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Research interests

My research interests are in the multi-scale asymptotic analysis of materials and media. The main objective of such analysis is to replace the complex medium in question by its "effective" counterpart possessing the physical properties of the original problem that are deemed important in a given application. I use a range of tools from the asymptotic analysis of partial differential equations and integral functionals, which are often linked to the kind of convergence ("topology") that preserves the energy stored in a medium for any data from a given function class. An example of a recent evolution of such asymptotic tools is provided by the analysis of the overall ("averaged", "homogenised") behaviour periodic composite media, where the increased contrast between component media leads to a loss of compactness of solutions (more generally, of bounded-energy sequences) in the classical Sobolev spaces.

Profile

It has recently become evident that in some cases there is no "natural" candidate for the effective medium, and one might think of the asymptotic approximation itself as the effective "model". I am currently engaged with the development of this idea as the mathematical equivalent of what physicists refer to as a "metamaterial". Here, each of the physical contexts (acoustics, electromagnetism, elasticity) requires new asymptotic techniques in the corresponding area of analysis (operator theory, calculus of variations). I am motivated by the fascinating interplay between physical objects and mathematical concepts that becomes evident as a result of the development of such techniques.

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  • 2 Similar Profiles
Periodic Coefficients Mathematics
Composite Media Mathematics
Homogenization Mathematics
Resolvent Estimates Mathematics
Periodic Problem Mathematics
Maxwell's equations Mathematics
Elliptic Problems Mathematics
Asymptotic Behavior Mathematics

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Projects 2014 2019

OOFA: Operators, Operator Functions, and Asymptotics II

Cherednichenko, K.

1/06/181/03/19

Project: Research-related funding

homogenizing
dissipation
differential equations
operators
endoscopes

IAA - New-wave Damping Composites (IAA261)

Cherednichenko, K. & Cooper, S.

5/09/1628/02/17

Project: Research council

International Research Accelerator Scheme

Shaddick, G., Kyprianou, A., Milewski, P., Cherednichenko, K. & Majumdar, A.

1/09/161/09/18

Project: Research-related fundingInternational Relations Office Funding

Research Output 1997 2018

Open Access
Composite Media
Maxwell's equations
Asymptotic Behavior
Oscillating Coefficients
Electromagnetism

Extreme localisation of eigenfunctions to one-dimensional high-contrast periodic problems with a defect

Cherednichenko, K., Cherdantsev, M. & Cooper, S. 22 Aug 2018 (Accepted/In press) In : SIAM Journal on Mathematical Analysis (SIMA).

Research output: Contribution to journalArticle

Periodic Problem
Eigenvalues and eigenfunctions
Eigenfunctions
Extremes
Defects
1 Citations

Functional model for extensions of symmetric operators and applications to scattering theory

Cherednichenko, K. D., Kiselev, A. V. & Silva, L. O. 1 Jun 2018 In : Networks and Heterogeneous Media. 13, 2, p. 191-215

Research output: Contribution to journalArticle

Symmetric Operator
Functional Model
Scattering Theory
Scattering
Deficiency Index

Norm-resolvent convergence in perforated domains

Cherednichenko, K., Dondl, P. & Rösler, F. 10 Apr 2018 (Accepted/In press) In : Asymptotic Analysis.

Research output: Contribution to journalArticle