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.
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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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Collaborations and top research areas from the last five years
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LMS-Bath Symposium "Operators, Asymptotics, Waves"
1/08/22 → 30/11/23
Project: Research-related funding
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Quantitative tools for upscaling the micro-geometry of resonant media
Engineering and Physical Sciences Research Council
1/11/21 → 31/10/24
Project: Research council
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Collaborative research visit by Josip Žubrinic (University of Zagreb)
10/04/21 → 30/04/21
Project: UK charity
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Support of collaborative research with Dr I Velcic (University of Zagreb) Croatia
8/09/19 → 21/09/19
Project: UK charity
Research output
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Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast
Cherednichenko, K., Velčić, I. & Žubrinić, J., 1 Jun 2023, In: Calculus of Variations and Partial Differential Equations. 62, 5, 72 p., 147.Research output: Contribution to journal › Article › peer-review
Open Access -
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) -
Norm-resolvent 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
File6 Downloads (Pure) -
Operator-norm 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 › peer-review
Open Access -
Operator-Norm Resolvent Asymptotic Analysis of Continuous Media with High-Contrast Inclusions
Kiselev, A. V., Silva, L. O. & Cherednichenko, K., 30 Apr 2022, In: Mathematical Notes. 111, 3-4, p. 373-387 15 p.Research output: Contribution to journal › Article › peer-review
Open AccessFile2 Downloads (Pure)