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Reaction-subdiffusion and reaction-superdiffusion equations for evanescent particles performing continuous-time

E Abad¹, S B Yuste, Katja Lindenberg

¹Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain.

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

|April 7, 2010

Summary

This study derives general macroscopic integrodifferential equations for evanescent continuous-time random-walks (CTRWs). The findings simplify modeling particle behavior where particles can disappear during their random walk.

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Area of Science:

Mathematical Physics
Statistical Mechanics
Stochastic Processes

Background:

Continuous-time random-walks (CTRWs) model particle transport.
Particles can evanesce (die) during their walk, complicating macroscopic descriptions.
Existing models for evanescent CTRWs are limited to specific cases.

Purpose of the Study:

To derive general macroscopic integrodifferential equations for evanescent CTRWs.
To provide a more flexible framework for modeling particle transport with evanescence.
To extend the understanding of anomalous diffusion in systems with particle loss.

Main Methods:

Starting from a continuous-time random-walk (CTRW) model.
Developing a general derivation for macroscopic integrodifferential equations.
Analyzing the impact of particle evanescence on probability density evolution.

Main Results:

A generalized derivation for integrodifferential equations governing evanescent CTRWs.
The framework accommodates less stringent constraints than previous models.
Demonstrates how particle evanescence complicates standard diffusion and anomalous diffusion descriptions.

Conclusions:

The derived equations offer a more versatile tool for studying systems with particle loss.
This work advances the macroscopic description of stochastic processes with decaying elements.
The findings are applicable to various fields involving particle transport and decay.