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Research interests
My research interests are in the multiscale 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 boundedenergy 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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Projects

From functional models of operator theory to materials science: new vistas through BathUNAM partnership
Cherednichenko, K., Spence, E., Silva, L. O., Ballesteros, M. & Kiselev, A.
1/01/20 → 31/12/21
Project: Researchrelated funding

Joint research with I. Velčić (University of Zagreb)
Cherednichenko, K. & Velcic, I.
8/09/19 → 30/09/19
Project: Researchrelated funding

Support of collaborative research with Dr I Velcic (University of Zagreb) Croatia
8/09/19 → 21/09/19
Project: UK charity

BathChileMexico Network
Kyprianou, A., Cherednichenko, K., Cox, A., Musso, M., Del Pino, M., Maas, A., Jara, A., Rivero, V., Benítez, H. & Majumdar, A.
1/07/18 → 31/08/20
Project: Researchrelated funding

OOFA: Operators, Operator Functions, and Asymptotics II
1/06/18 → 1/03/19
Project: Researchrelated funding
Research Output

Effective behaviour of criticalcontrast PDEs: microresonances, frequency conversion, and time dispersive properties. I.
Cherednichenko, K., Ershova, Y. & Kiselev, A., 31 May 2020, In : Communications in Mathematical Physics. 375, 3, p. 18331884 52 p.Research output: Contribution to journal › Article
Open Access 
Scattering theory for a class of nonselfadjoint extensions of symmetric operators
Cherednichenko, K. D., Kiselev, A. V. & Silva, L. O., 15 Jul 2020, Operator Theory: Advances and Applications. Kurasov, P., Laptev, A., Naboko, S. & Simon, B. (eds.). Cham, Switzerland: Springer, p. 194230 37 p. (Operator Theory: Advances and Applications; vol. 276).Research output: Chapter in Book/Report/Conference proceeding › Chapter

Frequencydependent 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. 113 13 p., 20190218.Research output: Contribution to journal › Article
Open Access 
Homogenisation of thin periodic frameworks with highcontrast inclusions
Cherednichenko, K. & Evans, J. A., 15 May 2019, In : Journal of Mathematical Analysis and Applications. 473, 2, p. 658679 22 p.Research output: Contribution to journal › Article
Open Access1 Citation (Scopus) 
Stochastic homogenisation of highcontrast media
Cherednichenko, K., Cherdantsev, M. & Velcic, I., 2019, In : Applicable Analysis. 98, 12, p. 91117 28 p.Research output: Contribution to journal › Article
Open Access1 Citation (Scopus)