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 poster: larger version
The conference is supported by London Mathematical Society, University of Bath, EPSRC, and Bath Institute for Mathematical Innovation (BIMI)
- Yves Capdeboscq (University of Oxford, UK)
"Small volume asymptotics for Maxwell's equations"
- Giuseppe Cardone (University of Sannio, Italy)
"Boundary perturbations of planar waveguides: oscillating boundary, windows, non-periodic perforations''
- Maxence Cassier (University of Utah, USA)
"On the spectral theory and limiting amplitude principle for a transmission problem between a dielectric and a metamaterial''
- Tanya Christiansen (University of Missouri, USA) "Sharp lower bounds on a resonance counting function in even-dimensional Euclidean scattering"
- Shane Cooper (University of Bath, UK) "Asymptotic analysis of stratified elastic media in the space of functions with bounded deformation"
- Pavel Exner (Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Academy of Sciences) "Singular Schrödinger operators and Robin billiards: geometry, spectra and asymptotic expansions"
- Rostyslav Hryniv (University of Rzeszów, Poland, and Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine) "Schrödinger operators with δ'-like potentials"
- Andrii Khrabustovskyi (Karlsruhe Institute of Technology, Germany)"On the spectrum of a class of periodic quantum graphs"
- Alexander Kiselev (National Pedagogical Dragomanov University, Ukraine) "On the connections between the spectral theory of quantum graphs and homogenisation problems in low-dimensional structures"
- David Krejcirik (Nuclear Physics Institute, Czech Academy of Sciences) "Non-self-adjoint graphs"
- Stefan Neukamm (TU Dresden, Germany)
"Stochastic homogenization: An estimate for the two-scale expansion for correlated coefficients"
- Zhongwei Shen (University of Kentucky, USA) "Boundary regularity estimates in periodic homogenization"\li>
- Jari Taskinen (University of Helsinki, Finland) "Spectral gaps for elastic and piezoelectric waveguides"\li>
- Tatiana Suslina (St. Petersburg State University, Russia)
"Spectral approach to homogenization of non stationary Schrödinger-type
- Ricardo Weder (IIMAS-UNAM, Mexico) "Limiting absorption principle for singular solutions to Maxwell equations and plasma
- Aaron Welters (Florida Institute of Technology, USA) "Analyticity of the Dirichlet-to-Neumann map for Maxwell's equations in passive composite media"
- Ian Wood (University of Kent, UK) "Spectral information contained in abstract M-functions''
Kirill Cherednichenko (Bath), Fritz Gesztesy (Missouri), Peter Kuchment (Texas A&M), Marco Marletta (Cardiff), Graeme Milton (Utah), Leonid Parnovsky (UCL)
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)
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
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)
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
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)
(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.
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) .
On propagation of attenuated Rayleigh
along a fluid-solid interface of arbitrary shape. The
Quarterly Journal of Mechanics and Applied Mathematics 59,
(with V. P. Smyshlyaev and V. V. Zhikov) Non-local
homogenised limits for composite media with highly anisotropic periodic
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.
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
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),
(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).
(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
Department of Mathematical Sciences
University of Bath
Bath, BA2 7AY
Google Scholar Back to Academic Profile
LMS-Bath-WIMCS Analysis Day: 4 December 2015