Subdiffusion kinetics of nanoprecipitate growth and destruction in solid solutions
type: Item
instance of: scholarly article
title: Subdiffusion kinetics of nanoprecipitate growth and destruction in solid solutions
zbMATH Open document ID: 1334.82070
author: V. V. Svetukhin
author: R. T. Sibatov
published in: Theoretical and Mathematical Physics
publication date: 2015-09-30T00:00:00Z
review text: This paper is a study of fractional differential generalizations of the Ham and Aaron-Kotler precipitation models used for the kinetics of subdiffusion-limited growth and dissolution of new-phase precipitates. Diffusion models that are based on the concept of normal impurity diffusion were successfully used to describe many phenomena. However, there are many examples that anomalous diffusion (predominantly subdiffusion) is also a very important model of many practical applications. Classical diffusion \((\alpha = 1)\) is based on Gaussian statistics and the second Fick law and leads to the dependence \(\Delta(t)=\sqrt{\langle x^2(t)\rangle}\propto^{1/2}\), but there are also available cases where \(\alpha\neq 1\) leads to sub- or super-diffusions with anomalous self-similarity diffusion. Existing diffusion models of precipitation reflect rather incompletely the properties of transport phenomena occurring in actual materials, thus the authors study the subdiffusion-limited kinetics of the growth and decomposition of new-phase precipitates using fractional differential generalizations of classical models of precipitate growth and dissolution in solid solutions. The whole paper is divided into six sections. After the introduction, we have a presentation of the mathematical basis of random walks with impurity localization in Section 2, then a generalization of the Ham model (Section 3) with Monte Carlo simulations in the framework of the Ham approach (Section 4). In Section 5, there is a proposal of subdiffusion generalization of the Aaron-Kotler model in terms of fractional derivatives. A summary of the paper is provided in Section 6.
reviewed by: Dominik Strzałka
Mathematics Subject Classification ID: 82D20
Mathematics Subject Classification ID: 82D80
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 82C80
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 6487445
zbMATH Keywords: subdiffusion
zbMATH Keywords: nanoprecipitate
zbMATH Keywords: fractional derivative
zbMATH Keywords: supersaturated solid solution
zbMATH Keywords: Monte Carlo method
MaRDI profile type: Publication
full work available at URL: s11232-015-0301-3
OpenAlex ID: W1615135837
cites work: The random walk's guide to anomalous diffusion: A fractional dynamics approach
cites work: Fractional Kinetics in Solids
cites work: The fractional Fick's law for non-local transport processes
cites work: Continuous-time random walk and parametric subordination in fractional diffusion
cites work: Random Walks on Lattices. II
cites work: The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
cites work: Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
cites work: Free Energy of a Nonuniform System. I. Interfacial Free Energy
cites work: Monte Carlo simulations for spinodal decomposition
cites work: Analysis of fractional differential equations
cites work: Detailed error analysis for a fractional Adams method
cites work: Algorithms for the fractional calculus: a selection of numerical methods
cites work: The Finite Difference Methods for Fractional Ordinary Differential Equations
cites work: On Mittag-Leffler-type functions in fractional evolution processes
cites work: A fractional Poisson process in a model of dispersive charge transport in semiconductors
cites work: FRACTIONAL PROCESSES: FROM POISSON TO BRANCHING ONE
DOI: 10.1007/S11232-015-0301-3
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description: scientific article; zbMATH DE number 6487445