Home
Research
Publications and
Preprints
Cours
ERC
QUANTHOM






New:
 Linear waves in disordered media
 (with A. Benoit) Longtime homogenization and asymptotic ballistic transport of classical waves
(preprint), Ann. Scientifiques de l'ENS.
 (with M. Duerinckx and C. Shirley) Approximate FloquetBloch theory for
linear waves in disordered media, in preparation.
 Homogenization and linear elasticity
 (with M. Ruf) Loss of strong ellipticity through homogenization in 2D linear elasticity: A phase diagram
(preprint), Arch. Ration. Mech. Anal.
 Quantitative theory of stochastic homogenization for uncorrelated and correlated coefficient fields: weighted functional inequalities, largescale regularity, quantitative estimates (optimal scalings and nearlyoptimal stochastic integrability), and theory of fluctuations
 (with M. Duerinckx) Weighted functional inequalities: Concentration properties
(preprint).
 (with M. Duerinckx) Weighted functional inequalities: Constructive approach
(preprint).
 (with M. Duerinckx) Weighted secondorder Poincaré inequalities: Application to RSA models
(preprint).
 (with S. Neukamm and F. Otto) A regularity theory for random
elliptic operators (preprint).
 (with S. Neukamm and F. Otto) Quantitative stochastic homogenization for correlated coefficient fields (preprint).
 (with M. Duerinckx and F. Otto) The structure of fluctuations in stochastic homogenization (preprint).
 (with M. Duerinckx and F. Otto) Robustness of the pathwise structure of fluctuations in stochastic homogenization, in preparation.
 (with M. Duerinckx and J. Fischer) Scaling limit of the homogenization commutator
for correlated Gaussian coefficient fields, in preparation.
 (with F. Otto) The corrector in stochastic homogenization: optimal rates, stochastic integrability, and fluctuations (preprint).
Publications:
Qualitative homogenization of discrete elliptic equations and applications
 (with A. Braides) Exact Bounds on the Effective Behavior of a Conducting Discrete
Polycrystal, SIAM MMS, 6 (2008), No. 4, pp 11981216 (pdf).
 (with R. Alicandro and M. Cicalese) Variational description of bulk energies for
bounded and unbounded spin systems, Nonlinearity, 21 (2008), pp 18811910 (pdf).
 (with R. Alicandro and M. Cicalese) Mathematical derivation of a rubberlike stored energy functional, C. R. Acad. Sci. Paris, Série I, 345 (2007), No. 8, pp 479482 (pdf).
 (with R. Alicandro and M. Cicalese) Convergence analysis of the BolReese model for rubber, Proceedings of CMDS 11, Presse des Mines de Paris, 2008, pp 137142 (pdf).
 (with R. Alicandro and M. Cicalese) Integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity, Arch. Ration. Mech. Anal., 200 (2011), No 3, pp 881943 (pdf).
Quantitative stochastic homogenization of discrete elliptic equations
 (with F. Otto) An optimal variance estimate in stochastic homogenization of discrete elliptic equations, Ann. of Probab., 39 (2011), No 3, pp 779856 (pdf).
 (with F. Otto) An optimal error estimate in stochastic homogenization of discrete elliptic equations, Ann. Appl. Probab., 22 (2012), No 1, pp 128 (pdf).
 (with J.C. Mourrat) Spectral measure and approximation of
homogenized coefficients, Probab. Theory Related Fields, 154 (2012),
No. 1, pp 287326, (pdf).
 (with J.C. Mourrat) Quantitative version of the KipnisVaradhan
theorem and MonteCarlo approximation of homogenized coefficients,
Ann. Appl. Probab., 23 (2013), No. 4, pp 15441583 (pdf).
 (with S. Neukamm and F. Otto) Quantification of ergodicity in
stochastic homogenization: optimal bounds via spectral gap on Glauber
dynamics, Inventiones Mathematicae, 199 (2015), No. 2, pp 455515 (long
version,
short
version).
 (with S. Neukamm and F. Otto) A quantitative twoscale expansion
in stochastic homogenization of discrete linear elliptic equations,
M2AN Modél. Math. Anal. Numér, special issue 2014:
Multiscale problems and techniques (pdf).
 (with J. Nolen) A quantitative central limit theorem for the
effective conductance on the discrete torus, Commun. Pure and Appl. Math. (pdf)
 (with M. Duerinckx and F. Otto) The structure of fluctuations in stochastic homogenization (pdf).
Qualitative homogenization of
elliptic PDEs and integral functionals
 Stochastic diffeomorphisms and homogenization of multiple integrals, AMRX, Vol. 2008, Article ID abn001 (pdf).
 (with M. Barchiesi) New counterexamples to the cell formula in nonconvex homogenization, Arch. Ration. Mech. Anal., 195 (2010), No 3, pp 9911024 (pdf).
 (with S. Neukamm) Commutability of homogenization and linearization at identity in finite elasticity and applications, Ann. Inst. H. Poincaré Anal. Non Linéaire,
28 (2011), No 6, pp 941964 (pdf).
 (with M. Duerinckx) Analyticity of homogenized coefficients
under Bernoulli perturbations and the ClausiusMossotti
formulas, Arch. Ration. Mech. Anal. (pdf).
 (with M. Duerinckx) Stochastic homogenization of nonconvex
unbounded integral functionals with convex growth, Arch. Ration. Mech. Anal. (pdf).
 (with G. A. Francfort) Isotropy prohibits the loss of strong ellipticity through homogenization in linear elasticity
(pdf), CRAS.
Quantitative stochastic
homogenization of elliptic PDEs
 Fluctuation of solutions to linear elliptic equations with noisy
diffusion coefficients, Comm. Partial Differential Equations,
38 (2013), No 2, pp 304338 (pdf).
 (with F. Otto) Quantitative estimates on the periodic
approximation of the corrector in stochastic
homogenization,
Esaim Proc (pdf).
 (with F. Otto) Quantitative results on the corrector equation in
stochastic homogenization, J. Eur. Math. Soc. (pdf).
 (with D. Marahrens) Annealed estimates on the Green functions and
uncertainty quantification,
Ann. Inst. H. Poincaré Anal. Non Linéaire (pdf).
 (with S. Armstrong and T. Kuusi) Bounded correctors in almost periodic homogenization, Arch. Ration. Mech. Anal. (pdf).
Numerical analysis for homogenization problems
 A direct approach to numerical homogenization in nonlinear elasticity, NHM, 1 (2006), No.1, pp 109141 (pdf).
 Analytical framework for the numerical homogenization of elliptic monotone operators and quasiconvex energies, SIAM MMS, 5 (2006), No. 3, pp 9961043 (pdf).
 Analytical framework for numerical homogenization. Part 2: Windowing and oversampling, SIAM MMS, 7 (2008), No. 1, pp 274293 (pdf).
 Reduction of the resonance error. Part 1: Approximation of homogenized coefficients, Math. Models Methods Appl. Sci. (M3AS), 21 (2011), No. 3, pp 16011630 (abstract, pdf).
 Numerical approximation of effective coefficients in stochastic homogenization of discrete elliptic
equations, M2AN Modél. Math. Anal. Numér, 46 (2012), No. 1, pp 138 (pdf).
 (with T. Goudon and S. Krell) Numerical homogenization of a nonlinearly coupled ellipticparabolic system, reduced basis method, and
application to nuclear waste storage, Math. Models Methods
Appl. Sci. (M3AS), 23 (2013), No. 13, pp 25232560 (pdf).
 Numerical homogenization: survey, new results, and perspectives, ESAIM: Proc.
Volume 37, September 2012, Mathematical and numerical approaches for
multiscale problem (pdf).
 (with A.C. Egloffe, J.C. Mourrat, and T. N. Nguyen) Random walk in random environment, corrector equation, and homogenized
coefficients: from theory to numerics, back and forth,
IMA J. Num. Anal. (pdf).
 (with Z. Habibi) Reduction of the resonance error in numerical
homogenization II: correctors and extrapolation, Foundations of Computational Mathematics (pdf).
Multiscale modelling in rubber elasticity
 (with P. Le Tallec and M. Vidrascu) Foundation, analysis, and
numerical investigation of a variational networkbased model
for rubber, Cont. Mech. Thermodynamics, 26 (2014), No 1, pp 131 (pdf).
 (with M. de Buhan, P. Le Tallec, and M. Vidrascu) Reconstruction of a constitutive law for rubber from in silico experiments
using Ogden's laws, Int. Journal of Solids and Structures, 62 (2015), pp 158–173 (pdf).
Stochastic geometry and applications
 (with M. D. Penrose) Random parking, Euclidean functionals, and
rubber elasticity, Commun. Math. Phys., 321 (2013), No. 1, pp 131 (pdf).
 When are incrementstationary random point sets
stationary?, Electron. Commun. Probab. 19 (2014), no. 30, 1–14 (pdf).
Numerical analysis for hyperbolic problems
 (with J.F. Coulombel) Semigroup stability of finite difference schemes for
multidimensional hyperbolic initial boundary value problems (pdf), Math. Comp., 80 (2011), pp 165203.
Fluidstructure interaction problems
 (with M.A. Fernandez, J.F. Gerbeau and M. Vidrascu) Domain decomposition based Newton methods for fluidstructure interaction problems, ESAIM: Proceedings, special volume CANUM 2006, 22 (2007), pp 6782 (pdf)
 (with M.A. Fernandez, J.F. Gerbeau and M. Vidrascu) A partitioned Newton method for the interaction of a fluid and a 3D shell structure (pdf), Eur. J. Comp. Mech., 19 (2010), 57, pp.479512
