Open reaction-diffusion systems: bridging probabilistic theory and simulations across scales
arXiv:2404.07119 · doi:10.1088/1751-8121/adc520
Abstract
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual particle/agent level, and in realistic applications, they often display interaction with their environment through energy or material exchange with a reservoir. This requires intricate mathematical considerations, especially in the case of material exchange since the varying number of particles/agents results in ``on-the-fly'' modification of the system dimension. In this work, we first overview the probabilistic description of reaction-diffusion processes at the particle level, which readily handles varying number of particles. We then extend this model to consistently incorporate interactions with macroscopic material reservoirs. Based on the resulting expressions, we bridge the probabilistic description with macroscopic concentration-based descriptions for linear and nonlinear reaction-diffusion systems, as well as for an archetypal open reaction-diffusion system. Using these mathematical bridges across scales, we finally develop numerical schemes for open reaction-diffusion systems, which we implement in two illustrative examples. This work establishes a methodological workflow to bridge particle-based probabilistic descriptions with macroscopic concentration-based descriptions of reaction-diffusion in open settings, laying the foundations for a multiscale theoretical framework upon which to construct theory and simulation schemes that are consistent across scales.
References in corpus (18)
- Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions
- Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
- Master equations and the theory of stochastic path integrals
- A Convergent Reaction-Diffusion Master Equation
- Stochastic Simulation of Reaction-Diffusion Systems: A Fluctuating-Hydrodynamics Approach
- MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations
- An adaptive multi-level simulation algorithm for stochastic biological systems
- Mathematical modeling of spatio-temporal population dynamics and application to epidemic spreading
- A probabilistic framework for particle-based reaction-diffusion dynamics using classical Fock space representations
- An Unstructured Mesh Convergent Reaction-Diffusion Master Equation for Reversible Reactions
- Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics
- Chemical diffusion master equation: formulations of reaction--diffusion processes on the molecular level
- Grand canonical diffusion-influenced reactions: a stochastic theory with applications to multiscale reaction-diffusion simulations
- A Discrete Stochastic Formulation for Reversible Bimolecular Reactions via Diffusion Encounter
- Field theories and quantum methods for stochastic reaction-diffusion systems
- Detailed Balance for Particle Models of Reversible Reactions in Bounded Domains
- Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion
- Dynamics of systems with varying number of particles: from Liouville equations to general master equations for open systems