(with M. Cherdantsev and S. Cooper) Extreme localisation of eigenfunctions to one-dimensional high-contrast periodic problems with a defect. To appear in SIAM Journal on Mathematical Analysis.
(with A. V. Kiselev and L. O. Silva) Scattering theory for non-selfadjoint extensions of symmetric operators. To appear in Operator Theory: Advances and Applications ("Analysis as a Tool in mathematical Physics: in Memory of Boris Pavlov").
(with M.Cherdantsev and I. Velčić) Stochastic homogenisation of high-contrast media. To appear in Applicable Analysis.
(with P. Dondl and F. Rösler) Norm-resolvent convergence in perforated domains. To appear in Asymptotic Analysis.
(with S. D'Onofrio) Operator-norm convergence estimates for elliptic homogenisation problems on periodic singular structures. Journal of Mathematical Sciences 232(4), 558--572 (2018)
(with M. Waurick) Open Access: Resolvent estimates in homogenisation of periodic problems of fractional elasticity. Journal of Differential Equations 264(6), 3811--3835 (2018)
(with A. V. Kiselev and L. O. Silva) Open Access: Functional model for extensions of symmetric operators and applications to scattering theory. Networks and Heterogeneous Media 13(2), 191--215 (2018)
(with S. Cooper) Open Access: Asymptotic behaviour of the spectra of systems of Maxwell equations in periodic composite media with high contrast. Mathematika 64(2), 583--605 (2018)
(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).