Issue 4, 2018

On the approximation of independent pairs in diffusion kinetics: correlation of distances in a three-body system

Abstract

This study investigates the problem of diffusion kinetics in a three-body system, motivated by the theory of radiation chemical kinetics. The backward diffusion equation for the joint density of the distances is formulated, and an explicit formula for the infinitesimal covariance of two diffusing distances is derived. The Clifford–Green theorem is used to show how the infinitesimal covariance of two distances is linked to the covariance of the corresponding two squared distances as time evolves. In addition, computer simulations for the problem are presented, which indicate that hitting probabilities are also correlated. While the results indicate that more work is needed before a usable correction to the independence approximation is possible, clear progress has been made.

Graphical abstract: On the approximation of independent pairs in diffusion kinetics: correlation of distances in a three-body system

Supplementary files

Article information

Article type
Paper
Submitted
10 Oct 2017
Accepted
19 Dec 2017
First published
12 Jan 2018

Phys. Chem. Chem. Phys., 2018,20, 2872-2879

On the approximation of independent pairs in diffusion kinetics: correlation of distances in a three-body system

E. H. Al-Samra and N. J. B. Green, Phys. Chem. Chem. Phys., 2018, 20, 2872 DOI: 10.1039/C7CP06929D

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