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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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Network
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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
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Newton Mobility Grant -: Homogenisation of Degenerate Equations and Scattering for New Materials
1/02/17 → 31/01/19
Project: Research council
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IAA - New-wave Damping Composites
Cherednichenko, K., Blondel, P. & Cooper, S.
Engineering and Physical Sciences Research Council
5/09/16 → 28/02/17
Project: Research council
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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, p. 373-387 15 p.Research output: Contribution to journal › Article › peer-review
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Sharp operator-norm asymptotics for thin elastic plates with rapidly oscillating periodic properties
Cherednichenko, K. & Velcic, I., 30 Apr 2022, In: Journal of the London Mathematical Society. 105, 3, p. 1634-1680 47 p.Research output: Contribution to journal › Article › peer-review
Open Access -
Functional model for boundary-value problems
Cherednichenko, K., Kiselev, A. & Silva, L., 31 Jul 2021, In: Mathematika. 67, 3, p. 596 - 626 25 p.Research output: Contribution to journal › Article › peer-review
Open Access -
Operator-norm resolvent asymptotic analysis of continuous media with low-index inclusions
Cherednichenko, K., Kiselev, A. V. & Silva, L. O., 8 Sep 2021, (Acceptance date) Mathematical Notes 14 p.Research output: Contribution to specialist publication › Article