On 27 July 2021 I give a lecture at the QJMAM/IMA Summer School on Asymptotics of PDEs and Modelling of Waves. Accompanying notes can be found here.
The research proposal "Quantitative tools for upscaling the micro-geometry of resonant media" has been supported by EPSRC. This 3-year-long project, which will kick off in October 2021, will focus on the development of a quantitative framework for wave phenomena in electromagnetic composite media where some of the components exhibits resonant properties, this leading to non-classical behaviour on the macro-scale. It is situated at the triple point of mathematical analysis, wave mechanics, and materials science and envisages a full-time research associate joining the project team for 30 months. If you are interested in this opportunity, feel free to contact me at the email address below.
The paper "Functional model for boundary-value problems" by K. Cherednichenko, A. Kiselev, L. Silva, which has been accepted for publication in Mathematika, develops a quantitative framework for the analysis of boundary-value problems of mathematical physics, rooted in the works of M.S. Birman, M. G. Krein, M. I. Višik and inspired by a recent paper (which takes the abstract operator-theoretic perspective) of Vladimir Ryzhov.
As part of team of applied analysts, mathematical modellers, and geophysicists from UNAM, Bath, Keele, Yakutsk, and St.Petersburg, our research group has been awarded a 3-year CONACyT grant as part of the funding programme Ciencia de Frontera 2019. The supported research project "The evolution of active zones in tectonic plates: a mathematical approach based on low-frequency flexural vibrations" is an exciting opportunity to bring recent cutting-edge mathematical tools to bear on more effective simulation and detection of seismic waves.
The paper by K. Cherednichenko, A. Kiselev, L. Silva (Operator Theory: Advances and Applications -- Volume dedicated to the memory of B. S. Pavlov) develops a quantitative framework for the analysis of a wide class of problems of mathematical physics (self-adjoint, dissipative, and, most generally, non-selfadjoint non-dissipative), including useful representations for resolvents and scattering operators. These, in turn, provide new quantitative tools for practically relevant physics and engineering problems. The final version of our manuscript is available on arXiv here.
A new master's programme MSc Mathematics with Data Science for Industry is launching in 2021/22. The MSc focuses on mathematical problem solving skills in an industrial context, with understanding and practical knowledge of data science. Please feel free to email me (at the address below) for further info. You may also be interested in watching the webinar about the programme, which took place on 14 October.
Uzy Smilansky, Professor Emeritus at Weizmann Institute of Science, has been awarded a competitive David Parkin Visiting Professorship for 2020-21 and will visit Bath for 6 months in the coming academic year, travel restrictions due to COVID-19 permitting. Professor Smilansky is a recognised leader in several research areas on the physics-mathematics interface. He is known for raising important questions about the behaviour of complex system that have initiated substantial strands of research, as well as for solving open problems that have provided new insights.
The paper by K. Cherednichenko, A. Kiselev, Y. Ershova (Communications in Mathematical Physics) develops a new technique for the analysis of continuous media with resonant mictrostructures, providing explicit quantitaive information on the overall behaviour of composites ("dispersion relations"), which has been out of reach of the existing analytical methods. The paper links several research fields that have previously not been considered together, from time dispersive media on the physics side to the Birman-Krein-Vishik theory and generalised resolvents on the analysis side.
The paper by K. Cherednichenko, W. Graham (Philosophical Transactions of the Royal Society A) derives a generalisation of the Leontovich boundary condition on the boundary of a frequency-dispersive medium and analyses the associated surface waves.
Research seminar "Asymptotics, Operators, and Functionals'': Mondays at 16:15-18:45 on Zoom -- please let me know if you would like to join the email list for meeting links and videos of past talks.
We aim to discuss the latest results and techniques in the asymptotic analysis of operators, differential equations and functionals, as well as its applications to mechanics, materials and wave propagation.
The talk will usually focus on one or two aspects of a problem of current interest, and is meant to form the basis for an informal discussion during and after the talk. All welcome.
The next session will take place on 28 June -- the speaker is Alex Figotin (UCI). Please note the unusual starting time: 17:15 BST.
Links to other seminars:
One World PDE
London Analysis and Probability
Here is a link to my EPSRC Fellowship "Mathematical foundations of metamaterials: homogenisation, dissipation and operator theory", which I held in 2014--2019.
I am always happy to talk to anyone looking for a PhD project. Here are some of the possible research topics.
Please feel free to email me at K.Cherednichenko (at) bath.ac.uk if you are interested.
My curriculum vitae (in PDF format)
List of my publications (in PDF format) Brief research statement (in PDF format)
Rigorous analysis of problems in mechanics and electromagnetism
Homogenisation of partial differential equations and integral functionals
Applications of homogenisation to the mechanics of composite materials
Scale interaction effects in the description of the behaviour of heterogeneous media
Wave propagation in solid mechanics and electromagnetism
Dissipative operator theory and functional models
Scattering theory for differential equations with inhomogeneities
Asymptotic methods for periodic media with rapidly oscillating properties and for high-frequency problems
Variational methods in the mechanics of media with a microstructure
Theories for the description of dislocations as agents of plastic flow
Reynaldo Castaneira, 2018--2019 (supported by UUKi Rutherford Fund)
Yulia Ershova, 2016--2018
James Roberts, Nov 2016 -- Mar 2017
Marcus Waurick, 2015--2017 (now Professor at TU Bergakademie Freiberg)
Shane Cooper, 2012--2013 (now Lecturer at University College London)
Mikhail Cherdantsev, 2008--2010 (now Senior Lecturer at Cardiff University)
Komil Kuliev, 2012--2013
Current PhD students
William Graham (2017--2021), working on waves in electromagnetic composites (member of the SAMBa CDT)
Yi Sheng Lim (2019--2023), working on localisation phenomena for stochastic problems with resonant inclusions (member of the SAMBa CDT, supervised jointly with Hendrick Weber)
Aaron Pim (2017--2021), working on homogenisation techniques for liquid crystals and existence theorems for associated energy functionals (Supervised jointly with
Apala Majumdar and Jey Sivaloganathan)
Former PhD students
Serena D'Onofrio (University of Bath, 2016--2020): Operator-theoretic methods in
homogenisation of singular periodic structures.
Matthew Lewis (Cardiff University, 2014--2018): Stability of solutions of a one-dimensional p-Laplace equation with periodic potential (supervised jointly with Karl Michael Schmidt).
James Evans (Cardiff University, 2012--2016): Higher-order homogenisation for Maxwell equations and on homogenisation and spectral properties of periodic thin structures with high contrast.
Mikhail Cherdantsev (Cardiff University), Patrick Dondl (Universität Freiburg), Harsha Hutridurga (IIT Bombay) Alexander Kiselev (St.Petersburg), Karsten Matthies (Bath), Sergey Naboko (St.Petersburg), Frank Rösler (Cardiff), Luis Silva (IIMAS-UNAM, Mexico) Igor Velčić (Zagreb)
Published articles Submitted manuscripts In preparation
Employer: Department of Mathematical Sciences,
University of Bath
Job Title: Professor of Applied Analysis
Telephone: +44 1225 38 6891
E-mail Address: K.Cherednichenko (at) bath.ac.uk
Department of Mathematical Sciences
University of Bath
Bath, BA2 7AY
Google Scholar Academic Profile on UoB site
BUC-XVIII 21--22 January 2020 (CIMAT, Unidad Mérida)
BUC-XVI: 2--6 September 2019 (IIMAS-UNAM, Mexico City)
Conference "Operators, Operator Families and Asymptotics II": 14--17 January 2019
BUC-XV: 16--19 September 2018 (CIMAT, Guanajuato, Mexico)
BUC-XII: 12--14 March 2018 (University of Bath)
BUC-XI: 27 November -- 3 December 2017 (CIMAT-Mérida)
BUC-VII: Spring School 30 March -- 3 April 2017 (UNAM), Workshop 4 April -- 7 April 2017 (CIMAT-Mérida)
Conference "Operators, Operator Families and Asymptotics": 16--19 May 2016
LMS-Bath-WIMCS Analysis Day: 4 December 2015