Kirill Cherednichenko

Professor of Applied Analysis

NEW:

  • The 74th British Mathematical Colloquium will take place at the University of Bath on 3-6 April 2023.

  • 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.

  • A new master's programme MSc Mathematics with Data Science for Industry was launched 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.
  • Research seminar "Asymptotics, Operators, and Functionals'': Mondays at 15:15-18:15 in 4W1.7 (Wolfson Lecture Theatre).

    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 22 May -- the speaker is Benjamin Fehrman (Oxford) Note new start time: 15:15

    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

    Alexander Kiselev, 2022--2024

    Josip Žubrinić, 2021 (now Lecturer at the University of Zagreb)

    Reynaldo Castaneira, 2018--2019 (supported by UUKi Rutherford Fund)

    Yulia Ershova, 2016--2018 (now Research Fellow at Texas A&M University)

    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 student

    Yi Sheng Lim (2019--2023, member of SAMBa CDT), working on dispersion and localisation for wave propagation in media with resonant inclusions.

    Former PhD students

    William Graham (University of Bath, 2017--2021, member of SAMBa CDT): Asymptotic and numerical analysis of wave propagation in thin-structure waveguides.

    Aaron Pim (Univerzsity of Bath, 2017--2021): Asymptotic and variational methods for the study of defects in liquid crystals (Supervised jointly with Apala Majumdar and Jey Sivaloganathan).

    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

    Giacomo Canevari (Verona), Mikhail Cherdantsev (Cardiff University), Patrick Dondl (Universität Freiburg), Harsha Hutridurga (IIT Bombay), Stephen Shipman (Louisiana State University), Luis Silva (IIMAS-UNAM, Mexico), Igor Velčić (Zagreb), Arghir Zarnescu (BCAM, Bilbao), Josip Žubrinić (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-XX 4--10 January 2023 (CIMAT, Unidad Mérida)

  • BUC-XIX: Summer school at UMAR, Huatulco (12-15 July 2022) and a research workshop at IIMAS-UNAM, Mexico City (19-22 July 2022).

  • 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--7 April 2017 (CIMAT-Mérida)

  • Conference "Operators, Operator Families and Asymptotics": 16--19 May 2016

  • LMS-Bath-WIMCS Analysis Day: 4 December 2015