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

- 11 Finished

### Joint research with I. Velčić (University of Zagreb)

Cherednichenko, K. & Velcic, I.

8/09/19 → 30/09/19

Project: Research-related funding

### Support of collaborative research with Dr I Velcic (University of Zagreb) Croatia

8/09/19 → 21/09/19

Project: UK charity

### Bath – Chile - Mexico (BCM) Network

Cherednichenko, K., Kyprianou, A., Majumdar, A., Cox, A., Del Pino, M. & Musso, M.

1/07/18 → 1/07/19

Project: Research-related funding

### 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

## Research Output 1997 2019

### Frequency-dependent impedance and surface waves on the boundary of a stratified dielectric medium

Cherednichenko, K. & Graham, W., 2 Sep 2019, In : Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 377, 2156, p. 1-13 13 p., 20190218.Research output: Contribution to journal › Article

### 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 22 p.Research output: Contribution to journal › Article

### Stochastic homogenisation of high-contrast media

Cherednichenko, K., Cherdantsev, M. & Velcic, I., 2019, In : Applicable Analysis. 98, 1-2, p. 91-117 28 p.Research output: Contribution to journal › Article

### 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 journal › Article

### Unified approach to critical-contrast homogenisation with explicit links to time-dispersive media

Cherednichenko, K., Ershova, Y., Kiselev, A. & Naboko, S., 13 Sep 2019, (Accepted/In press) In : Transactions of the Moscow Mathematical Society.Research output: Contribution to journal › Article