Kirill Cherednichenko

Professor of Applied Analysis


NEW:

  • Uzy Smilansky, Professor Emeritus at Weizmann Institute of Science, who has been awarded a competitive David Parkin Visiting Professorship, is visiting Bath until March 2023. 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. As part of his stay, he will deliver a number of research talks, including the David Parkin Lecture "Computer Applications in Archaeology: Results, Prospects, Challenges, and Possible Pitfalls." The lecture will take place on 1 December 2021 in 4W1.7 (Wolfson Lecture Theatre) at the Department of Mathematical Sciences, University of Bath. If you wish to attend, please register here, as places are limited.

  • The paper "Operator-norm homogenisation estimates for the system of Maxwell equations on periodic singular structures" by K. Cherednichenko and S. D'Onofrio, which has been accepted for publication in Calculus of Variations and Partial Differential Equations, develops a set of techniques for proving uniform (i.e. operator-norm) convergence estimates for the homogenisation of periodic "singular" structures, which can model, for example, "thin" structures or "multistructures". The paper can also be viewed as one transferring the technique of the recent work by K. Cherednichenko and I. Velčić to the context of arbitrary periodic Borel measures.

  • The paper "Sharp operator-norm asymptotics for linearised elastic plates with rapidly oscillating periodic properties" by K. Cherednichenko and I. Velčić, which has been accepted for piblication in the Journal of the London Mathematical Society, develops a new approach to obtaining operator-norm error estimates in homogenisation, unspired by such classical tools as asymptotic expansions and Poincaré's inequality. As we demonstrate in the paper, the new technique is particularly convenient for the analysis of "anisotropic" geometries, such as those relevant to the study of rods, plates, and shells.

  • The paper "Operator-norm resolvent asymptotic analysis of continuous media with low-index inclusions" by K. Cherednichenko, A. Kiselev, L. Silva, which has been accepted for publication in Mathematical Notes, provides an explicit quantitative construction of the operator-norm resolvent asymptotics for solutions to boundary-value problems with high-contrast inclusions. The result of this construction is a time-dispersive (memory-like) asymptotic description, serving as direct quantitative link to a "metamaterial" behaviour for the corresponding physical system.

  • On 27 July 2021 I gave a lecture at the QJMAM/IMA Summer School on Asymptotics of PDEs and Modelling of Waves. Accompanying notes can be found here.

  • I have been chosen for Fellowship of the Insitute Mathematical Innovation (IMI). As IMI Fellow, look forward to taking to a new level my collaborations with colleagues at the departments of Mechanical Engineering and Physics, on bringing lastest mathematical results to bear on the development of new real-world technologies. As part of the Fellowship, during 2021 I am hosting the Physics and Mathematics lecture series of the Universities for Science Consortium.

  • 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.

  • 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 2020, and an introduction to the programme as well as a lecture by Chris Budd, which was broadcast on 19 May 2021.

  • 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.
  • 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 9 May -- the speaker is Petr Siegl (TU Graz)

    Seminar programme

    Links to other seminars:

    One World PDE       London Analysis and Probability       Cardiff Analysis


    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)
    Research interests:

  • 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


    Research group


    Postdocs

    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 new asymptotic and variational techiques for the study of defects in liquid crystals (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.


    Collaborators

    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


    E-mail Address: K.Cherednichenko (at) bath.ac.uk
    Telephone: +44 1225 38 6891

    Postal Address:
    Department of Mathematical Sciences
    University of Bath
    Claverton Down
    Bath, BA2 7AY
    United Kingdom


    MathSciNet       Research Gate       Google Scholar       Academic Profile on UoB site
    Past events:

  • 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