Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
149 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Chemical Continuous Time Random Walks under Anomalous Diffusion (2406.18869v2)

Published 27 Jun 2024 in physics.chem-ph

Abstract: Chemical master equation plays an important role to describe the time evolution of homogeneous chemical system. In addition to the reaction process, it is also accompanied by physical diffusion of the reactants in complex system that is generally not homogeneous, which will result in non-exponential waiting times for particle reactions and diffusion. In this paper we shall introduce a chemical continuous time random walk under anomalous diffusion model based on renewal process to describe the general reaction-diffusion process in the heterogeneous system, where the waiting times are arbitrary distributed. According to this model, we will develop the systematic stochastic theory including generalizing the chemical diffusion master equation, deriving the corresponding mass action law, and extending the Gillespie algorithm. As an example, we analyze the monomolecular $A\leftrightarrow B$ reaction-diffusion system for exponential and power-law waiting times respectively, and show the strong fractional memory effect of the concentration of the reactants on the history of the concentration in power-law case.

Summary

We haven't generated a summary for this paper yet.