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Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates.

Weinan E1, Di Liu, Eric Vanden-Eijnden

  • 1Department of Mathematics and Program in Applied and Computational Mathematics (PACM), Princeton University, Princeton, NJ 08544, USA. weinan@princeton.edu

The Journal of Chemical Physics
|December 3, 2005
PubMed
Summary

A novel simulation algorithm efficiently models chemical kinetics by nesting stochastic simulation algorithms (SSA). This method accurately captures slow processes using fast reaction rates for improved computational efficiency.

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Area of Science:

  • Computational Chemistry
  • Chemical Kinetics
  • Algorithm Development

Background:

  • Simulating chemical kinetic systems with disparate rates presents computational challenges.
  • Classical stochastic simulation algorithms (SSA) are widely used but can be inefficient for systems with wide rate separation.

Purpose of the Study:

  • To develop an efficient and general simulation algorithm for chemical kinetic systems with disparate rates.
  • To improve upon the classical stochastic simulation algorithm (SSA) by incorporating a nested approach.

Main Methods:

  • A nested stochastic simulation algorithm (SSA) approach is proposed.
  • An outer SSA simulates slow processes, with rates determined by an inner SSA simulating fast reactions.
  • The method is a modification of the Gillespie algorithm.

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Main Results:

  • The proposed nested SSA algorithm demonstrates efficiency for systems with separated time scales.
  • The algorithm can be generalized to systems with multiple disparate time scales.
  • Convergence and efficiency are supported by error estimates and examples.

Conclusions:

  • The nested SSA provides an efficient and general method for simulating chemical kinetics with disparate rates.
  • This approach offers a seamless modification to classical SSA, enhancing computational performance.
  • The algorithm's applicability extends to complex systems with multiple time scales.