Projects per year

## Personal profile

### 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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## Projects 2014 2019

### OOFA: Operators, Operator Functions, and Asymptotics II

1/06/18 → 1/03/19

Project: Research-related funding

### Newton Mobility Grant -: Homogenisation of Degenerate Equations and Scattering for New Materials

1/02/17 → 31/01/19

Project: Research council

### Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

23/07/14 → 22/06/19

Project: Research council

### IAA - New-wave Damping Composites (IAA261)

Cherednichenko, K. & Cooper, S.

5/09/16 → 28/02/17

Project: Research council

### International Research Accelerator Scheme

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

1/09/16 → 1/09/18

Project: Research-related funding › International Relations Office Funding

## Research Output 1997 2018

### 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. 583-605Research output: Contribution to journal › Article

### 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 journal › Article

### 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. 191-215Research output: Contribution to journal › Article

### 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 journal › Article

### Operator-norm convergence estimates for elliptic homogenization problems on periodic singular structures

Cherednichenko, K. & D'Onofrio, S. 1 Jul 2018 In : Journal of Mathematical Sciences N.Y.. 232, 4, p. 558-572Research output: Contribution to journal › Article