CompuCell3d manual and Tutorial Version 2
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The constraint energy is zero if  (the constraint is satisfied) and grows as value diverges from . The constraint is elastic because the exponent of 2 effectively creates an ideal spring pushing on the cells and driving them to satisfy the constraint.  is the spring constant (a positive real number), which determines the constraint strength. Smaller values of allow the pattern to deviate more from the equilibrium condition (i.e., the condition satisfying the constraint). Because the constraint energy decreases smoothly to a minimum when the constraint is satisfied, the energy-minimizing dynamics used in the GGH automatically drives any configuration towards one that satisfies the constraint. However, because of the stochastic simulation method, the cell lattice need not satisfy the constraint exactly at any given time, resulting in random fluctuations. In addition, multiple constraints may conflict, leading to configurations which only partially satisfy some constraints.
Because biological cells have a given volume at any time, most GGH simulations employ a volume constraint, which restricts volume variations of generalized cells from their target volumes: Directory: BinDoc -> cc3d binaries -> Manuals Manuals -> 111Equation Chapter 1 Section 1 CompuCell3d reference Manual Version 4 Download 6.67 Mb. Share with your friends:
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