111Equation Chapter 1 Section 1 CompuCell3d reference Manual Version 4
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- KernelDiffusionSolver
- ReactionDiffusionSolver
FastDiffusionSolver2DFastDiffusionSolver2DFE steppable is a simplified version of the FlexibleDiffusionSolverFE steppable. It runs several times faster that flexible solver but lacks some of its features. Typical syntax is shown below: Demos/diffusion/diffusion_2D_fast_box.pulse.txt In particular for fast solver you cannot specify cells into which diffusion is prohibited. However, you may specify cell types where diffusant decay is prohibited For exmplanation how ExtraTimesPerMCS works see section on FlexibleDiffusionSolverFE. KernelDiffusionSolverThis diffusion solver has the advantage over previous solvers that it can handle large diffusion constants. It is also stable. However, it does not accept options like Simply put KernelDiffusionSolver solves diffusion equation 
With fixed, periodic boundary conditions on the edges of the lattice. This is different from FlexibleDiffusionSolver where the boundary conditions evolve. You also need to choose a proper Kernel range (K) according to the value of diffusion constant. Usually when K2 e-(K^2 / (4D) ) is small (this is the main part of the integrand), the approximation convergers to the exact value. The syntax for this solver is as follows: Demos/diffusion/diffusion_2D.pulse.txt Inside For example: Demos/diffusion/diffusion_2D.pulse.txt ReactionDiffusionSolverThe reaction diffusion solver solves the following system of N reaction diffusion equations: 
Let's consider a simple example of such system: 
It can be coded as follows: Demos/diffusion/diffusion_2D.pulse.txt Notice how we implement functions f from the general system of reaction diffusion equations. We simply use This means that function f will depend also on CellType . CellType hodls the value of the type of the cell at particular location - x, y, z - of the lattice. The inclusion of the cell type might be useful if you want to use additional terms which may change depending of the cell type. Then all you have to do is to either use if statements inside For example, let's assume that additional term for second equation is the following: 
In such a case additional term would be coded as follows: Notice that we have used here, so called ternary operator which might be familiar to you from other programing languages such as C or C++ and is equivalent to if-then-else statement The syntax of the ternary (aka if-then-else statement) is as follows: condition ? expression if condition is true : expression if condition false Important: If change the above expression to we will get an XML parsing error. Why? Because XML parser will think that <1 is the beginning of the new XML elelement. To fix this you could use two approaches: 1.Present your expression as CDATA CellType<1 ? 0.01*F : 0.15*F ]]>
In this case XML parser will correctly interpret the expression enclosed between and ]]> . 2. Replace XML using equivalent Python syntax, in which case you would code the above XML element as: DiffusionDataElmnt_2.ElementCC3D("AdditionalTerm",{}," CellType<1 ? 0.01*F : 0.15*F ") The moral from this story is that if like to use muParser in the XML file make sure to use this general syntax: YOUR EXPRESSION ]]>
One thing to remember is that computing time of the additional term depends on the level of complexity of this term. Thus you might get some performance degradation for very complex expressions coded in muParser Similarly as in the case of FlexibleDiffusionSolverwe may use AutoscaleDiffusion tag tells CC3D to automatically rescale diffusion constant. See section FlexibleDiffusionSolver or the Appendix for more information. Download 0.81 Mb. Share with your friends:
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