On the numerical accuracy of the Fokker-Planck approximation to the hierarchy of master equations
type: Item
instance of: scholarly article
title: On the numerical accuracy of the Fokker-Planck approximation to the hierarchy of master equations
zbMATH Open document ID: 0766.65113
author: M. Vicanek
author: Christopher A. Stone
author: Nasr M. Ghoniem
published in: Journal of Computational Physics
publication date: 1993-05-16T00:00:00Z
review text: This paper deals with the process of agglomeration of atomic clusters on clean surfaces during the early stages of the thin film formation. The evolution of the size distribution of the clusters is described by moments that are derived from both the hierarchical master equation and the equivalent Fokker-Planck approximation. The accuracy of the numerical moment solutions obtained with the two formulations in the following context is analyzed: only single atoms are mobile and the dissociation rate of clusters containing two or more atoms is negligible compared to the aggregation rate. The results show that a Fokker-Planck solution is a good approximation to the corresponding master equation.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 82C31
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 168641
zbMATH Keywords: birth and death processes
zbMATH Keywords: Langevin equations
zbMATH Keywords: Brownian motion
zbMATH Keywords: thermodynamic limit
zbMATH Keywords: Fokker-Planck equation
zbMATH Keywords: agglomeration of atomic clusters
zbMATH Keywords: thin film formation
zbMATH Keywords: moments
zbMATH Keywords: Fokker-Planck approximation
zbMATH Keywords: master equation
reviewed by: L. Vázquez
MaRDI profile type: Publication
full work available at URL: jcph.1993.1043
OpenAlex ID: W1968749975
DOI: 10.1006/JCPH.1993.1043
description: scientific article; zbMATH DE number 168641