Kirill Cherednichenko


  • Research seminar "Asymptotics, operators and functionals'': Mondays at 16:15-18:15 in Wolfson Lecture Theatre 4W 1.7.

    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.

    Next talk is by Fritz Gesztesy on 17 June 2016.

    Seminar programme



  • Mini-course by Professor Ricardo Weder (Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, UNAM, Mexico City)

    Dates and venue: 23--28 May 2016, Department of Mathematical Sciences, University of Bath. Room: 4W 1.1

    Information on timetable to follow.

    Course title: ``High-velocity estimates, inverse scattering and topological effects''. Link to course outline. Professor Weder's visit is supported by University of Bath and EPSRC.


  • I am organising the conference ``Operators, Operator Families and Asymptotics'' at the University of Bath, from Monday 16 May to Thursday 19 May 2016. The registration deadline has passed, but feel free to email me if you wish to attend.

    List of registered participants

    Conference programme

    Conference poster: larger version


    The conference is supported by London Mathematical Society, University of Bath, EPSRC, and Bath Institute for Mathematical Innovation (BIMI)

    Confirmed speakers:

    Programme committee:

    Kirill Cherednichenko (Bath), Fritz Gesztesy (Missouri), Peter Kuchment (Texas A&M), Marco Marletta (Cardiff), Graeme Milton (Utah), Leonid Parnovsky (UCL)

    Conference summary:

    The conference is aimed at making an overview of the state of the art in a rapidly developing area of analysis concerned with application of the techniques of operator theory to the asymptotic analysis of parameter-dependent differential equations and boundary-value problems. From the physical point of view, the parameter normally represents a length-scale in the situation modelled by the equation: for example, a wavelength in wave propagation, or the inhomogeneity size in the theory of periodic composites. The theory of linear operators in a Hilbert space (symmetric, self-adjoint, dissipative, non-selfadjoint), which has enjoyed several decades of outstanding progress, had been, for much of its time, restricted to abstract analysis of general classes of operators, accompanied by ad-hoc examples and applications to perturbations of the Laplace operator. The meeting is aimed at making a step-change in re-assessing the existing body of knowledge in the related areas, as a modern operator-theoretic version of the classical asymptotic analysis. This will generate new research directions in the asymptotic study of operator families, where the abstract and applied streams are aligned with each other.


    I am EPSRC Fellow and Reader in Mathematics

    Here is a link to my 5-year EPSRC-supported project "Mathematical foundations of metamaterials: homogenisation, dissipation and operator theory"

    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)
    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


    Postdocs

    Yulia Ershova, 2016--2018

    Marcus Waurick, 2015--2017

    Shane Cooper, 2012--2013 (now EPSRC Research Fellow at the University of Bath)

    Mikhail Cherdantsev, 2008--2010 (now Lecturer at Cardiff University)

    Komil Kuliev


    PhD students

    James Evans (Cardiff University, 2012-2015), working on higher-order homogenisation for Maxwell equations and on homogenisation and spectral properties of periodic thin structures with high contrast

    Matthew Lewis (Cardiff University, 2014-2017), working on eigenvalue problems for the nonlinear p-Laplace equation and its versions with rapidly oscillating coefficients (Supervised jointly with Karl Michael Schmidt)

    Serena D'Onofrio (University of Bath, 2016-2020), working on new analytical techniques in homogenisation and scattering for composite media


    Collaborators

    Michel Bellieud (Université Montpellier 2), Richard Craster (Imperial), Alexander Kiselev (Kyiv), Karsten Matthies (Bath) Graeme Milton (Utah), Stefan Neukamm (TU Dresden), Luis Silva (UNAM), Valery Smyshlyaev (UCL), John Willis (Cambridge), Vasily Zhikov (Vladimir)


    Publications

    Journal articles:

  • (with A. Kiselev) Norm-resolvent convergence of one-dimensional high-contrast periodic problems to a Kronig-Penney dipole-type model. To appear in Communications in Mathematical Physics.

  • (with M. Cherdantsev) Open Access: Bending of thin periodic plates. Calculus of Variations and Partial Differential Equations 54(4), 4079--4117 (2015)

  • (with S. Cooper) Open Access: On the existence of high-frequency boundary resonances in layered elastic media. Proceedings of the Royal Society A (2015); DOI: 10.1098/rspa.2014.0878

  • (with S. Cooper) Open Access: Resolvent estimates for high-contrast homogenisation problems. Archive for Rational Mechanics and Analysis (2015); DOI: 10.1007/s00205-015-0916-4

  • (with S. Cooper) Open Access: Homogenisation of the system of high-contrast Maxwell equations. Mathematika 61(2: V. G. Maz'ya Anniversary Issue), 475--500 (2015)

  • (with S. Cooper and S. Guenneau) Open Access: Spectral analysis of one-dimensional high-contrast elliptic problems with periodic coefficients. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal. 13(1), 72--98 (2015)

  • Some analogues of the double-porosity models and the associated effect of micro-resonance. Journal of Mathematical Sciences 176, 818--827 (2012)

  • (with M. Cherdantsev) Two-scale Γ-convergence of integral functionals and its application to homogenisation of nonlinear high-contrast periodic composites. Archive for Rational Mechanics and Analysis 204, 445--478 (2012)

  • (with S. D. M. Adams, R. V. Craster and S. Guenneau) High-frequency spectral analysis of thin periodic acoustic strips: theory and numerics. European Journal of Applied Mathematics 21(6), 557--590 (2010)

  • An approach to constitutive modelling of elasto-plasticity via ensemble averaging of the dislocation transport. Journal of the Mechanics and Physics of Solids 58(5), 798--809 (2010)

  • (with N. F. Britton, C. Carrillo and M. Mogie) Dynamic coexistence of sexual and asexual invasion fronts via a system of integro-difference equations. Bulletin of Mathematical Biology 71(7), 1612--1625 (2009)

  • (with F. J. Sabina) On the existence of waves guided by a cavity in an elastic layer. Quarterly Journal of Mechanics and Applied Mathematics 62(3), 221-233 (2009)

  • (with G. W. Milton, N.-A. P. Nicorovici, R. C. McPhedran and Z. Jacob) Open Access: Solutions in folded geometries and associated cloaking due to anomalous resonance. New Journal of Physics 10(11), 115021 (2008)

  • (with S. Guenneau) Bloch-wave homogenisation for spectral asymptotic analysis of the periodic Maxwell operator. Waves in Random and Complex Media 17, 627--651 (2007)

  • Asymptotic expansion of the boundary-layer type for flexural waves along the curved edge of a Kirchhoff-Love plate. Zapiski Nauchnykh Seminarov POMI, 332, 286--298 (2006), in Russian. English version in: J. Math. Sci. (N. Y.) 142 (6), 2682--2688 (2007).

  • Two-scale asymptotics for non-local effects in composites with highly anisotropic fibres. Asymptotic analysis, 49, 39--59 (2006) .

  • Open Access: On propagation of attenuated Rayleigh waves along a fluid-solid interface of arbitrary shape. The Quarterly Journal of Mechanics and Applied Mathematics 59, 75--94 (2006).

  • (with V. P. Smyshlyaev and V. V. Zhikov) Non-local homogenised limits for composite media with highly anisotropic periodic fibres. Proceedings of the Royal Society of Edinburgh: Section A 136(1), 87--114 (2006).

  • On propagation of Scholte-Gogoladze surface waves along a fluid-solid interface of arbitrary shape. Zapiski Nauchnykh Seminarov POMI 324, 229--247 (2005), in Russian. English version in: J. Math. Sci. (N. Y.), 138(2), 5613--5622 (2006).

  • (with P. Padilla) On derivation of the density of states for periodic operators by the method of asymptotic expansion. Proceedings of the Edinburgh Mathematical Society 48(1), 51-60 (2005).

  • (with V. P. Smyshlyaev) On full two-scale expansion of the solutions of nonlinear periodic rapidly oscillating problems and higher-order homogenised variational problems. Archive for Rational Mechanics and Analysis 174(3), 385--442 (2004).

  • (with V. M. Babich) On a differential equation with a singular point of regular type and a large parameter. Integral Transforms and Special Functions 11(2), 101--112 (2001).

  • (with V. P. Smyshlyaev) On rigorous derivation of strain gradient effects in the overall behaviour of periodic heterogeneous media. Journal of the Mechanics and Physics of Solids 48(6--7), 1325-1357 (2000).

  • (with V. M. Babich) On Fock's type asymptotics of Legendre functions. Integral Transforms and Special Functions 5(1--2), 1--18 (1997).

    Submitted papers:

  • (with M. Cherdantsev and S. Neukamm) Homogenisation in finite elasticity for composites with a high contrast in the vicinity of rigid-body motions.

  • (with J. Evans) Full two-scale asymptotic expansion and higher-order constitutive laws in the homogenisation of the system of Maxwell equations.

  • (with S. Cooper) Asymptotic behaviour of the spectra of systems of Maxwell equations in periodic composite media with high contrast.

  • (with J. Evans) Homogenisation of thin periodic frameworks with high-contrast inclusions.

    Papers in preparation:

  • Two-scale series expansions for travelling wave packets in one-dimensional periodic media.

  • Space-time ray expansions for linearised conservation laws near a curved phase boundary.

  • (with L. Silva and A. Kiselev) Functional model for extensions of symmetric operators and applications to scattering theory.

  • (with K. Matthies) Exponential homogenisation for nonlinear elliptic problems.

  • (with S. Cooper) ``High-frequency homogenisation'': a rigorous framework for two-scale behaviour of generalised eigenfunctions.

  • (with M. Cherdantsev and S. Cooper) The spectrum of one dimensional problems high-contrast problems with a defect.


    Employer: Department of Mathematical Sciences, University of Bath
    Job Title: Reader in Mathematics
    Telephone: +44 1225 38 6891

    E-mail Address: K.Cherednichenko (at) bath.ac.uk

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


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