https://github.com/pdieterle/diffWavePropAndInit
Tip revision: f8d9feffd57d05f47c8c14c6d9850643b2858d0a authored by pdieterle on 18 December 2020, 14:53:17 UTC
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Tip revision: f8d9fef
figureCode.nb
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In this notebook, we calculate the dynamics of the wave front with a \
Heaviside activation function; we explicitly plot the concentration profiles \
from figures 1 and 2 and the concentration gradients a la figure 4 of \
Dieterle et al. (2020).\
\>", "Subsubsection",
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First, we define the system parameters; vBase is the desired wave speed, Dc \
is the diffusion constant, cellDim is the number of dimensions in which the \
cells live, diffDim is the number of dimensions in which diffusion takes \
place, Cth is the threshold concentration (implicitly normalized by the \
emission rate, a, and cell density, rho) which gives the desired wave speed \
vBase given the other system parameters, and rInv is the initial signaling \
radius.\
\>", "Text",
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Next, we write down the Green's function for each dimensionality; this \
calculation assumes a spherically symmetric environment. The Green's function \
describes the concentration generated at radius r by a spherical (circular \
ring for sources in 2D, point for sources in 1D) shell at radius R; the shell \
is assumed to have made a momentary emission at time tt and the concentration \
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desired Green\[CloseCurlyQuote]s function given diffDim and cellDim. gradGF \
is the radial gradient of these functions\
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Next, we calculate the initiation time of the wave by finding the time at \
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We then compute the location of the wave front at every subsequent time point \
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