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TMF, 2015, Volume 183, Number 3, Pages 460–476 (Mi tmf8832)  

This article is cited in 1 scientific paper (total in 1 paper)

Subdiffusion kinetics of nanoprecipitate growth and destruction in solid solutions

R. T. Sibatov, V. V. Svetukhin

Ulyanovsk State University, Laboratory of Diffusion Process Modeling, Ulyanovsk, Russia

Abstract: Based on fractional differential generalizations of the Ham and Aaron–Kotler precipitation models, we study the kinetics of subdiffusion-limited growth and dissolution of new-phase precipitates. We obtain the time dependence of the number of impurities and dimensions of new-phase precipitates. The solutions agree with the Monte Carlo simulation results.

Keywords: subdiffusion, nanoprecipitate, fractional derivative, supersaturated solid solution, Monte Carlo method

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-99674
Ministry of Education and Science of the Russian Federation 1643, 3.1862.2014K

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/tmf8832

Full text: PDF file (1352 kB)
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English version:
Theoretical and Mathematical Physics, 2015, 183:3, 846–859

Bibliographic databases:

PACS: 81.40.Cd;
MSC: 82C24; 82C41
Received: 03.12.2014

Citation: R. T. Sibatov, V. V. Svetukhin, “Subdiffusion kinetics of nanoprecipitate growth and destruction in solid solutions”, TMF, 183:3 (2015), 460–476; Theoret. and Math. Phys., 183:3 (2015), 846–859

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf8832
  • http://mi.mathnet.ru/eng/tmf/v183/i3/p460

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. H. Sun, Y. Zhang, D. Baleanu, W. Chen, Ya. Chen, “A new collection of real world applications of fractional calculus in science and engineering”, Commun. Nonlinear Sci. Numer. Simul., 64 (2018), 213–231  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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