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 on 17 July by James Roberts.
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
Luke Young (University of Bath, 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 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
Collaborators
Patrick Dondl (Universität Freiburg), Alexander Kiselev (Kyiv), Karsten Matthies (Bath), Stefan Neukamm (TU Dresden), Luis Silva (IIMAS-UNAM, Mexico) Igor Velčić (Zagreb)
Publications
Journal articles:
(with M. Cherdantsev and S. Neukamm) Homogenisation in finite elasticity for composites with a high contrast in the vicinity of rigid-body motions. To appear in Asymptotic Analysis (2017)
(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 349, 441--480 (2017); DOI: 10.1007/s00220-016-2698-4
(with J. Evans) Open Access: Full two-scale asymptotic expansion and higher-order constitutive laws in the homogenisation of the system of Maxwell equations. Multiscale Modeling and Simulation (SIAM) 14(4), 1513--1539 (2016); DOI:10.1137/15M1042103
(with S. Cooper) Open Access: Resolvent estimates for high-contrast homogenisation problems. Archive for Rational Mechanics and Analysis 219(3), 1061--1086 (2016); DOI: 10.1007/s00205-015-0916-4
(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: 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 (SIAM) 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. Waurick) Resolvent estimates in homogenisation of periodic problems of fractional elasticity.
(with A. V. Kiselev and L. O. Silva) Functional model for extensions of symmetric operators and applications to scattering theory.
(with M. Cherdantsev and S. Cooper) Extreme localisation of eigenfunctions to one-dimensional high-contrast periodic problems with a defect.
(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 P. Dondl and F. Rösler) Norm-resolvent convergence in perforated domains
(with Y. Ershova and A. Kiselev) Derivation of quantum graph models with generalised vertex conditions via periodic homogenisation
(with S. Cooper and J. Roberts) Surface waves in stratified piezoeelctric media.
(with S. Cooper) Operator-norm resolvent convergence estimates for a system of high-contrast Maxwell equations.
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 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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BUC7: 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
