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%%Copyright: Copyright 1987-1994 Adobe Systems Incorporated. All Rights Reserved.
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def
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/Tj {
userdict /$$copystring 2 index put
_Tj
} bd
/iTm { _ctm setmatrix _tm concat 0 _rise translate _hs 1 scale } bd
/Tm { _tm astore pop iTm 0 0 moveto } bd
/Td { _mtx translate _tm _tm concatmatrix pop iTm 0 0 moveto } bd
/TD { dup /_ld xdd Td } bd
/Tf {
dup 1000 div /_fScl xdd
exch findfont exch scalefont setfont
} bd
/TL { neg /_ld xdd } bd
/Tw { /_cx xdd } bd
/Tc { /_ax xdd } bd
/Ts { /_rise xdd currentpoint iTm moveto } bd
/Tz { 100 div /_hs xdd iTm } bd
/Tk { exch pop _fScl mul neg 0 rmoveto } bd
/T* { 0 _ld Td } bd
/' { T* Tj } bd
/" { exch Tc exch Tw ' } bd
/TJ {
{
dup type /stringtype eq
{ Tj }
{ 0 exch Tk }
ifelse
} forall
} bd
/T- { _hy Tj } bd
/d0/setcharwidth ld
/d1 { setcachedevice /sfc{}dd /ssc{}dd } bd
/nND {{/.notdef} repeat} bd
/T3Defs {
/BuildChar
{
1 index /Encoding get exch get
1 index /BuildGlyph get exec
}
def
/BuildGlyph {
exch begin
GlyphProcs exch get exec
end
} def
} bd
/MakeBold {
findfont dup dup length 2 add dict
begin
CopyFont
/PaintType 2 def
/StrokeWidth .03 0 FontMatrix idtransform pop def
/dummybold currentdict
end
definefont
8 dict begin
/_basefont exch def
/_basefonto exch def
/FontType 3 def
/FontMatrix[1 0 0 1 0 0]def
/FontBBox[0 0 1 1]def
/Encoding StandardEncoding def
/BuildChar
{
exch begin
_basefont setfont
( )dup 0 4 -1 roll put
dup stringwidth
1 index 0 ne { exch .03 add exch }if
setcharwidth
0 0 moveto
gsave
dup show
grestore
_basefonto setfont
show
end
}bd
currentdict
end
definefont pop
}bd
/MakeItalic {
findfont _italMtx makefont
dup length dict
begin
CopyFont
currentdict
end
definefont pop
}bd
/MakeBoldItalic {
/dummybold exch
MakeBold
/dummybold
MakeItalic
}bd
currentdict readonly pop end
%%EndFile
PDFText begin
[39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis
/Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute
/egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde
/oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex
/udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls
/registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash
/.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef
/.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash
/questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef
/guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe
/endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide
/.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright
/fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand
/Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex
/Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex
/Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla
/hungarumlaut/ogonek/caron
0 TE
[1/dotlessi/caron 39/quotesingle 96/grave 
127/bullet/bullet/bullet/quotesinglbase/florin/quotedblbase/ellipsis
/dagger/daggerdbl/circumflex/perthousand/Scaron/guilsinglleft/OE
/bullet/bullet/bullet/bullet/quoteleft/quoteright/quotedblleft
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/guilsinglright/oe/bullet/bullet/Ydieresis/space/exclamdown/cent/sterling
/currency/yen/brokenbar/section/dieresis/copyright/ordfeminine
/guillemotleft/logicalnot/hyphen/registered/macron/degree/plusminus
/twosuperior/threesuperior/acute/mu/paragraph/periodcentered/cedilla
/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters
/questiondown/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla
/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis
/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply/Oslash
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/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla/egrave/eacute
/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis/eth/ntilde
/ograve/oacute/ocircumflex/otilde/odieresis/divide/oslash/ugrave/uacute
/ucircumflex/udieresis/yacute/thorn/ydieresis
1 TE
end
%%BeginFile: pdfimage.prc
%%Copyright: Copyright 1987-1993 Adobe Systems Incorporated. All Rights Reserved.
PDF /PDFImage 38 dict put
PDF /PDFIVars 20 dict put
PDF /PDFImage get begin
/initialize { PDFImage begin } bd
/terminate { end } bd
/nulldict 0 dict def
/gv { PDFIVars exch get } bd
/pv { PDFIVars 3 1 roll put } bd
/BI { save /savelevel exch pv mark } bd
/EI { /savelevel gv restore } bd
end
%%EndFile
%%BeginFile: pdfimg2.prc
%%Copyright: Copyright 1987-1993 Adobe Systems Incorporated. All Rights Reserved.
PDF /PDFImage get begin
Level2? StartLoad {
/ID {
5 counttomark 2 idiv
dup 3 1 roll add
dict begin
{ def } repeat
cleartomark
currentdict
end
begin
/ImageType 1 def
/ImageMatrix [ Width 0 0 Height neg 0 Height ] def
/ImageMask here { not } { true } ifelse
{ /ImageMask false def } if
ImageMask not { ColorSpace setcolorspace } if
/Intent here { ri } if
/Decode here { pop } {
/Decode [
ImageMask {
0 1
} {
currentcolorspace 0 get /Indexed eq {
0 2 BitsPerComponent exp 1 sub
} {
mark currentcolor counttomark
dup 2 add 1 roll cleartomark
{ 0 1 } repeat
} ifelse
} ifelse
] def
} ifelse
[
/DataSource here { pop } {
currentfile
/Filter here {
dup type /arraytype eq { length } { pop 1 } ifelse
1 sub 0 1 3 -1 roll {
/DecodeParms here {
dup type /arraytype eq {
1 index get
} if
dup null eq { pop } { exch } ifelse
} if
Filter dup type /arraytype eq
{ exch get } { exch pop } ifelse
filter
dup
} for
} if
/DataSource exch def
} ifelse
currentdict
/ImageMask here not { false } if
{ sfc imagemask } { image } ifelse
counttomark
{ dup status
{ dup flushfile closefile }
{ pop }
ifelse
}
repeat
pop
end
} bd
currentdict readonly pop
} EndLoad
end
%%EndFile
currentdict readonly pop
end end
/currentpacking where {pop setpacking}if
PDFVars/InitAll{[PDF PDFText PDFImage]{/initialize get exec}forall initgs 0 Tr}put
PDFVars/TermAll{[PDFImage PDFText PDF]{/terminate get exec}forall}put
PDFVars begin PDF begin PDFVars/InitAll get exec
/N13 <<
/SA false 
/OP false 
>> /ExtGState defineRes pop
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11 dict begin
/FontInfo 12 dict dup begin
/ItalicAngle 0 def
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/UnderlinePosition -100 def
/UnderlineThickness 50 def
/version (001.000) readonly def
/Notice (Copyright (c) 1990 Adobe Systems Incorporated.  All Rights Reserved.) readonly def
/FullName (MathematicalPi-One) readonly def
/FamilyName (MathematicalPi) readonly def
/Weight (Medium) readonly def
/BaseFontName (MathematicalPi-One) def
end readonly def
/FontName /BGNPKG+MathematicalPi-One def
/FontType 1 def
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/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/FontBBox { -30 -210 1000 779 } readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 35 /numbersign put
dup 36 /dollar put
dup 44 /comma put
dup 46 /period put
dup 49 /one put
dup 50 /two put
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dup 53 /five put
dup 54 /six put
dup 57 /nine put
dup 63 /question put
dup 68 /D put
dup 70 /F put
dup 93 /bracketright put
dup 97 /a put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 104 /h put
dup 112 /p put
dup 114 /r put
dup 126 /asciitilde put
readonly def
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% End encoding-delta
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11 dict begin
/FontInfo 12 dict dup begin
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/version (001.004) readonly def
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New Century Schoolbook is a trademark of Linotype Company.) readonly def
/FullName (New Century Schoolbook Bold Italic) readonly def
/FamilyName (New Century Schoolbook) readonly def
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/ItalicAngle -16 def
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/UnderlineThickness 54 def
/BaseFontName (NewCenturySchlbk-BoldItalic) def
end readonly def
/FontName /BGODJE+NewCenturySchlbk-BoldItalic def
/FontType 1 def
/PaintType 0 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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/FontBBox { -205 -250 1147 991 } readonly def
currentdict end
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/N8 1 Tf
1 0 TD
(F)Tj
/N6 1 Tf
1.047 0 TD
0.037 Tc
[(.)-10607 (\(2\))]TJ
6.5 0 0 6 143.02 551 Tm
3.4754 Tc
(00)Tj
10 0 0 10 318 542.5 Tm
0 Tc
[(second-)-385.2 (and)-385.1 (third-order)-385.2 (terms)-385.1 (are)-385 (formed)-385.1 (from)]TJ
-24 -1.05 TD
[(Using)-753.1 (compact)-753.2 (notation,)-753.2 (the)-753 (\256rst)-753.1 (three)-753.1 (divided)]TJ
/N7 1 Tf
28.048 -1.1 TD
(m)Tj
/N6 1 Tf
0.99 0 TD
(\()Tj
/N8 1 Tf
0.37 0 TD
(F)Tj
/N10 1 Tf
1.05 0 TD
(2)Tj
/N8 1 Tf
1 0 TD
(F)Tj
/N6 1 Tf
0.932 0 TD
(\))Tj
-32.39 -0.1 TD
[(differences)-385.2 (are)-385 (de\256ned)-385.1 (by)]TJ
/N7 1 Tf
6.5 0 0 6 366.02 518.5 Tm
1.642 Tc
[(ji)-1233.9 (j)]TJ
/N6 1 Tf
-6.3631 -0.25 TD
0.0925 Tc
[(\(2\))-15820.7 (\()-0.7 (1\))]TJ
/N10 1 Tf
30 0 0 10 357.37 512.5 Tm
0 Tc
(]]])Tj
7.5 0 0 10 402.37 512.5 Tm
(])Tj
/N8 1 Tf
10 0 0 10 318 512 Tm
(F)Tj
/N10 1 Tf
1.771 0 TD
0.333 Tc
[(52)-4898 (2)]TJ
/N6 1 Tf
8.229 0 TD
0 Tc
(6)Tj
/N7 1 Tf
0.5 0 TD
(a)Tj
/N8 1 Tf
0.721 0 TD
(F)Tj
/N10 1 Tf
1.772 0 TD
(2)Tj
/N6 1 Tf
1 0 TD
(3)Tj
/N7 1 Tf
0.5 0 TD
(b)Tj
/N8 1 Tf
0.537 0 TD
(F)Tj
/N7 1 Tf
6.5 0 0 6 324.66 509.5 Tm
0.0558 Tc
(ij)Tj
/N6 1 Tf
9.0769 0 TD
0 Tc
(3)Tj
/N7 1 Tf
8.1877 0 TD
0.0558 Tc
[(ij)-5153.9 (ij)]TJ
10 0 0 10 376.81 504.5 Tm
0 Tc
(R)Tj
6.5 0 0 6 134.91 502 Tm
(k)Tj
/N10 1 Tf
0.5369 0 TD
(2)Tj
/N6 1 Tf
0.8877 0 TD
(1)Tj
/N7 1 Tf
8.8831 0 TD
(k)Tj
/N10 1 Tf
0.5354 0 TD
(2)Tj
/N6 1 Tf
0.8892 0 TD
(1)Tj
/N8 1 Tf
10 0 0 10 127.14 497 Tm
(D)Tj
/N6 1 Tf
2.064 0 TD
([)Tj
/N7 1 Tf
0.333 0 TD
(t)Tj
/N6 1 Tf
0.715 0 TD
(,)Tj
/N7 1 Tf
0.472 0 TD
(t)Tj
/N6 1 Tf
1.616 0 TD
(])Tj
/N10 1 Tf
0.5 0 TD
(2)Tj
/N8 1 Tf
0.999 0 TD
(D)Tj
/N6 1 Tf
2.065 0 TD
([)Tj
/N7 1 Tf
0.333 0 TD
(t)Tj
/N6 1 Tf
0.714 0 TD
(,)Tj
/N7 1 Tf
0.472 0 TD
(t)Tj
/N6 1 Tf
0.658 0 TD
(])Tj
6.5 0 0 6 154.45 494.5 Tm
(0)Tj
/N7 1 Tf
1.7877 0 TD
(k)Tj
/N10 1 Tf
0.5369 0 TD
(2)Tj
/N6 1 Tf
0.8877 0 TD
6.5954 Tc
(11)Tj
/N7 1 Tf
8.8831 0 TD
0 Tc
(k)Tj
-22.6615 -0.0833 TD
(k)Tj
/N6 1 Tf
45.0723 -0.25 TD
0.0925 Tc
[(\(1\))-2820.7 (\()0.9 (1\))]TJ
/N10 1 Tf
30 0 0 10 126.02 489.5 Tm
0 Tc
(]]]]]]])Tj
19.5 0 0 10 231.02 489.5 Tm
(])Tj
/N8 1 Tf
10 0 0 10 78 489 Tm
(D)Tj
/N6 1 Tf
1.126 0 TD
([)Tj
/N7 1 Tf
0.333 0 TD
(t)Tj
/N6 1 Tf
0.714 0 TD
(,)Tj
/N7 1 Tf
0.472 0 TD
(t)Tj
/N6 1 Tf
0.658 0 TD
(])Tj
/N10 1 Tf
0.5 0 TD
(5)Tj
/N6 1 Tf
12.497 0 TD
(,)Tj
/N7 1 Tf
11.748 -0.15 TD
(m)Tj
/N6 1 Tf
0.99 0 TD
(\()Tj
/N8 1 Tf
0.37 0 TD
(F)Tj
/N10 1 Tf
1.771 0 TD
(2)Tj
/N8 1 Tf
1 0 TD
(F)Tj
/N6 1 Tf
1.654 0 TD
(\))Tj
6.5 0 0 6 95.92 486.5 Tm
(0)Tj
/N7 1 Tf
1.7877 0 TD
(k)Tj
39.7662 -0.25 TD
1.6789 Tc
[(ji)-2307.7 (j)]TJ
10 0 0 10 171.12 483.5 Tm
0 Tc
(t)Tj
/N10 1 Tf
0.88 0 TD
(2)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N6 1 Tf
6.5 0 0 6 324.66 483.5 Tm
0.0926 Tc
[(\(3\))-18323.6 (\()-0.6 (2\))-4697.5 (\(1\))]TJ
-23.1092 -0.4167 TD
0 Tc
(0)Tj
/N7 1 Tf
2.8569 0 TD
(k)Tj
/N10 1 Tf
30 0 0 10 357.37 479 Tm
(]]]])Tj
6.5 0 0 10 417.37 479 Tm
(])Tj
/N8 1 Tf
10 0 0 10 318 478.5 Tm
(F)Tj
/N10 1 Tf
1.771 0 TD
0.333 Tc
[(52)-6525 (2)]TJ
/N6 1 Tf
10.041 0 TD
0 Tc
(9)Tj
/N7 1 Tf
0.5 0 TD
(a)Tj
/N8 1 Tf
0.537 0 TD
(F)Tj
/N10 1 Tf
1.771 0 TD
(2)Tj
/N6 1 Tf
1.184 0 TD
(9)Tj
/N7 1 Tf
0.5 0 TD
(b)Tj
/N8 1 Tf
0.537 0 TD
(F)Tj
/N7 1 Tf
6.5 0 0 6 324.66 476 Tm
0.0558 Tc
(ij)Tj
/N6 1 Tf
10.1861 0 TD
0 Tc
(3)Tj
/N7 1 Tf
9.5815 0 TD
0.0559 Tc
[(ij)-5473.8 (ij)]TJ
10 0 0 10 384.02 471 Tm
0 Tc
(R)Tj
/N6 1 Tf
-29.602 -0.425 TD
(\()Tj
/N7 1 Tf
0.296 0 TD
(k)Tj
/N10 1 Tf
0.647 0 TD
(5)Tj
/N6 1 Tf
1 0 TD
0.037 Tc
[(1)37 (,)-185 (2)37 (,)-185 (3\))-14566 (\(3\))]TJ
/N10 1 Tf
23.994 -1.1 TD
0 Tc
(2)Tj
/N6 1 Tf
1 0 TD
(3)Tj
/N7 1 Tf
0.5 0 TD
(c)Tj
/N8 1 Tf
0.481 0 TD
(F)Tj
/N6 1 Tf
1.096 0 TD
0.037 Tc
[(,)-14059 (\(6\))]TJ
/N7 1 Tf
6.5 0 0 6 373.61 453.25 Tm
0.0543 Tc
(ij)Tj
/N6 1 Tf
-39.4323 -0.4167 TD
0 Tc
(0)Tj
10 0 0 10 78 445.75 Tm
(where)Tj
/N8 1 Tf
3.152 0 TD
(D)Tj
/N11 1 Tf
1.306 0 TD
(;)Tj
/N8 1 Tf
0.999 0 TD
(F)Tj
/N6 1 Tf
1.321 0 TD
[(and)-710.1 (square)-709.1 (brackets)-710.2 (refer)-710.1 (to)-710 (the)]TJ
6.5 0 0 6 199.02 438.75 Tm
(2)Tj
10 0 0 10 78 433.75 Tm
[(appropriate)-392.3 (time)-393.1 (intervals)-393.2 (\()]TJ
/N8 1 Tf
11.324 0 TD
(D)Tj
/N6 1 Tf
1.139 0 TD
([)Tj
/N7 1 Tf
0.333 0 TD
(t)Tj
/N6 1 Tf
0.714 0 TD
(,)Tj
/N7 1 Tf
0.643 0 TD
(t)Tj
/N6 1 Tf
0.714 0 TD
[(])-393 (i)0 (s)-393 (evaluated)-393.2 (at)]TJ
6.5 0 0 6 209.29 431.25 Tm
1.5877 Tc
(13)Tj
10 0 0 10 318 431 Tm
0 Tc
(with)Tj
6.5 0 0 6 142.24 426.75 Tm
16.1862 Tc
(43)Tj
/N7 1 Tf
10 0 0 10 78 421.75 Tm
0 Tc
(t)Tj
/N6 1 Tf
0.751 0 TD
[(\).)-308 (The)-308.1 (term)]TJ
/N8 1 Tf
4.895 0 TD
(D)Tj
/N6 1 Tf
1.447 0 TD
[(is)-308 (de\256ned)-308.1 (similarly)-308.2 (by)]TJ
/N8 1 Tf
9.399 0 TD
(D)Tj
/N6 1 Tf
1.139 0 TD
([)Tj
/N7 1 Tf
0.333 0 TD
(t)Tj
/N6 1 Tf
0.278 0 TD
(,)Tj
/N7 1 Tf
0.558 0 TD
(t)Tj
/N6 1 Tf
0.714 0 TD
[(])-309 (and)]TJ
6.5 0 0 6 81.33 419.25 Tm
28.4246 Tc
(12)Tj
0.6831 -0.7917 TD
0 Tc
(3)Tj
41.8646 -0.5833 TD
(2)Tj
/N8 1 Tf
10 0 0 10 78 409.5 Tm
(D)Tj
/N6 1 Tf
1.138 0 TD
([)Tj
/N7 1 Tf
0.333 0 TD
(t)Tj
/N6 1 Tf
0.714 0 TD
(,)Tj
/N7 1 Tf
0.574 0 TD
(t)Tj
/N6 1 Tf
0.714 0 TD
[(].)-324 (Conversion)-324.2 (of)-324 (the)-324 (force)-324.1 (polynomial)-324.3 (into)-324.1 (a)]TJ
/N8 1 Tf
26.154 0 TD
(R)Tj
/N10 1 Tf
0.889 0 TD
(?)Tj
/N6 1 Tf
0.5 0 TD
(\()Tj
/N8 1 Tf
0.37 0 TD
(F)Tj
/N10 1 Tf
1.05 0 TD
(2)Tj
/N8 1 Tf
0.999 0 TD
(F)Tj
/N6 1 Tf
0.933 0 TD
(\))Tj
/N7 1 Tf
-7.846 -0.15 TD
(V)Tj
/N6 1 Tf
6.5 0 0 6 96.05 407 Tm
1.4815 Tc
(03)Tj
/N7 1 Tf
46.4969 0 TD
2.8759 Tc
(ij)Tj
/N6 1 Tf
6.9323 -0.25 TD
0 Tc
(2)Tj
/N10 1 Tf
16.5 0 0 10 342.1 401 Tm
(])Tj
30 0 0 10 373.16 401 Tm
(]]])Tj
15.5 0 0 10 418.16 401 Tm
(])Tj
/N11 1 Tf
31.5 0 0 23 335.21 400.75 Tm
0.2615 Tc
(SD)Tj
/N7 1 Tf
10 0 0 10 318 400.5 Tm
0 Tc
(b)Tj
/N10 1 Tf
0.887 0 TD
2.797 Tc
[(51)-2832 (1)]TJ
/N7 1 Tf
11.091 0 TD
0 Tc
(a)Tj
/N6 1 Tf
6.5 0 0 6 401.44 398 Tm
(2)Tj
10 0 0 10 78 397.5 Tm
[(Taylor)-480.1 (series)-480.1 (provides)-480.2 (simple)-480.1 (expressions)-480.3 (for)-481.1 (inte-)]TJ
/N7 1 Tf
26.522 -0.25 TD
(R)Tj
5.137 -0.2 TD
(R)Tj
/N6 1 Tf
-31.659 -0.75 TD
[(grating)-336.1 (coordinates)-337.3 (and)-336.1 (velocities.)-337.2 (Equating)-336.2 (terms)-337.1 (in)]TJ
6.5 0 0 6 428.34 381 Tm
0.0929 Tc
[(\(1\))-2820.3 (\()1.3 (1\))]TJ
10 0 0 10 335.58 376 Tm
0 Tc
(3)Tj
/N8 1 Tf
0.5 0 TD
(V)Tj
/N10 1 Tf
0.778 0 TD
(?)Tj
/N6 1 Tf
0.499 0 TD
(\()Tj
/N8 1 Tf
0.37 0 TD
(F)Tj
/N10 1 Tf
1.05 0 TD
(2)Tj
/N8 1 Tf
1 0 TD
(F)Tj
/N6 1 Tf
0.932 0 TD
(\))Tj
/N8 1 Tf
1.722 0 TD
(R)Tj
/N10 1 Tf
0.888 0 TD
(?)Tj
/N6 1 Tf
0.5 0 TD
(\()Tj
/N8 1 Tf
0.37 0 TD
(F)Tj
/N10 1 Tf
1.772 0 TD
(2)Tj
/N8 1 Tf
0.999 0 TD
(F)Tj
/N6 1 Tf
1.654 0 TD
(\))Tj
-38.792 -0.25 TD
[(the)-742 (successive)-742.2 (time)-742.1 (derivatives)-743.2 (of)-742 (\()-37 (2)-37 (\))-742 (with)-743.1 (an)]TJ
/N7 1 Tf
6.5 0 0 6 363.48 373.5 Tm
2.8743 Tc
[(ij)-3673.9 (i)-1110.8 (j)]TJ
/N6 1 Tf
24.5908 -0.25 TD
0 Tc
(2)Tj
/N10 1 Tf
30 0 0 10 334.47 367.5 Tm
(]]])Tj
23.5 0 0 10 379.47 367.5 Tm
(])Tj
30 0 0 10 402.98 367.5 Tm
(]]]])Tj
14.5 0 0 10 462.98 367.5 Tm
(])Tj
/N7 1 Tf
10 0 0 10 318 367 Tm
(c)Tj
/N10 1 Tf
0.647 0 TD
6.018 Tc
[(51)-1054 (1)]TJ
/N7 1 Tf
15.756 0 TD
0 Tc
(a)Tj
/N6 1 Tf
0.5 0 TD
0.037 Tc
(\(3)Tj
/N7 1 Tf
0.87 0 TD
0 Tc
(b)Tj
/N10 1 Tf
0.703 0 TD
(2)Tj
/N6 1 Tf
1 0 TD
(4)Tj
/N7 1 Tf
0.5 0 TD
(a)Tj
/N6 1 Tf
0.954 0 TD
(\).)Tj
6.5 0 0 6 364.69 364.5 Tm
10.8508 Tc
(22)Tj
10 0 0 10 78 361.5 Tm
0 Tc
[(equivalent)-367.2 (Taylor)-368.1 (series)-367.1 (and)-368.1 (setting)]TJ
/N7 1 Tf
15.058 0 TD
(t)Tj
/N10 1 Tf
0.481 0 TD
(5)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N6 1 Tf
1.082 0 TD
[(yields)-368.1 (the)]TJ
/N7 1 Tf
10.363 -0.2 TD
6.767 Tc
(RR)Tj
/N6 1 Tf
6.5 0 0 6 246.73 359 Tm
0 Tc
(0)Tj
10 0 0 10 78 349.5 Tm
[(force)-385.1 (derivatives)]TJ
44.36 -0.525 TD
0.037 Tc
(\(7\))Tj
6.5 0 0 6 84.66 333.5 Tm
0.0928 Tc
[(\(1\))-3740.4 (4)-4093.4 (3)-4661 (2)-4511.8 (1)]TJ
/N10 1 Tf
10 0 0 11 125.49 328.75 Tm
3.083 Tc
[(99)98 (9)]TJ
/N8 1 Tf
10 0 0 10 78 328.5 Tm
0 Tc
(F)Tj
/N10 1 Tf
1.747 0 TD
(5)Tj
/N6 1 Tf
1.142 0 TD
(\()Tj
/N8 1 Tf
0.37 0 TD
(D)Tj
/N7 1 Tf
1.138 0 TD
(t)Tj
/N10 1 Tf
0.908 0 TD
(1)Tj
/N8 1 Tf
0.999 0 TD
(D)Tj
/N6 1 Tf
1.176 0 TD
(\))Tj
/N7 1 Tf
0.333 0 TD
(t)Tj
/N10 1 Tf
0.907 0 TD
(1)Tj
/N8 1 Tf
1 0 TD
(D)Tj
/N7 1 Tf
1.411 0 TD
(t)Tj
/N10 1 Tf
0.907 0 TD
(1)Tj
/N8 1 Tf
1 0 TD
(D)Tj
/N11 1 Tf
9.5 0 0 12.5 103.8 328.25 Tm
8.3438 Tc
(sd)Tj
/N6 1 Tf
6.5 0 0 6 125.49 326 Tm
4.7554 Tc
[(32)150.8 (1)]TJ
10 0 0 10 318 320.75 Tm
0 Tc
[(A)-498 (second)-499.1 (double)-499.1 (summation)-499.2 (then)-499.1 (gives)-499.1 (the)-499 (corre-)]TJ
6.5 0 0 6 84.66 314.75 Tm
0.0928 Tc
[(\(2\))-4709.6 (4)-14402.6 (3)-8050.3 (2)]TJ
50.1631 -0.1667 TD
0.0925 Tc
[(\(2\))-4800.7 (\()0.9 (3\))]TJ
/N10 1 Tf
10 0 0 11 134.75 310 Tm
0.4073 Tc
[(99)-1166.7 (99)-1166.7 (99)-2971.7 (9)-1166.7 (9)]TJ
/N8 1 Tf
10 0 0 10 78 309.75 Tm
0 Tc
(F)Tj
/N10 1 Tf
1.747 0 TD
(5)Tj
/N6 1 Tf
1 0 TD
(2!)Tj
/N8 1 Tf
1.141 0 TD
(D)Tj
/N6 1 Tf
1.139 0 TD
(\()Tj
/N7 1 Tf
0.296 0 TD
0.462 Tc
(tt)Tj
/N10 1 Tf
1.647 0 TD
0 Tc
(1)Tj
/N7 1 Tf
1 0 TD
0.463 Tc
(tt)Tj
/N10 1 Tf
1.648 0 TD
0 Tc
(1)Tj
/N7 1 Tf
1 0 TD
0.462 Tc
(tt)Tj
/N6 1 Tf
1.518 0 TD
0 Tc
(\))Tj
/N10 1 Tf
0.499 0 TD
(1)Tj
/N8 1 Tf
1 0 TD
(D)Tj
/N6 1 Tf
1.139 0 TD
(\()Tj
/N7 1 Tf
0.296 0 TD
(t)Tj
/N10 1 Tf
0.907 0 TD
(1)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N6 1 Tf
0.777 0 TD
(\))Tj
/N10 1 Tf
0.5 0 TD
(1)Tj
/N8 1 Tf
1 0 TD
(D)Tj
/N11 1 Tf
9.5 0 0 12.5 113.8 309.5 Tm
17.326 Tc
(sd)Tj
/N6 1 Tf
10 0 0 10 318 308.75 Tm
0 Tc
[(sponding)-516.2 (values)-517.1 (of)]TJ
/N8 1 Tf
8.605 0 TD
(F)Tj
/N6 1 Tf
2.098 0 TD
(and)Tj
/N8 1 Tf
1.961 0 TD
(F)Tj
/N6 1 Tf
2.098 0 TD
[(for)-517.1 (all)-517 (particles.)]TJ
6.5 0 0 6 134.75 307.25 Tm
0.639 Tc
[(12)-1794.8 (23)-1794.8 (13)-4571.8 (1)-1794.8 (2)]TJ
10 0 0 10 318 296.75 Tm
0 Tc
[(This)-476.1 (pair-wise)-476.2 (boot-strapping)-477.3 (procedure)-476.2 (provides)-477.2 (a)]TJ
6.5 0 0 6 84.66 296 Tm
0.0928 Tc
[(\(3\))-4709.6 (4)-10984.1 (3)]TJ
/N10 1 Tf
10 0 0 11 134.75 291.25 Tm
1.5735 Tc
(999)Tj
/N8 1 Tf
10 0 0 10 78 291 Tm
0 Tc
(F)Tj
/N10 1 Tf
1.747 0 TD
(5)Tj
/N6 1 Tf
1 0 TD
(3!)Tj
/N8 1 Tf
1.141 0 TD
(D)Tj
/N6 1 Tf
1.139 0 TD
(\()Tj
/N7 1 Tf
0.296 0 TD
(t)Tj
/N10 1 Tf
0.907 0 TD
(1)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N10 1 Tf
0.907 0 TD
(1)Tj
/N7 1 Tf
0.999 0 TD
(t)Tj
/N6 1 Tf
0.778 0 TD
(\))Tj
/N10 1 Tf
0.5 0 TD
(1)Tj
/N8 1 Tf
0.999 0 TD
(D)Tj
/N11 1 Tf
9.5 0 0 12.5 113.8 290.75 Tm
9.0733 Tc
(sd)Tj
/N6 1 Tf
6.5 0 0 6 134.75 288.5 Tm
2.4331 Tc
(123)Tj
10 0 0 10 318 284.75 Tm
0 Tc
[(convenient)-359.3 (starting)-360.2 (algorithm,)-360.2 (since)-360.1 (the)-360 (extra)-360.1 (cost)-360.1 (is)]TJ
6.5 0 0 6 84.66 277.25 Tm
0.0928 Tc
[(\(4\))-4234.2 (4)]TJ
10 0 0 10 318 272.75 Tm
0 Tc
[(usually)-385.1 (small.)]TJ
/N8 1 Tf
-24 -0.05 TD
(F)Tj
/N10 1 Tf
1.747 0 TD
(5)Tj
/N6 1 Tf
1 0 TD
(4!)Tj
/N8 1 Tf
0.833 0 TD
(D)Tj
/N6 1 Tf
1.138 0 TD
(,)Tj
20.282 -1.15 TD
[(Appropriate)-647.3 (initial)-648.1 (time-steps)]TJ
/N10 1 Tf
13.219 0 TD
(D)Tj
/N7 1 Tf
0.667 0 TD
(t)Tj
/N6 1 Tf
1.198 0 TD
[(are)-648 (now)-648.1 (de-)]TJ
/N7 1 Tf
6.5 0 0 6 469.96 258.25 Tm
(i)Tj
/N6 1 Tf
10 0 0 10 281.6 256 Tm
0.037 Tc
(\(4\))Tj
3.64 -0.725 TD
0 Tc
[(termined,)-320.2 (using)-320.1 (the)-320.1 (general)-321.2 (criterion)-320.2 (discussed)-320.2 (in)-321 (the)]TJ
0 -1.2 TD
[(next)-444.1 (subsection.)-444.3 (Setting)]TJ
/N7 1 Tf
10.36 0 TD
(t)Tj
/N10 1 Tf
0.881 0 TD
(5)Tj
/N6 1 Tf
1 0 TD
[(0,)-444 (the)-444 (backward)-445.2 (times)]TJ
/N10 1 Tf
10 0 0 11 110.08 235.25 Tm
(9)Tj
/N6 1 Tf
10 0 0 10 78 235 Tm
(where)Tj
/N7 1 Tf
2.856 0 TD
(t)Tj
/N10 1 Tf
0.912 0 TD
(5)Tj
/N7 1 Tf
0.999 0 TD
(t)Tj
/N10 1 Tf
0.881 0 TD
(2)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N6 1 Tf
0.653 0 TD
[(.)-413 (Eq.)-413.1 (\()-37 (4)-37 (\))-413 (is)-413 (mainly)-413.1 (used)-413.1 (to)-414 (obtain)]TJ
6.5 0 0 6 424.94 234.25 Tm
(0)Tj
/N7 1 Tf
-48.44 -0.2917 TD
(k)Tj
/N6 1 Tf
2.9123 0 TD
(0)Tj
/N7 1 Tf
2.8554 0 TD
(k)Tj
/N6 1 Tf
10 0 0 10 318 224.75 Tm
[(are)-327 (initialized)-328.2 (by)]TJ
/N7 1 Tf
7.203 0 TD
(t)Tj
/N10 1 Tf
0.825 0 TD
0.334 Tc
(52)Tj
/N7 1 Tf
2.166 0 TD
0 Tc
(k)Tj
/N10 1 Tf
0.772 0 TD
(D)Tj
/N7 1 Tf
0.667 0 TD
(t)Tj
/N6 1 Tf
0.93 0 TD
(\()Tj
/N7 1 Tf
0.296 0 TD
(k)Tj
/N10 1 Tf
0.648 0 TD
(5)Tj
/N6 1 Tf
1 0 TD
[(1,)-184 (2,)-184 (3)-37 (\))0 (.)-328 (Inversion)]TJ
-38.507 -0.175 TD
[(the)-641 (Taylor)-642.1 (series)-641.1 (derivatives)-642.2 (at)]TJ
/N7 1 Tf
14.483 0 TD
(t)Tj
/N10 1 Tf
0.481 0 TD
(5)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N6 1 Tf
0.714 0 TD
[(,)-642 (when)-642.1 (the)]TJ
/N7 1 Tf
6.5 0 0 6 393.13 222.25 Tm
6.3698 Tc
(ki)Tj
/N6 1 Tf
-23.4077 -0.2917 TD
0 Tc
(0)Tj
10 0 0 10 318 212.75 Tm
[(of)-490 (\()-37 (4)-37 (\))-491 (to)-491 (third)-491.1 (order)-491.1 (yields)-491.1 (starting)-491.2 (values)-491.1 (for)-491.1 (the)]TJ
-24 -0.175 TD
[(fourth)-384.1 (difference)-385.2 (is)-384 (not)-385.1 (yet)-384.1 (known.)-385.2 (Thus)-384.1 (the)-385 (contri-)]TJ
6.5 0 0 6 139.7 204 Tm
(4)Tj
10 0 0 10 318 200.75 Tm
[(divided)-385.2 (differences,)]TJ
-24 -0.175 TD
[(bution)-446.1 (from)]TJ
/N8 1 Tf
5.392 0 TD
(D)Tj
/N6 1 Tf
1.586 0 TD
[(to)-446 (each)-446.1 (order)-447.1 (is)-446 (only)-447.1 (added)-446.1 (at)-447 (the)]TJ
-6.978 -1.2 TD
[(end)-606.1 (of)-606 (an)-606 (integration)-606.2 (step.)-606.1 (This)-606.1 (so-called)-606.2 (`semi-)]TJ
26.939 -0.95 TD
3.894 Tc
(11)Tj
-26.939 -0.25 TD
0 Tc
[(iteration')-332.2 (gives)-333.1 (increased)-332.2 (accuracy)-333.2 (at)-332 (little)-333.1 (extra)-333.1 (cost)]TJ
6.5 0 0 6 325.77 175 Tm
5.0754 Tc
[(1\()4983.8 (3)4981.6 (\))-333.1 (\()4983.8 (2)4981.6 (\))56.1 (\()4982.2 (1)4983.1 (\))]TJ
/N10 1 Tf
14 0 0 10 346.28 170.5 Tm
2.6386 Tc
(]])Tj
/N11 1 Tf
31.5 0 0 23 339.38 170.25 Tm
0 Tc
(S)Tj
/N10 1 Tf
10 0 0 11 374.67 170.25 Tm
(9)Tj
/N11 1 Tf
31.5 0 0 23 414.73 170.25 Tm
(D)Tj
/N10 1 Tf
10 0 0 11 425.15 170.25 Tm
(9)Tj
/N8 1 Tf
10 0 0 10 318 170 Tm
(D)Tj
/N10 1 Tf
1.305 0 TD
(5)Tj
/N8 1 Tf
2.429 0 TD
(F)Tj
/N7 1 Tf
1.581 0 TD
(t)Tj
/N10 1 Tf
0.907 0 TD
(2)Tj
/N8 1 Tf
1.906 0 TD
(F)Tj
/N7 1 Tf
2.235 0 TD
(t)Tj
/N10 1 Tf
0.907 0 TD
(1)Tj
/N8 1 Tf
1 0 TD
(F)Tj
/N6 1 Tf
6.5 0 0 6 374.67 167.5 Tm
7.2661 Tc
(11)Tj
10 0 0 10 347.39 164.5 Tm
3.894 Tc
(62)Tj
-26.939 -0.15 TD
0 Tc
[(\()37 (o)0 (n)-385 (scalar)-385.1 (machines)36.8 (\))-385 (and)-385.1 (no)-385 (extra)-385.1 (memory.)]TJ
1 -1.2 TD
[(W)56 (e)-738 (now)-737.1 (describe)-738.2 (the)-737 (initialization)-738.3 (procedure,)]TJ
26.582 -0.1 TD
6.467 Tc
(11)Tj
6.5 0 0 6 325.77 147.5 Tm
6.0646 Tc
[(2\()5973 (3)5972.3 (\))-3302.4 (\()5971.4 (2)5972.3 (\))]TJ
/N10 1 Tf
14 0 0 10 352.71 143 Tm
4.4764 Tc
(]])Tj
10 0 0 11 384.06 142.75 Tm
1.574 Tc
(99)Tj
/N8 1 Tf
10 0 0 10 318 142.5 Tm
0 Tc
(D)Tj
/N10 1 Tf
1.305 0 TD
0.333 Tc
(52)Tj
/N8 1 Tf
3.072 0 TD
0 Tc
(F)Tj
/N6 1 Tf
1.581 0 TD
(\()Tj
/N7 1 Tf
0.296 0 TD
(t)Tj
/N10 1 Tf
0.907 0 TD
(1)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N6 1 Tf
0.777 0 TD
(\))Tj
/N10 1 Tf
0.5 0 TD
(1)Tj
/N8 1 Tf
1.906 0 TD
(F)Tj
/N6 1 Tf
6.5 0 0 6 384.06 140 Tm
2.4338 Tc
(12)Tj
10 0 0 10 78 139 Tm
0 Tc
[(assuming)-632.2 (one)-633.1 (force)-632.1 (polynomial.)-633.3 (From)-632.1 (the)-633 (initial)]TJ
27.582 -0.2 TD
6.467 Tc
(62)Tj
-27.582 -1 TD
0 Tc
(conditions)Tj
/N7 1 Tf
4.888 0 TD
(m)Tj
/N6 1 Tf
0.99 0 TD
(,)Tj
/N8 1 Tf
0.434 0 TD
(r)Tj
/N6 1 Tf
0.712 0 TD
(,)Tj
/N18 1 Tf
0.434 0 TD
(v)Tj
/N6 1 Tf
0.786 0 TD
[(,)-722 (the)-721 (respective)-722.2 (Taylor)-722.1 (series)]TJ
/N7 1 Tf
6.5 0 0 6 134.42 124.5 Tm
1.4835 Tc
[(jj)-117 (j)]TJ
/N6 1 Tf
10 0 0 10 342.16 122.5 Tm
0 Tc
(1)Tj
6.5 0 0 6 325.77 120 Tm
4.2692 Tc
[(3\()4176 (3)4176.9 (\))]TJ
/N10 1 Tf
14 0 0 10 341.04 115.5 Tm
0 Tc
(])Tj
/N6 1 Tf
10 0 0 10 78 115 Tm
[(derivatives)-354.2 (are)-354 (formed)-355.1 (by)-354 (successive)-355.2 (differentiations)]TJ
/N8 1 Tf
24 0 TD
(D)Tj
/N10 1 Tf
1.305 0 TD
(5)Tj
/N8 1 Tf
1.906 0 TD
(F)Tj
/N6 1 Tf
1.581 0 TD
0.037 Tc
[(.)-15281 (\(8\))]TJ
-2.376 -0.55 TD
0 Tc
(6)Tj
ET
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33 33 546 744 RC
BT
/N7 1 Tf
8 0 0 8 222.26 705 Tm
0 g
/N13 /ExtGState findRes gs
0 Tc
0 Tw
(S)Tj
/N6 1 Tf
8 0 2.144 8 226.26 705 Tm
(.)Tj
/N7 1 Tf
8 0 0 8 228.7 705 Tm
(J)Tj
/N6 1 Tf
8 0 2.144 8 232.25 705 Tm
(.)Tj
/N7 1 Tf
8 0 0 8 237.78 705 Tm
(Aarseth)Tj
/N6 1 Tf
3.6063 0 TD
(/)Tj
/N7 1 Tf
0.7375 0 TD
[(New)-440.8 (Astronomy)]TJ
/N6 1 Tf
8 0 2.144 8 328.02 705 Tm
[(6)-385 (\()-37 (2001)-37.5 (\))-384.5 (277)]TJ
8 0 0 8 373.29 705 Tm
(\261)Tj
8 0 2.144 8 377.73 705 Tm
(291)Tj
8 0 0 8 522 705 Tm
(279)Tj
10 0 2.68 10 78 679 Tm
(2.2.)Tj
/N7 1 Tf
10 0 0 10 98.55 679 Tm
[(Individual)-385.2 (time)]TJ
/N6 1 Tf
6.218 0 TD
(-)Tj
/N7 1 Tf
0.333 0 TD
(steps)Tj
/N6 1 Tf
15.394 0 TD
[(ticles)-487.1 (and)-487.1 (at)-487 (the)-487 (end)-487.1 (of)-487 (each)-487.1 (integration)-487.2 (cycle)-487.1 (for)]TJ
0 -1.2 TD
(particle)Tj
/N7 1 Tf
3.384 0 TD
(i)Tj
/N6 1 Tf
0.278 0 TD
[(.)-273 (W)55 (e)-385 (adopt)-385.1 (the)-385 (composite)-385.2 (criterion)]TJ
-26.662 -1.2 TD
[(Stellar)-546.1 (systems)-547.2 (are)-547 (characterized)-547.3 (by)-547 (a)-547 (range)-547.1 (in)]TJ
6.5 0 0 6 448.02 650.75 Tm
0.1664 Tc
(1/2)Tj
-9.4615 -0.0417 TD
0.0925 Tc
[(\(2\))-3465.3 (\()-0.7 (1\))-389.9 (2)]TJ
/N10 1 Tf
10 0 2.68 10 355.44 645.5 Tm
0 Tc
(h)Tj
/N6 1 Tf
10 0 0 10 361.55 645.5 Tm
(\()Tj
/N11 1 Tf
0.37 0 TD
(u)Tj
/N8 1 Tf
0.222 0 TD
(F)Tj
/N11 1 Tf
0.611 0 TD
0.184 Tc
(uu)Tj
/N8 1 Tf
0.628 0 TD
0 Tc
(F)Tj
/N11 1 Tf
1.58 0 TD
(u)Tj
/N10 1 Tf
0.389 0 TD
(1)Tj
/N11 1 Tf
1 0 TD
(u)Tj
/N8 1 Tf
0.222 0 TD
(F)Tj
/N11 1 Tf
1.581 0 TD
(u)Tj
/N6 1 Tf
0.675 0 TD
(\))Tj
-35.633 -0.25 TD
[(density)-403.1 (which)-404.1 (gives)-404.1 (rise)-403.1 (to)-404 (different)-404.2 (time-scales)-404.3 (for)]TJ
/N10 1 Tf
30 0 0 10 352.53 638.25 Tm
(]]]]])Tj
26 0 0 10 427.53 638.25 Tm
(])Tj
10 0 0 10 318 637.75 Tm
(D)Tj
/N7 1 Tf
0.667 0 TD
(t)Tj
/N10 1 Tf
0.913 0 TD
(5)Tj
/N6 1 Tf
12.505 0 TD
[(,)-5525 (\()-37 (10)-37 (\))]TJ
/N11 1 Tf
31.5 0 0 31 345.63 635.75 Tm
2.792 Tc
(SD)Tj
/N7 1 Tf
6.5 0 0 6 327.76 635.25 Tm
0 Tc
(i)Tj
/N6 1 Tf
5.9185 -0.0417 TD
0.0921 Tc
[(\(1\))-1956.4 (\()0.5 (3\))-3467.2 (\(2\))-391.8 (2)]TJ
10 0 0 10 78 631 Tm
0 Tc
[(signi\256cant)-280.2 (changes)-281.2 (of)-281 (the)-281 (orbital)-281.1 (parameters.)-281.3 (In)-281 (order)]TJ
27.564 -0.1 TD
(\()Tj
/N11 1 Tf
0.37 0 TD
(u)Tj
/N8 1 Tf
0.222 0 TD
(F)Tj
/N11 1 Tf
1.581 0 TD
0.184 Tc
(uu)Tj
/N8 1 Tf
0.628 0 TD
0 Tc
(F)Tj
/N11 1 Tf
1.581 0 TD
(u)Tj
/N10 1 Tf
0.389 0 TD
(1)Tj
/N11 1 Tf
0.999 0 TD
(u)Tj
/N8 1 Tf
0.222 0 TD
(F)Tj
/N11 1 Tf
1.581 0 TD
(u)Tj
/N6 1 Tf
0.676 0 TD
(\))Tj
-35.813 -1.1 TD
[(to)-356 (exploit)-357.2 (this)-357.1 (feature,)-357.2 (and)-356.1 (economize)-357.2 (on)-357 (the)-357 (expen-)]TJ
24 -0.825 TD
(where)Tj
/N10 1 Tf
10 0 2.68 10 345.26 610.75 Tm
(h)Tj
/N6 1 Tf
10 0 0 10 355.5 610.75 Tm
[(is)-377 (a)-376 (dimensionless)-376.3 (accuracy)-376.2 (parameter.)-377.2 (For)]TJ
-27.75 -0.375 TD
[(sive)-487.1 (force)-487.1 (calculation,)-487.3 (each)-487.1 (particle)-487.2 (is)-487 (assigned)-488.2 (its)]TJ
24 -0.825 TD
[(this)-357.1 (purpose,)-357.2 (only)-357.1 (the)-358 (last)-357.1 (two)-357.1 (terms)-358.1 (of)-357 (the)-357.1 (\256rst)-358.1 (and)]TJ
-24 -0.375 TD
[(own)-450.1 (time-step)-450.2 (which)-450.1 (is)-451 (related)-450.1 (to)-450 (the)-450 (orbital)-451.1 (time-)]TJ
24 -0.825 TD
[(second)-524.1 (force)-524.1 (derivatives)-524.2 (in)-525 (\()-37 (4)-37 (\))-524 (are)-524 (included.)-525.2 (This)]TJ
-24 -0.375 TD
[(scale.)-385.1 (Thus)-385.1 (the)-385 (aim)-385 (is)-385 (to)-385 (ensure)-385.1 (the)-385 (convergence)-386.3 (of)]TJ
24 -0.825 TD
[(expression)-348.2 (ensures)-348.2 (that)-348.1 (all)-349 (the)-348 (force)-348.1 (derivatives)-349.2 (play)]TJ
-24 -0.375 TD
[(the)-369 (force)-369.1 (polynomial)-369.3 (\()-37 (2)-37 (\))-369 (with)-369.1 (the)-369 (minimum)-369.2 (number)]TJ
24 -0.825 TD
[(a)-356 (role)-357.1 (and)-357.1 (is)-357 (also)-357.1 (well)-356.1 (de\256ned)-357.1 (for)-357.1 (special)-357.2 (cases)-357.1 (\()-37 (i.e.)]TJ
-24 -0.375 TD
[(of)-447 (force)-447.1 (evaluations.)-447.3 (Since)-448.1 (all)-447 (interactions)-447.3 (must)-448.1 (be)]TJ
24 -0.825 TD
[(starting)-506.1 (from)-506.1 (rest)-507.1 (or)]TJ
/N11 1 Tf
9.246 0 TD
(u)Tj
/N8 1 Tf
0.222 0 TD
(F)Tj
/N11 1 Tf
0.611 0 TD
0.167 Tc
(u.)Tj
/N6 1 Tf
1.389 0 TD
0 Tc
[(0)-37 (\))0 (.)-506 (Although)-507.2 (successive)]TJ
-35.468 -0.375 TD
[(added)-399.1 (consistently)-399.3 (in)-400 (a)-399 (direct)-400.1 (integration)-399.2 (method,)-400.2 (it)]TJ
24 -0.825 TD
[(time-steps)-288.2 (normally)-288.2 (change)-288.1 (smoothly,)-288.2 (it)-288 (is)-288 (prudent)-289.2 (to)]TJ
-24 -0.375 TD
[(is)-758 (necessary)-758.2 (to)-758 (include)-758.2 (a)-758 (temporary)-759.2 (coordinate)]TJ
24 -0.825 TD
[(restrict)-533.1 (the)-533 (growth)-533.1 (by)-534 (a)-533 (stability)-533.2 (factor)-534.1 (\()-37 (presently)]TJ
-24 -0.375 TD
[(prediction)-372.2 (of)-372 (the)-372 (other)-372.1 (particles.)-372.2 (However,)-372.2 (the)-373 (addi-)]TJ
24 -0.825 TD
[(1.2)-37 (\).)]TJ
-24 -0.375 TD
[(tional)-464.1 (cost)-464.1 (of)-464 (low-order)-464.2 (predictions)-464.2 (still)-464.1 (leads)-464.1 (to)-465 (a)]TJ
25 -0.825 TD
[(In)-320 (summary,)-320.2 (the)-320 (scheme)-321.2 (requires)-320.2 (the)-320 (following)-321.2 (30)]TJ
-25 -0.375 TD
[(signi\256cant)-387.2 (saving)-387.1 (since)-388.1 (this)-387.1 (permits)-387.2 (arbitrarily)-388.2 (large)]TJ
6.5 0 0 6 505.1 495.5 Tm
0.0927 Tc
[(\(1\))-2060.5 (1)]TJ
10 0 0 10 318 490.5 Tm
0 Tc
[(variables)-336.2 (for)-337 (each)-336.1 (particle:)]TJ
/N7 1 Tf
11.231 0 TD
(m)Tj
/N6 1 Tf
0.722 0 TD
(,)Tj
/N8 1 Tf
0.586 0 TD
(r)Tj
/N6 1 Tf
0.881 0 TD
(,)Tj
/N8 1 Tf
0.586 0 TD
(r)Tj
/N6 1 Tf
0.712 0 TD
(,)Tj
/N18 1 Tf
0.586 0 TD
(v)Tj
/N6 1 Tf
0.955 0 TD
(,)Tj
/N8 1 Tf
0.587 0 TD
(F)Tj
/N6 1 Tf
0.611 0 TD
(,)Tj
/N8 1 Tf
0.586 0 TD
(F)Tj
/N6 1 Tf
1.581 0 TD
(,)Tj
/N8 1 Tf
0.587 0 TD
(D)Tj
/N6 1 Tf
1.139 0 TD
(,)Tj
6.5 0 0 6 448.39 488 Tm
(0)Tj
/N7 1 Tf
2.22 0 TD
(t)Tj
/N6 1 Tf
2.1492 0 TD
(0)Tj
10 0 0 10 78 487 Tm
[(time-step)-385.2 (ratios.)]TJ
6.5 0 0 6 325.77 483.5 Tm
2.1354 Tc
(23)Tj
/N8 1 Tf
10 0 0 10 318 478.5 Tm
0 Tc
(D)Tj
/N6 1 Tf
1.138 0 TD
(,)Tj
/N8 1 Tf
0.575 0 TD
(D)Tj
/N6 1 Tf
1.138 0 TD
(,)Tj
/N10 1 Tf
0.575 0 TD
(D)Tj
/N7 1 Tf
0.667 0 TD
(t)Tj
/N6 1 Tf
0.278 0 TD
(,)Tj
/N7 1 Tf
0.574 0 TD
(t)Tj
/N6 1 Tf
0.714 0 TD
(,)Tj
/N7 1 Tf
0.574 0 TD
(t)Tj
/N6 1 Tf
0.714 0 TD
(,)Tj
/N7 1 Tf
0.575 0 TD
(t)Tj
/N6 1 Tf
0.714 0 TD
(,)Tj
/N7 1 Tf
0.574 0 TD
(t)Tj
/N6 1 Tf
0.714 0 TD
[(.)-325 (I)0 (t)-324 (i)0 (s)-324 (also)-325.1 (useful)-324.1 (to)-324 (employ)-325.2 (a)]TJ
6.5 0 0 6 370.78 476 Tm
1.4827 Tc
(0123)Tj
10 0 0 10 88 475 Tm
0 Tc
[(Following)-455.2 (the)-455 (polynomial)-455.3 (initialization)-456.3 (discussed)]TJ
23 -0.85 TD
[(secondary)-385.2 (velocity,)]TJ
/N18 1 Tf
8.296 0 TD
(v)Tj
/N6 1 Tf
0.786 0 TD
[(,)-385 (for)-385 (dual)-385.1 (purposes.)]TJ
/N7 1 Tf
6.5 0 0 6 406.46 464 Tm
(t)Tj
/N6 1 Tf
10 0 0 10 78 463 Tm
[(above,)-629.1 (the)-630 (integration)-630.2 (cycle)-630.1 (itself)-630.1 (begins)-630.1 (by)-630 (de-)]TJ
0 -1.2 TD
[(termining)-375.2 (the)-375 (next)-375.1 (particle)-376.2 (\()]TJ
/N7 1 Tf
11.647 0 TD
(i)Tj
/N6 1 Tf
0.371 0 TD
[(\))-375 (t)0 (o)-375 (b)0 (e)-375 (advanced.)-376.2 (Thus)]TJ
10 0 2.68 10 318 440.5 Tm
(2.3.)Tj
/N7 1 Tf
10 0 0 10 338.55 440.5 Tm
[(Neighbour)-385.2 (scheme)]TJ
/N6 1 Tf
-26.055 -0.15 TD
[(in)-343 (general,)]TJ
/N7 1 Tf
4.657 0 TD
(i)Tj
/N10 1 Tf
0.481 0 TD
(5)Tj
/N6 1 Tf
1 0 TD
[(min)-468.1 (\()]TJ
/N7 1 Tf
2.32 0 TD
(t)Tj
/N10 1 Tf
0.729 0 TD
0.167 Tc
(1D)Tj
/N7 1 Tf
1.667 0 TD
0 Tc
(t)Tj
/N6 1 Tf
0.599 0 TD
[(\),)-343 (where)]TJ
/N7 1 Tf
3.712 0 TD
(t)Tj
/N6 1 Tf
0.906 0 TD
[(is)-343 (the)-343.1 (time)-343.1 (of)]TJ
/N7 1 Tf
6.5 0 0 6 155.25 436.5 Tm
1.3266 Tc
[(jj)-2080 (j)-5029.2 (j)]TJ
/N6 1 Tf
10 0 0 10 78 427 Tm
0 Tc
[(the)-453 (last)-454.1 (force)-454.1 (evaluation.)-454.3 (It)-454 (is)-454 (convenient)-454.3 (to)-454 (de\256ne)]TJ
25 -1.05 TD
[(Having)-411.1 (introduced)-412.2 (the)-411 (basic)-412.1 (tools)-411.1 (for)-412.1 (direct)-412.1 (inte-)]TJ
-25 -0.15 TD
[(the)-437 (present)-437.2 (epoch)-437.1 (\()37 (o)0 (r)-437 (`global')-438.2 (time)36.9 (\))-437 (b)0 (y)]TJ
/N7 1 Tf
16.927 0 TD
(t)Tj
/N10 1 Tf
0.482 0 TD
(5)Tj
/N7 1 Tf
0.999 0 TD
(t)Tj
/N10 1 Tf
0.729 0 TD
0.167 Tc
(1D)Tj
/N7 1 Tf
1.667 0 TD
0 Tc
(t)Tj
/N6 1 Tf
0.546 0 TD
(,)Tj
/N7 1 Tf
6.5 0 0 6 265.18 412.5 Tm
3.4066 Tc
(ii)Tj
/N6 1 Tf
10 0 0 10 318 404.5 Tm
0 Tc
[(gration,)-415.2 (we)-416 (now)-415.1 (turn)-416.1 (to)-416 (the)-415 (AC)-416 (neighbour)-416.2 (scheme.)]TJ
-24 -0.15 TD
[(rather)-385.1 (than)-385.1 (relating)-385.2 (it)-385 (to)-385 (the)-385 (previous)-385.2 (value.)]TJ
24 -1.05 TD
[(Here)-709.1 (the)-709 (main)-709.1 (idea)-710.1 (is)-709 (to)-709 (reduce)-709.1 (the)-709 (effort)-710.1 (of)]TJ
-23 -0.15 TD
[(The)-448.1 (individual)-448.2 (time-step)-449.2 (scheme)-448.2 (\()37 (Aarseth,)-449.2 (1963)-37.1 (\))]TJ
23 -1.05 TD
[(evaluating)-508.2 (the)-508 (force)-508.1 (contribution)-508.3 (from)-508.1 (distant)-508.1 (par-)]TJ
-24 -0.15 TD
[(uses)-419.1 (two)-419.1 (types)-420.1 (of)-419 (coordinates)-420.3 (for)-419.1 (each)-420.1 (particle.)-308.2 (W)55 (e)]TJ
24 -1.05 TD
[(ticles)-748.1 (by)-748 (employing)-748.2 (two)-748.1 (polynomials)-748.3 (based)-749.1 (on)]TJ
-24 -0.15 TD
[(de\256ne)-335.1 (primary)-335.2 (and)-335.1 (secondary)-335.2 (coordinates,)]TJ
/N8 1 Tf
17.643 0 TD
(r)Tj
/N6 1 Tf
1.216 0 TD
(and)Tj
/N8 1 Tf
1.779 0 TD
(r)Tj
/N6 1 Tf
0.712 0 TD
(,)Tj
6.5 0 0 6 259.43 364.5 Tm
(0)Tj
/N7 1 Tf
4.5692 0 TD
(t)Tj
/N6 1 Tf
10 0 0 10 318 356.5 Tm
[(separate)-518.2 (time-scales.)-519.3 (Splitting)-519.2 (the)-518 (total)-519.1 (force)-519.1 (on)-519 (a)]TJ
-24 -0.15 TD
[(evaluated)-444.2 (at)]TJ
/N7 1 Tf
5.443 0 TD
(t)Tj
/N6 1 Tf
1.159 0 TD
(and)Tj
/N7 1 Tf
1.889 0 TD
(t)Tj
/N6 1 Tf
0.278 0 TD
[(,)-444 (respectively,)-445.3 (where)-445.1 (the)-445 (latter)]TJ
6.5 0 0 6 135.77 352.5 Tm
(0)Tj
10 0 0 10 318 344.5 Tm
[(given)-457.1 (particle)-458.1 (into)-457.1 (an)-458 (irregular)-458.2 (and)-457.1 (a)-458 (regular)-458.2 (com-)]TJ
-24 -0.15 TD
[(are)-372 (derived)-373.2 (from)-373.1 (the)-373 (former)-373.1 (by)-373 (the)-373 (predictor.)-373.2 (In)-373 (the)]TJ
24 -1.05 TD
(ponent,)Tj
-24 -0.15 TD
[(present)-276.2 (treatment)-277.2 (where)-277.1 (high)-276.1 (precision)-277.2 (is)-277 (not)-277.1 (normal-)]TJ
6.5 0 0 6 269.62 324 Tm
(\()Tj
/N8 1 Tf
0.4262 0 TD
(1)Tj
/N6 1 Tf
0.5923 0 TD
(\))Tj
10 0 0 10 78 319 Tm
[(ly)-385 (required,)-385.2 (we)-385 (predict)-385.2 (coordinates)-385.3 (to)-385 (order)]TJ
/N8 1 Tf
18.496 0 TD
(F)Tj
/N6 1 Tf
1.965 0 TD
(by)Tj
/N8 1 Tf
3.539 -0.55 TD
(F)Tj
/N10 1 Tf
0.777 0 TD
(5)Tj
/N8 1 Tf
1 0 TD
(F)Tj
/N10 1 Tf
1.574 0 TD
(1)Tj
/N8 1 Tf
1 0 TD
(F)Tj
/N6 1 Tf
1.624 0 TD
[(,)-13635 (\()-37 (11)-37 (\))]TJ
6.5 0 0 6 342.43 311 Tm
0.056 Tc
[(irr)-2849.5 (r)1.3 (eg)]TJ
-35.6015 -1.4167 TD
0.092 Tc
(\(1\))Tj
/N8 1 Tf
10 0 0 10 105.48 298.5 Tm
3.961 Tc
(\304\304)Tj
/N10 1 Tf
10 0 0 11 130.71 296 Tm
3.385 Tc
[(99)296 (9)]TJ
/N8 1 Tf
10 0 0 10 78 295.75 Tm
0 Tc
(r)Tj
/N10 1 Tf
0.883 0 TD
(5)Tj
/N6 1 Tf
0.999 0 TD
-0.037 Tc
(\(\()Tj
/N8 1 Tf
0.666 0 TD
0 Tc
(F)Tj
/N10 1 Tf
10 0 2.68 10 121.63 295.75 Tm
(d)Tj
/N7 1 Tf
10 0 0 10 127.19 295.75 Tm
(t)Tj
/N10 1 Tf
0.924 0 TD
(1)Tj
/N8 1 Tf
0.999 0 TD
(F)Tj
/N6 1 Tf
0.759 0 TD
(\))Tj
/N10 1 Tf
10 0 2.68 10 158.81 295.75 Tm
(d)Tj
/N7 1 Tf
10 0 0 10 164.37 295.75 Tm
(t)Tj
/N10 1 Tf
0.924 0 TD
(1)Tj
/N8 1 Tf
0.999 0 TD
(v)Tj
/N6 1 Tf
0.463 0 TD
(\))Tj
/N10 1 Tf
10 0 2.68 10 193.03 295.75 Tm
(d)Tj
/N7 1 Tf
10 0 0 10 198.59 295.75 Tm
(t)Tj
/N10 1 Tf
0.924 0 TD
(1)Tj
/N8 1 Tf
1 0 TD
(r)Tj
/N6 1 Tf
0.88 0 TD
0.037 Tc
[(,)-5210 (\(9\))]TJ
9.137 -0.075 TD
0 Tc
[(we)-297 (can)-297.1 (replace)-297.1 (the)-298 (full)]TJ
/N7 1 Tf
9.538 0 TD
(N)Tj
/N6 1 Tf
1.001 0 TD
[(summation)-298.2 (in)-297 (\()-37 (1)-37 (\))-297 (by)-297 (a)-298 (sum)]TJ
/N7 1 Tf
6.5 0 0 6 82.75 293.25 Tm
7.1005 Tc
[(tj)1658.5 (j)2113.9 (j)]TJ
/N6 1 Tf
21.5492 0 TD
0 Tc
(0)Tj
10 0 0 10 318 283 Tm
[(over)-286.1 (the)]TJ
/N7 1 Tf
3.571 0 TD
(n)Tj
/N6 1 Tf
0.823 0 TD
[(nearest)-287.2 (particles)-286.2 (together)-286.2 (with)-286.1 (a)-287 (prediction)]TJ
6.5 0 0 6 116.9 277.75 Tm
0.092 Tc
(\(1\))Tj
5.0969 -0.2917 TD
0.0928 Tc
(\(1\))Tj
-1.7938 -0.25 TD
6.2631 Tc
(11)Tj
/N8 1 Tf
10 0 0 10 111.36 273.75 Tm
5.082 Tc
(\304\304)Tj
/N10 1 Tf
9 0 0 6 137.7 271.25 Tm
4.3844 Tc
(]])Tj
10 0 0 11 230.45 271.25 Tm
0 Tc
(9)Tj
/N6 1 Tf
10 0 0 10 78 271 Tm
(where)Tj
/N8 1 Tf
3.136 0 TD
(F)Tj
/N10 1 Tf
1.835 0 TD
(5)Tj
/N8 1 Tf
1.566 0 TD
(F)Tj
/N6 1 Tf
1.581 0 TD
(,)Tj
/N8 1 Tf
0.434 0 TD
(F)Tj
/N10 1 Tf
0.814 0 TD
(5)Tj
/N8 1 Tf
1.567 0 TD
(F)Tj
/N6 1 Tf
1.304 0 TD
(and)Tj
/N10 1 Tf
10 0 2.68 10 221.38 271 Tm
(d)Tj
/N7 1 Tf
10 0 0 10 226.93 271 Tm
(t)Tj
/N10 1 Tf
0.912 0 TD
(5)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N10 1 Tf
0.482 0 TD
(2)Tj
/N7 1 Tf
0.999 0 TD
(t)Tj
/N6 1 Tf
1.24 0 TD
[(\()37 (with)-2400.1 (of)-415 (the)-416 (distant)-415.1 (contribution.)-416.3 (This)-415.1 (procedure)-416.2 (can)-416.1 (lead)]TJ
/N7 1 Tf
6.5 0 0 6 230.45 268.5 Tm
4.8774 Tc
(jj)Tj
/N6 1 Tf
-14.1662 -0.0833 TD
6.2631 Tc
(62)Tj
/N10 1 Tf
10 0 0 11 87.07 259.25 Tm
0 Tc
(9)Tj
10 0 2.68 10 78 259 Tm
(d)Tj
/N7 1 Tf
10 0 0 10 83.55 259 Tm
(t)Tj
/N10 1 Tf
0.924 0 TD
0.167 Tc
(,D)Tj
/N7 1 Tf
1.667 0 TD
0 Tc
(t)Tj
/N6 1 Tf
0.599 0 TD
[(\).)-333 (The)-333.1 (coordinates)-333.3 (and)-333.1 (velocities)-333.2 (of)-333 (particle)-2400.2 (to)-677 (a)-677 (signi\256cant)-677.2 (gain)-678.1 (in)-677 (ef\256ciency,)-677.2 (provided)-678.2 (the)]TJ
/N7 1 Tf
6.5 0 0 6 87.07 256.5 Tm
3.642 Tc
(jj)Tj
/N6 1 Tf
18.0446 -0.75 TD
0.0927 Tc
(\(3\))Tj
/N7 1 Tf
10 0 0 10 78 247 Tm
0 Tc
(i)Tj
/N6 1 Tf
0.646 0 TD
[(are)-332 (then)-332.1 (improved)-332.2 (to)-332 (order)]TJ
/N8 1 Tf
11.323 0 TD
(F)Tj
/N6 1 Tf
1.913 0 TD
[(by)-332 (standard)-332.2 (Taylor)-2400.1 (respective)-296.2 (time-scales)-297.2 (are)-297.1 (well)-297.1 (separated)-297.2 (and)]TJ
/N7 1 Tf
28.615 0 TD
(n)Tj
/N22 1 Tf
0.704 0 TD
(<)Tj
/N7 1 Tf
1.482 0 TD
(N)Tj
/N6 1 Tf
0.667 0 TD
(.)Tj
-45.35 -1.2 TD
[(series)-564.1 (integration)-564.2 (\()37 (cf.)-564 (\()-37 (4)-37 (\))37 (\),)-564 (whereupon)-564.2 (the)-564 (current)-3400.2 (To)-378 (implement)-379.2 (the)-379 (AC)-378 (scheme,)-379.2 (we)-379 (form)-378.1 (a)-379 (list)-379.1 (for)]TJ
T*
[(force)-377.1 (may)-377.1 (be)-378 (obtained)-377.2 (by)-377 (direct)-378.1 (summation.)-377.3 (At)-378 (this)-2400.1 (each)-348.1 (particle)-348.2 (containing)-348.2 (all)-349 (members)-348.2 (inside)-348.1 (a)-349 (sphere)]TJ
T*
[(stage)-413.1 (the)-414 (four)-413.1 (times)]TJ
/N7 1 Tf
8.764 0 TD
(t)Tj
/N6 1 Tf
1.072 0 TD
[(are)-414 (updated)-413.2 (to)-414 (be)-414 (consistent)-2400.2 (of)-477 (radius)]TJ
/N7 1 Tf
18.395 0 TD
(R)Tj
/N6 1 Tf
0.951 0 TD
[(.)-478 (I)0 (n)-477 (addition,)-477.2 (we)-478 (include)-477.1 (any)-478.1 (particles)]TJ
/N7 1 Tf
6.5 0 0 6 168.74 208.5 Tm
30.0175 Tc
(ks)Tj
/N6 1 Tf
46.3646 -0.75 TD
0.1672 Tc
(1/3)Tj
10 0 0 10 78 199 Tm
0 Tc
[(with)-493.1 (the)-494 (de\256nition)-493.2 (that)]TJ
/N7 1 Tf
10.308 0 TD
(t)Tj
/N6 1 Tf
1.207 0 TD
[(denotes)-494.2 (the)-493 (time)-494.1 (of)-494 (the)-2400 (within)-276.1 (a)-276 (surrounding)-276.3 (shell)-276.1 (of)-277 (radius)-276.1 (2)]TJ
/N7 1 Tf
28.964 0 TD
(R)Tj
/N6 1 Tf
1.232 0 TD
(satisfying)Tj
6.5 0 0 6 184.41 196.5 Tm
(0)Tj
/N7 1 Tf
46.8923 0 TD
(s)Tj
/N6 1 Tf
-18.2108 -0.75 TD
(2)Tj
10 0 0 10 78 187 Tm
[(most)-531.1 (recent)-532.1 (force)-532.1 (evaluation.)-532.3 (New)-532.1 (differences)-532.2 (are)]TJ
/N8 1 Tf
24 0 TD
(R)Tj
/N10 1 Tf
0.888 0 TD
(?)Tj
/N8 1 Tf
0.389 0 TD
(V)Tj
/N10 1 Tf
0.888 0 TD
(,)Tj
/N6 1 Tf
1 0 TD
(0.1)Tj
/N7 1 Tf
1.434 0 TD
(R)Tj
/N6 1 Tf
1.177 0 TD
(/)Tj
/N10 1 Tf
0.296 0 TD
(D)Tj
/N7 1 Tf
0.667 0 TD
(T)Tj
/N6 1 Tf
0.824 0 TD
[(,)-548 (where)]TJ
/N10 1 Tf
3.789 0 TD
(D)Tj
/N7 1 Tf
0.667 0 TD
(T)Tj
/N6 1 Tf
1.376 0 TD
[(denotes)-548.2 (the)-548 (regular)]TJ
/N7 1 Tf
6.5 0 0 6 370.84 184.5 Tm
2.7541 Tc
[(si)-5089.4 (i)]TJ
/N6 1 Tf
-22.5138 -0.75 TD
0 Tc
(4)Tj
10 0 0 10 78 175 Tm
[(now)-475.1 (formed)-475.1 (\()37 (cf.)-475 (\()-37 (3)-37 (\))37 (\),)-475 (including)]TJ
/N8 1 Tf
13.873 0 TD
(D)Tj
/N6 1 Tf
1.138 0 TD
[(.)-475 (Together)-476.2 (with)-2400.1 (time-step.)-559.2 (This)-559.1 (ensures)-559.2 (that)-559.1 (fast)-559.1 (approaching)-559.3 (par-)]TJ
6.5 0 0 6 120.06 168 Tm
0.0927 Tc
(\(4\))Tj
10 0 0 10 78 163 Tm
0 Tc
[(the)-325 (new)]TJ
/N8 1 Tf
3.539 0 TD
(F)Tj
/N6 1 Tf
1.581 0 TD
[(,)-326 (these)-326.1 (correction)-326.2 (terms)-326.1 (are)-326 (combined)-326.2 (to)-2400 (ticles)-385.1 (are)-385 (selected)-385.2 (from)-385.1 (the)-385 (buffer)-385.1 (zone.)]TJ
-5.12 -1.2 TD
[(improve)-591.2 (the)-591 (current)-592.2 (coordinates)-591.3 (and)-591.1 (velocities)-592.2 (to)-3400 (The)-289.1 (size)-289.1 (of)-289 (the)-290 (neighbour)-289.2 (sphere)-289.1 (is)-289 (modi\256ed)-289.2 (at)-290 (the)]TJ
T*
[(highest)-281.2 (order,)-282.1 (whereupon)-281.2 (the)-282 (primary)-281.2 (coordinates)-282.3 (are)-2400 (end)-561.1 (of)-562 (each)-562.1 (regular)-562.2 (time-step)-562.2 (when)-562.1 (a)-562 (total)-562.1 (force)]TJ
T*
[(initialized)-385.2 (by)]TJ
/N8 1 Tf
5.77 0 TD
(r)Tj
/N10 1 Tf
1.046 0 TD
(5)Tj
/N8 1 Tf
1 0 TD
(r)Tj
/N6 1 Tf
0.712 0 TD
[(.)-15222 (summation)-363.2 (is)-364 (carried)-364.1 (out.)-252.1 (W)55 (e)-363 (have)-364.1 (adopted)-364.2 (a)-364 (neigh-)]TJ
6.5 0 0 6 140.69 124.5 Tm
(0)Tj
/N7 1 Tf
3.1108 0 TD
(t)Tj
/N6 1 Tf
10 0 0 10 88 115 Tm
[(New)-435.1 (time-steps)-435.2 (are)-436 (assigned)-435.2 (initially)-436.2 (for)-435 (all)-436 (par-)-2400.1 (bour)-586.1 (criterion)-586.2 (mainly)-586.1 (based)-587.1 (on)-586 (distance)-586.2 (for)-587 (con-)]TJ
ET
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33 33 546 744 RC
BT
/N6 1 Tf
8 0 0 8 78 705 Tm
0 g
/N13 /ExtGState findRes gs
0 Tc
(280)Tj
/N7 1 Tf
18.0325 0 TD
0 Tw
(S)Tj
/N6 1 Tf
8 0 2.144 8 226.26 705 Tm
(.)Tj
/N7 1 Tf
8 0 0 8 228.7 705 Tm
(J)Tj
/N6 1 Tf
8 0 2.144 8 232.25 705 Tm
(.)Tj
/N7 1 Tf
8 0 0 8 237.78 705 Tm
(Aarseth)Tj
/N6 1 Tf
3.6063 0 TD
(/)Tj
/N7 1 Tf
0.7375 0 TD
[(New)-440.8 (Astronomy)]TJ
/N6 1 Tf
8 0 2.144 8 328.02 705 Tm
[(6)-385 (\()-37 (2001)-37.5 (\))-384.5 (277)]TJ
8 0 0 8 373.29 705 Tm
(\261)Tj
8 0 2.144 8 377.73 705 Tm
(291)Tj
6.5 0 0 6 348.82 681 Tm
0.0554 Tc
[(new)-3419.5 (o)0 (ld)-2849.2 (new)-3418 (o)-1.5 (ld)]TJ
10 0 0 10 78 679 Tm
0 Tc
[(venience.)-654.2 (However,)-654.2 (some)-654.1 (modi\256cation)-654.3 (would)-654.1 (be)]TJ
/N8 1 Tf
26.416 -0.3 TD
(F)Tj
/N10 1 Tf
2.043 0 TD
(2)Tj
/N6 1 Tf
1 0 TD
(\()Tj
/N8 1 Tf
0.37 0 TD
(F)Tj
/N10 1 Tf
1.792 0 TD
(2)Tj
/N8 1 Tf
0.999 0 TD
(F)Tj
/N6 1 Tf
1.915 0 TD
(\))Tj
/N10 1 Tf
0.499 0 TD
(2)Tj
/N8 1 Tf
1 0 TD
(F)Tj
/N6 1 Tf
6.5 0 0 6 348.82 673.5 Tm
0.0557 Tc
[(reg)-3808.9 (i)1.4 (rr)-3183.6 (irr)-4140.5 (r)-0.5 (eg)]TJ
-3.5462 -0.25 TD
0 Tc
(1)Tj
/N10 1 Tf
30 0 0 10 341.04 667.5 Tm
(]]]]]]])Tj
18 0 0 10 446.04 667.5 Tm
(])Tj
/N6 1 Tf
10 0 0 10 78 667 Tm
[(desirable)-398.2 (for)-399.1 (very)-398.1 (large)-399.1 (mass)-399.1 (ratios)-398.1 (\()37 (say)]TJ
/N10 1 Tf
17.359 0 TD
(.)Tj
/N6 1 Tf
1 0 TD
[(100)-37.1 (\).)-399 (A)]TJ
/N8 1 Tf
5.641 0 TD
(D)Tj
/N10 1 Tf
1.305 0 TD
(5)Tj
/N6 1 Tf
12.409 0 TD
[(,)-5896 (\()-37 (15)-37 (\))]TJ
/N7 1 Tf
-6.914 -0.55 TD
(t)Tj
/N10 1 Tf
0.482 0 TD
(2)Tj
/N7 1 Tf
1 0 TD
(T)Tj
/N6 1 Tf
6.5 0 0 6 406.93 659 Tm
(0)Tj
10 0 0 10 78 655 Tm
[(selection)-324.2 (criterion)-324.2 (based)-324.1 (on)-325 (the)-324 (local)-324.1 (number)-325.2 (density)]TJ
6.5 0 0 6 351.95 644 Tm
0.0556 Tc
(old)Tj
10 0 0 10 78 643 Tm
0 Tc
[(contrast)-391.2 (has)-392.1 (proved)-391.1 (itself)-392.1 (for)-391.1 (a)-392 (variety)-391.1 (of)-392 (problems,)]TJ
24 -0.4 TD
(where)Tj
/N8 1 Tf
2.728 0 TD
(F)Tj
/N6 1 Tf
1.911 0 TD
[(denotes)-286.2 (the)-286 (old)-286 (regular)-286.2 (force,)-286.1 (evaluated)-286.2 (at)]TJ
6.5 0 0 6 351.95 636.5 Tm
0.0554 Tc
(reg)Tj
10 0 0 10 78 631 Tm
0 Tc
[(but)-276.1 (may)-276.1 (need)-276.1 (modi\256cation)-276.3 (for)-276.1 (interacting)-277.2 (subsystems)]TJ
24 -0.4 TD
(time)Tj
/N7 1 Tf
2.147 0 TD
(T)Tj
/N6 1 Tf
0.992 0 TD
[(,)-370 (and)-369.1 (the)-370 (net)-370.1 (change)-369.1 (in)-370 (the)-369 (irregular)-370.2 (force)-370.1 (is)]TJ
6.5 0 0 6 345.59 624.5 Tm
(0)Tj
10 0 0 10 78 619 Tm
[(or)-294 (massive)-295.2 (particles.)-295.2 (To)-295 (suf\256cient)-295.2 (approximation,)-295.4 (the)]TJ
24 -0.4 TD
[(contained)-407.2 (in)-408 (the)-407.1 (middle)-408.1 (brackets.)-407.2 (In)-408 (the)-408.1 (subsequent)]TJ
-24 -0.8 TD
[(local)-385.1 (number)-385.2 (density)-385.1 (contrast)-385.2 (is)-385 (given)-385.1 (by)]TJ
24 -0.4 TD
[(discussions,)-586.3 (regular)-587.2 (times)-586.1 (and)-587.1 (time-steps)-586.2 (are)-587 (dis-)]TJ
0 -1.2 TD
[(tinguished)-475.2 (using)-476.1 (upper)-476.1 (case)-476.1 (characters.)-476.2 (All)-476.1 (current)]TJ
6.5 0 0 6 141.19 589.75 Tm
(3)Tj
10 0 0 10 97.81 586.75 Tm
(2)Tj
/N7 1 Tf
0.5 0 TD
1.514 Tc
(nR)Tj
/N6 1 Tf
6.5 0 0 6 108.37 584.25 Tm
0 Tc
(1)Tj
/N7 1 Tf
3.2323 0 TD
(h)Tj
/N10 1 Tf
32 0 0 10 96.7 579.25 Tm
(])Tj
23.5 0 0 10 121.84 579.25 Tm
(])Tj
/N6 1 Tf
10 0 0 10 318 579 Tm
[(force)-480.1 (components)-480.3 (are)-481 (obtained)-480.2 (using)-480.1 (the)]TJ
/N7 1 Tf
17.823 0 TD
(predicted)Tj
-41.823 -0.025 TD
(C)Tj
/N10 1 Tf
0.87 0 TD
(5)Tj
/N6 1 Tf
5.81 0 TD
[(,)-12930 (\()-37 (12)-37 (\))]TJ
/N11 1 Tf
31.5 0 0 26.5 114.95 577.5 Tm
0.3745 Tc
(SD)Tj
/N7 1 Tf
10 0 0 10 101.38 573.25 Tm
1.527 Tc
(NR)Tj
6.5 0 0 6 129.74 570.75 Tm
0 Tc
(s)Tj
/N6 1 Tf
10 0 0 10 318 567 Tm
[(coordinates)-455.3 (\()37 (which)-455.1 (must)-456.1 (be)-455 (saved)-37.1 (\),)-456 (rather)-455.1 (than)-456.1 (the)]TJ
6.5 0 0 6 485.61 560 Tm
(4)Tj
10 0 0 10 318 555 Tm
[(corrected)-294.2 (values)-295.1 (based)-294.1 (on)-295 (the)-294 (irregular)]TJ
/N8 1 Tf
15.984 0 TD
(D)Tj
/N6 1 Tf
1.433 0 TD
[(term)-295.1 (since)]TJ
-41.417 -0.45 TD
(where)Tj
/N7 1 Tf
2.909 0 TD
(n)Tj
/N6 1 Tf
1.402 0 TD
[(is)-466 (the)-466 (current)-466.2 (membership)-467.3 (and)]TJ
/N7 1 Tf
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/N6 1 Tf
1.493 0 TD
[(is)-467 (the)]TJ
6.5 0 0 6 112.64 548 Tm
(1)Tj
/N7 1 Tf
22.9677 0 TD
(h)Tj
/N6 1 Tf
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[(otherwise)-298.2 (\()-37 (1)0 (5)-37 (\))-298 (would)-298.1 (contain)-298.2 (a)-298 (spurious)-298.2 (force)-299.1 (differ-)]TJ
-24 -0.45 TD
[(half-mass)-568.2 (radius.)-569.1 (In)-568 (order)-569.1 (to)-568 (limit)-569.1 (the)-568 (range,)-569.1 (we)]TJ
24 -0.75 TD
[(ence.)-693.1 (The)-694.1 (higher)-694.1 (differences)-694.2 (are)-694 (formed)-694.1 (in)-694 (the)]TJ
-24 -0.45 TD
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24 -0.75 TD
[(standard)-356.2 (way,)-356.1 (whereupon)-356.2 (the)-356 (regular)-356.2 (force)-356.1 (corrector)]TJ
6.5 0 0 6 149.16 509.25 Tm
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10 0 0 10 318 507 Tm
0 Tc
[(is)-385 (applied)-385.2 (\()-37 (i)0 (f)-385 (desired)-37.1 (\).)]TJ
/N7 1 Tf
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/N10 1 Tf
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(5)Tj
/N7 1 Tf
0.999 0 TD
(n)Tj
/N6 1 Tf
1.803 0 TD
[(\()-37 (0.04)]TJ
/N7 1 Tf
2.12 0 TD
(C)Tj
/N6 1 Tf
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0.037 Tc
[(\))-1065 (,)-11373 (\(1)37 (3\))]TJ
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0 Tc
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3.2415 0 TD
0.0559 Tc
(max)Tj
10 0 0 10 328 495 Tm
0 Tc
[(A)-693 (complication)-693.3 (arises)-694.1 (because)-693.2 (any)-693.1 (change)-694.1 (in)]TJ
-1 -1.2 TD
[(neighbours)-465.2 (requires)-465.2 (appropriate)-466.3 (corrections)-465.2 (of)-466 (both)]TJ
-24 -0.25 TD
[(subject)-463.2 (to)]TJ
/N7 1 Tf
4.538 0 TD
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/N6 1 Tf
1.38 0 TD
[(being)-464.1 (within)-463.1 ([0.2)]TJ
/N7 1 Tf
7.288 0 TD
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/N6 1 Tf
1.803 0 TD
[(,)-463 (0.9)]TJ
/N7 1 Tf
1.963 0 TD
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/N6 1 Tf
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[(],)-464 (with)]TJ
/N7 1 Tf
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13.3738 0 TD
0.0548 Tc
[(max)-3906.7 (m)-1 (ax)]TJ
10 0 0 10 318 471 Tm
0 Tc
[(force)-340.1 (polynomials;)-340.3 (i.e.)-340.1 (using)-340.1 (the)-340 (principle)-340.2 (of)-341 (succes-)]TJ
/N7 1 Tf
-24 -0.25 TD
(n)Tj
/N6 1 Tf
2.338 0 TD
[(denoting)-536.2 (the)-536 (maximum)-536.2 (permitted)-536.2 (value.)-536.1 (The)]TJ
6.5 0 0 6 83.55 466 Tm
0.0559 Tc
(max)Tj
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0 Tc
[(sive)-528.1 (differentiation)-528.3 (of)-529 (\()-37 (1)0 (1)-37 (\))0 (.)-528 (The)-528.1 (respective)-529.2 (Taylor)]TJ
-24 -0.25 TD
[(new)-419.1 (neighbour)-419.2 (sphere)-420.1 (radius)-419.1 (is)-420 (then)-419.1 (adjusted)-420.2 (using)]TJ
24 -0.95 TD
[(series)-565.1 (derivatives)-565.2 (\()-37 (5)-37 (\))-566 (and)-565.1 (\()-37 (6)-37 (\))-566 (are)-565 (accumulated)-566.3 (to)]TJ
-24 -0.25 TD
[(the)-385 (corresponding)-385.3 (volume)-385.2 (ratio,)-385.1 (which)-385.1 (gives)]TJ
24 -0.95 TD
[(yield)-685.1 (the)-685.1 (net)-686.1 (change.)-685.2 (Each)-686.1 (force)-685.1 (polynomial)-686.3 (is)]TJ
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0.1664 Tc
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18.289 -0.125 TD
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(p)Tj
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0 Tc
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(R)Tj
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(5)Tj
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[(.)-11090 (\()-37 (14)-37 (\))]TJ
/N11 1 Tf
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0.3472 Tc
(SD)Tj
/N7 1 Tf
6.5 0 0 6 84.85 412.75 Tm
4.3279 Tc
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/N6 1 Tf
10 0 0 10 318 411 Tm
0 Tc
[(terms)-387.1 (to)-388 (the)-388.1 (corresponding)-387.3 (Taylor)-388.1 (series)-388.1 (derivatives)]TJ
/N7 1 Tf
-18.301 -0.125 TD
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/N6 1 Tf
6.5 0 0 6 140.55 407.25 Tm
(1)Tj
39.1031 -0.5417 TD
(4)Tj
10 0 0 10 318 399 Tm
[(\()-37 (4)-37 (\))-360 (\()37 (without)-360.2 (the)]TJ
/N8 1 Tf
6.894 0 TD
(D)Tj
/N6 1 Tf
1.499 0 TD
[(term)36.9 (\),)-360 (followed)-360.2 (by)-360 (a)-361 (conversion)]TJ
-31.393 -1.2 TD
[(An)-395 (alternative)-396.2 (and)-395.1 (simpler)-396.2 (strategy)-395.2 (is)-396 (to)-396 (stabilize)-2400.2 (to)-385 (standard)-385.2 (differences)-385.3 (using)-385.1 (\()-37 (8)-37 (\))0 (.)]TJ
-1 -1.2 TD
[(all)-600 (neighbour)-600.2 (memberships)-601.3 (on)-600 (the)-600 (same)-601.1 (constant)-3400.2 (Implementation)-563.4 (of)-564 (the)-563 (AC)-564 (scheme)-563.2 (requires)-564.2 (the)]TJ
T*
(value)Tj
/N7 1 Tf
2.852 0 TD
(n)Tj
/N10 1 Tf
1.083 0 TD
(5)Tj
/N7 1 Tf
1 0 TD
(n)Tj
/N6 1 Tf
1.622 0 TD
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/N8 1 Tf
37.168 0 TD
(F)Tj
/N6 1 Tf
1.625 0 TD
(,)Tj
/N7 1 Tf
6.5 0 0 6 111.83 360.5 Tm
(p)Tj
/N6 1 Tf
3.2415 0 TD
(0)Tj
59.8492 0 TD
0.0554 Tc
(reg)Tj
-30.1769 -0.75 TD
2.5292 Tc
(123)Tj
10 0 0 10 78 351 Tm
0 Tc
[(number)-379.2 (of)-380 (re\256nements)-380.3 (are)-380 (also)-380.1 (included)-380.2 (as)-380 (follows:)]TJ
/N8 1 Tf
24 0 TD
(D)Tj
/N6 1 Tf
1.138 0 TD
(,)Tj
/N8 1 Tf
0.83 0 TD
(D)Tj
/N6 1 Tf
1.139 0 TD
(,)Tj
/N8 1 Tf
0.83 0 TD
(D)Tj
/N6 1 Tf
1.139 0 TD
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/N10 1 Tf
0.83 0 TD
(D)Tj
/N7 1 Tf
0.667 0 TD
(T)Tj
/N6 1 Tf
0.556 0 TD
(,)Tj
/N7 1 Tf
0.83 0 TD
(T)Tj
/N6 1 Tf
0.993 0 TD
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/N7 1 Tf
0.83 0 TD
(T)Tj
/N6 1 Tf
0.992 0 TD
(,)Tj
/N7 1 Tf
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(T)Tj
/N6 1 Tf
0.992 0 TD
(,)Tj
/N7 1 Tf
0.831 0 TD
(T)Tj
/N6 1 Tf
0.992 0 TD
[(,)-580 (a)0 (s)-580 (well)-580.1 (as)-581 (the)]TJ
6.5 0 0 6 403.71 348.5 Tm
2.3035 Tc
(0123)Tj
10 0 0 10 318 339 Tm
0 Tc
[(neighbour)-300.2 (sphere)-301.1 (radius)]TJ
/N7 1 Tf
10.011 0 TD
(R)Tj
/N6 1 Tf
1.256 0 TD
[(and)-301.1 (neighbour)-301.2 (list)]TJ
/N7 1 Tf
7.625 0 TD
(L)Tj
/N6 1 Tf
0.857 0 TD
[(\()37 (size)]TJ
/N7 1 Tf
6.5 0 0 6 424.54 336.5 Tm
(s)Tj
10 0 0 10 318 327 Tm
(n)Tj
/N10 1 Tf
1.969 0 TD
(1)Tj
/N6 1 Tf
0.999 0 TD
0.037 Tc
[(1\))37 (.)]TJ
6.5 0 0 6 323.55 324.5 Tm
0.0559 Tc
(max)Tj
/N9 1 Tf
10 0 0 10 80.9 323 Tm
0 Tc
(\267)Tj
/N6 1 Tf
0.96 0 TD
[(In)-477 (order)-477.1 (to)-478 (avoid)-477.1 (a)-478 (resonance)-477.2 (oscillation)-477.2 (in)]TJ
/N7 1 Tf
19.149 0 TD
(R)Tj
/N6 1 Tf
0.951 0 TD
(,)Tj
/N7 1 Tf
6.5 0 0 6 288.41 320.5 Tm
(s)Tj
/N6 1 Tf
-25.5569 -0.75 TD
0.1672 Tc
(1/6)Tj
10 0 0 10 92.34 311 Tm
0 Tc
(\()Tj
/N7 1 Tf
0.296 0 TD
(n)Tj
/N6 1 Tf
1.023 0 TD
(/)Tj
/N7 1 Tf
0.352 0 TD
(n)Tj
/N6 1 Tf
0.973 0 TD
[(\))-1499 (i)0 (s)-398 (used)-398.1 (in)-398 (\()-37 (1)0 (4)-37 (\))-397 (if)-398 (the)-398 (predicted)-398.2 (mem-)]TJ
/N7 1 Tf
6.5 0 0 6 100.61 308.5 Tm
(p)Tj
/N6 1 Tf
2.1523 0 TD
(1)Tj
10 0 0 10 90.5 299 Tm
[(bership)-385.1 (lies)-385.1 (between)-385.2 (the)-385 (old)-385 (and)-385.1 (new)-385.1 (value.)]TJ
/N9 1 Tf
-0.96 -1.2 TD
(\267)Tj
/N7 1 Tf
0.96 0 TD
(R)Tj
/N6 1 Tf
1.331 0 TD
[(is)-376 (modi\256ed)-376.2 (by)-376 (a)-376 (radial)-376.1 (velocity)-376.2 (factor)-376.1 (outside)]TJ
/N8 1 Tf
21.419 0 TD
[(3.)-500 (Program)-385.2 (structure)]TJ
/N7 1 Tf
6.5 0 0 6 96.92 284.5 Tm
(s)Tj
/N6 1 Tf
10 0 0 10 90.5 275 Tm
[(the)-385 (core.)]TJ
/N9 1 Tf
-0.96 -1.2 TD
(\267)Tj
/N6 1 Tf
0.96 0 TD
[(The)-405.1 (volume)-405.2 (factor)-405.1 (is)-406 (only)-405.1 (allowed)-405.2 (to)-405 (change)-406.1 (by)-3400 (This)-514.1 (section)-515.1 (describes)-515.2 (the)-515.1 (structure)-515.2 (of)-515 (the)-515.1 (code)]TJ
0 -1.2 TD
[(25%,)-435.1 (subject)-435.2 (to)-436 (a)-435 (time-step)-436.2 (dependent)-435.2 (cut-off)-436.1 (if)-2400 (and)-408.1 (de\256nes)-409.2 (the)-409 (main)-409.1 (input)-408.1 (parameters)-409.2 (and)-409.1 (some)-409.1 (of)]TJ
/N10 1 Tf
T*
(D)Tj
/N7 1 Tf
0.667 0 TD
(T)Tj
/N10 1 Tf
1.007 0 TD
(,)Tj
/N6 1 Tf
0.999 0 TD
(0.01)Tj
/N7 1 Tf
1.934 0 TD
(T)Tj
/N6 1 Tf
1.593 0 TD
(\()Tj
/N7 1 Tf
0.296 0 TD
(T)Tj
/N6 1 Tf
1.594 0 TD
[(is)-385 (the)-385 (crossing)-385.2 (time)36.9 (\).)-5959 (the)-385.1 (options.)]TJ
/N7 1 Tf
6.5 0 0 6 103.04 236.5 Tm
(i)Tj
/N6 1 Tf
6.1 0 TD
0.0553 Tc
[(cr)-2019.4 (cr)]TJ
/N9 1 Tf
10 0 0 10 80.9 227 Tm
0 Tc
(\267)Tj
/N6 1 Tf
0.96 0 TD
(If)Tj
/N7 1 Tf
1.249 0 TD
(n)Tj
/N10 1 Tf
1.103 0 TD
(#)Tj
/N6 1 Tf
0.999 0 TD
[(3)-584 (and)-583.1 (the)-583 (neighbours)-584.2 (are)-583 (moving)-584.2 (out-)]TJ
6.5 0 0 6 108.54 224.5 Tm
(1)Tj
10 0 0 10 90.5 215 Tm
[(wards,)-584.1 (the)-585 (standard)-585.2 (sphere)]TJ
/N7 1 Tf
12.197 0 TD
(R)Tj
/N6 1 Tf
1.54 0 TD
[(is)-585 (increased)-585.2 (by)]TJ
/N7 1 Tf
6.5 0 0 6 218.89 212.5 Tm
(s)Tj
/N6 1 Tf
10 0 2.68 10 318 211 Tm
(3.1.)Tj
/N7 1 Tf
10 0 0 10 338.55 211 Tm
(Routines)Tj
/N6 1 Tf
-24.805 -0.8 TD
(10%.)Tj
23.75 -1.6 TD
[(The)-363.1 (program)-364.2 (contains)-364.2 (some)-364.1 (2307)-364.1 (lines)-364.1 (of)-364 (Fortran)]TJ
-24 -1.2 TD
[(The)-547.1 (gain)-548.1 (or)-548 (loss)-548.1 (of)-547 (particles)-548.2 (is)-548 (recorded)-548.2 (when)-2400.1 (statements)-379.2 (and)-380.1 (another)-380.2 (1203)-379.1 (lines)-380.1 (of)-380 (comments)-380.2 (and)]TJ
-1 -1.2 TD
[(comparing)-328.2 (the)-328 (old)-328 (and)-328.1 (new)-328.1 (neighbour)-328.2 (list,)-328.1 (following)-2400.2 (spaces.)-326.2 (It)-326 (is)-326 (divided)-326.2 (into)-326.1 (38)-326 (routines,)-326.2 (many)-326.1 (of)-327 (which)]TJ
T*
[(the)-352 (re-calculation)-353.3 (of)-353 (the)-352 (regular)-353.2 (force.)-353.1 (Regular)-353.2 (force)-2400.1 (are)-499 (optional)-499.2 (and)-499.1 (not)-499.1 (required)-499.2 (for)-499.1 (standard)-499.2 (simula-)]TJ
T*
[(differences)-531.2 (are)-532 (\256rst)-531.1 (evaluated,)-532.2 (assuming)-531.2 (there)-532.1 (has)-2400.1 (tions.)-357.1 (All)-357.1 (the)-357 (routines)-357.2 (are)-357 (listed)-357.1 (in)-357 (Table)-357.1 (1,)-357 (together)]TJ
T*
[(been)-335.1 (no)-336 (change)-335.1 (of)-336 (neighbours.)-335.3 (This)-336.1 (gives)-335.1 (rise)-336.1 (to)-336 (the)-2400 (with)-332.1 (the)-332 (main)-333.1 (calling)-332.1 (sequence)-333.2 (and)-332.1 (an)-333 (outline)-332.1 (of)-333 (the)]TJ
T*
[(provisional)-385.3 (new)-385.1 (regular)-385.2 (force)-385.1 (difference)-7355.2 (purpose)-385.2 (\()]TJ
/N11 1 Tf
27.847 0 TD
([)Tj
/N6 1 Tf
1.218 0 TD
[(denotes)-385.2 (an)-385 (option)36.9 (\).)]TJ
ET
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33 33 546 744 RC
BT
/N7 1 Tf
8 0 0 8 222.26 705 Tm
0 g
/N13 /ExtGState findRes gs
0 Tc
0 Tw
(S)Tj
/N6 1 Tf
8 0 2.144 8 226.26 705 Tm
(.)Tj
/N7 1 Tf
8 0 0 8 228.7 705 Tm
(J)Tj
/N6 1 Tf
8 0 2.144 8 232.25 705 Tm
(.)Tj
/N7 1 Tf
8 0 0 8 237.78 705 Tm
(Aarseth)Tj
/N6 1 Tf
3.6063 0 TD
(/)Tj
/N7 1 Tf
0.7375 0 TD
[(New)-440.8 (Astronomy)]TJ
/N6 1 Tf
8 0 2.144 8 328.02 705 Tm
[(6)-385 (\()-37 (2001)-37.5 (\))-384.5 (277)]TJ
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(\261)Tj
8 0 2.144 8 377.73 705 Tm
(291)Tj
8 0 0 8 522 705 Tm
(281)Tj
-55.5 -3 TD
[(Table)-384.3 (1)]TJ
0 -1.25 TD
[(Names)-384.3 (of)-385.8 (routines)]TJ
ET
1 i
78 666 15 -0.5 re
f 
93 666 15 -0.5 re
f 
108 666 15 -0.5 re
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123 666 15 -0.5 re
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138 666 15 -0.5 re
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153 666 15 -0.5 re
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168 666 15 -0.5 re
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183 666 15 -0.5 re
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198 666 15 -0.5 re
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213 666 15 -0.5 re
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228 666 15 -0.5 re
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243 666 15 -0.5 re
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273 666 15 -0.5 re
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288 666 15 -0.5 re
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303 666 15 -0.5 re
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318 666 15 -0.5 re
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333 666 15 -0.5 re
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438 666 15 -0.5 re
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453 666 15 -0.5 re
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468 666 15 -0.5 re
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483 666 15 -0.5 re
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498 666 15 -0.5 re
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513 666 21 -0.5 re
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BT
8 0 0 8 78 656 Tm
[(Routine)-14159.3 (Called)-385.3 (by)-17865 (Description)]TJ
ET
78 651 15 -0.5 re
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93 651 15 -0.5 re
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108 651 15 -0.5 re
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123 651 15 -0.5 re
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138 651 15 -0.5 re
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153 651 15 -0.5 re
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168 651 15 -0.5 re
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183 651 15 -0.5 re
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198 651 15 -0.5 re
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213 651 15 -0.5 re
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228 651 15 -0.5 re
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273 651 15 -0.5 re
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288 651 15 -0.5 re
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348 651 15 -0.5 re
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468 651 15 -0.5 re
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483 651 15 -0.5 re
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498 651 15 -0.5 re
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513 651 21 -0.5 re
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BT
/N7 1 Tf
8 0 0 8 78 641 Tm
(BLOCK)Tj
/N6 1 Tf
39.1875 0 TD
[(Block)-384.8 (data)-385.3 (initialization)]TJ
/N7 1 Tf
-39.1875 -1.25 TD
[(BODIES)-13827.3 (OU)-37.3 (TPU)-37.3 (T)]TJ
/N6 1 Tf
39.1875 0 TD
[(Output)-365.8 (of)-365.8 (binaries)-365.3 (and)-366 (particles)-365.8 (\()]TJ
/N11 1 Tf
13.7337 0 TD
([)Tj
/N6 1 Tf
1.1987 0 TD
0.3654 Tc
[(6&9)327.9 (\))]TJ
/N7 1 Tf
-54.12 -1.25 TD
0 Tc
[(CHECK)-13992.3 (OU)-37.3 (TPU)-37.3 (T)]TJ
/N6 1 Tf
39.1875 0 TD
[(Error)-385 (control)-384.5 (and)-384.8 (restart)-386 (\()]TJ
/N11 1 Tf
10.7212 0 TD
([)Tj
/N6 1 Tf
1.2188 0 TD
[(2)-385 (&)-384.5 (11)-37.5 (\))]TJ
/N7 1 Tf
-51.1275 -1.25 TD
[(CMCORR)-13215.3 (OU)-37.3 (TPU)-37.3 (T)]TJ
/N6 1 Tf
39.1875 0 TD
[(Centre)-385.3 (of)-384.5 (mass)-385 (corrections)-384.6 (\()]TJ
/N11 1 Tf
11.7775 0 TD
([)Tj
/N6 1 Tf
1.2188 0 TD
[(18)-36.3 (\))]TJ
/N7 1 Tf
-52.1837 -1.25 TD
[(CO)-54.8 (AL)-14715.5 (M)-55.8 (AIN)]TJ
/N6 1 Tf
39.1875 0 TD
[(Inelastic)-384.5 (two-body)-385.8 (collision)-385 (\()]TJ
/N11 1 Tf
12.1162 0 TD
([)Tj
/N6 1 Tf
1.2188 0 TD
[(12)-36.3 (\))]TJ
/N7 1 Tf
-52.5225 -1.25 TD
[(CORE)-14715.3 (OU)-37.3 (TPU)-37.3 (T)]TJ
/N6 1 Tf
39.1875 0 TD
[(Core)-384.8 (radius)-384.8 (and)-384.8 (density)-386 (centre)-384.5 (\()]TJ
/N11 1 Tf
13.385 0 TD
([)Tj
/N6 1 Tf
1.2175 0 TD
0.0375 Tc
(8\))Tj
/N7 1 Tf
-53.79 -1.25 TD
0 Tc
[(CPU)-36.3 (TIM)-13568 (OU)-37.3 (TPU)-37.3 (T)]TJ
/N6 1 Tf
21.6762 0 TD
(&)Tj
/N7 1 Tf
1.0525 0 TD
(INTGRT)Tj
/N6 1 Tf
16.4587 0 TD
[(CPU)-385 (time)-384.5 (in)-385.8 (minutes)-384.3 (\()36.8 (machine)-384.5 (dependent)-37.6 (\))]TJ
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[(DA)19.2 (T)-36.3 (A)]TJ
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[(ZERO)-14826.3 (ST)-56.5 (ART)]TJ
/N6 1 Tf
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[(Initialization)-385.3 (of)-384.5 (global)-385 (scalars)]TJ
ET
78 266 15 -0.5 re
f 
93 266 15 -0.5 re
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108 266 15 -0.5 re
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123 266 15 -0.5 re
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138 266 15 -0.5 re
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153 266 15 -0.5 re
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168 266 15 -0.5 re
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183 266 15 -0.5 re
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483 266 15 -0.5 re
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513 266 21 -0.5 re
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-1 -1.2 TD
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T*
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/N6 1 Tf
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/N6 1 Tf
2.574 0 TD
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[(,)-2400 (spaces)-318.1 (are)-319 (used)-318.1 (to)-319 (improve)-319.2 (readability)-318.2 (of)-319 (the)-319 (Fortran)]TJ
/N7 1 Tf
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[(F)-18 (POLY)]TJ
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3.13 0 TD
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/N7 1 Tf
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[(F)-19 (POLY)]TJ
/N6 1 Tf
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/N7 1 Tf
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[(\()-37 (initialization)36.7 (\);)-905 (and)-2400.1 (statements,)-497.3 (where)-497.1 (blocks)-497.1 (of)-497 (code)-497.1 (inside)]TJ
/N7 1 Tf
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/N7 1 Tf
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[(\()-37 (integration)36.8 (\).)-332 (The)-2400.1 (and)-385.1 (logical)]TJ
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14.472 0 TD
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-29.972 -1.2 TD
[(main)-327.1 (calling)-328.1 (sequence)-328.2 (\()]TJ
/N7 1 Tf
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[(ST)-55 (ART)]TJ
/N6 1 Tf
2.889 0 TD
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/N7 1 Tf
0.578 0 TD
[(OU)-37 (TPU)-37.1 (T)]TJ
/N6 1 Tf
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(,)Tj
/N7 1 Tf
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/N6 1 Tf
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(\))Tj
-21.267 -1.2 TD
[(originates)-382.2 (in)-383 (routine)]TJ
/N7 1 Tf
8.703 0 TD
[(M)-56 (AIN)]TJ
/N6 1 Tf
2.5 0 TD
[(,)-382 (whereas)-383.2 (routine)]TJ
/N7 1 Tf
7.507 0 TD
[(ST)-56 (ART)]TJ
/N6 1 Tf
10 0 2.68 10 318 151 Tm
(3.2.)Tj
/N7 1 Tf
10 0 0 10 338.55 151 Tm
[(COMMON)-385.2 (variables)]TJ
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[(acts)-359.1 (as)-360 (driver)-360.1 (for)-360 (both)-360.1 (input)-360.1 (and)-360.1 (polynomial)-360.3 (initiali-)]TJ
T*
[(zation)-418.1 (and)-418.1 (routine)]TJ
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7.975 0 TD
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3.9 0 TD
[(controls)-418.2 (the)-419 (subsequent)-3400.3 (In)-572 (principle,)-572.2 (the)-572.1 (program)-572.2 (can)-572.1 (be)-572 (used)-572.1 (for)-573 (any)]TJ
-11.875 -1.2 TD
[(program)-385.2 (\257ow.)-18199.1 (particle)-327.2 (number,)-328.2 (subject)-327.2 (to)-328 (available)-327.2 (computer)-328.2 (mem-)]TJ
ET
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33 33 546 744 RC
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18.0325 0 TD
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/N7 1 Tf
8 0 0 8 228.7 705 Tm
(J)Tj
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8 0 0 8 237.78 705 Tm
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/N6 1 Tf
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[(6)-385 (\()-37 (2001)-37.5 (\))-384.5 (277)]TJ
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(\261)Tj
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(291)Tj
10 0 0 10 78 679 Tm
[(ory)-379.1 (and)-380.1 (CPU)-380.1 (time.)-380.1 (The)-380.1 (size)-379.1 (of)-380 (all)-380 (particle)-380.2 (arrays)-380.1 (is)-2400 (The)-326.1 (integration)-326.2 (parameters)]TJ
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35.254 0 TD
[(ET)-55 (AI)]TJ
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2.259 0 TD
(5)Tj
/N6 1 Tf
0.888 0 TD
[(0.03)-327.1 (and)]TJ
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3.847 0 TD
[(ET)-55 (AR)]TJ
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2.519 0 TD
(5)Tj
/N6 1 Tf
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[(controlled)-540.2 (by)-540 (the)-541 (parameter)]TJ
/N7 1 Tf
12.436 0 TD
[(NM)-56 (AX)]TJ
/N6 1 Tf
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[(,)-540 (together)-541.2 (with)-2400.1 (0.06)-341.1 (usually)-341.1 (give)-341.1 (reasonable)-341.2 (results,)-341.2 (although)-341.2 (slight-)]TJ
/N7 1 Tf
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[(LM)-55 (AX)]TJ
/N6 1 Tf
3.111 0 TD
[(which)-407.1 (is)-407 (used)-408.1 (for)-407 (the)-408 (neighbour)-407.2 (lists.)-408.1 (These)-2400.1 (ly)-383 (smaller)-383.2 (values)-383.1 (are)-383 (preferable.)-383.2 (Further)-384.2 (discussions)]TJ
-3.111 -1.2 TD
[(parameters)-364.2 (must)-364.1 (be)-364 (speci\256ed)-364.2 (in)-364 (the)-364 (auxiliary)-365.2 (header)-2400.1 (of)-353 (time-step)-353.2 (criteria)-354.1 (and)-353.1 (accuracy)-353.2 (in)-354 (the)-353.1 (AC)-354 (method)]TJ
T*
(\256le)Tj
/N32 1 Tf
1.646 0 TD
(params.h)Tj
/N6 1 Tf
5.168 0 TD
[(at)-368 (compile)-369.2 (time)-368.1 (since)-368.1 (most)-369.1 (routines)-2400.2 (have)-340.1 (been)-340.1 (given)-340.1 (elsewhere)-340.2 (\()-37 (M)0.1 (akino,)-340.2 (1991a;)-340.2 (Makino)]TJ
-6.814 -1.2 TD
[(communicate)-781.3 (via)-782 (the)-781 (global)]TJ
/N7 1 Tf
13.458 0 TD
(COMMON)Tj
/N6 1 Tf
5.281 0 TD
[(blocks,)-2400.2 (and)-355.1 (Aarseth,)-356.2 (1992)-37.1 (\).)-355 (The)-356.1 (optimum)-355.2 (size)-356.1 (of)-355 (the)-356 (neigh-)]TJ
-18.739 -1.2 TD
[(rather)-531.1 (than)-531.1 (by)-532 (general-purpose)-531.4 (arguments.)-531.3 (All)-532.1 (the)-2400 (bour)-859.1 (sphere)-860.1 (depends)-860.2 (on)-859 (the)-860 (problem;)-860.2 (usually)]TJ
6.5 0 0 6 400.03 600 Tm
0.1664 Tc
(1/2)Tj
/N7 1 Tf
10 0 0 10 78 595 Tm
0 Tc
(COMMON)Tj
/N6 1 Tf
4.947 0 TD
[(variables)-467.2 (are)-467 (de\256ned)-467.1 (in)-466 (a)-467 (TEX)-467.1 (\256le)-467.1 (for)]TJ
/N7 1 Tf
19.053 0 TD
[(NNBM)-55.1 (AX)]TJ
/N11 1 Tf
4.259 0 TD
(.)Tj
/N6 1 Tf
0.999 0 TD
(10)Tj
/N10 1 Tf
1.167 0 TD
(1)Tj
/N7 1 Tf
1 0 TD
(N)Tj
/N6 1 Tf
2.242 0 TD
[(is)-381 (suf\256cient)-381.2 (for)-381 (small)]TJ
/N7 1 Tf
9.246 0 TD
(N)Tj
/N6 1 Tf
0.667 0 TD
[(.)-381 (For)]TJ
6.5 0 0 6 129.36 588 Tm
(1)Tj
10 0 0 10 78 583 Tm
[(convenience.)-18752.3 (larger)]TJ
/N7 1 Tf
26.71 0 TD
(N)Tj
/N6 1 Tf
1.046 0 TD
(\()Tj
/N10 1 Tf
0.536 0 TD
(.)Tj
/N6 1 Tf
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[(1000)-37.1 (\),)-379 (Makino)-378.2 (and)-379.1 (Hut)-378.1 (\()-37 (1988)-37.1 (\))-379 (suggest)]TJ
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ET
1 i
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BT
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ET
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33 33 546 744 RC
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93 666 15 -0.5 re
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108 666 15 -0.5 re
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[(NF)-18.3 (IX)]TJ
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[(Output)-384.5 (frequency)-384.6 (of)-385.8 (data)-385.3 (save)-384.3 (or)-385.8 (binaries)-384 (\()]TJ
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[(3&6)347.3 (\))]TJ
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-51.0675 -1.25 TD
0 Tc
[(NR)-54.5 (AND)]TJ
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[(Random)-384.8 (number)-385 (sequence)-385 (skip)]TJ
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[(NNBM)-54.5 (AX)]TJ
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[(LM)-54.8 (AX)]TJ
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[(NR)19.2 (U)-36.7 (N)]TJ
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[(Run)-384.3 (identi\256cation)-385.8 (index)]TJ
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[(ET)-55.5 (AI)]TJ
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[(Time-step)-385.1 (parameter)-384.6 (for)-385.3 (irregular)-384.6 (force)-384.8 (polynomial)]TJ
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[(ET)-55.5 (AR)]TJ
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[(Time-step)-385.1 (parameter)-384.6 (for)-385.3 (regular)-384.3 (force)-386 (polynomial)]TJ
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/N6 1 Tf
1.1663 0 TD
[(0)-30141.2 (Initial)-384.8 (neighbour)-385.1 (sphere)-385 (radius)]TJ
/N7 1 Tf
-1.1663 -1.25 TD
[(DELT)-55 (AT)]TJ
/N6 1 Tf
31.8075 0 TD
[(Output)-384.5 (time)-384.5 (interval)-385 (in)-385.8 (units)-385 (of)-384.5 (the)-385.5 (crossing)-384.5 (time)]TJ
/N7 1 Tf
-31.8075 -1.25 TD
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/N6 1 Tf
31.8075 0 TD
[(Termination)-384.8 (time)-384.5 (in)-385.8 (units)-385 (of)-384.5 (the)-385.5 (crossing)-384.5 (time)]TJ
/N7 1 Tf
-31.8075 -1.25 TD
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/N6 1 Tf
31.8075 0 TD
[(Energy)-384.5 (tolerance)-385 (\()36.8 (restart)-384.8 (if)]TJ
/N7 1 Tf
11.4988 0 TD
(DE)Tj
/N6 1 Tf
1.4438 0 TD
(/)Tj
/N7 1 Tf
0.3525 0 TD
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/N10 1 Tf
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/N6 1 Tf
1 0 TD
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/N7 1 Tf
1 0 TD
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/N6 1 Tf
1.755 0 TD
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/N11 1 Tf
1.8288 0 TD
([)Tj
/N6 1 Tf
1.2175 0 TD
(2)Tj
/N10 1 Tf
0.6675 0 TD
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/N6 1 Tf
0.9987 0 TD
0.0375 Tc
(1\))Tj
/N7 1 Tf
-54.4025 -1.25 TD
0 Tc
(EPS)Tj
/N6 1 Tf
31.8075 0 TD
[(Softening)-384.8 (parameter)-384.6 (\()36.8 (square)-385 (saved)-385.5 (in)]TJ
/N7 1 Tf
15.7725 0 TD
(EPS)Tj
/N6 1 Tf
1.7775 0 TD
0.0375 Tc
(2\))Tj
/N7 1 Tf
-49.3575 -1.875 TD
0 Tc
(KZ)Tj
/N6 1 Tf
1.2225 0 TD
(\()Tj
/N7 1 Tf
0.3512 0 TD
(J)Tj
/N6 1 Tf
0.5363 0 TD
[(\))-29364.5 (Non-zero)-384.1 (options)-385 (for)-385.3 (alternative)-385.3 (paths)]TJ
/N7 1 Tf
-2.11 -1.875 TD
[(XTP)55.5 (AR)]TJ
/N6 1 Tf
2.9625 0 TD
[(1)-28345 (Mass)-384 (of)-385.8 (external)-385.3 (Plummer)-384.3 (model)-385 (\()]TJ
/N11 1 Tf
43.3975 0 TD
([)Tj
/N6 1 Tf
1.2175 0 TD
(15)Tj
/N10 1 Tf
1.0563 0 TD
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/N6 1 Tf
0.8887 0 TD
[(1;)-384.5 (scaled)-384.8 (units)36.2 (\))]TJ
/N7 1 Tf
-49.5225 -1.25 TD
[(XTP)55.5 (AR)]TJ
/N6 1 Tf
2.9625 0 TD
[(2)-28345 (Length)-384.5 (scale)-384.8 (for)-385.3 (Plummer)-385.6 (model)]TJ
/N7 1 Tf
-2.9625 -1.25 TD
[(ZMG)-55.3 (AS)]TJ
/N6 1 Tf
31.8075 0 TD
[(Mass)-384 (scale)-386 (for)-384 (external)-385.3 (logarithmic)-385.3 (potential)-385 (\()]TJ
/N11 1 Tf
19.2138 0 TD
([)Tj
/N6 1 Tf
1.2175 0 TD
(15)Tj
/N10 1 Tf
1.0563 0 TD
(5)Tj
/N6 1 Tf
0.8875 0 TD
0.0375 Tc
(2\))Tj
/N7 1 Tf
-54.1825 -1.25 TD
0 Tc
[(RG)-54.5 (AS)]TJ
/N6 1 Tf
31.8075 0 TD
[(Length)-384.5 (scale)-384.8 (for)-385.3 (logarithmic)-385.3 (potential)]TJ
/N7 1 Tf
-31.8075 -1.875 TD
[(ALPH)-55 (AS)]TJ
/N6 1 Tf
31.8075 0 TD
[(Power-law)-384.3 (index)-385.5 (for)-385.3 (initial)-384.8 (mass)-385 (function)-384.5 (\()36.8 (routine)]TJ
/N7 1 Tf
21.21 0 TD
0.0192 Tc
[(DA)19.2 (T)-36.3 (A)]TJ
/N6 1 Tf
2.5375 0 TD
0 Tc
(\))Tj
/N7 1 Tf
-55.555 -1.25 TD
(BODY)Tj
/N6 1 Tf
2.6663 0 TD
[(1)-28641.2 (Maximum)-384.3 (particle)-384.8 (mass)-385 (before)-386 (scaling)]TJ
/N7 1 Tf
-2.6663 -1.25 TD
(BODYN)Tj
/N6 1 Tf
31.8075 0 TD
[(Minimum)-384 (particle)-386 (mass)-385 (before)-384.8 (scaling)]TJ
/N7 1 Tf
-31.8075 -1.875 TD
(Q)Tj
/N6 1 Tf
31.8075 0 TD
[(Virial)-384.5 (ratio)-384.5 (\()36.8 (routine)]TJ
/N7 1 Tf
8.45 0 TD
[(SC)-55.5 (ALE)]TJ
/N6 1 Tf
3.0375 0 TD
(;)Tj
/N7 1 Tf
0.6625 0 TD
(Q)Tj
/N10 1 Tf
0.815 0 TD
(5)Tj
/N6 1 Tf
0.8875 0 TD
[(0.5)-385 (for)-385.3 (equilibrium)36.9 (\))]TJ
/N7 1 Tf
-45.66 -1.25 TD
[(VXROT)-28696.5 (XY)]TJ
/N6 1 Tf
33.0112 0 TD
[(-velocity)-385 (scaling)-384.5 (factor)-385.5 (\()]TJ
/N10 1 Tf
10.4113 0 TD
(.)Tj
/N6 1 Tf
1 0 TD
[(0)-385 (for)-385.3 (solid-body)-384.6 (rotation)37.2 (\))]TJ
/N7 1 Tf
-44.4225 -1.25 TD
[(VZROT)-28751.5 (Z)]TJ
/N6 1 Tf
32.4 0 TD
[(-velocity)-385 (scaling)-384.5 (factor)-385.5 (\()36.8 (not)-384.5 (used)-385.8 (if)]TJ
/N7 1 Tf
14.9737 0 TD
(VXROT)Tj
/N10 1 Tf
3.2038 0 TD
(5)Tj
/N6 1 Tf
0.8887 0 TD
0.0362 Tc
(0\))Tj
/N7 1 Tf
-51.4662 -1.25 TD
0 Tc
[(RB)-55.5 (AR)]TJ
/N6 1 Tf
31.8075 0 TD
[(Virial)-384.5 (radius)-384.8 (in)-385.8 (pc)-384.8 (\()-37 (for)-385.3 (scaling)-384.5 (to)-384.5 (physical)-385.8 (units)37.5 (\))]TJ
/N7 1 Tf
-31.8075 -1.25 TD
[(ZMB)-55 (AR)]TJ
/N6 1 Tf
31.8075 0 TD
[(Mean)-384.3 (mass)-385 (in)-385.8 (solar)-384.8 (units)-385 (\()-37 (for)-385.3 (scaling)-37 (\))]TJ
/N7 1 Tf
-31.8075 -1.875 TD
(XCM)Tj
/N6 1 Tf
31.8075 0 TD
[(Displacement)-384.8 (of)-384.5 (subsystem)-385.6 (\()36.8 (routine)]TJ
/N7 1 Tf
15.1675 0 TD
[(SU)-18 (BSYS)]TJ
/N6 1 Tf
3.445 0 TD
(;)Tj
/N11 1 Tf
0.6625 0 TD
([)Tj
/N6 1 Tf
1.2175 0 TD
[(17)-37.5 (\))]TJ
/N7 1 Tf
-52.3 -1.25 TD
(ECC)Tj
/N6 1 Tf
31.8075 0 TD
[(Eccentricity)-384.3 (of)-385.8 (relative)-384.8 (motion)-384.8 (for)-385.3 (subsystem)-384.3 (\()]TJ
/N7 1 Tf
19.4363 0 TD
(ECC)Tj
/N10 1 Tf
2.1675 0 TD
(#)Tj
/N6 1 Tf
1 0 TD
0.0362 Tc
(1\))Tj
ET
78 321 15 -0.5 re
f 
93 321 15 -0.5 re
f 
108 321 15 -0.5 re
f 
123 321 15 -0.5 re
f 
138 321 15 -0.5 re
f 
153 321 15 -0.5 re
f 
168 321 15 -0.5 re
f 
183 321 15 -0.5 re
f 
198 321 15 -0.5 re
f 
213 321 15 -0.5 re
f 
228 321 15 -0.5 re
f 
243 321 15 -0.5 re
f 
258 321 15 -0.5 re
f 
273 321 15 -0.5 re
f 
288 321 15 -0.5 re
f 
303 321 15 -0.5 re
f 
318 321 15 -0.5 re
f 
333 321 15 -0.5 re
f 
348 321 15 -0.5 re
f 
363 321 15 -0.5 re
f 
378 321 15 -0.5 re
f 
393 321 15 -0.5 re
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408 321 15 -0.5 re
f 
423 321 15 -0.5 re
f 
438 321 15 -0.5 re
f 
453 321 15 -0.5 re
f 
468 321 15 -0.5 re
f 
483 321 15 -0.5 re
f 
498 321 15 -0.5 re
f 
513 321 21 -0.5 re
f 
BT
10 0 0 10 78 283 Tm
0 Tc
[(distribution,)-518.3 (where)]TJ
/N10 1 Tf
10 0 2.68 10 161.41 283 Tm
(a)Tj
10 0 0 10 172.08 283 Tm
(5)Tj
/N6 1 Tf
1 0 TD
[(2.35)-518.1 (gives)-518.1 (a)-519 (Salpeter-type)-2400.3 (units)-362.1 (are)-363 (introduced)-362.2 (in)-363 (routine)]TJ
/N7 1 Tf
26.458 0 TD
[(SC)-56 (ALE)]TJ
/N6 1 Tf
3.038 0 TD
[(;)-362 (however,)-363.2 (all)]TJ
/N7 1 Tf
6.5 0 0 6 167.28 280.5 Tm
(s)Tj
/N6 1 Tf
10 0 0 10 78 271 Tm
[(function.)-20417.2 (scaling)-471.1 (can)-471.1 (be)-472 (bypassed)-471.2 (if)-471 (desired)-472.1 (\()37 (cf.)-471 (option)-472.1 (16)-37 (\).)]TJ
1 -1.2 TD
[(In)-317 (the)-318 (simplest)-318.2 (case)-317.1 (\()]TJ
/N7 1 Tf
8.676 0 TD
(KZ)Tj
/N6 1 Tf
1.223 0 TD
0.037 Tc
(\(5\))Tj
/N10 1 Tf
1.296 0 TD
0 Tc
(5)Tj
/N6 1 Tf
0.888 0 TD
[(0)-37 (\))0 (,)-318 (a)-318 (uniform)-318.1 (spheri-)-2400.2 (Once)-407.1 (the)-408 (initial)-408.1 (conditions)-407.2 (have)-408.1 (been)-408.1 (generated,)-408.2 (all)]TJ
-13.083 -1.2 TD
[(cal)-297.1 (system)-297.1 (is)-298 (produced)-297.2 (by)-297 (choosing)]TJ
/N7 1 Tf
14.727 0 TD
(x)Tj
/N6 1 Tf
0.444 0 TD
(,)Tj
/N7 1 Tf
0.64 0 TD
(y)Tj
/N6 1 Tf
0.444 0 TD
(,)Tj
/N7 1 Tf
0.547 0 TD
(z)Tj
/N6 1 Tf
0.723 0 TD
[(at)-298 (random)-2400.1 (coordinates)-535.3 (and)-536.1 (velocities)-536.2 (are)-536 (\256rst)-536.1 (expressed)-536.2 (with)]TJ
-17.525 -1.2 TD
[(inside)-600.1 (a)-600 (unit)-601.1 (sphere)-600.1 (with)-600.1 (corresponding)-601.3 (isotropic)-2400.2 (respect)-385.2 (to)-385 (the)-385 (centre)-385.1 (of)-385 (mass)-385.1 (rest)-385.1 (frame.)]TJ
T*
[(velocities)-461.2 (having)-462.1 (randomized)-461.3 (magnitudes)-462.3 (in)-461 ([0,)-462.1 (1].)-3400.1 (W)56 (e)-518 (introduce)-517.2 (the)-518 (so-called)-517.2 (`standard')-518.2 (units)-518.1 (rec-)]TJ
T*
[(The)-369.1 (second)-369.1 (choice)-370.1 (\()]TJ
/N7 1 Tf
8.346 0 TD
(KZ)Tj
/N6 1 Tf
1.223 0 TD
0.037 Tc
(\(5\))Tj
/N10 1 Tf
1.295 0 TD
0 Tc
(5)Tj
/N6 1 Tf
0.889 0 TD
[(1)-37 (\))-369 (provides)-370.2 (for)-369.1 (a)-370 (Plum-)-2400.1 (ommended)-325.2 (by)-326 (Heggie)-325.1 (and)-326.1 (Mathieu)-325.2 (\()-37 (1986)-37.1 (\),)-326 (in)-326 (which)]TJ
-11.753 -1.2 TD
[(mer)-518.1 (model)-518.1 (with)-519.1 (isotropic)-518.2 (velocity)-518.2 (distribution)-519.3 (\()37 (cf.)]TJ
/N7 1 Tf
24 0 TD
(G)Tj
/N10 1 Tf
0.925 0 TD
(5)Tj
/N6 1 Tf
1 0 TD
(1,)Tj
/N7 1 Tf
1.227 0 TD
(M)Tj
/N10 1 Tf
1.399 0 TD
(5)Tj
/N6 1 Tf
1 0 TD
(1,)Tj
/N7 1 Tf
1.227 0 TD
(E)Tj
/N10 1 Tf
1.177 0 TD
0.333 Tc
(52)Tj
/N6 1 Tf
2.166 0 TD
0 Tc
[(1)-111 (/)-111 (4)0 (,)-477 (where)]TJ
/N7 1 Tf
5.147 0 TD
(M)Tj
/N6 1 Tf
1.71 0 TD
[(is)-477 (the)-478 (total)]TJ
6.5 0 0 6 358.04 196.5 Tm
4.7354 Tc
[(00)-8169.2 (0)]TJ
10 0 0 10 78 187 Tm
0 Tc
[(Aarseth)-385.2 (et)-385 (al.,)-385.1 (1974)-385.1 (for)-385 (a)-385 (detailed)-385.2 (algorithm)36.8 (\).)-5040 (mass)-488.1 (and)]TJ
/N7 1 Tf
28.421 0 TD
(E)Tj
/N6 1 Tf
1.499 0 TD
[(is)-488 (the)-489 (initial)-489.1 (energy.)-488.2 (These)-489.1 (units)-489.1 (are)]TJ
6.5 0 0 6 368.5 184.5 Tm
(0)Tj
10 0 0 10 318 175 Tm
[(suitable)-677.2 (for)-677 (most)-677.1 (types)-677.1 (of)-677 (bound)-677.1 (systems.)-677.2 (This)]TJ
10 0 2.68 10 78 163 Tm
(4.2.)Tj
/N7 1 Tf
10 0 0 10 98.55 163 Tm
(Scaling)Tj
/N6 1 Tf
21.945 0 TD
[(choice)-619.1 (corresponds)-619.3 (to)-619 (a)-619 (virial)-619.1 (equilibrium)-619.2 (radius)]TJ
/N10 1 Tf
11.361 -0.6 TD
(])Tj
/N11 1 Tf
19 0 0 10 423.28 153.5 Tm
(\316)Tj
/N7 1 Tf
10 0 0 10 318 151 Tm
(R)Tj
/N10 1 Tf
1.206 0 TD
(5)Tj
/N6 1 Tf
1 0 TD
[(1,)-338 (rms)-338.1 (velocity)]TJ
/N7 1 Tf
6.411 0 TD
(V)Tj
/N10 1 Tf
1.077 0 TD
(5)Tj
/N6 1 Tf
1.667 0 TD
[(2)-111 (/)-111 (2)-338 (and)-338.1 (a)-338 (mean)-338.1 (crossing)]TJ
/N36 1 Tf
6.5 0 0 6 324.42 148.5 Tm
12.5395 Tc
(vv)Tj
/N10 1 Tf
10 0 0 10 501.29 145 Tm
0 Tc
(])Tj
/N6 1 Tf
6.5 0 0 6 419 144 Tm
0.1665 Tc
[(5/2)-5087.3 (3)-1.2 (/2)]TJ
/N11 1 Tf
19 0 0 10 492.96 141.5 Tm
0 Tc
(\316)Tj
/N6 1 Tf
10 0 0 10 88 139 Tm
[(Results)-344.2 (of)]TJ
/N7 1 Tf
4.466 0 TD
(N)Tj
/N6 1 Tf
0.704 0 TD
[(-body)-344.1 (simulations)-344.3 (are)-344 (often)-345.1 (presented)-2400.2 (time)]TJ
/N7 1 Tf
20.573 0 TD
(T)Tj
/N10 1 Tf
1.375 0 TD
(5)Tj
/N6 1 Tf
0.999 0 TD
(2)Tj
/N7 1 Tf
0.5 0 TD
(R)Tj
/N6 1 Tf
1.147 0 TD
(/)Tj
/N7 1 Tf
0.315 0 TD
(V)Tj
/N10 1 Tf
1.077 0 TD
(5)Tj
/N7 1 Tf
1 0 TD
(M)Tj
/N6 1 Tf
2.158 0 TD
0.074 Tc
[(/\()37 (2)]TJ
/N11 1 Tf
1.406 0 TD
0 Tc
(u)Tj
/N7 1 Tf
0.222 0 TD
(E)Tj
/N11 1 Tf
1.01 0 TD
(u)Tj
/N6 1 Tf
0.259 0 TD
(\))Tj
/N10 1 Tf
1.601 0 TD
(5)Tj
/N6 1 Tf
1 0 TD
[(2)-1017 (2)0 (.)-966 (The)]TJ
6.5 0 0 6 351.54 136.5 Tm
0.056 Tc
(cr)Tj
/N36 1 Tf
4.4708 0 TD
1.5302 Tc
(vv)Tj
/N6 1 Tf
5.9077 0 TD
4.84 Tc
(00)Tj
10 0 0 10 78 127 Tm
0 Tc
[(in)-373 (a)-374 (variety)-374.1 (of)-374 (units)-374.1 (which)-374.1 (hinders)-374.2 (comparison)-374.3 (with)-2400.1 (scaling)-283.1 (to)-283 (internal)-283.2 (units)-283.1 (is)-283 (carried)-283.1 (out)-283.1 (in)-283 (four)-284.1 (separate)]TJ
0 -1.2 TD
[(other)-375.1 (work.)-376.1 (In)-376 (the)-376 (present)-376.2 (code,)-376.1 (a)-376 (convenient)-376.3 (set)-376.1 (of)-2400 (stages:)]TJ
ET
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33 33 546 744 RC
BT
/N6 1 Tf
8 0 0 8 78 705 Tm
0 g
/N13 /ExtGState findRes gs
0 Tc
(284)Tj
/N7 1 Tf
18.0325 0 TD
0 Tw
(S)Tj
/N6 1 Tf
8 0 2.144 8 226.26 705 Tm
(.)Tj
/N7 1 Tf
8 0 0 8 228.7 705 Tm
(J)Tj
/N6 1 Tf
8 0 2.144 8 232.25 705 Tm
(.)Tj
/N7 1 Tf
8 0 0 8 237.78 705 Tm
(Aarseth)Tj
/N6 1 Tf
3.6063 0 TD
(/)Tj
/N7 1 Tf
0.7375 0 TD
[(New)-440.8 (Astronomy)]TJ
/N6 1 Tf
8 0 2.144 8 328.02 705 Tm
[(6)-385 (\()-37 (2001)-37.5 (\))-384.5 (277)]TJ
8 0 0 8 373.29 705 Tm
(\261)Tj
8 0 2.144 8 377.73 705 Tm
(291)Tj
6.5 0 0 6 281.91 684 Tm
0.0556 Tc
(old)Tj
10 0 0 10 78 679 Tm
0 Tc
[(1.)-500 (Scale)-383.1 (all)-383 (the)-383 (masses)-383.2 (by)-383 (the)-384 (old)-383 (total)-383.1 (mass,)]TJ
/N7 1 Tf
19.447 0 TD
(M)Tj
/N6 1 Tf
1.903 0 TD
[(,)-2400 (5)0 (.)-500 (Combine)-393.2 (polynomials)-393.3 (for)]TJ
/N7 1 Tf
14.857 0 TD
(i)Tj
/N6 1 Tf
0.708 0 TD
[(and)-393.1 (predict)]TJ
/N8 1 Tf
5.007 0 TD
(r)Tj
/N6 1 Tf
1.109 0 TD
(and)Tj
/N18 1 Tf
1.837 0 TD
(v)Tj
/N6 1 Tf
6.5 0 0 6 281.91 676.5 Tm
(0)Tj
/N7 1 Tf
33.8554 0 TD
4.3712 Tc
(tt)Tj
/N6 1 Tf
-19.7277 -0.75 TD
0.0928 Tc
(\(3\))Tj
10 0 0 10 90.5 667 Tm
0 Tc
[(to)-385 (give)]TJ
/N7 1 Tf
3.27 0 TD
(M)Tj
/N10 1 Tf
1.398 0 TD
(5)Tj
/N6 1 Tf
1 0 TD
[(1.)-17582 (to)-385 (order)]TJ
/N8 1 Tf
21.99 0 TD
(F)Tj
/N6 1 Tf
1.58 0 TD
(.)Tj
6.5 0 0 6 131.71 664.5 Tm
(0)Tj
50.1185 -0.75 TD
0.0556 Tc
(old)Tj
10 0 0 10 78 655 Tm
0 Tc
[(2.)-500 (Calculate)-591.2 (the)-591 (total)-591.1 (kinetic,)-591.2 (potential)-591.2 (and)-591.1 (virial)-2400.1 (6.)-500 (Evaluate)-453.2 (the)-454 (irregular)-453.2 (force)]TJ
/N8 1 Tf
37.282 0 TD
(F)Tj
/N6 1 Tf
2.078 0 TD
[(and)-454.1 (update)-454.1 (the)]TJ
6.5 0 0 6 457.48 652.5 Tm
0.056 Tc
(irr)Tj
10 0 0 10 90.5 643 Tm
0 Tc
[(energies.)-20418.2 (times)]TJ
/N7 1 Tf
26.552 0 TD
(t)Tj
/N6 1 Tf
0.653 0 TD
(.)Tj
/N7 1 Tf
6.5 0 0 6 359.11 640.5 Tm
(k)Tj
/N6 1 Tf
10 0 0 10 78 631 Tm
[(3.)-500 (Scale)-280.1 (the)-281 (velocities)-280.2 (by)-281 (the)-280.1 (speci\256ed)-281.2 (virial)-281.1 (theorem)-2400.2 (7.)-500 (Form)-503.1 (new)-504.1 (irregular)-504.2 (differences)-503.3 (and)-504.1 (include)-504.2 (the)]TJ
6.5 0 0 6 338.27 624 Tm
(4)Tj
10 0 0 10 90.5 619 Tm
[(ratio)-385.1 (\()]TJ
/N7 1 Tf
2.588 0 TD
(Q)Tj
/N6 1 Tf
0.814 0 TD
(\).)Tj
/N8 1 Tf
20.598 0 TD
(D)Tj
/N6 1 Tf
1.523 0 TD
(term.)Tj
-26.773 -1.2 TD
[(4.)-500 (Rescale)-558.2 (coordinates)-559.3 (and)-559.1 (velocities)-559.2 (to)-559 (yield)-559.1 (the)-2400 (8.)-500 ([Case)-330.1 (\()-37 (1)-37 (\))-330 (only.])-330.1 (Extrapolate)-330.2 (the)-330 (regular)-330.2 (force)-330.1 (and)]TJ
6.5 0 0 6 461.66 600 Tm
0.0928 Tc
(\(1\))Tj
10 0 0 10 90.5 595 Tm
0 Tc
[(desired)-385.1 (total)-385.1 (energy.)-15593.2 (\256rst)-344.1 (derivative)-345.2 (to)-344 (give)]TJ
/N8 1 Tf
33.433 0 TD
(F)Tj
/N6 1 Tf
1.228 0 TD
(and)Tj
/N8 1 Tf
1.788 0 TD
(F)Tj
/N6 1 Tf
1.605 0 TD
[(;)-345 (g)0 (o)-344 (t)0 (o)-345 (step)-345.1 (15.)]TJ
/N7 1 Tf
6.5 0 0 6 431.25 592.5 Tm
4.4005 Tc
(tt)Tj
/N6 1 Tf
14.0292 -0.75 TD
0.0557 Tc
(new)Tj
10 0 0 10 318 583 Tm
0 Tc
[(9.)-500 (Obtain)-413.1 (the)-414 (new)-413.1 (irregular)-414.2 (and)-414.1 (regular)-413.2 (force,)]TJ
/N8 1 Tf
19.778 0 TD
(F)Tj
/N6 1 Tf
6.5 0 0 6 522.44 580.5 Tm
0.056 Tc
(irr)Tj
-25.5554 -0.75 TD
0.0557 Tc
(new)Tj
10 0 0 10 330.5 571 Tm
0 Tc
(and)Tj
/N8 1 Tf
1.916 0 TD
(F)Tj
/N6 1 Tf
1.877 0 TD
[(,)-473 (and)-473.1 (form)-473.1 (a)-472 (temporary)-473.2 (neighbour)-473.2 (list.)]TJ
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0.0554 Tc
(reg)Tj
10 0 0 10 78 565 Tm
0 Tc
[(Having)-762.1 (transformed)-762.3 (to)-763 (scaled)-762.1 (units,)-762.1 (the)-763 (output)]TJ
25.25 -0.6 TD
[(Check)-385.1 (for)]TJ
/N7 1 Tf
4.491 0 TD
(n)Tj
/N10 1 Tf
1.102 0 TD
(5)Tj
/N6 1 Tf
1 0 TD
0.385 Tc
[(0o)385 (r)]TJ
/N7 1 Tf
2.103 0 TD
0 Tc
(n)Tj
/N10 1 Tf
1.103 0 TD
(.)Tj
/N7 1 Tf
0.999 0 TD
(n)Tj
/N6 1 Tf
1.742 0 TD
(.)Tj
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5.9692 Tc
(11)Tj
/N7 1 Tf
9.6677 0 TD
0.0552 Tc
(max)Tj
/N6 1 Tf
10 0 0 10 78 553 Tm
0 Tc
[(interval)-553.2 (\()]TJ
/N7 1 Tf
3.904 0 TD
[(DELT)-56.1 (AT)]TJ
/N6 1 Tf
3.816 0 TD
[(\))-553 (and)-554.1 (termination)-553.3 (time)-553.1 (\()]TJ
/N7 1 Tf
10.675 0 TD
(TCRIT)Tj
/N6 1 Tf
2.872 0 TD
(\))Tj
2.733 -0.6 TD
[(10.Adjust)-501.2 (the)-501 (neighbour)-501.2 (sphere)]TJ
/N7 1 Tf
13.808 0 TD
(R)Tj
/N6 1 Tf
1.457 0 TD
[(and)-501.1 (update)-502.1 (the)]TJ
/N7 1 Tf
6.5 0 0 6 462.51 544.5 Tm
(s)Tj
/N6 1 Tf
10 0 0 10 78 541 Tm
[(are)-440 (re-de\256ned)-440.2 (in)-440 (terms)-440.1 (of)-440 (the)-440 (crossing)-440.2 (time.)-440.1 (Using)]TJ
25.25 -0.6 TD
(times)Tj
/N7 1 Tf
2.552 0 TD
(T)Tj
/N6 1 Tf
0.931 0 TD
(.)Tj
/N7 1 Tf
6.5 0 0 6 361.89 532.5 Tm
(k)Tj
/N6 1 Tf
10 0 0 10 78 529 Tm
[(the)-378 (input)-379.1 (parameters)-379.2 (for)-379 (the)-378 (virial)-379.1 (radius)-379.1 (\()]TJ
/N7 1 Tf
17.555 0 TD
[(RB)-55 (AR)]TJ
/N6 1 Tf
2.555 0 TD
0.379 Tc
[(\)i)379 (n)]TJ
3.89 -0.6 TD
0 Tc
[(11.Construct)-318.3 (new)-319.1 (regular)-318.2 (differences)-319.2 (and)-318.1 (include)-319.2 (the)]TJ
-24 -0.6 TD
[(pc)-278 (and)-278.1 (mean)-278.1 (mass)-278.1 (\()]TJ
/N7 1 Tf
7.962 0 TD
-0.0001 Tc
[(ZMB)-55.2 (A)-0.1 (R)]TJ
/N6 1 Tf
3.333 0 TD
0 Tc
[(\))-278 (i)0 (n)-278 (solar)-278.1 (masses,)-278.2 (we)-278 (also)]TJ
6.5 0 0 6 338.27 516 Tm
(4)Tj
/N8 1 Tf
10 0 0 10 330.5 511 Tm
(D)Tj
/N6 1 Tf
1.523 0 TD
(term.)Tj
-26.773 -0.6 TD
[(introduce)-434.2 (scaling)-434.1 (factors)-434.1 (for)-434 (conversion)-434.2 (to)-434 (physical)]TJ
6.5 0 0 6 438.41 504 Tm
0.0927 Tc
(\(1\))Tj
10 0 0 10 318 499 Tm
0 Tc
(12.Set)Tj
/N8 1 Tf
3.095 0 TD
(F)Tj
/N6 1 Tf
1.45 0 TD
[(from)-567.1 (\()-37 (1)0 (1)-37 (\))-568 (and)]TJ
/N8 1 Tf
6.83 0 TD
(F)Tj
/N6 1 Tf
2.172 0 TD
[(using)-567.1 (\()-37 (4)-37 (\))-567 (for)-568.1 (both)]TJ
6.5 0 0 6 290.75 498 Tm
(6)Tj
/N7 1 Tf
9.9415 -0.25 TD
12.4974 Tc
(tt)Tj
/N6 1 Tf
10 0 0 10 78 493 Tm
0 Tc
[(units.)-332.1 (This)-332.1 (gives)-332.1 (rise)-332.1 (to)-332 (the)-332 (time)-332.1 (unit)]TJ
/N7 1 Tf
15.518 0 TD
[(TST)-55.1 (AR)]TJ
/N6 1 Tf
3.221 0 TD
0.037 Tc
[(\(i)37 (n)-295 (1)37 (0)]TJ
6.511 -0.6 TD
0 Tc
(types.)Tj
/N10 1 Tf
6.5 0 0 6 212.16 486 Tm
(2)Tj
/N6 1 Tf
0.8892 0 TD
(1)Tj
10 0 0 10 78 481 Tm
[(yr)37 (\),)-459 (velocity)-459.2 (unit)]TJ
/N7 1 Tf
7.46 0 TD
[(VST)-56.1 (AR)]TJ
/N6 1 Tf
3.404 0 TD
[(\()-37 (k)0 (m)-460 (s)-1031 (\))-459 (and)-459.1 (a)-460 (re-scaled)]TJ
13.136 -0.6 TD
[(13.Identify)-732.2 (the)-733 (loss)-733.1 (or)-733 (gain)-733.1 (of)-733 (neighbours)-733.2 (and)]TJ
-24 -0.6 TD
[(mass)-385.1 (unit)]TJ
/N7 1 Tf
4.326 0 TD
-0.0001 Tc
[(ZMB)-55.2 (A)-0.1 (R)]TJ
/N6 1 Tf
3.662 0 TD
0.037 Tc
[(\(M)-653 (\))37 (.)]TJ
/N40 1 Tf
6.5 0 0 6 171.03 466.5 Tm
0 Tc
(\()Tj
/N6 1 Tf
10 0 0 10 330.5 463 Tm
[(accumulate)-797.2 (derivative)-797.2 (corrections;)-797.3 (update)-797.1 (the)]TJ
0 -1.2 TD
[(neighbour)-385.2 (list)-385.1 (and)-385.1 (convert)-385.2 (to)-385 (differences)-385.3 (by)-385 (\()-37 (8)-37 (\))]TJ
-1.25 -1.2 TD
[(14.Prescribe)-385.3 (the)-385.1 (new)-385.1 (regular)-385.2 (time-step)]TJ
/N10 1 Tf
16.338 0 TD
(D)Tj
/N7 1 Tf
0.667 0 TD
(T)Tj
/N6 1 Tf
0.823 0 TD
(.)Tj
/N7 1 Tf
6.5 0 0 6 493.92 436.5 Tm
(i)Tj
/N6 1 Tf
10 0 2.68 10 78 433 Tm
(4.3.)Tj
/N7 1 Tf
10 0 0 10 98.55 433 Tm
[(Integration)-385.2 (algorithm)]TJ
/N6 1 Tf
21.945 -0.6 TD
[(15.Update)-385.2 (the)-385 (new)-385.1 (irregular)-385.2 (time-step)]TJ
/N10 1 Tf
16.116 0 TD
(D)Tj
/N7 1 Tf
0.667 0 TD
(t)Tj
/N6 1 Tf
0.545 0 TD
(.)Tj
/N7 1 Tf
6.5 0 0 6 488.92 424.5 Tm
(i)Tj
/N6 1 Tf
10 0 0 10 318 415 Tm
[(16.Repeat)-516.2 (the)-516 (cycle)-516.1 (at)-517 (step)-516.1 (1)-516 (until)-516.1 (termination)-517.3 (or)]TJ
-23 -0.6 TD
[(W)56 (e)-434 (begin)-434.1 (by)-434 (summarizing)-434.3 (the)-434 (starting)-434.2 (procedure)]TJ
24.25 -0.6 TD
(output.)Tj
-25.25 -0.6 TD
[(of)-282 (the)-281 (AC)-282 (method.)-282.2 (Given)-282.1 (the)-282 (initial)-282.1 (conditions)]TJ
/N7 1 Tf
19.116 0 TD
(m)Tj
/N6 1 Tf
0.99 0 TD
(,)Tj
/N8 1 Tf
0.532 0 TD
(r)Tj
/N6 1 Tf
0.712 0 TD
(,)Tj
/N7 1 Tf
6.5 0 0 6 276.7 394.5 Tm
1.6343 Tc
(ii)Tj
/N18 1 Tf
10 0 0 10 78 385 Tm
0 Tc
(v)Tj
/N6 1 Tf
1.163 0 TD
[(and)-372.1 (a)-373 (suitable)-372.2 (value)-372.1 (of)]TJ
/N7 1 Tf
9.86 0 TD
(R)Tj
/N6 1 Tf
0.95 0 TD
[(,)-373 (the)-372 (two)-372.1 (force)-373.1 (polyno-)]TJ
/N7 1 Tf
6.5 0 0 6 83.5 382.5 Tm
16.822 Tc
(is)Tj
/N6 1 Tf
10 0 0 10 318 379 Tm
0 Tc
[(Here)-522.1 (both)-523.1 (force)-523.1 (polynomials)-523.3 (are)-523.1 (integrated)-523.2 (to)-523 (the)]TJ
-24 -0.6 TD
[(mials)-406.1 (are)-406 (\256rst)-407.1 (initialized)-406.2 (according)-406.2 (to)-407 (\()-37 (5)-37 (\))-406 (while)-407.1 (the)]TJ
24 -0.6 TD
[(same)-281.1 (order;)-282.1 (however,)-282.2 (two)-281.1 (separate)-282.2 (time-step)-282.2 (parame-)]TJ
-24 -0.6 TD
[(neighbour)-377.2 (list)-377.1 (is)-378 (constructed.)-266.3 (W)56 (e)-378 (also)-377.1 (form)-377.1 (the)-378 (total)]TJ
24 -0.6 TD
[(ters)-617.1 (are)-617.1 (used)-618.1 (in)-617 (\()-37 (1)0 (0)-37 (\))0 (.)-618 (Note)-617.1 (that)-618.1 (the)-617 (decision)-618.2 (to)]TJ
-24 -0.6 TD
[(force)-543.1 (\()-37 (1)0 (1)-37 (\))-543 (and)-544.1 (its)-543 (\256rst)-544.1 (derivative,)-543.2 (to)-544 (be)-543 (used)-544.1 (for)]TJ
24 -0.6 TD
[(re-calculate)-492.3 (the)-493 (regular)-492.2 (force)-493.1 (is)-492 (based)-493.1 (on)-492 (the)-493 (next)]TJ
-24 -0.6 TD
[(coordinate)-685.2 (predictions)-686.2 (and)-686.1 (neighbour)-686.2 (corrections.)]TJ
/N7 1 Tf
24 -0.6 TD
(estimated)Tj
/N6 1 Tf
4.214 0 TD
[(irregular)-326.2 (time-step.)-326.2 (Force)-326.1 (polynomials)-327.3 (and)]TJ
-28.214 -0.6 TD
[(During)-339.1 (the)-340 (second)-340.1 (stage,)-340.1 (the)-340 (next)-340.1 (two)-340.1 (orders)-340.1 (\()-37 (6)-37 (\))-340 (are)]TJ
24 -0.6 TD
[(their)-407.1 (derivatives)-408.2 (must)-407.1 (be)-408 (combined)-407.2 (with)-408.1 (care.)-408.1 (Thus)]TJ
-24 -0.6 TD
[(calculated)-401.2 (for)-402.1 (each)-402.1 (component,)-401.3 (using)-402.1 (the)-402 (neighbour)]TJ
24 -0.6 TD
[(the)-351 (second)-351.1 (regular)-352.1 (difference)-351.2 (required)-351.2 (at)-352 (step)-351.1 (5)-352 (\()37 (and)]TJ
-24 -0.6 TD
[(list)-401.1 (for)-401.1 (identi\256cation.)-401.3 (The)-401.1 (initialization)-401.3 (procedure)-402.2 (is)]TJ
24 -0.6 TD
[(at)-350 (output)-351.1 (times)36.9 (\))-351 (i)0 (s)-351 (obtained)-350.2 (from)-351.1 (a)-351 (differentiation)-351.3 (of)]TJ
-24 -0.6 TD
[(completed)-406.2 (by)-406 (specifying)-407.2 (irregular)-406.2 (and)-406.1 (regular)-407.2 (time-)]TJ
6.5 0 0 6 527.88 288 Tm
(3)Tj
10 0 0 10 318 283 Tm
0.037 Tc
[(\(4\))-561 (a)37 (t)]TJ
/N7 1 Tf
3.159 0 TD
0 Tc
(t)Tj
/N12 1 Tf
0.482 0 TD
(\261)Tj
/N7 1 Tf
0.999 0 TD
(T)Tj
/N6 1 Tf
1.591 0 TD
[(which)-599.1 (yields)-599.1 (an)-599 (extra)-598.1 (term)-599.1 (in)]TJ
/N8 1 Tf
13.98 0 TD
(D)Tj
/N6 1 Tf
1.139 0 TD
(.)Tj
6.5 0 0 6 370.52 280.5 Tm
(0)Tj
10 0 0 10 78 277 Tm
(steps,)Tj
/N10 1 Tf
2.571 0 TD
(D)Tj
/N7 1 Tf
0.667 0 TD
(t)Tj
/N6 1 Tf
0.872 0 TD
(and)Tj
/N10 1 Tf
1.765 0 TD
(D)Tj
/N7 1 Tf
0.667 0 TD
(T)Tj
/N6 1 Tf
0.824 0 TD
[(,)-322 (according)-321.2 (to)-322 (\()-37 (1)0 (0)-37 (\))0 (,)-321 (whereupon)-322.2 (the)]TJ
/N7 1 Tf
6.5 0 0 6 113.47 274.5 Tm
5.2343 Tc
(ii)Tj
/N6 1 Tf
10 0 0 10 318 271 Tm
0 Tc
[(Likewise)-483.2 (for)-484.1 (step)-484.1 (8,)-484 (the)-484 (regular)-483.2 (force)-484.1 (and)-484.1 (its)-484 (\256rst)]TJ
-24 -0.6 TD
[(divided)-572.2 (differences)-572.2 (are)-572 (formed)-572.1 (by)-572 (\()-37 (8)-37 (\))0 (.)-572 (The)-572.1 (main)]TJ
24 -0.6 TD
[(derivative)-729.2 (are)-729 (evaluated)-729.2 (to)-730 (highest)-729.2 (order)-729.1 (at)-730 (an)]TJ
-24 -0.6 TD
[(integration)-313.2 (cycle)-313.1 (consists)-313.2 (of)-313 (the)-313 (following)-314.2 (signi\256cant)]TJ
24 -0.6 TD
[(intermediate)-360.3 (time)-360.1 (before)-360.1 (the)-360.1 (contributions)-360.3 (are)-360 (added)]TJ
-24 -0.6 TD
(steps:)Tj
24 -0.6 TD
[(to)-385 (the)-385 (respective)-385.2 (irregular)-385.2 (parts.)]TJ
1 -1.2 TD
[(V)112 (arious)-499.1 (stratagems)-500.2 (may)-499.1 (be)-499 (used)-499.1 (to)-499 (increase)-499.2 (the)]TJ
-25 -1.2 TD
[(1.)-500 (Select)-530.1 (the)-530 (next)-531.1 (particle,)]TJ
/N7 1 Tf
12.008 0 TD
(i)Tj
/N6 1 Tf
0.278 0 TD
[(,)-530 (t)0 (o)-531 (b)0 (e)-530 (advanced)-531.2 (and)-2400.1 (ef\256ciency)-618.2 (of)-618 (determining)-618.3 (the)-618 (next)-618.1 (particle)-618.2 (to)-618 (be)]TJ
-11.036 -1.2 TD
[(de\256ne)-385.1 (the)-385 (current)-385.2 (epoch)-385.1 (by)]TJ
/N7 1 Tf
11.995 0 TD
(t)Tj
/N10 1 Tf
0.481 0 TD
(5)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N10 1 Tf
0.729 0 TD
0.167 Tc
(1D)Tj
/N7 1 Tf
1.667 0 TD
0 Tc
(t)Tj
/N6 1 Tf
0.545 0 TD
[(.)-6083 (advanced.)-882.2 (The)-882.1 (earlier)-882.1 (scheduling)-882.2 (algorithm)-882.2 (of)]TJ
/N7 1 Tf
6.5 0 0 6 228.35 196.5 Tm
3.4082 Tc
(ii)Tj
/N6 1 Tf
28.6431 -0.75 TD
0.1672 Tc
(1/2)Tj
10 0 0 10 78 187 Tm
0 Tc
[(2.)-500 (Make)-538.1 (a)-538 (new)-539.1 (sorted)-538.1 (time-step)-538.2 (list)-539.1 (if)]TJ
/N7 1 Tf
17.405 0 TD
(t)Tj
/N10 1 Tf
0.482 0 TD
(.)Tj
/N7 1 Tf
0.999 0 TD
(t)Tj
/N6 1 Tf
1.27 0 TD
[(and)-2400.1 (searching)-344.2 (a)-344 (list)-345.1 (of)]TJ
/N11 1 Tf
11.719 0 TD
(.)Tj
/N7 1 Tf
1 0 TD
(N)Tj
/N6 1 Tf
2.206 0 TD
[(pre-selected)-344.3 (members)-345.2 (has)]TJ
/N7 1 Tf
6.5 0 0 6 269.96 184.5 Tm
(L)Tj
/N6 1 Tf
10 0 0 10 90.5 175 Tm
(adjust)Tj
/N10 1 Tf
2.774 0 TD
(D)Tj
/N7 1 Tf
0.667 0 TD
(t)Tj
/N6 1 Tf
0.726 0 TD
[(.)-18333 (been)-367.1 (modi\256ed)-368.2 (to)-367 (include)-368.1 (sequential)-367.2 (sorting.)-368.2 (At)-368 (time)]TJ
/N7 1 Tf
6.5 0 0 6 128 172.5 Tm
(L)Tj
/N6 1 Tf
10 0 0 10 78 163 Tm
[(3.)-500 (Compare)]TJ
/N7 1 Tf
5.621 0 TD
(t)Tj
/N10 1 Tf
0.482 0 TD
0.166 Tc
(1D)Tj
/N7 1 Tf
1.666 0 TD
0 Tc
(t)Tj
/N6 1 Tf
1.268 0 TD
(with)Tj
/N7 1 Tf
2.484 0 TD
(T)Tj
/N10 1 Tf
1.158 0 TD
0.167 Tc
(1D)Tj
/N7 1 Tf
1.667 0 TD
0 Tc
(T)Tj
/N6 1 Tf
1.546 0 TD
[(to)-521 (decide)-522.1 (be-)]TJ
/N7 1 Tf
8.108 0 TD
(t)Tj
/N10 1 Tf
0.481 0 TD
($)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N6 1 Tf
1.017 0 TD
[(\()37 (with)]TJ
/N7 1 Tf
2.366 0 TD
(t)Tj
/N10 1 Tf
0.897 0 TD
(5)Tj
/N6 1 Tf
1 0 TD
[(0)-291 (initially)-37.2 (\),)-291 (a)-292 (list)-291.1 (is)-291 (formed)-291.1 (of)-291 (all)-292 (the)]TJ
/N7 1 Tf
6.5 0 0 6 158.79 160.5 Tm
(i)Tj
/N6 1 Tf
6.2354 0 TD
(0)Tj
/N7 1 Tf
4.3092 0 TD
16.4251 Tc
[(iL)11776.5 (L)]TJ
/N6 1 Tf
10 0 0 10 90.5 151 Tm
0 Tc
[(tween)-459.1 (a)-459 (regular)-459.2 (force)-459.1 (prediction)-459.2 ([case)-459.1 (\()-37 (1)-37 (\))0 (])-459 (o)0 (r)-460 (a)-2400 (particles)-384.2 (due)-384.1 (to)-384 (be)-384 (advanced)-384.2 (during)-384.1 (the)-384 (interval)-384.2 ([)]TJ
/N7 1 Tf
43.373 0 TD
(t)Tj
/N6 1 Tf
0.727 0 TD
(,)Tj
/N7 1 Tf
6.5 0 0 6 527.33 148.5 Tm
(L)Tj
/N6 1 Tf
10 0 0 10 90.5 139 Tm
[(new)-385.1 (total)-385.1 (force)-385.1 (summation)-385.2 ([case)-385.1 (\()-37 (2)-37 (\)].)]TJ
/N7 1 Tf
22.75 0 TD
(t)Tj
/N10 1 Tf
0.909 0 TD
0.167 Tc
(1D)Tj
/N7 1 Tf
1.667 0 TD
0 Tc
(t)Tj
/N6 1 Tf
0.743 0 TD
[(])-385 (and)-385.1 (the)-385 (list)-385.1 (is)-385 (then)-385.1 (ordered)-385.2 (sequentially.)]TJ
/N7 1 Tf
6.5 0 0 6 321.09 136.5 Tm
3.4071 Tc
(LL)Tj
/N6 1 Tf
10 0 0 10 78 127 Tm
0 Tc
[(4.)-500 (Predict)-310.2 (coordinates)-310.3 (of)-310 (neighbours)-310.2 ([case)-310.1 (\()-37 (1)-37 (\))0 (])-310 (o)0 (r)-310 (all)-3400 (To)-443 (include)-443.2 (the)-444 (case)-443.1 (of)-444 (repeated)-443.2 (small)-444.1 (time-steps)]TJ
1.25 -1.2 TD
[(particles)-385.2 ([case)-385.1 (\()-37 (2)-37 (\)].)-14715 (and)-387.1 (ensure)-388.1 (that)-388.1 (the)-387 (global)-388.1 (time)-388.1 (increases)-388.2 (monotoni-)]TJ
ET
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33 33 546 744 RC
BT
/N7 1 Tf
8 0 0 8 222.26 705 Tm
0 g
/N13 /ExtGState findRes gs
0 Tc
0 Tw
(S)Tj
/N6 1 Tf
8 0 2.144 8 226.26 705 Tm
(.)Tj
/N7 1 Tf
8 0 0 8 228.7 705 Tm
(J)Tj
/N6 1 Tf
8 0 2.144 8 232.25 705 Tm
(.)Tj
/N7 1 Tf
8 0 0 8 237.78 705 Tm
(Aarseth)Tj
/N6 1 Tf
3.6063 0 TD
(/)Tj
/N7 1 Tf
0.7375 0 TD
[(New)-440.8 (Astronomy)]TJ
/N6 1 Tf
8 0 2.144 8 328.02 705 Tm
[(6)-385 (\()-37 (2001)-37.5 (\))-384.5 (277)]TJ
8 0 0 8 373.29 705 Tm
(\261)Tj
8 0 2.144 8 377.73 705 Tm
(291)Tj
8 0 0 8 522 705 Tm
(285)Tj
/N10 1 Tf
10 0 0 11 490.28 679.25 Tm
(9)Tj
/N6 1 Tf
10 0 0 10 78 679 Tm
[(cally,)-749.1 (we)-749 (have)-749.1 (adopted)-749.2 (an)-749 (insert)-749.1 (procedure)-750.2 (to)-2400 (force)-452.1 (derivative)-452.2 (contains)-453.2 (an)-452 (extra)-452.1 (term)]TJ
/N7 1 Tf
40.876 0 TD
(t)Tj
/N10 1 Tf
0.907 0 TD
(5)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N10 1 Tf
0.88 0 TD
(2)Tj
/N7 1 Tf
1 0 TD
(T)Tj
/N6 1 Tf
6.5 0 0 6 490.28 676.5 Tm
2.4046 Tc
[(00)-416.9 (0)]TJ
-2.8354 -0.75 TD
0 Tc
(3)Tj
10 0 0 10 78 667 Tm
[(maintain)-308.2 (the)-308 (sequential)-308.2 (ordering.)-308.2 (Thus)-308.1 (the)-308.1 (index)-308.1 (of)-308 (a)-2400 (i)0 (n)-366 (the)-367 (corresponding)-366.3 (coef\256cient)-367.2 (of)]TJ
/N8 1 Tf
38.608 0 TD
(D)Tj
/N6 1 Tf
1.505 0 TD
[(\()37 (cf.)-366 (\()-37 (4)-37 (\))37 (\).)-367 (It)-367 (is)]TJ
-40.113 -1.2 TD
[(particle)-439.2 (satisfying)]TJ
/N7 1 Tf
7.767 0 TD
(t)Tj
/N10 1 Tf
0.482 0 TD
0.166 Tc
(1D)Tj
/N7 1 Tf
1.666 0 TD
0 Tc
(t)Tj
/N10 1 Tf
0.729 0 TD
(,)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N6 1 Tf
0.727 0 TD
[(,)-439 (evaluated)-440.2 (at)-440 (the)-440 (end)-2400.1 (required)-716.2 (for)-717 (the)-717 (prediction)-717.2 (of)-716 (particle)]TJ
/N7 1 Tf
29.536 0 TD
(i)Tj
/N6 1 Tf
1.032 0 TD
[(at)-717 (the)]TJ
/N7 1 Tf
6.5 0 0 6 180.25 652.5 Tm
2.382 Tc
(iL)Tj
/N6 1 Tf
10 0 0 10 78 643 Tm
0 Tc
[(of)-349 (the)-350 (cycle,)-350.1 (is)-350 (inserted)-350.2 (at)-350 (the)-350 (appropriate)-350.3 (sequential)-2400.2 (beginning)-455.2 (of)-456 (an)-456 (irregular)-456.2 (step)-456.1 (as)-456 (well)-456.1 (as)-456 (at)-456 (output)]TJ
0 -1.2 TD
[(location)-288.2 (\()37 (routine)]TJ
/N7 1 Tf
6.927 0 TD
(INSERT)Tj
/N6 1 Tf
3.427 0 TD
[(\).)-288 (An)-288 (updating)-289.2 (of)-288 (the)-289 (sorted)-2400.1 (and)-385.1 (other)-385.1 (high-order)-385.2 (predictions.)]TJ
-10.354 -1.2 TD
[(list)-408.1 (is)-409 (made)-409.1 (if)]TJ
/N7 1 Tf
6.301 0 TD
(t)Tj
/N10 1 Tf
0.482 0 TD
(.)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N6 1 Tf
0.726 0 TD
[(,)-409 (whereupon)-408.2 (the)-409.1 (interval)]TJ
/N10 1 Tf
10.605 0 TD
(D)Tj
/N7 1 Tf
0.667 0 TD
(t)Tj
/N6 1 Tf
1.152 0 TD
[(is)-3400 (Force)-531.1 (polynomials)-532.3 (based)-532.1 (on)-532 (divided)-532.1 (differences)]TJ
/N7 1 Tf
6.5 0 0 6 158.92 616.5 Tm
17.9025 Tc
(LL)Tj
/N6 1 Tf
10 0 0 10 78 607 Tm
0 Tc
[(stabilized)-340.2 (on)-340 (a)-340 (membership)-340.3 (chosen)-340.1 (as)-340 (a)-341 (compromise)-2400.3 (result)-435.1 (in)-435 (relatively)-436.2 (simple)-435.1 (code.)-436.1 (However,)-435.2 (the)-436 (inte-)]TJ
0 -1.2 TD
[(between)-290.2 (the)-290 (cost)-291.1 (of)-290 (sorting)-291.1 (the)-290 (quantities)]TJ
/N7 1 Tf
16.919 0 TD
(t)Tj
/N10 1 Tf
0.729 0 TD
0.167 Tc
(1D)Tj
/N7 1 Tf
1.667 0 TD
0 Tc
(t)Tj
/N6 1 Tf
0.841 0 TD
[(and)-2400.1 (gration)-387.1 (is)-388 (most)-388.1 (conveniently)-388.3 (carried)-387.1 (out)-388.1 (in)-388 (terms)-388.1 (of)]TJ
/N7 1 Tf
6.5 0 0 6 250.29 592.5 Tm
3.4066 Tc
(jj)Tj
/N6 1 Tf
10 0 0 10 78 583 Tm
0 Tc
[(inserting)-387.2 (a)-388 (small)-388.1 (number)-388.2 (of)-388 (particles)-388.2 (in)-388 (the)-388 (sequen-)-2400.2 (an)-336 (equivalent)-337.2 (Taylor)-337.1 (series,)-337.1 (with)-337.1 (\()37 (optimized)-37.2 (\))-337 (predic-)]TJ
6.5 0 0 6 380.65 575.75 Tm
0.0928 Tc
(\(3\))Tj
10 0 0 10 78 571 Tm
0 Tc
[(tial)-356.1 (list.)-356.1 (This)-357.1 (is)-356 (achieved)-356.2 (by)-357 (employing)-356.2 (two)-357.1 (variable)]TJ
24 -0.025 TD
[(tion)-385.1 (to)-385 (order)]TJ
/N8 1 Tf
5.599 0 TD
(F)Tj
/N6 1 Tf
1.965 0 TD
[(given)-385.1 (by)]TJ
-31.564 -1.175 TD
[(stabilization)-495.3 (factors)-496.1 (\()-37 (i)0 (n)-495 (the)-496 (range)-496.1 (0.25)-55.1 (\261)-56 (4.0)-37 (\))-496 (which)]TJ
35.436 -0.575 TD
(1)Tj
6.5 0 0 6 379.59 552.5 Tm
0.0926 Tc
[(\(3\))-3912.9 (\()-0.6 (2\))-6934.4 (\(1\))]TJ
/N8 1 Tf
10 0 0 10 374.05 548.5 Tm
3.149 Tc
[(\304\304)-1964 (\304)-654 (\304)]TJ
/N6 1 Tf
-29.605 -0.15 TD
0 Tc
[(are)-757 (used)-758.1 (to)-758 (determine)-758.2 (the)-758 (optimal)-758.2 (membership)]TJ
/N10 1 Tf
24 0 0 10 428.75 546.25 Tm
(])Tj
/N11 1 Tf
31.5 0 0 23 335.16 546 Tm
-0.0032 Tc
[(SSS)-3866.9 (D)-770.4 (D)]TJ
/N8 1 Tf
10 0 0 10 318 545.75 Tm
0 Tc
(r)Tj
/N10 1 Tf
0.883 0 TD
(5)Tj
/N6 1 Tf
2.902 0 TD
[(\()-37 (0.6)]TJ
/N8 1 Tf
1.62 0 TD
(F)Tj
/N7 1 Tf
1.668 0 TD
(t)Tj
/N10 1 Tf
0.315 0 TD
0.167 Tc
(91)Tj
/N8 1 Tf
1.499 0 TD
0 Tc
(F)Tj
/N6 1 Tf
1.633 0 TD
(\))Tj
/N7 1 Tf
1.999 0 TD
(t)Tj
/N10 1 Tf
0.315 0 TD
0.167 Tc
(91)Tj
/N8 1 Tf
1.5 0 TD
0 Tc
(F)Tj
/N7 1 Tf
2.321 0 TD
(t)Tj
/N10 1 Tf
0.315 0 TD
0.167 Tc
(91)Tj
/N8 1 Tf
1.499 0 TD
0 Tc
(F)Tj
/N7 1 Tf
1.301 0 TD
(t)Tj
/N10 1 Tf
0.315 0 TD
(9)Tj
/N7 1 Tf
6.5 0 0 6 322.75 543.25 Tm
(t)Tj
/N6 1 Tf
10 0 0 10 429.86 540.25 Tm
(12)Tj
-35.186 -0.525 TD
(\()Tj
/N10 1 Tf
0.37 0 TD
(~)Tj
/N7 1 Tf
0.667 0 TD
[(NNBM)-55.1 (AX)]TJ
/N6 1 Tf
4.148 0 TD
[(\).)-550 (In)-551 (spite)-551.1 (of)-551 (this)-551.1 (complication,)-551.3 (com-)]TJ
-5.185 -1.2 TD
[(parison)-754.1 (with)-754.1 (the)-754 (so-called)-754.2 (`heap-sort')-754.2 (algorithm)]TJ
/N11 1 Tf
31.5 0 0 23 353.96 519.5 Tm
(D)Tj
/N10 1 Tf
10 0 0 10 335.16 519.25 Tm
(1)Tj
/N8 1 Tf
1 0 TD
(v)Tj
/N7 1 Tf
1.57 0 TD
(t)Tj
/N10 1 Tf
0.315 0 TD
0.167 Tc
(91)Tj
/N8 1 Tf
1.499 0 TD
0 Tc
(r)Tj
/N6 1 Tf
6.5 0 0 6 350.71 516.75 Tm
4.6215 Tc
(00)Tj
10 0 0 10 78 511 Tm
0 Tc
[(advocated)-671.2 (by)-672 (Press)-672.1 (\()-37 (1986)-37.1 (\))-672 (favoured)-672.2 (the)-672 (present)]TJ
35.052 -1.075 TD
(1)Tj
6.5 0 0 6 378.25 499.5 Tm
0.0926 Tc
[(\(3\))-3912.9 (\()-0.6 (2\))-6731.3 (\(1\))]TJ
10 0 0 10 78 499 Tm
0 Tc
[(algorithm)-394.2 (above)]TJ
/N7 1 Tf
7.065 0 TD
(N)Tj
/N11 1 Tf
0.87 0 TD
(.)Tj
/N6 1 Tf
1 0 TD
[(100,)-394.1 (although)-394.2 (the)-394 (cost)-394.1 (of)-395 (both)]TJ
/N8 1 Tf
20.536 -0.35 TD
3.149 Tc
[(\304\304)-1832 (\304)]TJ
/N10 1 Tf
14 0 0 10 427.41 493.25 Tm
0 Tc
(])Tj
/N11 1 Tf
31.5 0 0 23 335.72 493 Tm
-0.003 Tc
[(SS)-3983.5 (D)]TJ
/N8 1 Tf
10 0 0 10 318 492.75 Tm
0 Tc
(v)Tj
/N10 1 Tf
0.939 0 TD
(5)Tj
/N6 1 Tf
2.212 0 TD
[(\()-37 (0.75)]TJ
/N8 1 Tf
2.12 0 TD
(F)Tj
/N7 1 Tf
1.668 0 TD
(t)Tj
/N10 1 Tf
0.315 0 TD
0.167 Tc
(91)Tj
/N8 1 Tf
1.5 0 TD
0 Tc
(F)Tj
/N6 1 Tf
1.632 0 TD
(\))Tj
/N7 1 Tf
1.499 0 TD
(t)Tj
/N10 1 Tf
0.315 0 TD
0.351 Tc
(91)Tj
/N8 1 Tf
1.868 0 TD
0 Tc
(F)Tj
/N6 1 Tf
2.321 0 TD
(1.5)Tj
/N7 1 Tf
1.25 0 TD
(t)Tj
/N10 1 Tf
0.315 0 TD
(9)Tj
/N7 1 Tf
6.5 0 0 6 323.31 490.25 Tm
(t)Tj
/N6 1 Tf
10 0 0 10 428.52 487.25 Tm
(9)Tj
-35.052 -0.025 TD
[(procedures)-385.2 (is)]TJ
/N10 1 Tf
5.824 0 TD
(~)Tj
/N7 1 Tf
0.906 0 TD
(N)Tj
/N6 1 Tf
1.292 0 TD
(log)Tj
/N7 1 Tf
2.099 0 TD
(N)Tj
/N6 1 Tf
0.667 0 TD
(.)Tj
6.5 0 0 6 171.55 484.5 Tm
(2)Tj
/N8 1 Tf
10 0 0 10 347.71 469 Tm
(\304)Tj
/N11 1 Tf
31.5 0 0 23 351.83 466.5 Tm
(D)Tj
/N10 1 Tf
10 0 0 10 335.72 466.25 Tm
(1)Tj
/N8 1 Tf
1 0 TD
(F)Tj
/N6 1 Tf
1.301 0 TD
(2)Tj
/N7 1 Tf
0.5 0 TD
(t)Tj
/N10 1 Tf
0.315 0 TD
0.166 Tc
(91)Tj
/N8 1 Tf
1.499 0 TD
0 Tc
(v)Tj
/N6 1 Tf
0.936 0 TD
[(.)-12287 (\()-37 (17)-37 (\))]TJ
6.5 0 0 6 387.43 463.75 Tm
(0)Tj
10 0 2.68 10 78 460.5 Tm
(4.4.)Tj
/N7 1 Tf
10 0 0 10 98.55 460.5 Tm
[(Force)-385.1 (polynomials)]TJ
/N6 1 Tf
21.945 -1.725 TD
[(Here)-302.1 (the)-303 (integration)-302.2 (factorials)-303.2 (in)-302 (\()-37 (9)-37 (\))-303 (and)-302.1 (factorials)-303.2 (in)]TJ
6.5 0 0 6 413.51 438 Tm
(\()Tj
/N7 1 Tf
0.3508 0 TD
(k)Tj
/N6 1 Tf
0.5369 0 TD
(\))Tj
10 0 0 10 88 436.5 Tm
[(At)-336 (several)-336.2 (stages,)-336.2 (it)-336 (is)-336 (necessary)-336.2 (to)-336 (combine)-336.2 (force)]TJ
/N8 1 Tf
31.997 -0.25 TD
(\304)Tj
/N6 1 Tf
-8.997 -0.275 TD
[(\()-37 (4)-37 (\))-487 (are)-487.1 (absorbed)-487.2 (in)]TJ
/N8 1 Tf
8.797 0 TD
(F)Tj
/N6 1 Tf
1.583 0 TD
[(,)-488 (and)]TJ
/N7 1 Tf
2.669 0 TD
(t)Tj
/N10 1 Tf
0.315 0 TD
0.166 Tc
(95)Tj
/N7 1 Tf
1.499 0 TD
0 Tc
(t)Tj
/N10 1 Tf
0.482 0 TD
(2)Tj
/N7 1 Tf
0.999 0 TD
(t)Tj
/N6 1 Tf
1.202 0 TD
(represents)Tj
6.5 0 0 6 484.78 428.75 Tm
(0)Tj
10 0 0 10 78 424.5 Tm
[(polynomials)-382.3 (and)-383.1 (their)-383.1 (derivatives.)-383.3 (The)-383.1 (prediction)-383.2 (of)]TJ
24 -0.525 TD
[(the)-385.1 (integration)-385.2 (interval.)]TJ
-24 -0.675 TD
[(the)-460 (regular)-461.2 (force)-461.1 (is)-460 (straightforward,)-461.4 (using)-461.1 (\()-37 (2)-37 (\))-461 (with)]TJ
25 -0.525 TD
[(The)-532.1 (coordinate)-533.2 (and)-533.1 (velocity)-533.2 (increments)-533.2 (of)-533 (\()-37 (1)0 (7)-37 (\))]TJ
-25 -0.675 TD
[(appropriate)-906.3 (time)-907.1 (arguments)]TJ
/N7 1 Tf
13.217 0 TD
(t)Tj
/N10 1 Tf
0.482 0 TD
(2)Tj
/N7 1 Tf
1 0 TD
(T)Tj
/N6 1 Tf
1.838 0 TD
[(\()37 (cf.)-907 (routine)]TJ
6.5 0 0 6 411.95 400.25 Tm
(4)Tj
/N7 1 Tf
-27.86 -0.375 TD
(k)Tj
/N6 1 Tf
10 0 0 10 318 395.25 Tm
[(due)-391.1 (to)-391 (the)-391 (corrector)]TJ
/N8 1 Tf
8.618 0 TD
(D)Tj
/N6 1 Tf
1.53 0 TD
[(contain)-391.1 (four)-391.1 (terms)-391.1 (since)-392.1 (all)]TJ
/N7 1 Tf
-34.148 -0.675 TD
(NBINT)Tj
/N6 1 Tf
2.982 0 TD
(\).)Tj
21.018 -0.525 TD
[(the)-722 (lower)-722.1 (derivatives)-723.2 (are)-722 (also)-723.1 (modi\256ed)-722.2 (in)-723 (\()-37 (4)-37 (\))0 (.)]TJ
-23 -0.675 TD
[(The)-340.1 (\256rst)-340.1 (force)-341.1 (derivatives)-340.2 (are)-341 (usually)-340.1 (evaluated)-341.2 (at)]TJ
23 -0.525 TD
[(Consequently,)-437.3 (we)-437 (combine)-437.2 (the)-437 (corresponding)-438.3 (time-)]TJ
-24 -0.675 TD
[(the)-452 (end)-453.1 (of)-453 (an)-453 (integration)-453.2 (step)-453.1 (of)-453 (either)-453.1 (type,)-453.1 (since)]TJ
24 -0.525 TD
[(step)-376.1 (factors)-376.1 (for)]TJ
/N8 1 Tf
6.626 0 TD
(r)Tj
/N6 1 Tf
1.093 0 TD
(and)Tj
/N18 1 Tf
1.82 0 TD
(v)Tj
/N6 1 Tf
1.168 0 TD
[(to)-376 (yield)-376.1 (\()-37 (i)0 (n)-376 (code)-377.1 (notation)36.8 (\))]TJ
/N7 1 Tf
6.5 0 0 6 389.02 356.75 Tm
4.3189 Tc
(tt)Tj
/N6 1 Tf
10 0 0 10 78 352.5 Tm
0 Tc
[(coordinates)-426.3 (or)-426 (velocities)-426.2 (at)-426 (a)-426 (general)-426.2 (time)]TJ
/N7 1 Tf
18.145 0 TD
(t)Tj
/N12 1 Tf
0.482 0 TD
(\261)Tj
/N7 1 Tf
0.999 0 TD
(t)Tj
/N6 1 Tf
1.141 0 TD
(or)Tj
6.5 0 0 6 277.6 350 Tm
(0)Tj
/N7 1 Tf
10 0 0 10 78 340.5 Tm
(t)Tj
/N12 1 Tf
0.481 0 TD
(\261)Tj
/N7 1 Tf
1 0 TD
(T)Tj
/N6 1 Tf
1.376 0 TD
[(are)-385 (obtained)-384.2 (by)-384 (an)-385 (expansion)-384.2 (with)-384.1 (respect)-385.2 (to)]TJ
25.148 -0.1 TD
8.714 Tc
[(21)6206 (1)]TJ
6.5 0 0 6 98.92 338 Tm
0 Tc
(0)Tj
/N10 1 Tf
14 0 0 10 356.94 332.5 Tm
(])Tj
24 0 0 10 446.58 332.5 Tm
(])Tj
14 0 0 10 479.16 332.5 Tm
(])Tj
/N11 1 Tf
31.5 0 0 23 336.25 332.25 Tm
-0.0032 Tc
[(SSS)-1120.2 (D)-1217.4 (D)-1649.1 (D)]TJ
/N7 1 Tf
10 0 0 10 318 332 Tm
0 Tc
(s)Tj
/N10 1 Tf
0.991 0 TD
(5)Tj
/N7 1 Tf
3.847 0 TD
(t)Tj
/N10 1 Tf
0.315 0 TD
0.167 Tc
(91)Tj
/N7 1 Tf
1.499 0 TD
0 Tc
(s)Tj
/N6 1 Tf
1.46 0 TD
(0.6)Tj
/N7 1 Tf
1.25 0 TD
(t)Tj
/N10 1 Tf
0.315 0 TD
0.167 Tc
(91)Tj
/N7 1 Tf
1.499 0 TD
2.737 Tc
(st)Tj
/N10 1 Tf
3.441 0 TD
0.167 Tc
(91)Tj
/N7 1 Tf
2.443 0 TD
1.071 Tc
(st)Tj
/N10 1 Tf
1.775 0 TD
0 Tc
(9)Tj
/N6 1 Tf
6.5 0 0 6 322.44 329.5 Tm
9.7354 Tc
[(65)3275.4 (4)1183.1 (3)]TJ
10 0 0 10 78 328.5 Tm
0 Tc
[(the)-700 (interval)]TJ
/N7 1 Tf
5.677 0 TD
(t)Tj
/N10 1 Tf
0.482 0 TD
(2)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N6 1 Tf
0.714 0 TD
[(.)-700 (I)0 (n)-701 (the)-700 (case)-701.1 (of)-700 (the)-701 (irregular)]TJ
20.132 -0.2 TD
8.464 Tc
[(31)8464 (2)6206 (6)]TJ
6.5 0 0 6 152.92 326 Tm
0 Tc
(0)Tj
10 0 0 10 78 316.5 Tm
(component,)Tj
/N7 1 Tf
5.115 0 TD
(t)Tj
/N10 1 Tf
0.482 0 TD
(5)Tj
/N7 1 Tf
0.999 0 TD
(t)Tj
/N6 1 Tf
1.136 0 TD
[(and)-421.1 (\()-37 (4)-37 (\))-421 (applies)-421.2 (directly;)-422.2 (likewise)]TJ
6.5 0 0 6 147.3 314 Tm
(0)Tj
10 0 0 10 424.4 313.25 Tm
(1)Tj
/N10 1 Tf
14 0 0 10 423.29 306.25 Tm
(])Tj
/N11 1 Tf
31.5 0 0 23 336.25 306 Tm
3.0853 Tc
(SD)Tj
/N7 1 Tf
10 0 0 10 318 305.75 Tm
0 Tc
(s)Tj
/N10 1 Tf
0.991 0 TD
(5)Tj
/N6 1 Tf
1.832 0 TD
(0.2)Tj
/N7 1 Tf
1.25 0 TD
(t)Tj
/N10 1 Tf
0.315 0 TD
0.166 Tc
(91)Tj
/N6 1 Tf
1.499 0 TD
0 Tc
(0.25)Tj
/N7 1 Tf
1.75 0 TD
0.689 Tc
(st)Tj
/N10 1 Tf
1.393 0 TD
0.167 Tc
(91)Tj
/N7 1 Tf
2.444 0 TD
1.07 Tc
(st)Tj
/N10 1 Tf
1.774 0 TD
0.167 Tc
(91)Tj
/N6 1 Tf
1.499 0 TD
0 Tc
(0.5)Tj
/N7 1 Tf
1.25 0 TD
(s)Tj
/N6 1 Tf
0.825 0 TD
[(,)-2788 (\()-37 (18)-37 (\))]TJ
/N11 1 Tf
9.5 0 0 10.5 343.14 305 Tm
5.8702 Tc
(sd)Tj
/N6 1 Tf
10 0 0 10 78 304.5 Tm
0 Tc
[(for)-610.1 (the)-610 (regular)-610.2 (component)-610.3 (at)-610 (an)-610 (end-point)-611.2 (when)]TJ
6.5 0 0 6 322.44 303.25 Tm
11.2508 Tc
[(75)5849.3 (4)4790.8 (3)]TJ
10 0 0 10 424.4 300.25 Tm
0 Tc
(3)Tj
/N7 1 Tf
-34.64 -0.775 TD
(t)Tj
/N10 1 Tf
0.481 0 TD
(5)Tj
/N7 1 Tf
1 0 TD
(T)Tj
/N6 1 Tf
0.992 0 TD
[(.)-392 (However,)-392.2 (the)-392 (prediction)-392.2 (of)-392 (the)-392 (regular)-392.2 (force)]TJ
6.5 0 0 6 98.92 290 Tm
(0)Tj
10 0 0 10 318 283 Tm
[(where)-423.1 (again)-423.1 (all)-423 (factorials)-423.2 (are)-423 (absorbed)-423.2 (in)-423 (the)-424 (force)]TJ
-24 -0.25 TD
[(derivative)-449.2 (at)-450 (the)-450 (end)-450.1 (of)-450 (a)-449 (sub-step)-450.2 (which)-450.1 (does)-450.1 (not)]TJ
24 -0.95 TD
[(derivatives.)-634.3 (The)-635.1 (coef\256cients)-634.3 (are)-635 (de\256ned)-634.2 (by)]TJ
/N7 1 Tf
19.775 0 TD
(s)Tj
/N10 1 Tf
0.992 0 TD
(5)Tj
/N6 1 Tf
-44.767 -0.25 TD
[(coincide)-758.2 (with)-758.1 (a)-758 (total)-758.1 (force)-758.1 (calculation)-759.2 (requires)]TJ
6.5 0 0 6 520.19 268.5 Tm
(3)Tj
/N10 1 Tf
10 0 0 11 321.52 259.25 Tm
1.574 Tc
[(9)1167 (9)1166 (9)-1810 (9)1167 (99)1166 (99)1167 (9)-1810 (999)]TJ
/N7 1 Tf
10 0 0 10 318 259 Tm
0.4625 Tc
(ttt)Tj
/N6 1 Tf
2.221 0 TD
0 Tc
(,)Tj
/N7 1 Tf
0.985 0 TD
(s)Tj
/N10 1 Tf
0.992 0 TD
(5)Tj
/N7 1 Tf
1 0 TD
0.462 Tc
(tt)Tj
/N10 1 Tf
1.648 0 TD
0 Tc
(1)Tj
/N7 1 Tf
0.999 0 TD
0.463 Tc
(tt)Tj
/N10 1 Tf
1.648 0 TD
0 Tc
(1)Tj
/N7 1 Tf
1 0 TD
0.462 Tc
(tt)Tj
/N6 1 Tf
1.481 0 TD
0 Tc
(,)Tj
/N7 1 Tf
0.985 0 TD
(s)Tj
/N10 1 Tf
0.992 0 TD
(5)Tj
/N7 1 Tf
0.999 0 TD
(t)Tj
/N10 1 Tf
0.907 0 TD
(1)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N10 1 Tf
0.907 0 TD
(1)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N6 1 Tf
0.741 0 TD
[(,)-735 (re-)]TJ
-43.505 -0.25 TD
[(special)-559.2 (care.)-559.1 (Applying)-559.2 (one)-559.1 (time)-559.1 (differentiation)-559.3 (of)]TJ
6.5 0 0 6 321.52 256.5 Tm
0.6391 Tc
[(123)-1657.8 (4)-1782.4 (12)-1794.7 (13)-1794.7 (23)-1657.8 (5)-1782.4 (1)-1794.7 (2)-1794.7 (3)]TJ
/N10 1 Tf
10 0 0 11 478.33 247.25 Tm
0 Tc
(9)Tj
/N6 1 Tf
10 0 0 10 318 247 Tm
[(spectively,)-294.2 (where)-295.1 (the)-294 (old)-295.1 (de\256nition)-294.2 (of)]TJ
/N7 1 Tf
15.681 0 TD
(t)Tj
/N6 1 Tf
1.04 0 TD
[(still)-295.1 (applies.)]TJ
-40.721 -0.25 TD
[(\()-37 (2)-37 (\))0 (,)-385 (w)0 (e)-385 (obtain)]TJ
/N7 1 Tf
6.5 0 0 6 478.33 244.5 Tm
(k)Tj
/N6 1 Tf
-12.9615 -0.75 TD
(2)Tj
/N10 1 Tf
10 0 0 11 390.39 235.25 Tm
(9)Tj
/N6 1 Tf
10 0 0 10 318 235 Tm
[(The)-333.1 (extra)-334.1 (factor)]TJ
/N7 1 Tf
6.886 0 TD
(t)Tj
/N6 1 Tf
1.416 0 TD
[(omitted)-334.2 (from)-334.1 (\()-37 (1)0 (8)-37 (\))-333 (is)-334 (included)-334.2 (in)]TJ
6.5 0 0 6 325.77 228 Tm
(4)Tj
-37.0938 -0.0417 TD
0.0928 Tc
[(\(1\))-3272.7 (3)-14402.6 (2)-8051.8 (1)]TJ
/N10 1 Tf
10 0 0 11 125.41 223 Tm
0.408 Tc
[(99)-1166 (99)-1165 (99)-2971 (9)-1166 (9)]TJ
/N8 1 Tf
10 0 0 10 318 223 Tm
0 Tc
(D)Tj
/N6 1 Tf
1.138 0 TD
[(.)-284 (The)-285.1 (semi-iteration)-284.3 (is)-284 (applied)-284.1 (to)-284 (both)-285.1 (polynomials)]TJ
/N8 1 Tf
-25.138 -0.025 TD
(F)Tj
/N10 1 Tf
1.955 0 TD
(5)Tj
/N8 1 Tf
1 0 TD
(D)Tj
/N6 1 Tf
1.138 0 TD
(\()Tj
/N7 1 Tf
0.296 0 TD
0.463 Tc
(tt)Tj
/N10 1 Tf
1.648 0 TD
0 Tc
(1)Tj
/N7 1 Tf
1 0 TD
0.463 Tc
(tt)Tj
/N10 1 Tf
1.648 0 TD
0 Tc
(1)Tj
/N7 1 Tf
0.999 0 TD
0.463 Tc
(tt)Tj
/N6 1 Tf
1.519 0 TD
0 Tc
(\))Tj
/N10 1 Tf
0.499 0 TD
(1)Tj
/N8 1 Tf
1 0 TD
(D)Tj
/N6 1 Tf
1.139 0 TD
(\()Tj
/N7 1 Tf
0.296 0 TD
(t)Tj
/N10 1 Tf
0.907 0 TD
(1)Tj
/N7 1 Tf
0.999 0 TD
(t)Tj
/N6 1 Tf
0.778 0 TD
(\))Tj
/N10 1 Tf
0.5 0 TD
(1)Tj
/N8 1 Tf
0.999 0 TD
(D)Tj
/N6 1 Tf
1.139 0 TD
(,)Tj
/N7 1 Tf
6.5 0 0 6 84.66 220.25 Tm
(t)Tj
/N6 1 Tf
6.2692 0 TD
0.64 Tc
[(01)-1793.8 (02)-1792.3 (12)-4570.8 (0)-1793.8 (1)]TJ
10 0 0 10 318 211 Tm
0 Tc
[(here.)-467.1 (However,)-468.2 (the)-467 (regular)-468.2 (corrections)-467.2 (may)-468.1 (not)-468.1 (be)]TJ
-4.14 -0.45 TD
0.037 Tc
[(\(1)37 (6\))]TJ
4.14 -0.75 TD
0 Tc
[(bene\256cial)-447.2 (if)-447 (there)-448.1 (are)-447 (large)-447.1 (force)-448.1 (derivatives,)-447.3 (as)-448 (in)]TJ
/N10 1 Tf
10 0 0 11 138.49 187.5 Tm
(9)Tj
/N6 1 Tf
10 0 0 10 78 187.25 Tm
[(where)-544.1 (again)]TJ
/N7 1 Tf
5.697 0 TD
(t)Tj
/N10 1 Tf
0.912 0 TD
(5)Tj
/N7 1 Tf
0.999 0 TD
(t)Tj
/N10 1 Tf
0.881 0 TD
(2)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N6 1 Tf
1.202 0 TD
[(denotes)-544.2 (the)-544.1 (relevant)-545.2 (time)]TJ
13.309 -0.025 TD
[(the)-405 (case)-406.1 (of)-406 (small)-406.1 (softening)-406.2 (parameters)-406.2 (\()-37 (i.e.)]TJ
/N10 1 Tf
10 0 2.68 10 502.85 187 Tm
(e)Tj
10 0 0 10 509.88 187 Tm
(,)Tj
/N7 1 Tf
0.999 0 TD
(R)Tj
/N6 1 Tf
1.135 0 TD
(/)Tj
/N7 1 Tf
6.5 0 0 6 138.49 184.75 Tm
(k)Tj
/N6 1 Tf
2.9123 0 TD
(0)Tj
/N7 1 Tf
2.8554 0 TD
(k)Tj
53.8954 -0.0417 TD
(h)Tj
/N6 1 Tf
10 0 0 10 78 175.25 Tm
[(intervals)-671.2 (\()37 (since)]TJ
/N7 1 Tf
7.137 0 TD
(t)Tj
/N10 1 Tf
0.88 0 TD
(5)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N6 1 Tf
0.986 0 TD
[(here)36.9 (\).)-671 (Setting)]TJ
/N7 1 Tf
6.443 0 TD
(t)Tj
/N10 1 Tf
0.825 0 TD
(5)Tj
/N7 1 Tf
0.999 0 TD
(T)Tj
/N6 1 Tf
1.608 0 TD
(then)Tj
/N7 1 Tf
4.122 -0.025 TD
(N)Tj
/N6 1 Tf
0.759 0 TD
(\).)Tj
6.5 0 0 6 152.7 172.75 Tm
(0)Tj
/N7 1 Tf
14.2846 0 TD
2.7914 Tc
(kk)Tj
/N6 1 Tf
10 0 0 10 78 163.25 Tm
0 Tc
[(yields)-324.1 (the)-325 (predicted)-324.2 (regular)-325.2 (force)-324.1 (derivative)-325.2 (which)-325.1 (is)]TJ
25 -0.025 TD
[(Although)-367.2 (the)-367 (AC)-367 (scheme)-367.2 (is)-367 (based)-367.1 (on)-367 (the)-367 (concept)]TJ
-25 -1.175 TD
[(added)-316.1 (to)-316 (its)-316 (irregular)-317.2 (counterpart,)-316.3 (obtained)-316.2 (by)-316 (\()-37 (4)-37 (\))0 (,)-317 (t)0 (o)]TJ
24 -0.025 TD
[(of)-368 (nearest)-368.2 (neighbours,)-368.3 (there)-368.1 (are)-368.1 (situations)-368.2 (when)-368.1 (this)]TJ
6.5 0 0 6 213.24 144 Tm
0.0928 Tc
(\(1\))Tj
10 0 0 10 78 139 Tm
0 Tc
[(form)-322.1 (the)-322 (total)-322.1 (force)-323.1 (derivative,)]TJ
/N8 1 Tf
12.858 0 TD
(F)Tj
/N6 1 Tf
1.581 0 TD
[(,)-322 (employed)-322.2 (in)-323 (the)-2400 (is)-494 (less)-495.1 (useful.)-495.2 (Thus)-495.1 (the)-495.1 (neighbour)-495.2 (sphere)-495.1 (determi-)]TJ
-14.439 -1.2 TD
[(subsequent)-385.3 (predictions.)-14477.3 (nation)-381.1 (for)-381.1 (a)-381 (distant)-381.1 (particle)-381.2 (may)-381.1 (lead)-381.1 (to)-381 (undesirable)]TJ
1 -1.2 TD
[(The)-452.1 (analogous)-453.2 (expression)-453.2 (for)-452.1 (the)-453 (second)-453.1 (regular)-2400.2 (oscillations)-314.3 (and)-315.1 (consequent)-315.3 (time-step)-315.2 (reduction.)-315.2 (This)]TJ
ET
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33 33 546 744 RC
BT
/N6 1 Tf
8 0 0 8 78 705 Tm
0 g
/N13 /ExtGState findRes gs
0 Tc
(286)Tj
/N7 1 Tf
18.0325 0 TD
0 Tw
(S)Tj
/N6 1 Tf
8 0 2.144 8 226.26 705 Tm
(.)Tj
/N7 1 Tf
8 0 0 8 228.7 705 Tm
(J)Tj
/N6 1 Tf
8 0 2.144 8 232.25 705 Tm
(.)Tj
/N7 1 Tf
8 0 0 8 237.78 705 Tm
(Aarseth)Tj
/N6 1 Tf
3.6063 0 TD
(/)Tj
/N7 1 Tf
0.7375 0 TD
[(New)-440.8 (Astronomy)]TJ
/N6 1 Tf
8 0 2.144 8 328.02 705 Tm
[(6)-385 (\()-37 (2001)-37.5 (\))-384.5 (277)]TJ
8 0 0 8 373.29 705 Tm
(\261)Tj
8 0 2.144 8 377.73 705 Tm
(291)Tj
10 0 0 10 78 679 Tm
[(problem)-730.2 (has)-730.1 (been)-730.1 (circumvented)-730.3 (by)-730 (including)-731.2 (a)-2400 (2)0 (.)-500 (Obtain)-431.1 (the)-431 (potential)-431.2 (energy)-432.1 (with)-431.1 (respect)-431.2 (to)-432 (both)]TJ
0 -1.2 TD
[(nominal)-415.2 (small)-416.1 (central)-416.1 (mass)-416.1 (in)-415 (the)-416 (irregular)-416.2 (force)-416.1 (if)-3650 (components.)]TJ
T*
[(there)-578.1 (are)-578 (no)-579 (neighbours)-578.2 (inside)-579.1 (a)-578 (large)-579.1 (neighbour)-2400.2 (3.)-500 (Form)-331.1 (the)-332 (two-body)-332.2 (binding)-332.2 (energy)]TJ
/N7 1 Tf
39.908 0 TD
(E)Tj
/N10 1 Tf
1.157 0 TD
0.333 Tc
(52)Tj
/N7 1 Tf
2.166 0 TD
0.268 Tc
(mm)Tj
/N6 1 Tf
2.091 0 TD
0 Tc
(/)Tj
/N7 1 Tf
6.5 0 0 6 483.13 652.5 Tm
4.84 Tc
[(bi)3594.9 (j)]TJ
/N6 1 Tf
10 0 0 10 78 643 Tm
0 Tc
[(sphere)-756.1 (\()]TJ
/N7 1 Tf
3.662 0 TD
(R)Tj
/N10 1 Tf
1.122 0 TD
(.)Tj
/N6 1 Tf
1 0 TD
(50)Tj
/N7 1 Tf
1.184 0 TD
(R)Tj
/N6 1 Tf
1.06 0 TD
[(\);)-756 (hence)-756.1 (adopting)]TJ
/N7 1 Tf
8.712 0 TD
(n)Tj
/N10 1 Tf
1.103 0 TD
(5)Tj
/N6 1 Tf
0.999 0 TD
[(0)-757 (still)-3650.1 (2)]TJ
/N7 1 Tf
6.908 0 TD
(a)Tj
/N6 1 Tf
0.5 0 TD
(.)Tj
/N7 1 Tf
6.5 0 0 6 121.04 640.5 Tm
4.6972 Tc
(sh)Tj
/N6 1 Tf
19.9862 0 TD
0 Tc
(1)Tj
10 0 0 10 78 631 Tm
[(permits)-385.2 (large)-385.1 (irregular)-385.2 (time-steps.)-10042.3 (4.)-500 (De\256ne)-285.1 (new)-286.1 (mass,)-286.1 (coordinates)-285.3 (and)-286.1 (velocities)-286.2 (using)]TJ
25.25 -1.2 TD
[(the)-385 (index)-385.1 (min\()]TJ
/N7 1 Tf
6.084 0 TD
(i)Tj
/N6 1 Tf
0.278 0 TD
(,)Tj
/N7 1 Tf
0.783 0 TD
(j)Tj
/N6 1 Tf
0.371 0 TD
(\).)Tj
-8.766 -1.2 TD
[(5.)-500 (Calculate)-623.2 (potential)-624.2 (energy)-624.1 (with)-623.1 (respect)-624.2 (to)-624 (the)]TJ
10 0 2.68 10 78 603.25 Tm
(4.5.)Tj
/N7 1 Tf
10 0 0 10 98.55 603.25 Tm
[(External)-385.2 (potentials)]TJ
/N6 1 Tf
23.195 -0.825 TD
[(composite)-385.2 (body.)]TJ
-1.25 -1.2 TD
[(6.)-500 (Subtract)-419.2 (the)-420 (two-body)-420.2 (energy)-420.1 (and)-420.1 (tidal)-420.1 (potential)]TJ
-23 -0.375 TD
[(W)56 (e)-300 (have)-299.1 (included)-300.2 (two)-299.1 (optional)-300.2 (external)-300.2 (potentials,)]TJ
24.25 -0.825 TD
[(energy)-385.1 (from)]TJ
/N7 1 Tf
5.435 0 TD
(E)Tj
/N6 1 Tf
0.841 0 TD
(.)Tj
/N7 1 Tf
6.5 0 0 6 390.9 568.5 Tm
(t)Tj
/N6 1 Tf
10 0 0 10 78 567.25 Tm
[(which)-496.1 (are)-496 (treated)-496.1 (in)-497 (a)-496 (similar)-496.1 (way.)-496.1 (The)-496.1 (\256rst)-497.1 (case)]TJ
24 -0.825 TD
[(7.)-500 (Reduce)]TJ
/N7 1 Tf
4.635 0 TD
(N)Tj
/N6 1 Tf
1.11 0 TD
[(by)-387 (1)-386 (and)-387.1 (update)-387.1 (all)]TJ
/N7 1 Tf
8.544 0 TD
(COMMON)Tj
/N6 1 Tf
4.868 0 TD
(arrays)Tj
-43.157 -0.375 TD
(\()Tj
/N7 1 Tf
0.296 0 TD
(KZ)Tj
/N6 1 Tf
1.223 0 TD
0.037 Tc
[(\(1)37 (5\))]TJ
/N10 1 Tf
1.795 0 TD
0 Tc
(5)Tj
/N6 1 Tf
0.889 0 TD
[(1)-37 (\))-385 (is)-385 (the)-385 (Plummer)-385.2 (potential)]TJ
21.047 -0.825 TD
[(\()37 (routine)]TJ
/N7 1 Tf
3.514 0 TD
[(REMO)36.9 (VE)]TJ
/N6 1 Tf
4.054 0 TD
(\).)Tj
/N7 1 Tf
-27.972 -1.175 TD
0.221 Tc
(GM)Tj
/N6 1 Tf
19.154 -0.025 TD
0 Tc
[(8.)-500 (Predict)-470.2 (coordinates)-471.3 (and)-470.1 (velocities)-471.2 (of)-471 (neighbours)]TJ
/N7 1 Tf
6.5 0 0 6 144.16 532.75 Tm
(b)Tj
/N6 1 Tf
35.32 -0.7917 TD
0.0928 Tc
(\(2\))Tj
/N10 1 Tf
30 0 0 10 112.54 527.75 Tm
0 Tc
(]]])Tj
7.5 0 0 10 157.54 527.75 Tm
(])Tj
10 0 2.68 10 78 527.25 Tm
(F)Tj
10 0 0 10 90.88 527.25 Tm
0.333 Tc
(52)Tj
/N6 1 Tf
7.285 0 TD
0 Tc
[(,)-11037 (\()-37 (19)-37 (\))]TJ
6.5 0 0 6 85.41 524.75 Tm
5.04 Tc
[(12)2335.4 (2)4386.2 (1)4873.8 (/)4873.4 (2)]TJ
10 0 0 10 330.5 523 Tm
0 Tc
[(to)-385 (order)]TJ
/N8 1 Tf
3.658 0 TD
(F)Tj
/N6 1 Tf
1.58 0 TD
(.)Tj
-26.923 -0.325 TD
(\()Tj
/N7 1 Tf
0.296 0 TD
(r)Tj
/N10 1 Tf
1.009 0 TD
(1)Tj
/N7 1 Tf
1 0 TD
(a)Tj
/N6 1 Tf
0.953 0 TD
(\))Tj
17.177 -0.875 TD
[(9.)-500 (Initialize)-308.2 (force)-309.1 (polynomials)-309.3 (and)-309.1 (time-steps)-309.2 (for)-309 (the)]TJ
-24 -1.1 TD
[(where)-444.1 (the)-445 (background)-445.3 (mass)]TJ
/N7 1 Tf
12.165 0 TD
(M)Tj
/N6 1 Tf
1.657 0 TD
[(and)-445.1 (length)-445.1 (scale)]TJ
/N7 1 Tf
7.278 0 TD
(a)Tj
/N6 1 Tf
4.15 -0.1 TD
[(new)-385.1 (body.)]TJ
/N7 1 Tf
6.5 0 0 6 207.92 497.5 Tm
(b)Tj
/N6 1 Tf
10 0 0 10 78 488 Tm
[(are)-465 (speci\256ed)-466.2 (as)-466 (input)-466.1 (\()37 (cf.)]TJ
/N7 1 Tf
11.317 0 TD
[(XTP)55.9 (AR)]TJ
/N6 1 Tf
2.963 0 TD
(1,)Tj
/N7 1 Tf
1.216 0 TD
[(XTP)55.9 (AR)]TJ
/N6 1 Tf
2.963 0 TD
[(2)-37 (\))0 (.)-466 (The)]TJ
-18.459 -1.2 TD
[(corresponding)-359.3 (force)-360.1 (is)-360 (evaluated)-360.2 (in)-359 (routine)]TJ
/N7 1 Tf
18.043 0 TD
(XTRNL)Tj
/N6 1 Tf
3.057 0 TD
(1)Tj
2.9 -0.4 TD
[(This)-563.1 (algorithm)-563.2 (maintains)-564.2 (fairly)-563.1 (good)-563.1 (energy)-564.1 (con-)]TJ
-24 -0.8 TD
[(and)-431.1 (added)-431.1 (to)-432 (the)-431 (regular)-432.2 (component.)-431.3 (For)-432.1 (initializa-)]TJ
24 -0.4 TD
[(servation)-562.2 (with)-562.1 (respect)-562.2 (to)-563 (the)-562 (newly)-562.1 (updated)-563.2 (total)]TJ
-24 -0.8 TD
[(tion,)-696.1 (the)-697 (same)-697.1 (routine)-697.1 (adds)-697.1 (the)-697 (force)-697.1 (and)-697.1 (\256rst)]TJ
24 -0.4 TD
[(energy)-607.1 (\()]TJ
/N7 1 Tf
3.624 0 TD
(E)Tj
/N6 1 Tf
0.879 0 TD
[(\).)-608 (Since)-608.1 (the)]TJ
/N7 1 Tf
5.851 0 TD
(COMMON)Tj
/N6 1 Tf
5.089 0 TD
[(arrays)-608.1 (are)-608 (ad-)]TJ
/N7 1 Tf
6.5 0 0 6 360.3 445.5 Tm
(t)Tj
/N6 1 Tf
10 0 0 10 78 440 Tm
[(derivative)-698.2 (to)-698 (the)-698 (regular)-698.2 (terms.)-698.1 (The)-698.1 (appropriate)]TJ
24 -0.4 TD
[(dressed)-418.2 (by)-418 (global)-418.1 (indices)-419.1 (\()37 (rather)-418.1 (than)-418.1 (pointers)36.8 (\),)-419 (the)]TJ
-24 -0.8 TD
[(contributions)-522.3 (are)-523 (added)-522.1 (to)-523 (the)-522 (potential)-523.2 (and)-523.1 (virial)]TJ
24 -0.4 TD
[(removal)-332.2 (of)-332 (variables)-333.2 (associated)-332.2 (with)-333.1 (a)-332 (given)-333.1 (particle)]TJ
-24 -0.8 TD
[(energies)-385.2 (\()37 (routine)]TJ
/N7 1 Tf
7.231 0 TD
(ENERGY)Tj
/N6 1 Tf
3.87 0 TD
(\).)Tj
12.899 -0.4 TD
(\()Tj
/N7 1 Tf
0.518 0 TD
(j)Tj
/N6 1 Tf
0.37 0 TD
[(\))-499 (entails)-500.1 (a)-499 (compressing)-499.3 (of)-499 (arrays)-499.1 (for)-499 (all)-500 (indices)]TJ
-23.888 -0.8 TD
[(W)56 (e)-406 (also)-406.1 (include)-406.2 (an)-406 (external)-406.2 (logarithmic)-407.3 (potential)]TJ
/N7 1 Tf
23 -0.4 TD
(k)Tj
/N10 1 Tf
0.647 0 TD
($)Tj
/N7 1 Tf
1 0 TD
(j)Tj
/N6 1 Tf
0.278 0 TD
[(,)-513 (performed)-512.2 (in)-513 (routine)]TJ
/N7 1 Tf
10.076 0 TD
[(REMO)36.9 (V)0 (E)]TJ
/N6 1 Tf
3.962 0 TD
[(.)-513 (I)0 (n)-513 (addition,)]TJ
-39.963 -0.8 TD
[(of)-385 (the)-385 (type)]TJ
24 -0.4 TD
[(the)-554.1 (neighbour)-555.2 (lists)-554.1 (require)-555.1 (reduction)-554.2 (by)-555 (1)-554 (for)-555 (all)]TJ
0 -1.2 TD
[(index)-607.1 (references)]TJ
/N10 1 Tf
7.71 0 TD
(.)Tj
/N7 1 Tf
1 0 TD
(j)Tj
/N6 1 Tf
0.278 0 TD
[(,)-607 (a)0 (s)-607 (well)-607.1 (as)-607 (removal)-607.2 (of)-607 (the)]TJ
/N7 1 Tf
-28.774 -0.375 TD
(GM)Tj
6.5 0 0 6 135.63 369.75 Tm
(g)Tj
/N6 1 Tf
10 0 0 10 318 364 Tm
[(speci\256ed)-385.2 (particle.)]TJ
/N10 1 Tf
30 0 0 10 100.87 363.75 Tm
(]]])Tj
24.5 0 0 10 145.87 363.75 Tm
(])Tj
10 0 2.68 10 78 363.25 Tm
(F)Tj
10 0 0 10 90.88 363.25 Tm
(5)Tj
/N6 1 Tf
6.966 0 TD
[(,)-11356 (\()-37 (20)-37 (\))]TJ
6.5 0 0 6 85.41 360.75 Tm
(2)Tj
/N7 1 Tf
10 0 0 10 101.98 357.5 Tm
(R)Tj
/N6 1 Tf
1.25 0 TD
[(log)-436 (\()]TJ
/N7 1 Tf
2.01 0 TD
(r)Tj
/N6 1 Tf
0.5 0 TD
(/)Tj
/N7 1 Tf
0.352 0 TD
(R)Tj
/N6 1 Tf
1.06 0 TD
(\))Tj
/N7 1 Tf
6.5 0 0 6 108.41 355 Tm
(g)Tj
/N6 1 Tf
2.9862 0 TD
(2)Tj
/N7 1 Tf
3.34 0 TD
(g)Tj
/N6 1 Tf
10 0 0 10 78 336.25 Tm
(where)Tj
/N7 1 Tf
2.733 0 TD
(M)Tj
/N6 1 Tf
1.503 0 TD
[(is)-291 (the)-291 (mass)-290.1 (scale)-291.1 (and)]TJ
/N7 1 Tf
8.786 0 TD
(R)Tj
/N6 1 Tf
1.318 0 TD
[(is)-290 (the)-291 (length)-291.1 (scale)]TJ
10 0 2.68 10 318 334 Tm
(4.7.)Tj
/N7 1 Tf
10 0 0 10 338.55 334 Tm
[(Escaper)-385.2 (removal)]TJ
6.5 0 0 6 113.61 333.75 Tm
15.0431 Tc
(gg)Tj
/N6 1 Tf
10 0 0 10 78 324.25 Tm
0 Tc
[(of)-416 (the)-417 (continuous)-416.2 (mass)-417.1 (distribution)-416.3 (\()]TJ
/N7 1 Tf
15.434 0 TD
(KZ)Tj
/N6 1 Tf
1.223 0 TD
0.037 Tc
[(\(1)37 (5\))]TJ
/N10 1 Tf
1.796 0 TD
0 Tc
(5)Tj
/N6 1 Tf
0.888 0 TD
0.037 Tc
[(2\))37 (.)-380 (A)]TJ
-19.341 -1.2 TD
0 Tc
[(second)-355.1 (routine)-356.1 (\()]TJ
/N7 1 Tf
6.617 0 TD
(XTRNL)Tj
/N6 1 Tf
3.057 0 TD
[(2)-37 (\))-355 (is)-356 (constructed)-356.2 (in)-356 (a)-356 (similar)]TJ
15.326 -0.225 TD
(Routine)Tj
/N7 1 Tf
3.531 0 TD
[(ESC)-56.1 (APE)]TJ
/N6 1 Tf
4.032 0 TD
[(\()37 (option)-365.1 (13)-37 (\))-365 (contains)-365.2 (procedures)]TJ
-32.563 -0.975 TD
[(way)-385.1 (as)-385 (above,)-385.1 (with)]TJ
/N7 1 Tf
8.455 0 TD
(C)Tj
/N10 1 Tf
1.213 0 TD
(5)Tj
/N7 1 Tf
0.999 0 TD
(M)Tj
/N6 1 Tf
1.32 0 TD
(/)Tj
/N7 1 Tf
0.352 0 TD
(R)Tj
/N6 1 Tf
1.408 0 TD
[(\()19 (denoted)]TJ
/N7 1 Tf
3.865 0 TD
[(CG)-56 (AS)]TJ
/N6 1 Tf
2.648 0 TD
(\).)Tj
3.74 -0.225 TD
[(for)-566 (the)-566 (removal)-567.2 (of)-566 (escaping)-567.2 (particles.)-566.2 (A)-567 (nominal)]TJ
/N7 1 Tf
6.5 0 0 6 169.16 297.75 Tm
3.16 Tc
[(gg)1373.8 (g)]TJ
/N6 1 Tf
10 0 0 10 318 286 Tm
0 Tc
[(tidal)-496.1 (radius,)]TJ
/N7 1 Tf
5.465 0 TD
(R)Tj
/N6 1 Tf
0.879 0 TD
[(,)-496 (i)0 (s)-497 (used)-497.1 (as)-496 (distance)-497.2 (criterion,)-497.2 (with)]TJ
/N7 1 Tf
6.5 0 0 6 379.07 283.5 Tm
(t)Tj
10 0 0 10 318 274 Tm
(R)Tj
/N10 1 Tf
1.05 0 TD
(5)Tj
/N6 1 Tf
0.999 0 TD
(10)Tj
/N7 1 Tf
1 0 TD
(R)Tj
/N6 1 Tf
1.023 0 TD
[(.)-325 (The)-325.1 (escape)-324.1 (algorithm)-325.2 (can)-325.1 (be)-325 (summarized)]TJ
10 0 2.68 10 78 272.75 Tm
(4.6.)Tj
/N7 1 Tf
10 0 0 10 98.55 272.75 Tm
[(Inelastic)-385.2 (collisions)]TJ
6.5 0 0 6 324.42 271.5 Tm
4.4143 Tc
(th)Tj
/N6 1 Tf
10 0 0 10 318 262 Tm
0 Tc
[(as)-385 (follows:)]TJ
-23 -1.325 TD
[(An)-506 (optional)-507.2 (procedure)-507.2 (\()37 (option)-507.1 (12)-37 (\))-507 (has)-507.1 (been)-507.1 (in-)]TJ
-1 -1.2 TD
[(cluded)-606.1 (for)-606 (the)-607 (coalescence)-606.3 (of)-607 (two)-606.1 (particles.)-607.2 (The)]TJ
24 -0.175 TD
[(1.)-500 (Select)-385.1 (a)-385 (candidate)-385.2 (\()]TJ
/N7 1 Tf
9.439 0 TD
(i)Tj
/N6 1 Tf
0.371 0 TD
[(\))-385 (for)-385 (escape)-385.1 (if)]TJ
/N11 1 Tf
6.499 0 TD
(u)Tj
/N8 1 Tf
0.222 0 TD
(r)Tj
/N11 1 Tf
0.728 0 TD
(u)Tj
/N10 1 Tf
0.389 0 TD
(.)Tj
/N6 1 Tf
0.999 0 TD
(2)Tj
/N7 1 Tf
0.5 0 TD
(R)Tj
/N6 1 Tf
0.879 0 TD
(.)Tj
/N7 1 Tf
6.5 0 0 6 488.06 232.5 Tm
4.0051 Tc
(it)Tj
/N6 1 Tf
-0.0769 -0.75 TD
0 Tc
(2)Tj
-1.6538 -0.25 TD
(1)Tj
10 0 0 10 78 224.75 Tm
[(neighbour)-376.2 (scheme)-376.2 (itself)-376.1 (facilitates)-376.2 (the)-377 (determination)]TJ
/N10 1 Tf
9 0 0 6 476.14 223.25 Tm
(])Tj
/N6 1 Tf
10 0 0 10 318 223 Tm
[(2.)-500 (Evaluate)-513.2 (the)-514.1 (binding)-513.2 (energy)]TJ
/N7 1 Tf
13.802 0 TD
(E)Tj
/N10 1 Tf
1.013 0 TD
(5)Tj
/N36 1 Tf
1.566 0 TD
(v)Tj
/N10 1 Tf
1.138 0 TD
(1)Tj
10 0 2.68 10 503.19 223 Tm
(f)Tj
/N6 1 Tf
10 0 0 10 512.03 223 Tm
[(;)-698 (ac-)]TJ
/N7 1 Tf
6.5 0 0 6 462.07 220.5 Tm
3.6435 Tc
[(ii)527.7 (i)]TJ
/N6 1 Tf
2.2677 -0.0833 TD
0 Tc
(2)Tj
10 0 0 10 78 212.75 Tm
[(of)-388 (a)-388 (collision)-389.2 (candidate)-388.2 (since)-388.1 (a)-389 (search)-388.1 (can)-388.1 (be)-389 (made)]TJ
25.25 -0.175 TD
[(cept)-385.1 (escaper)-385.2 (if)]TJ
/N7 1 Tf
6.43 0 TD
(E)Tj
/N10 1 Tf
1.025 0 TD
(.)Tj
/N6 1 Tf
0.999 0 TD
(0.)Tj
/N7 1 Tf
6.5 0 0 6 400.85 208.5 Tm
(i)Tj
/N6 1 Tf
10 0 0 10 78 200.75 Tm
[(during)-439.1 (the)-439 (irregular)-440.2 (force)-439.1 (loop.)-440.1 (Having)-439.2 (identi\256ed)-440.2 (a)]TJ
24 -0.175 TD
[(3.)-500 (Check)-344.1 (whether)-344.2 (nearest)-345.2 (particle)-344.2 (is)-345 (escaping)-344.2 (or)-345 (has)]TJ
-24 -1.025 TD
[(close)-456.1 (neighbour,)-457.2 (the)-457.1 (osculating)-457.2 (semi-major)-457.3 (axis,)]TJ
/N7 1 Tf
20.85 0 TD
(a)Tj
/N6 1 Tf
0.5 0 TD
(,)Tj
3.9 -0.175 TD
[(large)-385.1 (perturbation.)]TJ
-25.25 -1.025 TD
[(may)-450.1 (be)-451 (used)-450.1 (in)-451 (the)-450 (collision)-451.2 (criterion.)-450.2 (If)-451 (accepted,)]TJ
24 -0.175 TD
[(4.)-500 (Subtract)]TJ
/N7 1 Tf
5.117 0 TD
0.268 Tc
(mE)Tj
/N6 1 Tf
2.383 0 TD
0 Tc
[(from)-535.1 (the)-535 (total)-535.1 (energy)]TJ
/N7 1 Tf
9.805 0 TD
(E)Tj
/N6 1 Tf
1.381 0 TD
(and)Tj
/N7 1 Tf
1.979 0 TD
(m)Tj
6.5 0 0 6 376.71 172.5 Tm
1.0174 Tc
[(ii)-15932.3 (t)-4101.5 (i)]TJ
/N6 1 Tf
10 0 0 10 78 164.75 Tm
0 Tc
[(the)-313 (appropriate)-314.3 (global)-314.1 (index)-314.1 (is)-314 (saved)-314.1 (until)-314.1 (the)-314 (end)-314.1 (of)]TJ
25.25 -0.175 TD
(from)Tj
/N7 1 Tf
2.329 0 TD
(M)Tj
/N6 1 Tf
1.063 0 TD
(.)Tj
/N7 1 Tf
6.5 0 0 6 362.06 160.5 Tm
(t)Tj
/N6 1 Tf
10 0 0 10 78 152.75 Tm
[(the)-349 (integration)-350.2 (cycle.)-350.1 (The)-350.1 (main)-350.1 (steps)-350.1 (of)-350 (the)-350 (coalesc-)]TJ
24 -0.175 TD
[(5.)-500 (Correct)-344.2 (the)-345 (irregular)-345.2 (force)-344.1 (and)-345.1 (\256rst)-345.1 (difference)-345.2 (for)]TJ
-24 -1.025 TD
[(ence)-385.1 (procedure)-385.2 (\()37 (routine)]TJ
/N7 1 Tf
10.114 0 TD
[(CO)-55 (AL)]TJ
/N6 1 Tf
2.704 0 TD
[(\))-385 (are)-385 (as)-385 (follows:)]TJ
12.432 -0.175 TD
[(each)-385.1 (neighbour.)]TJ
-1.25 -1.2 TD
[(6.)-500 (Reduce)]TJ
/N7 1 Tf
4.635 0 TD
(N)Tj
/N6 1 Tf
1.11 0 TD
[(by)-387 (1)-386 (and)-387.1 (update)-387.1 (all)]TJ
/N7 1 Tf
8.544 0 TD
(COMMON)Tj
/N6 1 Tf
4.868 0 TD
(arrays)Tj
6.5 0 0 6 282.35 120 Tm
0.0928 Tc
(\(3\))Tj
10 0 0 10 78 115 Tm
0 Tc
[(1.)-500 (Improve)-360.2 (the)-360 (collision)-361.2 (candidate)-360.2 (\()]TJ
/N7 1 Tf
15.096 0 TD
(j)Tj
/N6 1 Tf
0.371 0 TD
[(\))-360 (t)0 (o)-360 (order)]TJ
/N8 1 Tf
4.302 0 TD
(F)Tj
/N6 1 Tf
1.581 0 TD
[(.)-3650 (\()37 (routine)]TJ
/N7 1 Tf
7.414 0 TD
[(REMO)36.9 (VE)]TJ
/N6 1 Tf
4.054 0 TD
(\).)Tj
ET
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33 33 546 744 RC
BT
/N7 1 Tf
8 0 0 8 222.26 705 Tm
0 g
/N13 /ExtGState findRes gs
0 Tc
0 Tw
(S)Tj
/N6 1 Tf
8 0 2.144 8 226.26 705 Tm
(.)Tj
/N7 1 Tf
8 0 0 8 228.7 705 Tm
(J)Tj
/N6 1 Tf
8 0 2.144 8 232.25 705 Tm
(.)Tj
/N7 1 Tf
8 0 0 8 237.78 705 Tm
(Aarseth)Tj
/N6 1 Tf
3.6063 0 TD
(/)Tj
/N7 1 Tf
0.7375 0 TD
[(New)-440.8 (Astronomy)]TJ
/N6 1 Tf
8 0 2.144 8 328.02 705 Tm
[(6)-385 (\()-37 (2001)-37.5 (\))-384.5 (277)]TJ
8 0 0 8 373.29 705 Tm
(\261)Tj
8 0 2.144 8 377.73 705 Tm
(291)Tj
8 0 0 8 522 705 Tm
(287)Tj
10 0 0 10 78 679 Tm
[(7.)-500 (Re-de\256ne)-475.2 (coordinates)-476.3 (and)-475.1 (velocities)-476.2 (in)-475 (the)-476 (c.m.)-2400.1 (5.)-500 (De\256ne)-966.1 (individual)-966.2 (mass)-967.1 (densities)]TJ
/N10 1 Tf
10 0 2.68 10 493.77 679 Tm
(r)Tj
10 0 0 10 502.79 679 Tm
(5)Tj
/N6 1 Tf
0.999 0 TD
(3)Tj
/N7 1 Tf
0.5 0 TD
(M)Tj
/N6 1 Tf
1.344 0 TD
(/)Tj
/N7 1 Tf
6.5 0 0 6 498.71 676.5 Tm
(i)Tj
/N6 1 Tf
4.2446 0 TD
(5)Tj
-26.9323 -0.75 TD
(3)Tj
10 0 0 10 90.5 667 Tm
[(frame)-385.1 (and)-385.1 (correct)]TJ
/N7 1 Tf
7.707 0 TD
(E)Tj
/N6 1 Tf
0.841 0 TD
15.202 Tc
[(.\()15165 (4)]TJ
/N10 1 Tf
10 0 2.68 10 339.2 667 Tm
0 Tc
(p)Tj
/N7 1 Tf
10 0 0 10 346.42 667 Tm
(r)Tj
/N6 1 Tf
0.899 0 TD
(\).)Tj
/N7 1 Tf
6.5 0 0 6 173.62 664.5 Tm
(t)Tj
/N6 1 Tf
27.3262 0 TD
(6)Tj
10 0 0 10 318 655 Tm
[(6.)-500 (Form)-385.1 (the)-385 (density)-385.1 (centre)]TJ
/N8 1 Tf
11.695 0 TD
(r)Tj
/N10 1 Tf
1.027 0 TD
(5)Tj
/N11 1 Tf
1 0 TD
(o)Tj
/N8 1 Tf
1.107 0 TD
(r)Tj
/N10 1 Tf
10 0 2.68 10 473.96 655 Tm
(r)Tj
/N6 1 Tf
10 0 0 10 482.38 655 Tm
(/)Tj
/N11 1 Tf
0.389 0 TD
(o)Tj
/N10 1 Tf
10 0 2.68 10 497.35 655 Tm
(r)Tj
/N6 1 Tf
10 0 0 10 504.65 655 Tm
(.)Tj
/N7 1 Tf
6.5 0 0 6 439.7 652.5 Tm
4.3231 Tc
[(di)3391.9 (i)1004.2 (i)]TJ
/N6 1 Tf
10 0 0 10 318 643 Tm
0 Tc
[(7.)-500 (Obtain)-437.1 (core)-437.1 (radius)]TJ
/N7 1 Tf
9.448 0 TD
(R)Tj
/N6 1 Tf
1.428 0 TD
[(and)-437.1 (average)-437.2 (core)-437.1 (density,)]TJ
-33.876 -0.075 TD
[(In)-439 (a)-439 (second)-439.1 (stage,)-440.1 (routine)]TJ
/N7 1 Tf
11.388 0 TD
(CMCORR)Tj
/N6 1 Tf
4.55 0 TD
[(\()37 (option)-440.1 (18)-37 (\))]TJ
/N7 1 Tf
6.5 0 0 6 418.9 640.5 Tm
(c)Tj
/N6 1 Tf
-7.0831 -0.75 TD
(2)Tj
/N11 1 Tf
10 0 0 10 330.5 631 Tm
(k)Tj
/N10 1 Tf
10 0 2.68 10 334.38 631 Tm
(r)Tj
/N11 1 Tf
10 0 0 10 340.31 631 Tm
(l)Tj
/N10 1 Tf
0.499 0 TD
(5)Tj
/N11 1 Tf
1 0 TD
(o)Tj
/N10 1 Tf
10 0 2.68 10 366.37 631 Tm
(r)Tj
/N6 1 Tf
10 0 0 10 377.77 631 Tm
(/)Tj
/N11 1 Tf
0.389 0 TD
(o)Tj
/N10 1 Tf
10 0 2.68 10 392.74 631 Tm
(r)Tj
/N6 1 Tf
10 0 0 10 400.05 631 Tm
(.)Tj
-32.205 -0.075 TD
[(adjusts)-284.1 (all)-285 (coordinates)-285.3 (and)-284.1 (velocities)-285.2 (to)-285 (the)-285 (centre-of-)]TJ
/N7 1 Tf
6.5 0 0 6 372.86 628.5 Tm
3.5405 Tc
(ii)Tj
/N6 1 Tf
10 0 0 10 78 618.25 Tm
0 Tc
[(mass)-605.1 (rest)-605.1 (frame.)-605.1 (Appropriate)-605.3 (modi\256cation)-605.3 (of)-606 (the)]TJ
0 -1.2 TD
[(total)-353.1 (energy)-353.1 (involves)-353.2 (a)-354 (correction)-353.2 (to)-353 (the)-353 (new)-354.1 (kinetic)]TJ
25 -0.325 TD
[(In)-426 (the)-426 (AC)-426 (scheme,)-427.2 (central)-426.2 (particles)-426.2 (tend)-426.1 (to)-427 (have)]TJ
6.5 0 0 6 481.66 596 Tm
(3)Tj
10 0 0 10 78 594.25 Tm
[(energy,)-320.2 (and)-320.1 (the)-320 (primary)-321.2 (integration)-320.2 (variables,)]TJ
/N36 1 Tf
18.917 0 TD
(v)Tj
/N6 1 Tf
1.239 0 TD
(and)Tj
6.5 0 0 6 272.55 591.75 Tm
(0)Tj
10 0 0 10 318 591 Tm
[(the)-647 (largest)-647.1 (neighbour)-647.2 (densities,)]TJ
/N7 1 Tf
14.282 0 TD
(n)Tj
/N6 1 Tf
1.047 0 TD
(/)Tj
/N7 1 Tf
0.352 0 TD
(R)Tj
/N6 1 Tf
1.07 0 TD
[(;)-647 (hence)-648.1 (an)]TJ
6.5 0 0 6 466.37 588.5 Tm
(1)Tj
/N7 1 Tf
2.3523 0 TD
(s)Tj
/N8 1 Tf
10 0 0 10 78 582.25 Tm
(r)Tj
/N6 1 Tf
1.265 0 TD
[(are)-385 (updated)-385.2 (consistently.)]TJ
6.5 0 0 6 82.99 579.75 Tm
(0)Tj
10 0 0 10 318 579 Tm
[(appropriate)-507.2 (averaging)-507.2 (would)-507.1 (also)-507.1 (yield)-507.1 (a)-507 (well)-507.1 (de-)]TJ
0 -1.2 TD
[(\256ned)-332.1 (density)-332.1 (centre.)-221.1 (Where)-332.1 (relevant,)-332.2 (any)-333.1 (discussions)]TJ
10 0 2.68 10 78 556.75 Tm
(4.8.)Tj
/N7 1 Tf
10 0 0 10 98.55 556.75 Tm
[(Density)-385.2 (centre)]TJ
/N6 1 Tf
21.945 -0.175 TD
[(\()37 (and)-846.1 (algorithms)36.8 (\))-846 (involving)-847.2 (the)-846.1 (central)-847.2 (distance)]TJ
0 -1.2 TD
[(should)-633.1 (be)-634 (interpreted)-634.2 (as)-634 (referring)-634.2 (to)-634 (the)-634 (density)]TJ
-23 -1.025 TD
[(Models)-304.2 (of)-304 (centrally)-305.2 (concentrated)-304.3 (systems)-304.2 (are)-305 (most)]TJ
23 -0.175 TD
[(centre)-654.1 (\()-37 (i.e.)-654.1 (using)]TJ
/N11 1 Tf
8.164 0 TD
(u)Tj
/N8 1 Tf
0.222 0 TD
(r)Tj
/N10 1 Tf
0.883 0 TD
(2)Tj
/N8 1 Tf
1 0 TD
(r)Tj
/N11 1 Tf
0.873 0 TD
(u)Tj
/N6 1 Tf
0.259 0 TD
[(\),)-654 (which)-654.1 (is)-654 (updated)-655.2 (at)]TJ
/N7 1 Tf
6.5 0 0 6 406.62 528.5 Tm
2.6174 Tc
(id)Tj
/N6 1 Tf
10 0 0 10 78 520.75 Tm
0 Tc
[(conveniently)-348.3 (analysed)-348.2 (with)-348.1 (respect)-348.2 (to)-348 (a)-348 (well)-349.1 (de\256ned)]TJ
24 -0.175 TD
[(output)-385.1 (times.)]TJ
-24 -1.025 TD
[(cluster)-392.1 (centre,)-393.2 (in)-393 (accordance)-393.2 (with)-393.1 (standard)-393.2 (observa-)]TJ
0 -1.2 TD
[(tional)-548.1 (practice.)-548.2 (Following)-548.2 (analytical)-548.2 (estimates)-549.2 (and)]TJ
10 0 2.68 10 318 487 Tm
(4.9.)Tj
/N7 1 Tf
10 0 0 10 338.55 487 Tm
[(Error)-385.1 (checking)]TJ
/N6 1 Tf
-26.055 -0.225 TD
[(extensive)-348.2 (numerical)-349.2 (experiments,)-348.3 (Casertano)-349.2 (and)-349.1 (Hut)]TJ
0 -1.2 TD
[(\()-37 (1985)-37.1 (\))-282 (have)-282.1 (proposed)-282.2 (an)-282 (operational)-282.3 (de\256nition)-282.2 (of)-282 (the)]TJ
25 -0.975 TD
[(In)-392 (standard)-393.2 (simulations,)-393.3 (energy)-393.1 (conservation)-393.3 (may)]TJ
-25 -0.225 TD
[(density)-385.1 (centre)-385.1 (and)-385.1 (corresponding)-385.3 (core)-385.1 (radius.)]TJ
24 -0.975 TD
[(be)-295 (employed)-296.2 (as)-296 (a)-295 (check)-296.1 (to)-296 (safeguard)-295.2 (the)-296 (results)-296.1 (from)]TJ
-23 -0.225 TD
[(The)-332.1 (original)-332.2 (de\256nition)-333.2 (of)-332 (the)-332.1 (core)-333.1 (radius)-332.1 (has)-333.1 (been)]TJ
23 -0.975 TD
[(any)-304.1 (spurious)-304.2 (procedures)-305.2 (such)-304.1 (as)-304 (force)-305.1 (discontinuities)]TJ
-24 -0.225 TD
[(modi\256ed)-570.2 (slightly)-570.2 (in)-570 (order)-570.1 (to)-570 (obtain)-570.1 (a)-570 (convergent)]TJ
24 -0.975 TD
[(or)-309 (inappropriate)-309.3 (program)-309.2 (usage.)-309.1 (Even)-309.1 (systems)-309.2 (which)]TJ
-24 -0.225 TD
[(result)-552.1 (using)-553.1 (a)-553 (smaller)-553.2 (\()37 (central)-37.1 (\))-552 (sample)-553.1 (\()]TJ
/N7 1 Tf
17.609 0 TD
(n)Tj
/N11 1 Tf
0.704 0 TD
(.)Tj
/N7 1 Tf
0.999 0 TD
(N)Tj
/N6 1 Tf
0.778 0 TD
0.112 Tc
[(/2)75 (\))112 (.)]TJ
3.91 -0.975 TD
0 Tc
[(include)-404.2 (collisions,)-404.2 (escape)-404.1 (and)-111.1 (/)-111 (o)0 (r)-404 (analytical)-405.2 (external)]TJ
-24 -0.225 TD
[(Thus)-665.1 (the)-666 (core)-665.1 (radius)-666.1 (is)-666 (determined)-665.2 (by)-666 (the)-666 (rms)]TJ
24 -0.975 TD
[(potentials)-347.2 (may)-348.1 (be)-348 (treated)-348.1 (in)-348 (this)-347.1 (way,)-348.1 (since)-348.1 (the)-348 (total)]TJ
-24 -0.225 TD
(expression)Tj
24 -0.975 TD
[(energy)-385.1 (is)-385 (adjusted)-385.2 (accordingly.)]TJ
/N7 1 Tf
6.5 0 0 6 110.87 386 Tm
(n)Tj
/N6 1 Tf
10.0369 -0.1667 TD
0.1664 Tc
(1/2)Tj
10 0 0 10 328 379 Tm
0 Tc
[(By)-575 (saving)-576.1 (all)]TJ
/N7 1 Tf
6.505 0 TD
(COMMON)Tj
/N6 1 Tf
5.056 0 TD
[(variables)-576.2 (at)-576 (speci\256ed)]TJ
6.5 0 0 6 153.34 378.5 Tm
1.0538 Tc
(22)Tj
/N11 1 Tf
24 0 0 24 107.17 373.5 Tm
0 Tc
(O)Tj
10 0 0 10 120.79 373.5 Tm
(u)Tj
/N8 1 Tf
0.222 0 TD
(r)Tj
/N10 1 Tf
0.883 0 TD
(2)Tj
/N8 1 Tf
1 0 TD
(r)Tj
/N11 1 Tf
0.873 0 TD
(u)Tj
/N10 1 Tf
10 0 2.68 10 156.95 373.5 Tm
(r)Tj
/N7 1 Tf
6.5 0 0 6 127.77 371 Tm
2.6189 Tc
[(id)528.1 (i)]TJ
/N6 1 Tf
10 0 0 10 318 367 Tm
0 Tc
[(intervals)-367.2 (\()37 (usually)-368.1 (each)-368.1 (output)-37.1 (\),)-368 (the)-368 (last)-368.1 (interval)-368.2 (may)]TJ
/N7 1 Tf
6.5 0 0 6 106.78 365.25 Tm
(i)Tj
/N10 1 Tf
0.3708 0 TD
(5)Tj
/N6 1 Tf
0.8877 0 TD
(1)Tj
/N10 1 Tf
30 0 0 10 105.67 360.25 Tm
(]]])Tj
34 0 0 10 150.67 360.25 Tm
(])Tj
/N7 1 Tf
10 0 0 10 78 359.75 Tm
(R)Tj
/N10 1 Tf
1.157 0 TD
(5)Tj
/N6 1 Tf
9.738 0 TD
[(,)-8715 (\()-37 (21)-37 (\))]TJ
/N7 1 Tf
6.5 0 0 6 84.42 357.25 Tm
(c)Tj
/N11 1 Tf
35 0 0 35 97.91 357.25 Tm
1.7749 Tc
(12)Tj
/N6 1 Tf
6.5 0 0 6 145.06 355.75 Tm
0 Tc
(2)Tj
10 0 0 10 318 355 Tm
[(be)-767 (re-calculated)-768.3 (with)-767.1 (reduced)-768.2 (time-steps)-767.2 (if)-768 (the)]TJ
/N11 1 Tf
24 0 0 24 125.15 350.75 Tm
(O)Tj
/N10 1 Tf
10 0 2.68 10 138.58 350.75 Tm
(r)Tj
/N7 1 Tf
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(i)Tj
/N6 1 Tf
10 0 0 10 318 343 Tm
[(energy)-716.1 (change)-716.1 (exceeds)-716.2 (the)-716 (prescribed)-716.2 (tolerance.)]TJ
-24 -1.15 TD
(where)Tj
/N8 1 Tf
3.08 0 TD
(r)Tj
/N6 1 Tf
1.499 0 TD
[(denotes)-638.2 (the)-638.1 (coordinates)-638.3 (of)-638 (the)-638 (density)]TJ
19.421 -0.05 TD
[(Since)-492.1 (unit)-492.1 (1)-492 (\()37 (option)-492.1 (1)-37 (\))-492 (is)-492 (reserved)-492.2 (for)]TJ
/N7 1 Tf
17.156 0 TD
(COMMON)Tj
6.5 0 0 6 113.56 329 Tm
(d)Tj
/N6 1 Tf
10.4262 -0.75 TD
(3)Tj
10 0 0 10 78 319.5 Tm
[(centre)-503.1 (and)]TJ
/N10 1 Tf
10 0 2.68 10 126.94 319.5 Tm
(r)Tj
10 0 0 10 135.96 319.5 Tm
(5)Tj
/N6 1 Tf
1 0 TD
[(15)-111 (/)-74 (\()-37 (4)]TJ
/N10 1 Tf
10 0 2.68 10 169.29 319.5 Tm
(p)Tj
/N7 1 Tf
10 0 0 10 176.52 319.5 Tm
(r)Tj
/N6 1 Tf
0.899 0 TD
[(\))-504 (i)0 (s)-504 (the)-504 (density)-504.1 (estimator)]TJ
13.249 -0.05 TD
[(save)-620.1 (at)-620 (termination,)-620.3 (unit)-621.1 (2)-620 (i)0 (s)-620 (employed)-620.2 (for)-621 (this)]TJ
/N7 1 Tf
6.5 0 0 6 131.89 317 Tm
(i)Tj
/N6 1 Tf
7.6062 0 TD
(6)Tj
10 0 0 10 78 307.5 Tm
[(de\256ned)-368.1 (with)-368.1 (respect)-368.2 (to)-368 (the)-368 (sixth)-368.1 (nearest)-368.2 (particle,)]TJ
/N7 1 Tf
20.524 0 TD
(r)Tj
/N6 1 Tf
0.826 0 TD
(.)Tj
2.65 -0.05 TD
[(purpose.)-578.2 (Thus)-578.1 (if)]TJ
/N7 1 Tf
7.761 0 TD
(KZ)Tj
/N6 1 Tf
1.223 0 TD
0.037 Tc
(\(2\))Tj
/N10 1 Tf
1.296 0 TD
0 Tc
(5)Tj
/N6 1 Tf
0.888 0 TD
[(1,)-578 (a)]TJ
/N7 1 Tf
2.35 0 TD
(COMMON)Tj
/N6 1 Tf
5.059 0 TD
[(save)-579.1 (is)]TJ
6.5 0 0 6 287.69 305 Tm
(6)Tj
10 0 0 10 78 295.5 Tm
[(W)56 (e)-428 (also)-427.1 (generalize)-428.2 (the)-427 (density)-428.1 (estimator)-427.2 (to)-428 (include)]TJ
24 -0.05 TD
[(performed)-318.2 (every)-319.1 (output,)-318.2 (provided)-319.2 (the)-318.1 (relative)-319.2 (energy)]TJ
-24 -1.15 TD
[(the)-747 (actual)-748.1 (mass)-748.1 (of)-747 (the)]TJ
/N7 1 Tf
11.403 0 TD
(\256ve)Tj
/N6 1 Tf
2.173 0 TD
[(nearest)-748.2 (neighbours)]TJ
10.424 -0.05 TD
(error)Tj
/N7 1 Tf
2.338 0 TD
(DE)Tj
/N6 1 Tf
1.728 0 TD
[(\()37 (scaled)-395.1 (by)-395 (the)-395.1 (kinetic)-395.1 (or)-395 (potential)-396.2 (energy)-37.1 (\))]TJ
-28.066 -1.15 TD
[(\()-37 (Spurzem,)-430.2 (1991)-37.1 (\))-431 (i)0 (n)-430 (order)-431.1 (to)-431 (be)-430 (consistent)-431.2 (with)-431.1 (the)]TJ
24 -0.05 TD
(satis\256es)Tj
/N7 1 Tf
3.836 0 TD
(DE)Tj
/N10 1 Tf
1.556 0 TD
(,)Tj
/N6 1 Tf
0.999 0 TD
(5*)Tj
/N7 1 Tf
1 0 TD
(QE)Tj
/N6 1 Tf
1.333 0 TD
[(,)-670 (where)]TJ
/N7 1 Tf
4.033 0 TD
(QE)Tj
/N6 1 Tf
2.059 0 TD
[(is)-670 (the)-670 (speci\256ed)]TJ
-38.816 -1.15 TD
[(original)-310.2 (expression)-311.2 (for)-310 (equal)-311.1 (masses)-311.1 (\()37 (cf.)-310 (Eq.)-311.1 (\()-37 (V)167 (.3)-37 (\))-311 (o)0 (f)]TJ
24 -0.05 TD
(tolerance.)Tj
-24 -1.15 TD
[(Casertano)-569.2 (and)-569.1 (Hut)-37.1 (\).)-569 (The)-570.1 (density)-569.1 (centre)-569.1 (and)-570.1 (core)]TJ
25 -0.05 TD
[(Modi\256cations)-676.3 (of)-677 (the)-676 (accuracy)-677.2 (parameters)-677.2 (take)]TJ
-25 -1.15 TD
[(radius)-498.1 (are)-499 (determined)-499.2 (in)-499 (routine)]TJ
/N7 1 Tf
14.269 0 TD
(CORE)Tj
/N6 1 Tf
3.11 0 TD
[(\()37 (option)-499.1 (8)-37 (\))]TJ
6.621 -0.05 TD
[(place)-329.1 (if)]TJ
/N7 1 Tf
3.38 0 TD
(KZ)Tj
/N6 1 Tf
1.223 0 TD
0.037 Tc
(\(2\))Tj
/N10 1 Tf
1.295 0 TD
0 Tc
(5)Tj
/N6 1 Tf
0.889 0 TD
[(2.)-329 (Thus)-330.1 (if)]TJ
/N7 1 Tf
4.35 0 TD
(DE)Tj
/N10 1 Tf
1.555 0 TD
(.)Tj
/N6 1 Tf
0.999 0 TD
(5*)Tj
/N7 1 Tf
1 0 TD
(QE)Tj
/N6 1 Tf
1.333 0 TD
[(,)-330 (the)-330 (previous)]TJ
-40.024 -1.15 TD
[(according)-385.2 (to)-385 (the)-385 (schematic)-385.2 (algorithm:)]TJ
/N7 1 Tf
24 -0.05 TD
(COMMON)Tj
/N6 1 Tf
4.986 0 TD
[(variables)-506.2 (are)-506.1 (read)-506.1 (from)-506.1 (unit)-506.1 (2,)-506 (where-)]TJ
-4.986 -1.2 TD
(upon)Tj
/N7 1 Tf
2.374 0 TD
[(ET)-56 (AI)]TJ
/N6 1 Tf
2.578 0 TD
(and)Tj
/N7 1 Tf
1.818 0 TD
[(ET)-56 (AR)]TJ
/N6 1 Tf
2.838 0 TD
[(are)-374.1 (reduced)-375.2 (by)-374 (a)-375 (factor)-374.1 (of)-375 (2,)]TJ
-33.608 -1.2 TD
[(1.)-500 (Select)-460.1 (all)-461 (particles)-460.2 (inside)-461.1 (max)-184.1 (\()-37 (3)]TJ
/N7 1 Tf
15.089 0 TD
(R)Tj
/N6 1 Tf
0.987 0 TD
(,)Tj
/N7 1 Tf
0.71 0 TD
(R)Tj
/N6 1 Tf
1.06 0 TD
[(\))-461 (a)0 (s)-461 (data)-2400.1 (and)-712.1 (the)-712 (current)-712.2 (time-steps)-712.2 (are)-712 (reduced)-712.2 (partially)]TJ
/N7 1 Tf
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2.1668 Tc
(ch)Tj
/N6 1 Tf
10 0 0 10 90.5 187 Tm
0 Tc
[(sample.)-19667.2 (\()37 (subject)-456.2 (to)]TJ
/N10 1 Tf
27.569 0 TD
(D)Tj
/N7 1 Tf
0.667 0 TD
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/N10 1 Tf
0.729 0 TD
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0.999 0 TD
(t)Tj
/N10 1 Tf
0.482 0 TD
(2)Tj
/N7 1 Tf
1 0 TD
(t)Tj
/N6 1 Tf
0.599 0 TD
[(\).)-456 (A)-456 (second)-456.1 (restart)-456.1 (is)-457 (carried)]TJ
/N7 1 Tf
6.5 0 0 6 375.95 184.5 Tm
4.6605 Tc
(ii)Tj
/N6 1 Tf
10 0 0 10 78 175 Tm
0 Tc
[(2.)-500 (Form)-335.1 (a)-336 (list)-335.1 (of)-336 (the)-335 (six)-336 (nearest)-335.2 (neighbours)-336.2 (for)-336 (each)-2400.1 (out)-471.1 (if)-471 (this)-472.1 (procedure)-471.2 (does)-471.1 (not)-472.1 (satisfy)-471.1 (the)-472 (accuracy)]TJ
1.25 -1.2 TD
[(selected)-385.2 (particle.)-15895.2 (criterion)-375.2 (\()37 (using)-375.1 (the)-376 (counter)]TJ
/N7 1 Tf
34.323 0 TD
[(NDU)-37.1 (MP)]TJ
/N6 1 Tf
3.666 0 TD
[(\).)-375 (If)-376 (a)-375 (restart)-376.1 (is)]TJ
-39.239 -1.2 TD
[(3.)-500 (Sort)-489.1 (the)-490 (list)-489.1 (of)-490 (six)-489 (square)-490.1 (distances)-489.2 (to)-490 (\256nd)-490.1 (the)-2400 (not)-457.1 (required)-457.2 (but)]TJ
/N7 1 Tf
31.259 0 TD
(DE)Tj
/N10 1 Tf
1.555 0 TD
(.)Tj
/N7 1 Tf
1 0 TD
(QE)Tj
/N6 1 Tf
1.333 0 TD
[(,)-457 (the)-457 (integration)-458.2 (parame-)]TJ
6.5 0 0 6 128.78 144 Tm
(2)Tj
49.3677 0 TD
0.1664 Tc
(1/2)Tj
10 0 0 10 90.5 139 Tm
0 Tc
[(largest)-385.1 (\()]TJ
/N7 1 Tf
3.347 0 TD
(r)Tj
/N6 1 Tf
0.899 0 TD
[(\).)-17921 (ters)-404.1 (are)-404 (decreased)-404.2 (by)-404 (\()]TJ
/N7 1 Tf
28.097 0 TD
(QE)Tj
/N6 1 Tf
1.444 0 TD
(/)Tj
/N7 1 Tf
0.352 0 TD
(DE)Tj
/N6 1 Tf
1.426 0 TD
[(\))-1102 (,)-404 (whereas)-404.2 (a)-405 (small)]TJ
6.5 0 0 6 128.78 136.5 Tm
(6)Tj
10 0 0 10 78 127 Tm
[(4.)-500 (Obtain)-552.1 (the)-552 (total)-552.1 (mass)-553.1 (\()]TJ
/N7 1 Tf
11.477 0 TD
(M)Tj
/N6 1 Tf
1.269 0 TD
0.552 Tc
[(\)o)552 (ft)552 (h)552 (e)]TJ
/N7 1 Tf
4.044 0 TD
0 Tc
(\256ve)Tj
/N6 1 Tf
1.978 0 TD
[(nearest)-2400.2 (increase)-589.2 (is)-590 (allowed)-590.2 (if)]TJ
/N7 1 Tf
15.311 0 TD
(DE)Tj
/N10 1 Tf
1.555 0 TD
(,)Tj
/N6 1 Tf
1 0 TD
(0.2*)Tj
/N7 1 Tf
1.75 0 TD
(QE)Tj
/N6 1 Tf
1.96 0 TD
(and)Tj
/N7 1 Tf
2.034 0 TD
[(ET)-55 (AI)]TJ
/N10 1 Tf
2.389 0 TD
(,)Tj
/N6 1 Tf
6.5 0 0 6 201.28 124.5 Tm
(5)Tj
10 0 0 10 90.5 115 Tm
(neighbours.)Tj
/N7 1 Tf
22.75 0 TD
[(ET)-55 (A)]TJ
/N6 1 Tf
1.833 0 TD
[(0)-385 (\()-37 (initial)-385.1 (value)-385.1 (of)]TJ
/N7 1 Tf
7.743 0 TD
[(ET)-56 (AI)]TJ
/N6 1 Tf
2.259 0 TD
(\).)Tj
ET
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33 33 546 744 RC
BT
/N6 1 Tf
8 0 0 8 78 705 Tm
0 g
/N13 /ExtGState findRes gs
0 Tc
(288)Tj
/N7 1 Tf
18.0325 0 TD
0 Tw
(S)Tj
/N6 1 Tf
8 0 2.144 8 226.26 705 Tm
(.)Tj
/N7 1 Tf
8 0 0 8 228.7 705 Tm
(J)Tj
/N6 1 Tf
8 0 2.144 8 232.25 705 Tm
(.)Tj
/N7 1 Tf
8 0 0 8 237.78 705 Tm
(Aarseth)Tj
/N6 1 Tf
3.6063 0 TD
(/)Tj
/N7 1 Tf
0.7375 0 TD
[(New)-440.8 (Astronomy)]TJ
/N6 1 Tf
8 0 2.144 8 328.02 705 Tm
[(6)-385 (\()-37 (2001)-37.5 (\))-384.5 (277)]TJ
8 0 0 8 373.29 705 Tm
(\261)Tj
8 0 2.144 8 377.73 705 Tm
(291)Tj
/N8 1 Tf
10 0 0 10 78 679 Tm
[(5.)-500 (Practical)-385.2 (aspects)]TJ
/N6 1 Tf
24 0 TD
[(1964;)-418.1 (Goodman)-418.2 (et)-418 (al.,)-418.1 (1993)-37.1 (\).)-418 (However,)-418.2 (in)-418 (view)-418.1 (of)]TJ
0 -1.2 TD
[(the)-423 (chaotic)-424.1 (nature)-424.1 (of)-424 (the)]TJ
/N7 1 Tf
10.783 0 TD
(N)Tj
/N6 1 Tf
0.704 0 TD
[(-body)-424.1 (problem,)-424.2 (it)-424 (is)-424 (not)]TJ
-34.487 -1.2 TD
[(The)-332.1 (\256nal)-332.1 (section)-333.1 (is)-332 (devoted)-332.2 (to)-333 (practical)-332.2 (aspects)-333.2 (of)-2400 (justi\256ed)-408.2 (to)-409 (aim)-408 (for)-409.1 (the)-409 (highest)-408.2 (possible)-409.2 (accuracy)-409.2 (at)]TJ
/N7 1 Tf
-1 -1.2 TD
(N)Tj
/N6 1 Tf
0.704 0 TD
[(-body)-751.1 (simulations,)-752.3 (and)-751.1 (also)-752.1 (summarizes)-752.3 (some)-2400.1 (the)-617.1 (expense)-618.2 (of)-618 (curtailing)-618.2 (the)-618 (integration)-618.2 (time)-618.1 (or)]TJ
-0.704 -1.2 TD
[(features)-385.2 (of)-385 (a)-385 (test)-385.1 (calculation.)-11991.3 (particle)-475.2 (number.)-476.2 (This)-476.1 (is)-475 (particularly)-476.2 (relevant)-476.2 (when)]TJ
24 -1.2 TD
[(using)-720.1 (an)-721 (approximate)-721.3 (model)-721.1 (for)-721.1 (the)-721 (interaction)]TJ
10 0 2.68 10 78 607 Tm
(5.1.)Tj
/N7 1 Tf
10 0 0 10 98.55 607 Tm
[(Performance)-385.3 (and)-441.1 (Accuracy)]TJ
/N6 1 Tf
21.945 0 TD
(potential.)Tj
1 -1.2 TD
[(The)-573.1 (most)-573.1 (noticeable)-573.2 (systematic)-573.2 (errors)-573.1 (are)-573 (con-)]TJ
-24 -1.2 TD
[(The)-322.1 (litmus)-322.1 (test)-322.1 (of)-322 (a)-323 (good)-322.1 (code)-322.1 (lies)-322.1 (in)-322 (its)-322 (ability)-323.1 (to)-2400 (nected)-280.1 (with)-280.1 (the)-281 (integration)-280.2 (of)-280 (binaries,)-281.2 (and)-280.1 (this)-281.1 (effect)]TJ
-1 -1.2 TD
[(produce)-447.2 (satisfactory)-447.3 (solutions)-447.2 (in)-447 (a)-447 (given)-447.1 (time.)-448.1 (The)-2400.1 (is)-308 (also)-308.1 (present)-308.2 (when)-308.1 (using)-309.1 (a)-308 (softening)-308.2 (parameter.)-197.2 (W)55 (e)]TJ
T*
[(CPU)-646.1 (time)-647.1 (requirement)-647.3 (is)-647 (particularly)-647.3 (crucial)-647.2 (for)-2400.1 (can)-356.1 (measure)-357.2 (the)-356 (characteristic)-357.3 (error)-356.1 (of)-357 (the)-357 (two-body)]TJ
/N7 1 Tf
T*
(N)Tj
/N6 1 Tf
0.704 0 TD
[(-body)-608.1 (simulations,)-608.3 (which)-608.1 (are)-608 (often)-608.1 (designed)-608.2 (to)-2400 (motion)-470.1 (by)-470 (studying)-471.2 (binaries)-470.2 (in)-471 (isolation,)-470.2 (using)-471.1 (the)]TJ
-0.704 -1.2 TD
[(make)-465.1 (full)-465.1 (use)-466.1 (of)-465 (the)-465 (available)-466.2 (resources,)-465.2 (as)-465 (in)-466 (the)-2400 (equivalent)-576.2 (formulation)-576.3 (with)-576.1 (one)-576.1 (force)-576.1 (polynomial)]TJ
T*
[(case)-363.1 (of)-364 (dedicated)-364.2 (workstations.)-364.3 (In)-363 (view)-364.1 (of)-364 (the)-364 (time-)-2400.1 (\()-37 (program)]TJ
/N7 1 Tf
28.184 0 TD
(NBODY)Tj
/N6 1 Tf
3.333 0 TD
[(1)-37 (\))0 (.)-427 (For)-426.1 (a)-426 (binary)-426.1 (with)-427.1 (eccentricity)]TJ
-31.517 -1.2 TD
[(consuming)-420.2 (nature)-420.1 (of)-420 (such)-420.1 (calculations,)-420.3 (code)-420.1 (design)-2400.1 (0.8)-391 (\()37 (and)-391.1 (no)-392 (softening)-37.2 (\))-391 (the)-391 (systematic)-392.2 (error)-391.1 (in)-392 (semi-)]TJ
/N10 1 Tf
6.5 0 0 6 503.81 504 Tm
(2)Tj
/N6 1 Tf
0.8892 0 TD
(5)Tj
10 0 0 10 78 499 Tm
[(must)-594.1 (inevitably)-594.2 (be)-594 (based)-595.1 (on)-594 (a)-594 (trade-off)-595.2 (between)-2400.2 (major)-301.1 (axis)-302.1 (per)-302.1 (revolution)-302.2 (is)]TJ
/N10 1 Tf
10 0 2.68 10 432.71 499 Tm
(d)Tj
/N7 1 Tf
10 0 0 10 438.26 499 Tm
(a)Tj
/N6 1 Tf
0.611 0 TD
(/)Tj
/N7 1 Tf
0.353 0 TD
(a)Tj
/N10 1 Tf
0.703 0 TD
0.334 Tc
(52)Tj
/N6 1 Tf
2.166 0 TD
0 Tc
(3)Tj
/N10 1 Tf
0.667 0 TD
(3)Tj
/N6 1 Tf
0.999 0 TD
[(10)-1297 (with)]TJ
/N10 1 Tf
6.5 0 0 6 418.87 492 Tm
(2)Tj
/N6 1 Tf
0.8892 0 TD
(6)Tj
10 0 0 10 78 487 Tm
[(speed)-385.1 (and)-385.1 (accuracy.)]TJ
/N10 1 Tf
10 0 2.68 10 318 487 Tm
(h)Tj
10 0 0 10 326.14 487 Tm
(5)Tj
/N6 1 Tf
1 0 TD
[(0.02)-753.1 (\()37 (o)0 (r)]TJ
/N10 1 Tf
4.552 0 TD
(2)Tj
/N6 1 Tf
1 0 TD
(6)Tj
/N10 1 Tf
0.666 0 TD
(3)Tj
/N6 1 Tf
1 0 TD
[(10)-1747 (with)]TJ
/N10 1 Tf
10 0 2.68 10 460.18 487 Tm
(h)Tj
10 0 0 10 468.33 487 Tm
(5)Tj
/N6 1 Tf
0.999 0 TD
[(0.01)-37.1 (\),)-754 (which)]TJ
-39.032 -1.2 TD
[(In)-593 (the)-593 (present)-593.2 (version,)-593.2 (we)-593 (have)-593.1 (made)-593.1 (a)-593 (com-)-2400.1 (corresponds)-361.3 (to)-361 (about)-361.1 (140)-362.1 (\()-37 (200)-37.1 (\))-361 (integration)-361.2 (steps)-362.1 (for)]TJ
-1 -1.2 TD
[(promise)-362.2 (by)-361 (de\256ning)-362.2 (the)-362 (basic)-362.1 (variables)]TJ
/N8 1 Tf
16.558 0 TD
(r)Tj
/N6 1 Tf
0.88 0 TD
(,)Tj
/N8 1 Tf
0.612 0 TD
(r)Tj
/N6 1 Tf
0.712 0 TD
(,)Tj
/N18 1 Tf
0.612 0 TD
(v)Tj
/N6 1 Tf
0.955 0 TD
(,)Tj
/N7 1 Tf
0.612 0 TD
(t)Tj
/N6 1 Tf
3.059 0 TD
[(each)-385.1 (component.)]TJ
6.5 0 0 6 248.58 460.5 Tm
(0)Tj
/N7 1 Tf
2.2585 0 TD
(t)Tj
/N6 1 Tf
2.1877 0 TD
1.5415 Tc
(00)Tj
10 0 0 10 78 451 Tm
0 Tc
[(\()37 (and)-462.1 (global)-463.1 (time)36.9 (\))-463 (i)0 (n)-463 (full)-463.1 (double)-463.1 (precision,)-463.2 (with)-463.1 (all)]TJ
0 -1.2 TD
[(other)-360.1 (variables)-360.2 (in)-360 (standard)-360.2 (precision.)-360.2 (This)-360.1 (gives)-360.1 (rise)]TJ
10 0 2.68 10 318 427.25 Tm
(5.2.)Tj
/N7 1 Tf
10 0 0 10 338.55 427.25 Tm
[(Sof)-19.1 (tening)]TJ
/N6 1 Tf
-26.055 -0.025 TD
[(to)-283 (a)-284 (faster)-284.1 (force)-284.1 (calculation)-284.2 (while)-284.1 (the)-284 (dominant)-284.2 (terms)]TJ
0 -1.2 TD
[(of)-283 (the)-284 (Taylor)-283.1 (series)-284.1 (are)-283 (retained)-284.2 (to)-283 (higher)-284.1 (accuracy)-284.2 (at)]TJ
25 -1.175 TD
[(The)-719.1 (force)-719.1 (law)-719 (\()-37 (1)-37 (\))-719 (is)-719 (based)-719.1 (on)-719 (the)-720.1 (softened)]TJ
-25 -0.025 TD
[(little)-347.1 (extra)-347.1 (cost.)-347.1 (Assuming)-348.2 (a)-347 (Fortran)-347.2 (77)-347 (compiler)-348.2 (\()37 (o)0 (r)]TJ
6.5 0 0 6 399.95 396 Tm
2.9277 Tc
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/N7 1 Tf
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[(/)-833 (2)0 (,)-299 (inside)-300.1 (which)]TJ
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[(Actual)-324.1 (CPU)-324.1 (times)-324.1 (are)-325 (problem)-324.2 (dependent)-324.2 (and)-325.1 (any)-2400.1 (the)-385.1 (interaction)-385.2 (tends)-385.1 (to)-385 (a)-385 (harmonic)-385.2 (oscillator.)]TJ
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T*
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T*
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/N7 1 Tf
34.93 0 TD
(N)Tj
/N6 1 Tf
0.667 0 TD
[(,)-400 (thereby)-400.2 (reducing)-400.2 (close)]TJ
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T*
[(for)-711.1 (Plummer)-712.2 (models)-711.2 (near)-712.1 (equilibrium)-711.2 (over)-712.1 (one)-2400.1 (systems)-339.2 (in)-339 (virial)-339.1 (equilibrium)-339.2 (lead)-339.1 (to)-339 (a)-339 (close)-340.1 (encoun-)]TJ
T*
[(crossing)-434.2 (time)-434.1 (with)]TJ
/N7 1 Tf
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[(in)-434 (the)-434 (range)-434.1 ([100,)-434.1 (2000])-435.1 (and)-2400.1 (ter)-346 (de\256nition)]TJ
/N7 1 Tf
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(r)Tj
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1.172 0 TD
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1 0 TD
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(N)Tj
/N6 1 Tf
1.069 0 TD
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0.0545 Tc
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4.6969 0 TD
0 Tc
(h)Tj
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[(softening)-543.2 (parameter)]TJ
/N10 1 Tf
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(e)Tj
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(5)Tj
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1 0 TD
(4)Tj
/N7 1 Tf
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(R)Tj
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1.146 0 TD
(/)Tj
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(N)Tj
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0.667 0 TD
[(.)-543 (A)-544 (least)-544.1 (square)-544.1 (\256t)-2400 (between)-311.2 (two)-312.1 (typical)-311.2 (particles.)-312.2 (On)-312 (the)-311 (other)-312.1 (hand,)-312.1 (the)]TJ
/N36 1 Tf
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(v)Tj
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0.056 Tc
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0 Tc
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10.488 0 TD
(T)Tj
/N10 1 Tf
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(~)Tj
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(N)Tj
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/N7 1 Tf
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(c)Tj
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[(coef\256cient)-710.2 (exceeding)-711.2 (0.9997.)-711.2 (Excluding)]TJ
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(N)Tj
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[(100)-2400.1 (general)-283.2 (discussion)-284.2 (of)-284 (these)-284.1 (aspects)-284.1 (has)-284.1 (been)-284.1 (given)-284.1 (by)]TJ
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T*
[(compared)-296.2 (with)-296.1 (an)-297 (older)-296.1 (test)-297.1 (for)]TJ
/N7 1 Tf
13.053 0 TD
(N)Tj
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1.019 0 TD
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1 -1.2 TD
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(5)Tj
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1 0 TD
[(0)-440 (a)0 (s)-439 (long)-440.1 (as)-440 (there)]TJ
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[(although)-360.2 (it)-360 (is)-360 (not)-360.1 (an)-361 (easy)-360.1 (one.)-360.1 (It)-360 (is)-360 (well)-360.1 (known)-361.1 (that)-2400.1 (are)-515 (no)-515 (critical)-515.1 (encounters)-515.2 (or)-515 (persistent)-515.2 (binaries)-515.2 (of)]TJ
T*
[(the)-442 (numerical)-443.2 (solutions)-443.2 (for)-443.1 (the)-443 (point-mass)-443.2 (problem)-2400.2 (high)-385.1 (eccentricity.)]TJ
T*
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ET
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33 33 546 744 RC
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0 g
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0 Tw
(S)Tj
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(.)Tj
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(J)Tj
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(.)Tj
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(Aarseth)Tj
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3.6063 0 TD
(/)Tj
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[(New)-440.8 (Astronomy)]TJ
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[(6)-385 (\()-37 (2001)-37.5 (\))-384.5 (277)]TJ
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(\261)Tj
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(291)Tj
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[(expressions)-733.3 (with)-734.1 (a)-733 (steeper)]TJ
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12.654 0 TD
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[(-dependence)-733.3 (in)-734 (the)-2400 (include)-749.1 (an)-749 (example)-749.2 (of)-749 (generating)-749.2 (two)-749.1 (separate)]TJ
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[(transition)-569.2 (region.)-569.2 (One)-570.1 (such)-569.1 (alternative)-570.2 (is)]TJ
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[(SU)-19 (BSYS)]TJ
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0.074 Tc
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(1)Tj
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(e)Tj
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[(tions)-376.1 (of)-376 (dwarf)-376.1 (galaxies)-377.2 (orbiting)-376.2 (the)-376 (Milky)-321.1 (W)56 (a)0 (y)-377 (\()-37 (Oh)-2400 (second)-458.1 (system)-459.1 (is)-458 (a)-459 (replica)-458.1 (of)-459 (the)-458 (\256rst)-459.1 (\()37 (after)-458.1 (it)-459 (has)]TJ
T*
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T*
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39.292 0 TD
(6)Tj
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0.833 0 TD
(XCM)Tj
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2.204 0 TD
[(\))-1160 (with)]TJ
-42.329 -1.2 TD
[(approximation)-303.3 (to)-303 (Newton's)-304.2 (Law)-303.1 (for)]TJ
/N7 1 Tf
14.959 0 TD
(r)Tj
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0.593 0 TD
(.)Tj
10 0 2.68 10 243.51 595 Tm
(e)Tj
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[(.)-304 (I)0 (n)-303 (the)-304 (AC)-2400 (speci\256ed)-437.2 (orbital)-438.1 (eccentricity)-437.3 (\()]TJ
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19.444 0 TD
(ECC)Tj
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2.038 0 TD
[(\),)-437 (whereupon)-438.2 (the)]TJ
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[(scheme,)-679.2 (the)-680 (steeper)-679.2 (fall-off)-680.2 (actually)-679.2 (permits)-680.2 (the)-2400 (particle)-426.2 (number)-426.2 (and)-426.1 (total)-426.1 (mass)-426.1 (are)-426 (updated.)-426.2 (In)-427 (this)]TJ
T*
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T*
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(2)Tj
10 0 0 10 78 547 Tm
[(identi\256cation)-385.3 (of)-385 (all)-385 (expressions)-385.3 (involving)]TJ
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10 0 2.68 10 253.36 547 Tm
(e)Tj
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10 0 0 10 262.89 547 Tm
[(.)-5261 (velocity)-278.2 (factor)-278.1 (outside)-278.1 (the)-278 (core)-278.1 (should)-278.1 (be)-278 (omitted)-278.2 (\()37 (cf.)]TJ
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[(The)-372.1 (interpretation)-372.3 (of)-372 (the)-372 (softening)-372.2 (as)-372 (an)-373 (effective)-2400.2 (option)-541.1 (10)-541 (in)-541 (routine)]TJ
/N7 1 Tf
32.331 0 TD
(REGINT)Tj
/N6 1 Tf
3.648 0 TD
[(\).)-541 (Likewise,)-541.2 (the)-541 (de-)]TJ
-36.979 -1.2 TD
[(half-mass)-304.2 (radius)-304.1 (has)-305.1 (been)-304.1 (subject)-305.2 (to)-304 (some)-305.1 (confusion.)-2400.2 (termination)-435.2 (of)-435 (the)-436 (density)-435.2 (centre)-436.1 (and)-435.1 (the)-436 (half-mass)]TJ
T*
[(Although)-546.2 (it)-546 (has)-547.1 (been)-546.1 (traditional)-547.2 (to)-546 (generalize)-547.2 (the)-2400 (radius)-358.1 (should)-358.1 (be)-359 (modi\256ed)-358.2 (accordingly)-359.3 (\()-37 (i.e.)-358.1 (by)-359 (using)]TJ
T*
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5.3969 Tc
[(22)2581.5 (2)]TJ
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0 Tc
(replacing)Tj
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(e)Tj
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10 0 0 10 135.75 487 Tm
(with)Tj
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(e)Tj
10 0 0 10 170.6 487 Tm
(1)Tj
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(e)Tj
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/N7 1 Tf
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3.0374 Tc
(ij)Tj
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10 0 0 10 78 475 Tm
0 Tc
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T*
[(motion)-530.1 (of)-531 (two)-531.1 (overlapping)-531.3 (Plummer)-531.2 (spheres.)-531.2 (The)-2400.1 (evaluation.)-319.2 (However,)-319.2 (the)-319 (frequency)-320.2 (of)-319 (full)]TJ
/N7 1 Tf
41.688 0 TD
(N)Tj
/N6 1 Tf
1.024 0 TD
(coordi-)Tj
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[(actual)-284.1 (force)-284.1 (law)-284 (of)-284 (such)-284.1 (interactions)-284.3 (is)-284 (rather)-284.1 (compli-)-2400.2 (nate)-406.1 (predictions)-406.2 (may)-407.1 (be)-406 (reduced)-406.2 (considerably)-407.3 (with-)]TJ
T*
[(cated)-408.1 (\()37 (cf.)-297 (Wielen,)-408.2 (1979)-37.1 (\),)-408 (but)-408.1 (alternatives)-408.3 (have)-408.1 (been)-2400.1 (out)-287.1 (unduly)-287.1 (affecting)-287.2 (the)-288 (accuracy)-287.2 (\()37 (option)-287.1 (14)-37 (\).)-287 (This)-288.1 (is)]TJ
T*
[(discussed)-484.2 (\()-37 (Dyer)-484.1 (and)-484.1 (Ip,)-485.1 (1993)-37.1 (\).)-484 (However,)-484.2 (this)-485.1 (still)-2400.1 (permissible)-343.3 (because)-343.2 (typical)-343.1 (neighbours)-343.3 (are)-344 (predicted)]TJ
T*
[(leaves)-353.1 (softened)-353.2 (potentials)-354.2 (as)-353 (a)-353 (useful)-354.1 (tool)-353.1 (for)-354 (reduc-)-2400.1 (a)-294 (number)-294.2 (of)-295 (times)-294.1 (at)-294 (each)-295.1 (irregular)-294.2 (force)-295.1 (summation,)]TJ
T*
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T*
[(simulations)-359.3 (of)-360 (collapsing)-359.2 (systems)-360.2 (may)-359.1 (relate)-360.1 (soften-)-2400.2 (members.)-366.2 (Consequently,)-366.3 (the)-366 (full)]TJ
/N7 1 Tf
37.742 0 TD
(N)Tj
/N6 1 Tf
1.07 0 TD
[(predictor)-366.2 (loop)-367.1 (is)]TJ
-38.812 -1.2 TD
[(ing)-385 (to)-385 (half-mass)-385.2 (radius)-385.1 (\()37 (cf.)-385 (Aarseth)-385.2 (et)-385 (al.,)-385.1 (1988)-37.1 (\).)-3535 (replaced)-459.2 (by)-459 (a)-460 (neighbour)-459.2 (prediction)-460.2 (if)-459 (the)-460 (member-)]TJ
24 -1.2 TD
(ship)Tj
/N7 1 Tf
2.402 0 TD
[(n)-1171 (exceeds)]TJ
/N6 1 Tf
5.552 0 TD
[(the)-735 (average)-735.2 (neighbour)-735.2 (number)]TJ
6.5 0 0 6 347.57 364.5 Tm
(1)Tj
10 0 2.68 10 78 355 Tm
(5.3.)Tj
/N7 1 Tf
10 0 0 10 98.55 355 Tm
[(Special)-385.2 (f)-19 (eatures)]TJ
/N6 1 Tf
21.945 0 TD
[(\()37 (updated)-322.2 (in)]TJ
/N7 1 Tf
4.885 0 TD
(KZ)Tj
/N6 1 Tf
1.223 0 TD
[(\()-37 (1)0 (4)-37 (\))-323 (every)-322.1 (output,)-323.2 (provided)-323.2 (the)-323 (initial)]TJ
-6.108 -1.2 TD
[(value)-341.1 (is)-342 (non-zero)36.8 (\).)-342 (Another)-341.2 (reduction)-342.2 (of)-342 (the)-342 (numeri-)]TJ
-23 -1.2 TD
[(It)-283 (is)-284 (often)-283.1 (desirable)-284.2 (to)-284 (perform)-283.1 (large)-284.1 (simulations)-284.3 (in)-2400 (cal)-474.1 (effort)-475.1 (is)-475 (made)-474.1 (during)-475.1 (initialization)-475.3 (by)-475 (omitting)]TJ
-1 -1.2 TD
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/N7 1 Tf
11.759 0 TD
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/N6 1 Tf
4.856 0 TD
[(variables)-375.2 (on)-2400 (distant)-498.1 (contributions)-499.3 (to)-499 (the)-498.1 (second)-499.1 (and)-499.1 (third)-499.1 (force)]TJ
-16.615 -1.2 TD
[(disc)-346.1 (or)-347 (tape.)-346.1 (This)-347.1 (can)-346.1 (be)-347 (done)-346.1 (by)-347 (specifying)-346.2 (the)-347 (run)-2400.1 (derivatives)-385.2 (in)-385 (\()-37 (6)-37 (\))-385 (\()-37 (i.e.)]TJ
/N7 1 Tf
33.538 0 TD
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/N10 1 Tf
0.796 0 TD
(.)Tj
/N6 1 Tf
0.999 0 TD
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/N7 1 Tf
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/N6 1 Tf
0.988 0 TD
(\).)Tj
/N7 1 Tf
6.5 0 0 6 444.6 304.5 Tm
(s)Tj
/N6 1 Tf
10 0 0 10 78 295 Tm
[(time)-620.1 (at)-620 (input)-620.1 (\()]TJ
/N7 1 Tf
6.712 0 TD
(TCOMP)Tj
/N6 1 Tf
3.463 0 TD
[(\),)-620 (together)-620.2 (with)-620.1 (option)-621.1 (1.)]TJ
-10.175 -1.2 TD
[(Alternatively,)-826.3 (on)-826 (Unix)-826.1 (machines)-826.2 (the)-826 (command)]TJ
10 0 2.68 10 318 283 Tm
(5.4.)Tj
/N7 1 Tf
10 0 0 10 338.55 283 Tm
[(Data)-385.1 (analysis)]TJ
/N6 1 Tf
-26.055 -1.2 TD
(`touch)Tj
/N7 1 Tf
3.011 0 TD
(STOP)Tj
/N6 1 Tf
2.426 0 TD
[(')-457 (creates)-457.1 (a)-456 (\256le)-457.1 (\()]TJ
/N7 1 Tf
6.954 0 TD
(STOP)Tj
/N6 1 Tf
2.463 0 TD
[(\))-457 (which)-457.1 (triggers)]TJ
-14.854 -1.2 TD
[(termination)-440.2 (at)-441 (the)-440 (next)-441.1 (timing)-441.1 (check)-440.1 (\()37 (every)]TJ
/N7 1 Tf
18.822 0 TD
[(NM)-56 (AX)]TJ
/N6 1 Tf
6.178 0 TD
[(The)-672.1 (emphasis)-673.2 (of)-672 (the)-673 (code)-672.1 (is)-673 (on)-672 (providing)-673.2 (a)]TJ
-25 -1.2 TD
[(steps)36.9 (\).)-21454 (versatile)-288.2 (integration)-288.2 (tool,)-289.1 (leaving)-288.1 (the)-289.1 (question)-288.2 (of)-289 (data)]TJ
1 -1.2 TD
[(A)-353 (standard)-354.2 (restart)-353.1 (is)-354 (made)-353.1 (after)-354.1 (reading)-353.2 (the)-354 (saved)-2400.1 (analysis)-287.2 (to)-287 (the)-287 (individual)-287.2 (user.)-287.1 (The)-287.1 (main)-287.1 (facility)-288.1 (here)]TJ
/N7 1 Tf
-1 -1.2 TD
(COMMON)Tj
/N6 1 Tf
4.829 0 TD
[(\256le)-331.1 (from)-330.1 (unit)-331.1 (1)-330 (\()37 (using)]TJ
/N7 1 Tf
9.393 0 TD
[(KST)-56.1 (ART)]TJ
/N10 1 Tf
3.65 0 TD
(5)Tj
/N6 1 Tf
0.888 0 TD
[(2)-37 (\))0 (.)-331 (For)-2400.1 (is)-358 (the)-359 (data)-358.1 (bank)-359.1 (\()37 (option)-358.1 (3)-37 (\))-359 (which)-358.1 (creates)-359.1 (a)-358 (\256le)-359.1 (\()37 (unit)]TJ
-18.76 -1.2 TD
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/N7 1 Tf
34.339 0 TD
(m)Tj
/N6 1 Tf
0.722 0 TD
(,)Tj
/N8 1 Tf
0.54 0 TD
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/N6 1 Tf
0.444 0 TD
(,)Tj
/N18 1 Tf
0.541 0 TD
(v)Tj
/N6 1 Tf
0.884 0 TD
[(and)-290.1 (the)-291 (identity)-37.2 (\))-291 (for)]TJ
-37.47 -1.2 TD
[(can)-509.1 (be)-510 (changed)-509.2 (at)-510 (restart)-510.1 (time.)-509.1 (Depending)-510.2 (on)-510 (the)-2400 (each)-659.1 (particle)-659.2 (at)-659 (output)-659.1 (times)]TJ
/N7 1 Tf
37.571 0 TD
(TNEXT)Tj
/N6 1 Tf
3.661 0 TD
[(\()-37 (frequency)]TJ
-41.232 -1.2 TD
[(value)-471.1 (of)-471 (the)-471 (control)-471.2 (index,)-472.1 (routine)]TJ
/N7 1 Tf
15.186 0 TD
[(MODIF)-18.2 (Y)]TJ
/N6 1 Tf
4.304 0 TD
(reads)Tj
/N7 1 Tf
4.51 0 TD
[(NF)-18 (IX)]TJ
/N6 1 Tf
2.333 0 TD
[(\).)-277 (This)-277.1 (data)-277.1 (may)-278.1 (be)-277 (read)-277.1 (by)-277 (a)-277 (separate)-278.2 (program,)]TJ
-26.333 -1.2 TD
[(one)-317.1 (or)-318 (two)-318.1 (input)-318.1 (lines)-318.1 (\()37 (with)-317.1 (the)-318 (convention)-318.2 (that)-318.1 (only)-2400.1 (with)-321.1 (the)-321 (\256rst)-322.1 (record)-321.1 (\()]TJ
/N7 1 Tf
32.691 0 TD
(N)Tj
/N6 1 Tf
0.667 0 TD
(,)Tj
/N7 1 Tf
0.572 0 TD
(MODEL)Tj
/N6 1 Tf
3.444 0 TD
(,)Tj
/N7 1 Tf
0.571 0 TD
[(NR)18 (U)-37 (N)]TJ
/N6 1 Tf
2.778 0 TD
[(\))-322 (containing)]TJ
-40.723 -1.2 TD
[(non-zero)-385.2 (variables)-385.2 (are)-385 (altered)-37.1 (\):)-11091 (the)-385.1 (size)-385.1 (\()]TJ
/N7 1 Tf
27.843 0 TD
(N)Tj
/N6 1 Tf
0.759 0 TD
[(\))-385 (o)0 (f)-385 (the)-385 (subsequent)-385.3 (arrays.)]TJ
-3.602 -1.2 TD
[(The)-416.1 (general)-417.2 (output)-417.1 (on)-416 (unit)-417.1 (6)-417 (\()37 (routine)]TJ
/N7 1 Tf
16.155 0 TD
[(OU)-37 (TPU)-37.1 (T)]TJ
/N6 1 Tf
4.112 0 TD
(\))Tj
/N9 1 Tf
-44.977 -1.2 TD
(\267)Tj
/N7 1 Tf
0.96 0 TD
[(DELT)-55.1 (AT)]TJ
/N6 1 Tf
3.667 0 TD
(,)Tj
/N7 1 Tf
0.635 0 TD
(TNEXT)Tj
/N6 1 Tf
3.001 0 TD
(,)Tj
/N7 1 Tf
0.635 0 TD
(TCRIT)Tj
/N6 1 Tf
2.723 0 TD
(,)Tj
/N7 1 Tf
0.635 0 TD
(QE)Tj
/N6 1 Tf
1.333 0 TD
(,)Tj
/N7 1 Tf
0.691 0 TD
(J)Tj
/N6 1 Tf
0.444 0 TD
(,)Tj
/N7 1 Tf
0.635 0 TD
(KZ)Tj
/N6 1 Tf
1.223 0 TD
(\()Tj
/N7 1 Tf
0.351 0 TD
(J)Tj
/N6 1 Tf
0.537 0 TD
[(\))-5907 (provides)-287.2 (a)-287 (summary)-287.2 (of)-287 (the)-287 (main)-287.1 (diagnostics.)-287.3 (Most)-287.1 (of)]TJ
-16.51 -1.2 TD
(\()Tj
/N7 1 Tf
0.296 0 TD
[(KST)-55.1 (ART)]TJ
/N10 1 Tf
3.649 0 TD
(5)Tj
/N6 1 Tf
0.888 0 TD
[(3)-385 (o)0 (r)-385 (5)-37 (\).)-14694 (this)-283.1 (output)-283.1 (refers)-283.1 (to)]TJ
/N7 1 Tf
26.104 0 TD
(COMMON)Tj
/N6 1 Tf
4.764 0 TD
[(variables.)-283.2 (Among)-284.2 (the)]TJ
/N9 1 Tf
-36.661 -1.2 TD
(\267)Tj
/N7 1 Tf
0.96 0 TD
[(ET)-55 (AI)]TJ
/N6 1 Tf
2.166 0 TD
(,)Tj
/N7 1 Tf
0.635 0 TD
[(ET)-56 (AR)]TJ
/N6 1 Tf
3.462 0 TD
(\()Tj
/N7 1 Tf
0.296 0 TD
[(KST)-56.1 (ART)]TJ
/N10 1 Tf
3.649 0 TD
(5)Tj
/N6 1 Tf
0.889 0 TD
[(4)-385 (o)0 (r)-385 (5)-37 (\).)-8430 (other)-483.1 (quantities)-483.2 (are)-483 (the)-483 (time)-483.1 (expressed)-483.2 (in)-483 (crossing)]TJ
ET
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33 33 546 744 RC
BT
/N6 1 Tf
8 0 0 8 78 705 Tm
0 g
/N13 /ExtGState findRes gs
0 Tc
(290)Tj
/N7 1 Tf
18.0325 0 TD
0 Tw
(S)Tj
/N6 1 Tf
8 0 2.144 8 226.26 705 Tm
(.)Tj
/N7 1 Tf
8 0 0 8 228.7 705 Tm
(J)Tj
/N6 1 Tf
8 0 2.144 8 232.25 705 Tm
(.)Tj
/N7 1 Tf
8 0 0 8 237.78 705 Tm
(Aarseth)Tj
/N6 1 Tf
3.6063 0 TD
(/)Tj
/N7 1 Tf
0.7375 0 TD
[(New)-440.8 (Astronomy)]TJ
/N6 1 Tf
8 0 2.144 8 328.02 705 Tm
[(6)-385 (\()-37 (2001)-37.5 (\))-384.5 (277)]TJ
8 0 0 8 373.29 705 Tm
(\261)Tj
8 0 2.144 8 377.73 705 Tm
(291)Tj
6.5 0 0 6 174.9 684 Tm
(6)Tj
10 0 0 10 78 679 Tm
[(times)-575.1 (\()]TJ
/N7 1 Tf
3.038 0 TD
(TC)Tj
/N6 1 Tf
1.315 0 TD
[(\))-576 (and)-575.1 (in)-575 (10)-992 (yr)-575 (\()]TJ
/N7 1 Tf
7.977 0 TD
(T)Tj
/N6 1 Tf
0.667 0 TD
[(6)-37 (\))0 (,)-575 (half-mass)-576.2 (radius)-2400.1 (relative)-476.2 (energy)-477.1 (errors)-477.1 (\()-37 (Column)-476.2 (8)-37 (\))0 (.)-477 (The)-477.1 (main)-477.1 (error)]TJ
-12.997 -1.2 TD
(\()Tj
/N11 1 Tf
0.37 0 TD
(k)Tj
/N7 1 Tf
0.333 0 TD
(R)Tj
/N11 1 Tf
0.629 0 TD
(l)Tj
/N6 1 Tf
0.37 0 TD
[(\),)-280 (maximum)-280.2 (neighbour)-280.2 (density)-280.1 (contrast)-279.2 (\()]TJ
/N7 1 Tf
16.444 0 TD
[(CM)-56 (AX)]TJ
/N6 1 Tf
2.871 0 TD
[(\),)-2400 (occurred)-448.2 (at)]TJ
/N7 1 Tf
8.1 0 TD
(t)Tj
/N10 1 Tf
0.482 0 TD
(5)Tj
/N6 1 Tf
1 0 TD
(2)Tj
/N7 1 Tf
0.5 0 TD
(T)Tj
/N6 1 Tf
1.657 0 TD
[(when)-449.1 (the)-449 (time-step)-449.2 (parameters)]TJ
6.5 0 0 6 395.1 664.5 Tm
0.056 Tc
(cr)Tj
10 0 0 10 78 655 Tm
0 Tc
[(time-weighted)-477.3 (neighbour)-478.2 (number)-478.2 (\()]TJ
/N11 1 Tf
14.69 0 TD
(k)Tj
/N7 1 Tf
0.333 0 TD
(Cn)Tj
/N11 1 Tf
1.204 0 TD
(l)Tj
/N6 1 Tf
0.37 0 TD
[(\),)-478 (centre-of-)-2400.2 (were)-532.1 (reduced)-533.2 (to)-533 (0.012)-533.1 (and)-532.1 (0.024)-533.1 (\()-37 (from)-533.1 (0.02)-533.1 (and)]TJ
-16.597 -1.2 TD
[(mass)-660.1 (displacements)-661.3 (\()]TJ
/N7 1 Tf
9.283 0 TD
(RCM)Tj
/N6 1 Tf
2.111 0 TD
(,)Tj
/N7 1 Tf
0.818 0 TD
(VCM)Tj
/N6 1 Tf
2.204 0 TD
[(\))-660 (and)]TJ
/N7 1 Tf
3.098 0 TD
(z)Tj
/N6 1 Tf
1.087 0 TD
[(angular)-2400.2 (0.04)-37.1 (\),)-564 (respectively;)-565.3 (this)-565.1 (was)-565.1 (followed)-565.2 (by)-565 (a)-565 (small)]TJ
-18.601 -1.2 TD
[(momentum)-385.2 (\()]TJ
/N7 1 Tf
5.292 0 TD
(AZ)Tj
/N6 1 Tf
1.26 0 TD
[(\).)-16865 (increase.)-457.2 (Note)-457.1 (that)-457.1 (the)-457 (half-mass)-457.2 (radius)-457.1 (\()]TJ
/N7 1 Tf
35.01 0 TD
[(RSC)-56.1 (ALE)]TJ
/N6 1 Tf
3.705 0 TD
(\))Tj
-44.267 -1.2 TD
[(Further)-414.2 (optional)-415.2 (diagnostic)-415.2 (output)-415.1 (is)-415 (provided)-415.2 (on)-2400 (should)-348.1 (be)-348 (updated)-348.2 (fairly)-348.1 (frequently)-348.2 (during)-348.1 (phases)-349.1 (of)]TJ
-1 -1.2 TD
[(unit)-316.1 (6)-317 (b)0 (y)-317 (routine)]TJ
/N7 1 Tf
7.156 0 TD
(BODIES)Tj
/N6 1 Tf
3.499 0 TD
[(.)-317 (Here)-317.1 (an)-317 (individual)-317.2 (line)-317.1 (is)-2400 (violent)-385.2 (relaxation)-385.2 (\()37 (cf.)-385 (\()-37 (1)0 (2)-37 (\))37 (\).)]TJ
-10.655 -1.2 TD
[(printed)-455.1 (for)-455 (each)-455.1 (particle)-455.2 (\()37 (using)-455.1 (option)-455.1 (9)-455 (t)0 (o)-455 (control)-3400.2 (The)-394.1 (test)-395.1 (calculation)-395.2 (required)-395.2 (a)-394 (total)-395.1 (CPU)-395.1 (time)-395.1 (of)]TJ
T*
[(the)-751 (amount)-37.2 (\).)-752 (Likewise,)-752.2 (a)-752 (search)-752.1 (for)-752.1 (signi\256cant)-2400.2 (35)-384 (s)-385 (o)0 (n)-385 (a)-385 (Sun)-385.1 (UltraSparc)-384.2 (1)-385 (workstation,)-385.3 (with)-385.1 (clock)]TJ
T*
[(binaries)-315.2 (is)-316 (made)-316.1 (at)-316 (each)-316.1 (output)-316.1 (time)-316.1 (or)-316 (at)-316 (a)-316 (speci\256ed)-2400.2 (speed)-311.1 (140)-311.1 (MHz)-311.1 (and)-312.1 (SPEC95)-311.2 (rating)-311.1 (of)-311 (7.9.)-312.1 (Although)]TJ
T*
(frequency,)Tj
/N7 1 Tf
4.662 0 TD
[(NF)-18 (IX)]TJ
/N6 1 Tf
2.655 0 TD
(\()Tj
/N7 1 Tf
0.296 0 TD
(KZ)Tj
/N6 1 Tf
1.223 0 TD
0.037 Tc
(\(6\))Tj
/N10 1 Tf
1.295 0 TD
0 Tc
(5)Tj
/N6 1 Tf
0.889 0 TD
[(1)-414 (o)0 (r)-415 (2)-37 (\).)-414 (Each)-414.1 (output)-415.1 (line)-2400.1 (the)-369 (AC)-369 (method)-370.2 (gains)-369.1 (in)-370 (ef\256ciency)-369.2 (with)-370.1 (respect)-369.2 (to)-370 (a)]TJ
-11.02 -1.2 TD
[(contains)-280.2 (the)-280 (identity)-281.2 (of)-280 (components)-281.3 (and)-280.1 (their)-281.1 (masses,)-2400.2 (single)-359.1 (polynomial)-360.3 (formulation)-360.3 (as)]TJ
/N7 1 Tf
37.939 0 TD
(N)Tj
/N6 1 Tf
1.082 0 TD
[(increases,)-360.2 (it)-360 (can)]TJ
-39.021 -1.2 TD
[(binding)-308.2 (energy)-308.1 (per)-308.1 (unit)-309.1 (mass,)-308.1 (semi-major)-308.3 (axis,)-309.1 (mean)-2400.1 (also)-530.1 (be)-530 (used)-530.1 (for)-530 (relatively)-530.2 (small)-530.1 (systems.)-530.2 (Thus)-531.1 (a)]TJ
T*
[(motion,)-359.2 (separation,)-360.3 (central)-360.2 (distance,)-360.2 (eccentricity)-360.3 (and)-2400.1 (second)-455.1 (similar)-455.1 (example)-456.2 (with)]TJ
/N7 1 Tf
36.542 0 TD
(N)Tj
/N10 1 Tf
0.871 0 TD
(5)Tj
/N6 1 Tf
1 0 TD
[(25)-455 (conserved)-456.2 (the)]TJ
/N10 1 Tf
6.5 0 0 6 433.14 516 Tm
(2)Tj
/N6 1 Tf
0.8892 0 TD
(5)Tj
10 0 0 10 78 511 Tm
[(neighbour)-385.2 (number.)-16255.2 (total)-323.1 (energy)-324.1 (to)-323 (about)-323.1 (3)]TJ
/N10 1 Tf
33.459 0 TD
(3)Tj
/N6 1 Tf
1 0 TD
[(10)-1317 (\()37 (using)]TJ
/N7 1 Tf
5.104 0 TD
[(NNBM)-55.1 (AX)]TJ
/N10 1 Tf
4.148 0 TD
(5)Tj
/N6 1 Tf
0.889 0 TD
(10)Tj
-43.6 -1.2 TD
[(Additional)-322.2 (information)-323.3 (about)-322.1 (the)-323 (radii)-322.1 (of)-323 (speci\256ed)-2400.2 (and)]TJ
/N10 1 Tf
10 0 2.68 10 337.68 499 Tm
(e)Tj
10 0 0 10 344.71 499 Tm
(5)Tj
/N6 1 Tf
1 0 TD
[(0.25)-37.1 (\))-524 (after)-524.1 (10389)-525.1 (and)-524.1 (5134)-524.1 (irregular)-525.2 (and)]TJ
-27.671 -1.2 TD
[(mass)-461.1 (percentiles,)-462.3 (including)-461.2 (the)-462 (half-mass)-461.2 (radius,)-462.1 (is)-2400 (regular)-385.2 (steps,)-385.1 (respectively.)]TJ
T*
[(provided)-373.2 (by)-374 (routine)]TJ
/N7 1 Tf
8.509 0 TD
[(L)-56 (AGR)]TJ
/N6 1 Tf
2.929 0 TD
[(\()37 (option)-374.1 (7)-37 (\))-374 (and)-374.1 (is)-374 (printed)]TJ
-11.438 -1.2 TD
[(on)-440 (unit)-441.1 (6)-441 (and)-111.1 (/)-111 (o)0 (r)-441 (7)0 (,)-441 (depending)-441.2 (on)-440 (the)-441 (value)-441.1 (of)-441 (the)]TJ
10 0 2.68 10 318 463 Tm
(5.6.)Tj
/N7 1 Tf
10 0 0 10 338.55 463 Tm
[(Program)-385.2 (modi\256cations)]TJ
/N6 1 Tf
-26.055 -1.2 TD
[(option.)-399.2 (Further)-399.2 (analysis)-399.2 (or)-400 (plotting)-399.2 (routines)-399.2 (may)-400.1 (be)]TJ
T*
[(called)-444.1 (from)-445.1 (routine)]TJ
/N7 1 Tf
8.499 0 TD
[(OU)-37 (TPU)-37.1 (T)]TJ
/N6 1 Tf
3.963 0 TD
[(,)-444 (since)-445.1 (all)-445 (the)-445 (current)-3400.2 (The)-303.1 (variety)-303.1 (of)-303 (problems)-303.2 (suitable)-303.2 (for)-303.1 (direct)]TJ
/N7 1 Tf
30.101 0 TD
(N)Tj
/N6 1 Tf
0.704 0 TD
(-body)Tj
-43.267 -1.2 TD
[(coordinates)-465.3 (and)-466.1 (velocities)-465.2 (\()]TJ
/N8 1 Tf
11.579 0 TD
(r,)Tj
/N18 1 Tf
1.16 0 TD
(v)Tj
/N6 1 Tf
0.556 0 TD
[(\))-465 (are)-466 (known)-465.1 (at)-466 (this)-2400.1 (simulations)-276.3 (is)-277 (so)-277 (large)-277.1 (that)-277.1 (one)-276.1 (code)-277.1 (cannot)-277.1 (deal)-277.1 (with)]TJ
-13.295 -1.2 TD
[(stage.)-21695.1 (all)-582 (the)-582 (requirements.)-582.3 (However,)-582.2 (the)-582.1 (basic)-582.1 (solution)]TJ
24 -1.2 TD
[(method)-348.2 (is)-348 (suf\256ciently)-348.2 (\257exible)-348.2 (for)-348 (new)-348.1 (procedures)-348.2 (to)]TJ
10 0 2.68 10 78 391 Tm
(5.5.)Tj
/N7 1 Tf
10 0 0 10 98.55 391 Tm
[(Test)-385.1 (calculation)]TJ
/N6 1 Tf
21.945 0 TD
[(be)-385 (included.)]TJ
1 -1.2 TD
[(Although)-411.2 (the)-412 (present)-412.2 (code)-411.1 (has)-412.1 (been)-412.1 (designed)-412.2 (for)]TJ
-24 -1.2 TD
[(It)-419 (is)-419 (instructive)-419.2 (to)-420 (illustrate)-419.2 (the)-419 (general)-420.2 (workings)-2400.2 (scalar)-308.1 (machines,)-308.2 (it)-308 (can)-308.1 (readily)-308.1 (be)-308 (modi\256ed)-308.2 (to)-308 (exploit)]TJ
-1 -1.2 TD
[(of)-453 (the)-454 (code)-454.1 (by)-454 (quoting)-453.2 (a)-454 (test)-454.1 (calculation,)-454.3 (although)-2400.2 (special)-420.2 (features)-421.2 (available)-420.2 (on)-421 (vector)-420.1 (processors.)-421.3 (The)]TJ
T*
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33 33 546 744 RC
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/N6 1 Tf
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[(6)-385 (\()-37 (2001)-37.5 (\))-384.5 (277)]TJ
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8 0 2.144 8 377.73 705 Tm
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0 -1.2 TD
[(lan,)-385.1 (1986;)-385.1 (Makino,)-385.2 (1991b)18.9 (\).)-12670 (separate)-280.2 (\256le,)-280.1 (using)-281.1 (scaled)-280.1 (integer)-280.1 (format)-281.1 (of)-280 (two)-281.1 (bytes)]TJ
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[(Since)-289.1 (the)-289 (square)-289.1 (root)-290.1 (calculation)-289.2 (is)-289 (by)-289 (far)-289 (the)-290 (most)-2400.1 (to)-487 (save)-487.1 (memory.)-487.2 (The)-487.1 (actual)-487.1 (movie)-487.1 (production)-487.2 (de-)]TJ
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13.195 0 TD
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/N6 1 Tf
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[(-body)-317.1 (code,)-317.1 (it)-318 (may)-2400.1 (pends)-326.1 (on)-326 (available)-326.2 (software;)-326.2 (by)-326 (now)-326.1 (it)-326 (is)-326 (possible)-327.2 (to)]TJ
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T*
[(Aarseth)-400.2 (et)-401 (al.,)-400.1 (1993)-37.1 (\).)-401 (This)-400.1 (algorithm)-401.2 (would)-400.1 (also)-401.1 (be)]TJ
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[(signi\256cant)-385.2 (loss)-385.1 (of)-385 (precision.)]TJ
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[(Aarseth,)-385 (S.J.,)-385 (1963.)-385 (MNRAS)-384.1 (126,)-385 (223.)]TJ
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[(Aarseth,)-715 (S.J.,)-715 (1985.)-716.3 (In:)-715.3 (Brackbill,)-715.6 (J.U.,)-715.3 (Cohen,)-715.3 (B.I.)-716.3 (\()-37 (Eds.)37.5 (\),)]TJ
10 0 0 10 88 547 Tm
[(The)-499.1 (code)-499.1 (may)-499.1 (readily)-499.1 (be)-499 (modi\256ed)-499.2 (to)-499 (include)-499.2 (a)]TJ
8 0 0 8 328 539 Tm
[(Multiple)-385 (Time)-384 (Scales.)-385 (Academic)-386.1 (Press,)-384 (New)-329.5 (Y)54.5 (ork,)-384.5 (p.)-385 (377.)]TJ
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[(population)-621.2 (of)-622 (massless)-621.2 (test)-622.1 (particles.)-621.2 (Now)-622.1 (all)]TJ
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20.933 0 TD
(N)Tj
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8 0 0 8 318 529 Tm
[(Aarseth,)-386.3 (S.J.,)-386.3 (Inagaki,)-386 (S.,)-385.3 (1986.)-386.3 (In:)-386.5 (Hut,)-386.3 (P)111 (.)0 (,)-386.3 (McMillan,)-386.3 (S.)-386.5 (\()-37 (Eds.)37.5 (\),)]TJ
10 0 0 10 78 523 Tm
[(particles)-308.2 (may)-308.1 (be)-308 (integrated)-308.2 (in)-308 (the)-308 (standard)-308.2 (way,)-309.1 (with)]TJ
8 0 0 8 328 519 Tm
[(The)-547.5 (Use)-548.8 (of)-548.3 (Supercomputers)-547.3 (in)-548.3 (Stellar)-547.8 (Dynamics.)-548.8 (Springer-)]TJ
10 0 0 10 78 511 Tm
[(the)-367 (force)-367.1 (loops)-368.1 (performed)-367.2 (over)-367.1 (a)-368 (smaller)-367.2 (number)-368.2 (of)]TJ
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[(V)112 (erlag,)-384.8 (New)-329.5 (Y)54.5 (ork,)-384.5 (p.)-385 (203.)]TJ
5.3525 -1.2188 TD
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10 0 0 10 78 499 Tm
[(massive)-276.2 (bodies.)-165.2 (When)-276.1 (modelling)-276.2 (close)-276.1 (interactions,)-277.3 (it)]TJ
8 0 0 8 318 499 Tm
[(Aarseth,)-385 (S.J.,)-385 (Henon,)-384 (M.,)-274.8 (Wielen,)-384.5 (R.,)-385.5 (1974.)-385 (A&A)-384.3 (37,)-385 (183.)]TJ
0 -1.25 TD
[(Aarseth,)-385 (S.J.,)-385 (Lin,)-384.8 (D)37 (.N.C.,)-384.8 (Papaloizou,)-384.8 (J.,)-384.8 (1988.)-385 (ApJ)-385.3 (324,)-385 (288.)]TJ
10 0 0 10 78 487 Tm
[(is)-442 (sometimes)-443.2 (desirable)-443.2 (to)-443 (include)-443.2 (partially)-443.2 (inelastic)]TJ
8 0 0 8 318 479 Tm
[(Aarseth,)-385 (S.J.,)-385 (Palmer,)-384.5 (P)111 (.L.,)-385.3 (Lin,)-384.8 (D)37 (.N.C.,)-384.8 (1993.)-385 (ApJ)-385.3 (403,)-385 (351.)]TJ
10 0 0 10 78 475 Tm
[(effects.)-318.2 (The)-318.1 (collision)-318.2 (determination)-318.3 (would)-318.1 (be)-318 (similar)]TJ
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[(Ahmad,)-384.8 (A.,)-384.3 (Cohen,)-385.3 (L.,)-385.3 (1973.)-385 (J.)-384.8 (Comput.)-385.8 (Phys.)-385 (12,)-385 (389.)]TJ
10 0 0 10 78 463 Tm
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[(Casertano,)-384.8 (S.,)-385.3 (Hut,)-385 (P)112.2 (.)0 (,)-385 (1985.)-385 (ApJ)-385.3 (298,)-385 (80.)]TJ
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[(The)-499.1 (effect)-499.1 (of)-499 (an)-500 (external)-499.2 (potential)-499.2 (may)-499.1 (also)-500.1 (be)]TJ
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[(Governato,)-384.1 (F.,)-385.3 (Bhatia,)-385.3 (R.,)-385.5 (Chinkarini,)-384.6 (G.,)-385.5 (1991.)-385 (ApJ)-384 (371,)-385 (L15.)]TJ
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[(Heggie,)-550.8 (D)37 (.C.,)-551.8 (Mathieu,)-550.8 (R.D)36.5 (.,)-551.3 (1986.)-551.3 (In:)-551.5 (Hut,)-551.3 (P)111 (.)0 (,)-552.5 (McMillan,)-551.3 (S.)]TJ
10 0 0 10 78 403 Tm
[(This)-353.1 (description)-353.2 (may)-353.1 (be)-353 (used)-353.1 (for)-353.1 (star)-353.1 (clusters)-354.2 (inside)]TJ
8 0 0 8 328 399 Tm
[(\()-37 (Eds.)37.5 (\),)-707 (The)-706.3 (Use)-707.5 (of)-707 (Supercomputers)-706.1 (in)-707 (Stellar)-707.8 (Dynamics.)]TJ
10 0 0 10 78 391 Tm
[(a)-298 (galaxy)-299.1 (or)-299 (dwarf)-299.1 (galaxies)-299.2 (orbiting)-298.2 (a)-299 (large)-299.1 (galaxy.)-299.2 (In)]TJ
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[(Springer-)111.9 (V)110.7 (erlag,)-384.8 (New)-329.5 (Y)55.7 (ork,)-385.8 (p.)-385 (233.)]TJ
10 0 0 10 78 379 Tm
[(the)-363 (case)-364.1 (of)-364 (open)-364.1 (clusters,)-363.2 (the)-364 (assumption)-364.3 (of)-364 (circular)]TJ
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[(Makino,)-456.5 (J.,)-457.3 (1986.)-457.5 (In:)-456.5 (Hut,)-457.5 (P)111 (.)0 (,)-457.5 (McMillan,)-457.6 (S.)-456.5 (\()-37 (Eds.)37.5 (\),)-458.3 (The)-456.3 (Use)-457.5 (of)]TJ
1.25 -1.25 TD
[(Supercomputers)-628.6 (in)-628.3 (Stellar)-629 (Dynamics.)-628.8 (Springer-)111.9 (V)110.8 (erlag,)-628.5 (New)]TJ
10 0 0 10 78 367 Tm
[(motion)-578.1 (near)-578.1 (the)-578 (plane)-578.1 (of)-578 (symmetry)-578.2 (permits)-578.2 (sim-)]TJ
8 0 0 8 328 359 Tm
[(Y)55.8 (ork,)-384.5 (p.)-385 (151.)]TJ
10 0 0 10 78 355 Tm
[(pli\256ed)-496.1 (expressions)-496.3 (for)-497.1 (the)-496 (tidal)-497.1 (force)-496.1 (\()37 (cf.)-497 (Aarseth,)]TJ
8 0 0 8 318 349 Tm
[(Makino,)-384 (J.,)-386 (1991a.)-384.8 (ApJ)-385.3 (369,)-385 (200.)]TJ
10 0 0 10 78 343 Tm
[(1985)-37.1 (\).)-737 (For)-737.1 (more)-737.1 (general)-738.2 (types)-737.1 (of)-737 (orbits,)-737.1 (it)-738 (is)]TJ
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[(Makino,)-384 (J.,)-386 (1991b.)-385 (P)112.2 (ASJ)-385.5 (43,)-385 (859.)]TJ
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[(convenient)-331.2 (to)-332 (employ)-332.2 (local)-332.1 (rotating)-332.2 (coordinates)-332.3 (with)]TJ
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[(it)-293 (stands)-293.1 (\()-37 (i.e.)]TJ
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