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A comparison between two-scale asymptotic expansions and Bloch wave expansions for the homogenization of periodic structures

Grégoire Allaire , Marc Briane , Muthusamy Vanninathan
SeMA Journal: Boletin de la Sociedad Española de Matemática Aplicada, 2016, 73 (3), pp.237-259. ⟨10.1007/s40324-016-0067-z⟩
Article dans une revue hal-01215580v2
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A new div-curl result. Applications to the homogenization of elliptic systems and to the weak continuity of the Jacobian

Marc Briane , Juan Casado-Diaz
Journal of Differential Equations, 2016, 260 (7), pp.5678-5725. ⟨10.1016/j.jde.2015.12.029⟩
Article dans une revue hal-01101745v1
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Reconstruction of isotropic conductivities from non smooth electric fields

Marc Briane
ESAIM: Mathematical Modelling and Numerical Analysis, 2018, 52 (18), pp.1173-1193. ⟨10.1051/m2an/2018013⟩
Article dans une revue hal-01705977v1
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First Bloch eigenvalue in high contrast media

Marc Briane , Muthusamy Vanninathan
Journal of Mathematical Physics, 2014, 55 (1), pp.1-15. ⟨10.1063/1.4859195⟩
Article dans une revue hal-00828333v1

New bounds on strong field magneto-transport in multiphase columnar composites

Marc Briane , Graeme W. Milton
SIAM Journal on Applied Mathematics, 2010, 70 (8), pp.3272-3286. ⟨10.1137/100798090⟩
Article dans une revue hal-00560455v1
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Isotropic realizability of fields and reconstruction of invariant measures under positivity properties. Asymptotics of the flow by a non-ergodic approach

Marc Briane
SIAM Journal on Applied Dynamical Systems, 2019, 18 (4), pp.1846-1866. ⟨10.1137/19M1240411⟩
Article dans une revue hal-01982014v1
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Bounds on strong field magneto-transport in three-dimensional composites

Marc Briane , Graeme W. Milton
Journal of Mathematical Physics, 2011, 52 (10), 18 p. ⟨10.1063/1.3644377⟩
Article dans une revue hal-00591081v1
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Isotropic realizability of a strain field for the two-dimensional incompressible elasticity system

Marc Briane
Inverse Problems, 2016, 32 (6), ⟨10.1088/0266-5611/32/6/065002⟩
Article dans une revue hal-01200804v1
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Specific properties of the ODE's flow in dimension two versus dimension three

Marc Briane , Loïc Hervé
Journal of Dynamics and Differential Equations, 2024, 36 (1), pp.421-461. ⟨10.1007/s10884-022-10154-1⟩
Article dans une revue hal-03412162v1

Expansion formulae for the homogenized determinant of anisotropic checkerboards

Marc Briane , Yves Capdeboscq
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2006, 462 (2073), pp.2759-2779. ⟨10.1098/rspa.2006.1690⟩
Article dans une revue hal-00447685v1

Homogenization of convex functionals which are weakly coercive and not equi-bounded from above

Marc Briane , Juan Casado-Diaz
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2013, 30 (4), pp.547-571. ⟨10.1016/j.anihpc.2012.10.005⟩
Article dans une revue hal-00878452v1

Towards a complete characterization of the effective elasticity tensors of mixtures of an elastic phase and an almost rigid phase

Graeme W. Milton , Davit Harutyunyan , Marc Briane
Mathematics and Mechanics of Complex Systems, 2017, 5 (1), pp.95-113. ⟨10.2140/memocs.2017.5.95⟩
Article dans une revue hal-01355783v1
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Homogenization of systems with equi-integrable coefficients

Marc Briane , Juan Casado-Diaz
ESAIM: Control, Optimisation and Calculus of Variations, 2014, 20 (4), pp.1214-1223. ⟨10.1051/cocv/2014013⟩
Article dans une revue hal-01102183v1
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Fine asymptotic expansion of the ODE's flow

Marc Briane , Loïc Hervé
Journal of Differential Equations, 2023, 373, pp.327 - 358. ⟨10.1016/j.jde.2023.07.013⟩
Article dans une revue hal-03923357v3
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Around the asymptotic properties of a two-dimensional parametrized Euler flow

Marc Briane
Discrete and Continuous Dynamical Systems - Series A, 2024, 44 (7), pp.1864-1877. ⟨10.3934/dcds.2024012⟩
Article dans une revue hal-04285793v1
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Homogenization of the two-dimensional Hall effect

Marc Briane , David Manceau , Graeme W. Milton
Journal of Mathematical Analysis and Applications, 2008, 339 (2), pp.1468 - 1484. ⟨10.1016/j.jmaa.2007.07.044⟩
Article dans une revue istex hal-00372692v2

Reversal of the Hall coefficient sign under homogenization

Marc Briane , Graeme Milton
Sixth International Congress on Industrial Applied Mathematics (IVIAM07) and GAMM annual meeting, Jul 2007, Zürich, Switzerland. pp.1050603 - 1050604, ⟨10.1002/pamm.200700493⟩
Communication dans un congrès hal-01543724v1
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Asymptotics of ODE's flows everywhere or almost-everywhere in the torus:from rotation sets to homogenization of transport equations

Marc Briane , Loïc Hervé
Journal of Differential Equations, 2021, 304, pp.165 - 190. ⟨10.1016/j.jde.2021.09.035⟩
Article dans une revue hal-03117545v1
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Homogenization of linear transport equations. A new approach

Marc Briane
Journal de l'École polytechnique — Mathématiques, 2020, Tome 7, p. 479-495. ⟨10.5802/jep.122⟩
Article dans une revue hal-02134511v2
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Two-dimensional Jacobians det and Det for bounded variation functions. Application

Marc Briane , Juan Casado-Díaz
2023
Pré-publication, Document de travail hal-04182568v1

Loss of ellipticity through homogenization in linear elasticity

Marc Briane , Gilles A. Francfort
Mathematical Models and Methods in Applied Sciences, 2015, 25 (5), pp.905-928. ⟨10.1142/S0218202515500220⟩
Article dans une revue hal-01102201v1

Théorie de l'intégration. Cours et exercices. Licence et master de mathématiques. 3è édition

Gilles Pagès , Marc Briane
Vuibert, pp.332, 2004
Ouvrages hal-00104953v1
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Which electric fields are realizable in conducting materials?

Marc Briane , Graeme W. Milton , Andrejs Treibergs
ESAIM: Mathematical Modelling and Numerical Analysis, 2014, 48 (2), pp.307-323. ⟨10.1051/m2an/2013109⟩
Article dans une revue hal-00771274v1
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Estimate of the pressure when its gradient is the divergence of a measure. Applications

Marc Briane , Juan Casado-Diaz
ESAIM: Control, Optimisation and Calculus of Variations, 2011, 17 (4), pp.1066-1087. ⟨10.1051/cocv/2010037⟩
Article dans une revue hal-00567605v1
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Magneto-resistance in three-dimensional composites.

Marc Briane , Laurent Pater
Asymptotic Analysis, 2014, 86 (3-4), pp.165-197. ⟨10.3233/ASY-131192⟩
Article dans une revue hal-00713779v1
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Some classes of singular ODEs flows

Marc Briane
2024
Pré-publication, Document de travail hal-04466222v2

Duality results in the homogenization of two-dimensional high-contrast conductivities

Marc Briane , David Manceau
Networks and Heterogeneous Media, 2008, 3 (3), pp.509-522
Article dans une revue hal-00360041v1
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Nonlocal effects in two-dimensional conductivity

Marc Briane
Archive for Rational Mechanics and Analysis, 2006, 182 (2), pp.255-267. ⟨10.1007/s00205-006-0427-4⟩
Article dans une revue hal-00447664v1

On cloaking for elasticity and physical equations with a transformation invariant form

Graeme W. Milton , Marc Briane , John R. Willis
New Journal of Physics, 2006, 8 (248), 19 p. ⟨10.1088/1367-2630/8/10/248⟩
Article dans une revue hal-00452194v1
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An optimal condition of compactness for elasticity problems involving one directional reinforcement

Marc Briane , Mohamed Camar-Eddine
Journal of Elasticity, 2012, 107 (1), pp.11-38. ⟨10.1007/s10659-011-9334-5⟩
Article dans une revue hal-00497567v1