Mikhail Cherdantsev

Mikhail Cherdantsev
Cardiff University | CU · School of Mathematics

PhD

About

12
Publications
862
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
77
Citations
Introduction
Homogenisation of PDEs: high-contrast homogenisation, periodic and random settings, spectral analysis, non-linear elasticity. Multiple scales problems in PDEs.
Additional affiliations
July 2013 - present
Cardiff University
Position
  • Lecturer
November 2010 - June 2013
Cardiff University
Position
  • EPSRC Research Fellow
Description
  • Fellowship project "Rigorous derivation of moderate and high-contrast nonlinear composite plate theories"
November 2008 - October 2010
Cardiff University
Position
  • Research Associate
Description
  • I was a co-investigator of the project "Variational Convergence for Non-linear High-contrast Homogenisation Problems"
Education
October 2005 - March 2009
University of Bath
Field of study
  • Mathematics
September 1999 - June 2004

Publications

Publications (12)
Preprint
Full-text available
We study the homogenisation problem for elliptic high-contrast operators A^ε whose coefficients degenerate as ε → 0 on a set of randomly distributed inclusions. In our earlier paper [Stochastic homogenisation of high-contrast media. Applicable Analysis (2019)] we proved the Hausdorff convergence of the spectra of A^ε to the spectrum of a two-scale...
Preprint
Full-text available
We study the properties of eigenvalues and corresponding eigenfunctions generated by a defect in the gaps of the spectrum of a high-contrast random operator. We consider a family of ellipitic operators $\mathcal{A}^\varepsilon$ in divergence form whose coefficients possess double porosity type scaling and are perturbed on a fixed-size compact domai...
Article
Full-text available
Using a suitable stochastic version of the compactness argument of [V. V. Zhikov, 2000. On an extension of the method of two-scale convergence and its applications. Sb. Math., 191(7--8), 973--1014], we develop a probabilistic framework for the analysis of heterogeneous media with high contrast. We show that an appropriately defined multiscale limit...
Article
Full-text available
We study the homogenisation of geometrically nonlinear elastic composites with high contrast. The composites we analyse consist of a perforated matrix material, which we call the "stiff" material, and a "soft" material that fills the remaining pores. We assume that the pores are of size 0 < ϵ ≪ 1 and are periodically distributed with period ϵ. We a...
Article
Full-text available
Following a number of recent studies of resolvent and spectral convergence of non-uniformly elliptic families of differential operators describing the behaviour of periodic composite media with high contrast, we study the corresponding one-dimensional version that includes a "defect": an inclusion of fixed size with a given set of material paramete...
Article
Full-text available
We show that nonlinearly elastic plates of thickness \(h\rightarrow 0\) with an \(\varepsilon \)-periodic structure such that \(\varepsilon ^{-2}h\rightarrow 0\) exhibit non-standard behaviour in the asymptotic two-dimensional reduction from three-dimensional elasticity: in general, their effective stored-energy density is “discontinuously anisotro...
Article
Full-text available
We present a multiscale asymptotic framework for the analysis of the macroscopic behaviour of periodic two-material composites with high contrast in a finite-strain setting. Our derivation starts with the geometrically nonlinear description of a composite consisting of a stiff material matrix and soft, periodically distributed inclusions, where the...
Article
Full-text available
An analytical framework is developed for passing to the homogenisation limit in (not necessarily convex) variational problems for composites whose material properties oscillate with a small period ε and that exhibit high contrast of order ε^{-1} between the constitutive, "stress-strain", response on different parts of the period cell. The approach...
Article
Full-text available
We consider an eigenvalue problem for a divergence-form elliptic operator Aε that has high-contrast periodic coefficients with period ε in each coordinate, where ε is a small parameter. The coefficients are perturbed on a bounded domain of “order one” size. The local perturbation of coefficients for such an operator could result in the emergence of...
Article
Full-text available
In this paper, we consider eigenvalue problems for the Laplace operator in three-dimensional domains with singularly perturbed boundary. Perturbations are generated by a complementary Dirichlet boundary condition on a small nonclosed surface inside the domain. The convergence and the asymptotic behavior of simple eigenvalues of the problem are cons...

Network

Cited By

Projects

Projects (2)
Project
Developing a theory for the named topic with focus on the behaviour of the spectra.
Archived project
We consider 1-d high contrast periodic problem for a divergence type operator with a fixed size defect. The focus of the work is the eigenmodes in the gaps of the essential spectrum localised on the defect.