Simulating Kinetic Processes in Time and Space on a Lattice

J. P. Gill; K. M. Shaw; B. L. Rountree; C. E. Kehl; H. J. Chiel

Mathematical Modelling of Natural Phenomena (2011)

  • Volume: 6, Issue: 6, page 159-197
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Gill, J. P., et al. "Simulating Kinetic Processes in Time and Space on a Lattice." Mathematical Modelling of Natural Phenomena 6.6 (2011): 159-197. <http://eudml.org/doc/222312>.

@article{Gill2011,
abstract = {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. },
author = {Gill, J. P., Shaw, K. M., Rountree, B. L., Kehl, C. E., Chiel, H. J.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {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; Michaelis-Menten; Lotka-Volterra; predator-prey model; biomathematics education},
language = {eng},
month = {10},
number = {6},
pages = {159-197},
publisher = {EDP Sciences},
title = {Simulating Kinetic Processes in Time and Space on a Lattice},
url = {http://eudml.org/doc/222312},
volume = {6},
year = {2011},
}

TY - JOUR
AU - Gill, J. P.
AU - Shaw, K. M.
AU - Rountree, B. L.
AU - Kehl, C. E.
AU - Chiel, H. J.
TI - Simulating Kinetic Processes in Time and Space on a Lattice
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/10//
PB - EDP Sciences
VL - 6
IS - 6
SP - 159
EP - 197
AB - 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.
LA - eng
KW - 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; Michaelis-Menten; Lotka-Volterra; predator-prey model; biomathematics education
UR - http://eudml.org/doc/222312
ER -

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