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
From functional models of operator theory to materials science: new vistas through Bath-UNAM partnership
Cherednichenko, K., Spence, E., Silva, L. O., Ballesteros, M. & Kiselev, A.
1/01/20 → 31/12/21
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
Joint research with I. Velčić (University of Zagreb)
Cherednichenko, K. & Velcic, I.
8/09/19 → 30/09/19
Project: Research-related funding
Strand 1a Larger Scale 2017-18.
Kyprianou, A., Cherednichenko, K., Cox, A., Musso, M., Del Pino, M., Maas, A., Jara, A., Rivero, V. & Benítez, H.
1/07/18 → 31/08/19
Project: Research-related funding
OOFA: Operators, Operator Functions, and Asymptotics II
1/06/18 → 1/03/19
Project: Research-related funding
Research Output
Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. I.
Cherednichenko, K., Ershova, Y. & Kiselev, A., 21 Feb 2020, In : Communications in Mathematical Physics.Research output: Contribution to journal › Article
Open Access
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
Open Access
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
Open Access
1
Citation
(Scopus)
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
Open Access
1
Citation
(Scopus)
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
Open Access
File
2
Citations
(Scopus)
31
Downloads
(Pure)