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Preprints of the Keldysh Institute of Applied Mathematics, 2020, 122, 34 pp.
DOI: https://doi.org/10.20948/prepr-2020-122
(Mi ipmp2913)
 

This article is cited in 6 scientific papers (total in 6 papers)

On the diffuse interface models for high codimension dispersed inclusions

E. V. Zipunova, E. B. Savenkov
Full-text PDF (901 kB) Citations (6)
References:
Abstract: Diffuse interface models are widely used to describe evolution of multi-phase system of different nature. Usually dispersed inclusions are three dimensional objects. When describing elastic fractute evolution, elements of the dispersed phase are effectively 2d objects. An example of the model which governs evolution of effectively 1d dispersed inclusions is phase field model for electric breakdown in solids. Phase field model is defined by appropriate free energy functional, which depends on phase field and its derivatives. In this work we show that codimension of the dispersed 'inclusion' significantly restrict the functional dependency of system energy on the derivatives of the problem state variables. It is shown that free energy of any phase field model suitable to describe 1d diffuse objects necessary depends on higher order derivatives of the phase field or need an additional smoothness of the solution — it should have first derivatives integrated with power greater then two. To support theoretical discussion, some numerical experience are presented.
Keywords: diffuse interface models, phase field, order parameter, electric breakdown.
Document Type: Preprint
Language: Russian
Citation: E. V. Zipunova, E. B. Savenkov, “On the diffuse interface models for high codimension dispersed inclusions”, Keldysh Institute preprints, 2020, 122, 34 pp.
Citation in format AMSBIB
\Bibitem{ZipSav20}
\by E.~V.~Zipunova, E.~B.~Savenkov
\paper On the diffuse interface models for high codimension dispersed inclusions
\jour Keldysh Institute preprints
\yr 2020
\papernumber 122
\totalpages 34
\mathnet{http://mi.mathnet.ru/ipmp2913}
\crossref{https://doi.org/10.20948/prepr-2020-122}
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  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Препринты Института прикладной математики им. М. В. Келдыша РАН
     
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