Continuous-time random-walk approach to normal and anomalous reaction-diffusion processes

2008/03/27 by Andrea Zoia, A. Zoia · 1 citation
Decision Sciences · Environmental Science · Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Groundwater flow and contamination studies #Probabilistic and Robust Engineering Design #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.77.041115

published as Phys. Rev. E 77, 041115 (2008) · 6 pages, 4 figures

arxiv created 2008/03/27 · openalex publication_date 2008/04/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the dynamics of a radioactive species flowing through a porous material, within the continuous-time random-walk (CTRW) approach to the modeling of stochastic transport processes. Emphasis is given to the case where radioactive decay is coupled to anomalous diffusion in locally heterogeneous media, such as porous sediments or fractured rocks. In this framework, we derive the distribution of the number of jumps each particle can perform before a decay event. On the basis of the obtained results, we compute the moments of the cumulative particle distribution, which can be then used to quantify the overall displacement and spread of the contaminant species.

Citations

• Normal and anomalous transport across an interface: Monte Carlo and analytical approach
• Continuous-time random walks and traveling fronts
• The Monte Carlo and fractional kinetics approaches to the underground anomalous subdiffusion of contaminants
• The random walk's guide to anomalous diffusion: a fractional dynamics approach
• Fractional Differential Equations

Cited by

• Continuous-time random-walk model of transport in variably saturated heterogeneous porous media