(with M. Waurick) Resolvent estimates in homogenisation of periodic problems of fractional elasticity. To appear in Journal of Differential Equations.
(with A. V. Kiselev and L. O. Silva) Functional model for extensions of symmetric operators and applications to scattering theory. To appear in Networks and Heterogeneous Media.
(with S. Cooper) Asymptotic behaviour of the spectra of systems of Maxwell equations in periodic composite media with high contrast. To appear
(with M. Cherdantsev and S. Neukamm) Open Access: High contrast homogenisation in nonlinear elasticity under small loads Asymptotic Analysis 104(1--2), 67--102 (2017); DOI: 10.3233/ASY-171430
(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) Open Access: 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 waves 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 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),
(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).