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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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LMSBath Symposium "Operators, Asymptotics, Waves"
1/08/22 → 30/11/23
Project: Researchrelated funding

Quantitative tools for upscaling the microgeometry of resonant media
Engineering and Physical Sciences Research Council
1/11/21 → 31/10/24
Project: Research council


Collaborative research visit by Josip Žubrinic (University of Zagreb)
10/04/21 → 30/04/21
Project: UK charity

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

Operatornorm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast
Cherednichenko, K., Velčić, I. & Žubrinić, J., 31 Mar 2023, (Acceptance date) In: Calculus of Variations and Partial Differential Equations. 59 p.Research output: Contribution to journal › Article › peerreview

Asymptotic analysis of operator families and applications to resonant media
Cherednichenko, K. D., Ershova, Y. Y., Kiselev, A. V., Ryzhov, V. A. & Silva, L. O., 27 Jul 2022, (Acceptance date) Operator Theory: Advances and Applications. Birkhäuser, 62 p. (Operator Theory: Advances and Applications).Research output: Chapter or section in a book/report/conference proceeding › Chapter or section
File8 Downloads (Pure) 
Normresolvent convergence for Neumann Laplacians on manifolds thinning to graphs
Cherednichenko, K. D., Ershova, Y. Y. & Kiselev, A. V., 9 May 2022.Research output: Working paper / Preprint › Preprint
File5 Downloads (Pure) 
Operatornorm homogenisation estimates for the system of Maxwell equations on periodic singular structures
Cherednichenko, K. & D'Onofrio, S., 7 Feb 2022, In: Calculus of Variations and Partial Differential Equations. 61, 2, 43 p., 67.Research output: Contribution to journal › Article › peerreview
Open Access 
OperatorNorm Resolvent Asymptotic Analysis of Continuous Media with HighContrast Inclusions
Kiselev, A. V., Silva, L. O. & Cherednichenko, K., 30 Apr 2022, In: Mathematical Notes. 111, 34, p. 373387 15 p.Research output: Contribution to journal › Article › peerreview
Open AccessFile