\name{p.exp} \alias{p.exp} \alias{p.lin} \alias{p.sig} \title{ Common Properties with Distance,to be used with setup.prop.1D } \description{ Functions that define an y-property as a function of the one-dimensional x-coordinate. These routines can be used to specify properties and parameters as a function of distance, e.g. depth in the water column or the sediment. They make a transition from an upper (or upstream) zone, with value \code{y.0} to a lower zone with a value \code{y.inf}. Particularly useful in combination with \link{setup.prop.1D} \itemize{ \item \code{p.exp}: exponentially decreasing transition \deqn{ y = y_{\inf} + (y_0-y_{\inf}) \exp(-\max(0,x-x_0)/x_a) }{ y=y0+(y0-yinf)*exp(-max(0,(x-x0))/xa} \item \code{p.lin}: linearly decreasing transition \deqn{ y = y_0; y = y_0 - (y_0-y_{inf})*(x-x_L)/x_{att}) ; y = y_{inf} }{y=y0 ; y=y0-(y0-yinf)(x-xl)/xatt ; y = yinf} for \eqn{0 \leq x \leq x_L}, \eqn{x_L \leq x \leq x_L + x_{att}} and \eqn{(x \geq x_L + x.att )} respectively. \item \code{p.sig}: sigmoidal decreasing transition \deqn{ y = y_{inf} + (y_0-y_{inf})\frac{\exp(-(x-(x_L + 0.5 x_{att}))/ (0.25 x_{att}))}{(1+\exp(-(x-(x_L+0.5*x_{att}))/(0.25 x_{att}))}) }{y=yinf+(y0-yinf)exp(-x-(xL+0.5xatt)/(0.25xatt)) / (1+exp(-x-(xL+0.5xatt)/(0.25xatt)))} } } \usage{ p.exp(x, y.0=1, y.inf=0.5, x.L=0, x.att=1) p.lin(x, y.0=1, y.inf=0.5, x.L=0, x.att=1) p.sig(x, y.0=1, y.inf=0.5, x.L=0, x.att=1) } \arguments{ \item{x }{the x-values for which the property has to be calculated. } \item{y.0 }{the y-value at the origin } \item{y.inf }{the y-value at infinity } \item{x.L }{the x-coordinate where the transition zone starts; for \code{x <= x.0}, the value will be equal to \code{y.0}. For \code{x >> x.L + x.att} the value will tend to \code{y.inf} } \item{x.att }{attenuation coefficient in exponential decrease, or the size of the transition zone in the linear and sigmoid decrease } } \value{ the property value, estimated for each x-value. } \details{ For \code{p.lin}, the width of the transition zone equals \code{x.att} and the depth where the transition zone starts is \code{x.L}. For \code{p.sig}, the transition is smooth, but most pronounced in the transition zone. For \code{p.exp}, there is no clearly demarcated transition zone; there is an abrupt change at \code{x.L} after which the property exponentially changes from \code{y.0} towards \code{y.L} with attenuation coefficient \code{x.att}; the larger \code{x.att} the less steep the change. } \author{ Filip Meysman , Karline Soetaert } \examples{ x<- seq(0,5,len=100) plot(x, p.exp(x,x.L=2),xlab="x.coordinate", ylab="y value",ylim=c(0,1)) lines(x, p.lin(x,x.L=2),col="blue") lines(x, p.sig(x,x.L=2),col="red") } \keyword{utilities}