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

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 di...

Full description

Saved in:
Bibliographic Details
Published in:Physical chemistry chemical physics : PCCP 2018, Vol.20 (4), p.2872-2879
Main Authors: Al-Samra, Eyad H, Green, Nicholas J B
Format: Article
Language:English
Subjects:
Approximation
Computer simulation
Covariance
Diffusion
Kinetics
Mathematical analysis
Reaction kinetics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1463-9076
1463-9084
DOI:10.1039/c7cp06929d