277201 Accelerated Kinetic Monte Carlo (KMC) Algorithm for off-Lattice Particle- Based Reaction-Diffusion Systems

Tuesday, October 30, 2012: 4:55 PM
327 (Convention Center )
Vikram Thapar, Chemical Engineering, Cornell University, Ithaca, NY and Paulette Clancy, Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY

Accelerated Kinetic Monte Carlo (KMC) Algorithm for Off-Lattice Particle- Based Reaction-Diffusion Systems

Vikram Thapar* and Paulette Clancy

School of Chemical and Biomolecular Engineering

Cornell University

Ithaca NY 14853

*vt87@cornell.edu

We present an accelerated stochastic algorithm for simulating off-lattice/particle-based reaction-diffusion network. Off-lattice Kinetic Monte Carlo models are widely acknowledged to be valuable for a wide range of applications (especially in materials growth applications and cell biology) for which a fixed geometry lattice-based approach is restrictive. The most popular current particle-based models include ChemCell, MCell, Smoldyn and DADOS. The first three models (used largely for biological applications) make use of a fixed, or adaptive-based, time step, whereas the commercial package DADOS (used almost exclusively for Si-based semiconductor applications) uses a variable time step. DADOS is based on a Gillespie SSA-like that "fires" just one reaction or diffusion event in a time step. This, inevitably, makes it computationally inefficient and limits its scope to complex problems.

Our newly developed algorithm offers a computationally efficient, open source, code that makes use of a variable time step. The "tau-leaping" approach developed by Gillespie for "well-mixed" systems lays the foundation for our algorithm. The idea of "tau leaping" is based on firing multiple reaction-diffusion events in a time interval chosen such that the rates of those events will not change by a significant amount. Hence, the most critical and challenging aspect is to select an appropriate value of tau. The expression for the time step we have implemented is derived from concepts of how one event affects another. A traditional (single event, rejection-free) KMC method is implemented for use as a "gold standard" comparison to our accelerated simulations. Neighbor lists and data structures are used to increase computational efficiency. The use of constrained binomial random numbers to calculate the number of executions for each event takes care of the issue of overlapping of particles and negative populations. Two interesting reaction-diffusion examples – Fisher's Equation and the Lotka-Volterra (Predator-Prey) Equations -- are used to check the performance and accuracy of the algorithm. We highlight improvements in computational efficiency obtained by implementing this approach. Major challenges applying this technique to a general reaction-diffusion system are discussed, and possible solutions are presented.


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See more of this Session: Multiscale Modeling: Methods and Applications
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