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Master equation for a bistable chemical system with perturbed particle velocity distribution function.

P Dziekan¹, A Lemarchand, B Nowakowski

¹Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland. pdziekan@ichf.edu.pl

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 3, 2012

Summary

A modified master equation accounts for reaction-induced changes in particle velocity, predicting dynamical regime shifts in gaseous systems. This approach, validated by simulations, offers a more efficient way to study complex chemical reactions.

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Area of Science:

Chemical kinetics
Non-equilibrium thermodynamics
Computational chemistry

Background:

Homogeneous gaseous reactive systems often assume equilibrium conditions.
Particle velocity distribution functions can be perturbed by reactions, leading to non-equilibrium states.
Understanding these non-equilibrium effects is crucial for accurately modeling complex chemical dynamics.

Purpose of the Study:

To develop a modified master equation incorporating non-equilibrium corrections for gaseous reactive systems.
To investigate the impact of reaction-induced perturbations on the particle velocity distribution function.
To analyze the resulting transitions between different dynamical regimes.

Main Methods:

Formulation of a modified master equation including non-equilibrium corrections.
Application of the modified approach to the Schlögl model.
Validation of predictions through comparison with direct simulation Monte Carlo (DSMC) microscopic simulations.

Main Results:

The modified master equation successfully predicts non-equilibrium-induced transitions between dynamical regimes.
Observed transitions include the conversion of monostable to bistable systems and vice versa.
Predictions align with results from DSMC simulations, confirming the model's validity.

Conclusions:

The modified master equation provides an accurate and efficient method for studying non-equilibrium effects in reactive systems.
This approach captures complex dynamical behaviors, such as regime transformations, not apparent in equilibrium models.
The method offers a significant computational advantage over direct microscopic simulations for similar analyses.