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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.

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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

Joint research with I. Velčić (University of Zagreb)

Cherednichenko, K. & Velcic, I.

8/09/1930/09/19

Project: Research-related funding

OOFA: Operators, Operator Functions, and Asymptotics II

Cherednichenko, K.

1/06/181/03/19

Project: Research-related funding

IAA - New-wave Damping Composites (IAA261)

Cherednichenko, K. & Cooper, S.

5/09/1628/02/17

Project: Research council

Research Output 1997 2019

Homogenisation of thin periodic frameworks with high-contrast inclusions

Cherednichenko, K. & Evans, J. A., 15 May 2019, In : Journal of Mathematical Analysis and Applications. 473, 2, p. 658-679

Research output: Contribution to journalArticle

Open Access

Time-dispersive behavior as a feature of critical-contrast media

Cherednichenko, K., Ershova, Y. & Kiselev, A. V., 2019, In : SIAM Journal on Applied Mathematics. 79, 2, p. 690-715 26 p.

Research output: Contribution to journalArticle

Open Access
File

Asymptotic behaviour of the spectra of systems of Maxwell equations in periodic composite media with high contrast

Cherednichenko, K. & Cooper, S., 2018, In : Mathematika. 64, 2, p. 583-605

Research output: Contribution to journalArticle

Open Access
Composite Media
Maxwell's equations
Asymptotic Behavior
Oscillating Coefficients
Electromagnetism
1 Citation (Scopus)

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

Cherdantsev, M., Cherednichenko, K. & Cooper, S., 31 Dec 2018, In : SIAM Journal on Mathematical Analysis (SIMA). 50, 6, p. 5825-5856 32 p.

Research output: Contribution to journalArticle

Open Access
File
Periodic Problem
Eigenvalues and eigenfunctions
Eigenfunctions
Extremes
Defects