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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

The British Scholarship Trust Award for Josip Žubrinić
Cherednichenko, K. & Žubrinić, J.
1/03/21 → 30/06/21
Project: UK charity

The evolution of active zones in tectonic plates: a mathematical approach based on lowfrequency flexural vibrations
Cherednichenko, K., Silva, L. O., Kiselev, A. V. & Kaplunov, J.
15/10/20 → 15/10/23
Project: Researchrelated funding

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

Quantitative tools for upscaling the microgeometry of resonant media
Engineering and Physical Sciences Research Council
1/10/21 → 30/09/24
Project: Research council

David Parkin Visiting Professorship for Uzy Smilansky
Cherednichenko, K. & Smilansky, U.
1/09/21 → 28/02/22
Project: Researchrelated funding
Research output

Functional model for boundaryvalue problems
Cherednichenko, K., Kiselev, A. & Silva, L., 20 Mar 2021, (Acceptance date) In: Mathematika. 25 p.Research output: Contribution to journal › Article › peerreview
Open AccessFile 
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 › peerreview
Open Access 
Global long wave approximations for elastic wave guides
Cherednichenko, K., Kaplunov, J. & Prikazchikov, D., 19 Oct 2020, EURODYN 2020, XI International Conference of Structural Dynamics, 2020.. Papadrakakis, M., Fragiadakis, M. & Papadimitriou, C. (eds.). ICMES, p. 24642474 11 p.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
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 › peerreview
Open Access1 Citation (Scopus)