Math. Model. Nat. Phenom.
Volume 6, Number 6, 2011Biomathematics Education
|Page(s)||159 - 197|
|Published online||05 October 2011|
Simulating Kinetic Processes in Time and Space on a Lattice
Department of Biology
2 Department of Neurosciences
3 Department of Biomedical Engineering, Case Western Reserve University, Cleveland, OH, 44106
4 Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA 94550
⋆ Corresponding author. E-mail: email@example.com
We have developed a chemical kinetics simulation that can be used as both an educational and research tool. The simulator is designed as an accessible, open-source project that can be run on a laptop with a student-friendly interface. The application can potentially be scaled to run in parallel for large simulations. The simulation has been successfully used in a classroom setting for teaching basic electrochemical properties. We have shown that this can be used for simulating fundamental molecular and chemical processes and even simplified models of predator–prey interactions. By giving the simulated entities spatial extent in the lattice, the particles do not interpenetrate, and clusters of particles can spatially exclude one another. Our simulation demonstrates that spatial inhomogeneity leads to different results than those that are obtained by using standard ordinary differential equation models, as previously reported.
Mathematics Subject Classification: 97M60 / 82C22 / 92C45 / 92D25 / 92B05
Key words: education in biomathematics / lattice models / artificial chemistry / simulation / open-source / autopoiesis / origin of life / diffusion / Nernst potential / resting potential / Donnan equilibrium / chemical reactions / kinetics / Michaelis–Menten / enzyme kinetics / Lotka–Volterra / predator–prey model
© EDP Sciences, 2011
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