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 session of the seminar is on 9 January. In the meantime, please note the workshop "Partially ordered materials", where I speak on an extreme localisation property for eigenfunctions of one-dimensional high-contrast periodic problems with a defect, my joint work with Mikhail Cherdantsev and Shane Cooper.

    Seminar programme


    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)      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


    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

    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


    Former PhD student

    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


    Publications

    Journal articles:

  • (with J. Evans) Full two-scale asymptotic expansion and higher-order constitutive laws in the homogenisation of the system of Maxwell equations. To appear in Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 26 pp, (2016)

  • (with A. Kiselev) Open Access: Norm-resolvent convergence of one-dimensional high-contrast periodic problems to a Kronig-Penney dipole-type model. Communications in Mathematical Physics, DOI: 10.1007/s00220-016-2698-4 (2016)

  • (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 471: 20140878 (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 219(3), 1061--1086 (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 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.

  • (with S. Cooper) Operator-norm resolvent convergence estimates for a system of high-contrast Maxwell equations.

  • (with S. Cooper and M. Waurick) Resolvent estimates in homogenisation of fractional elasticity.

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

  • (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.

  • (with S. Cooper and W. Graham) Surface waves in stratified electromagnetic media.

    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       Conference "Operators, Operator Families and Asymptotics"