In the context of the construction of the European landscape of research, Inria and ULB (Université Libre de Bruxelles) signed in 2013 an agreement to foster joint research teams on topics of mutual interests. The team MEPHYSTO, a joint project of Inria, the Université Lille 1 and CNRS, and the Université Libre de Bruxelles, is the first such collaboration, in applied mathematics. It operates in two locations: Lille and Brussels.
The main objective of the team is to develop mathematical and numerical tools to study in a quantitative way some specific physical models which display random and/or multiscale features. The emphasis is put on the interplay between analysis, probability, and numerics.
We focus our efforts on two prototypical examples: stochastic homogenization and the Schrödinger equations.
Whereas many models in physics involve randomness, they behave deterministically in suitable asymptotic regimes when stochastic effects average out. The qualitative and quantitative understanding of this deterministic behavior is the main challenge of this project.
From a mathematical point of view, our main fields of interest are stochastic homogenization of PDEs and random or deterministic one-dimensional nonlinear Schrödinger equations. These topics involve two challenges identified in the strategic plan of Inria “Objectif 2020": randomness and multiscale modeling.
From a physical point of view, the problems we shall consider find their origin in
the statistical physics of random polymer-chain networks;
light propagation in optical fibers.
Stochastic homogenization
Homogenization is a theory which deals with oscillations in PDEs.
Let
for some suitable r. h. s.
The homogenized coefficients
In the periodic case, these correctors are well-behaved by standard PDE theory.
The convergence of
One of our initial motivations to develop a quantitative stochastic homogenization theory
is the derivation of nonlinear elasticity from polymer physics, which is presented in the research program and application section.
We plan to develop a complete quantitative theory of stochastic homogenization of elliptic equations.
In particular we aim at quantifying how well
Schrödinger equations
The linear Schrödinger equation, with an appropriate choice of geometry and boundary conditions, has been central to the description of all non-relativistic quantum mechanical systems for almost a century now. In addition, its nonlinear variant arises in the mean field description of Bose-Einstein condensates, where it is known as the Gross-Pitaevskii equation, but also in nonlinear classical optics, and in particular in fiber optics. The quantitative and qualitative description of its solutions (for both the evolution and the stationary equations), their time-asymptotic behavior, their stability or instability in terms of the parameters of the initial conditions and/or the potentials and boundary conditions continue to pose numerous physical and mathematical problems (see and for general references).
In view of our collaboration with the Lille laser physics laboratory PhLAM, we will focus more particularly on the one-dimensional nonlinear Schrödinger equation (NLS). Indeed, (NLS) drives the envelope of the propagation of a laser pulse in a Kerr medium, such as an optical fiber . Many phenomena on (NLS) (and variants thereof, with higher order derivatives, various types of initial conditions, external fields, etc.) are put in evidence by physical experiments at PhLAM, are not fully understood, and raise exciting questions from the numerical and analytical perspectives.
The same type of equation also describes Bose-Einstein condensates, for which questions related to Anderson localization are also of interest theoretically and experimentally at PhLAM.
Whereas numerical methods in nonlinear elasticity are well-developed and reliable, constitutive laws used for rubber in practice are phenomenological and generally not very precise. On the contrary, at the scale of the polymer-chain network, the physics of rubber is very precisely described by statistical physics. The main challenge in this field is to understand how to derive macroscopic constitutive laws for rubber-like materials from statistical physics.
At the continuum level, rubber is modelled by an energy
Our aim is to relate qualitatively and quantitatively the (precise but unpractical) statistical physics picture to explicit macroscopic constitutive laws that can be used for practical purposes.
In collaboration with R. Alicandro (Univ. Cassino, Italy) and M. Cicalese (Univ. Munich, Germany), A. Gloria analyzed in
the (asymptotic)
These preliminary results show that the variational model has the potential to explain qualitatively and quantitatively how rubber elasticity emerges from polymer physics. In order to go further and obtain more quantitative results and rigorously justify the model, we have to address several questions of analysis, modelling, scientific computing, inverse problems, and physics.
Whereas the approximation of homogenized coefficients is an easy task in periodic homogenization, this is a highly nontrivial task for stochastic coefficients. This is in order to analyze numerical approximation methods of the homogenized coefficients that F. Otto (MPI for mathematics in the sciences, Leipzig, Germany) and A. Gloria obtained the first quantitative results in stochastic homogenization . The development of a complete stochastic homogenization theory seems to be ripe for the analysis and constitutes the second major objective of this section.
In order to develop a quantitative theory of stochastic homogenization, one needs to quantitatively understand the corrector equation ().
Provided
They also proved that the variance of spatial averages of the energy density
The proof of these results, which is inspired by , is based on the insight that coefficients such as the Poisson random inclusions are special in the sense that the associated probability measure satisfies a spectral gap estimate. Combined with elliptic regularity theory, this spectral gap estimate quantifies ergodicity in stochastic homogenization. This systematic use of tools from statistical physics has opened the way to the quantitative study of stochastic homogenization problems, which we plan to fully develop.
As well known, the (non)linear Schrödinger equation
with coupling constants
When in the equation () above one sets
where
If
If now
In the course of developing a quantitative theory of stochastic homogenization of discrete elliptic equations, we have introduced new tools to quantify ergodicity in partial differential equations. These tools are however not limited to PDEs, and could also have an impact in other fields where an evolution takes place in a (possibly dynamic) random environment and an averaging process occurs. The goal is then to understand the asymptotics of the motion of the particle/process.
For a random walker in a random environment, the Kipnis-Varadhan theorem ensures that the expected squared-position of the random walker after time
Similar questions arise when the medium is reactive (that is, when the potential is modified by the particle itself). The approach to equilibrium in such systems was observed numerically and explained theoretically, but not completely proven, in .
The mechanics of heterogeneous materials aims at characterizing the macroscopic properties of heterogeneous materials using the properties of their constituents.
The homogenization theory is a natural tool for this task. In particular, for linear problems (linear conductivity or linear elasticity), the macroscopic properties are encoded into a single (conductivity or elasticity) homogenized tensor. The numerical approximation of this homogenized tensor is a typical objective of quantitative homogenization.
For nonlinear problems, such as rubber elasticity, the macroscopic properties are no longer characterized by a single tensor, but rather by a nonlinear energy density. Our aim is to relate qualitatively and quantitatively the (precise but unpractical) statistical physics picture to explicit macroscopic constitutive laws that can be used for practical purposes. This endeavor is relevant both in science and technology. The rigorous derivation of rubber elasticity from polymer-physics was indeed emphasized by John Ball as an important open problem of nonlinear elasticity in his survey on the field. Its solution could shed light on some aspects of polymer-physics. The associated ab initio derivation of constitutive laws (as an alternative to phenomenological laws) would also be of interest to computational mechanics and rubber industry.
For this application domain, we work in close collaboration with physicists (François Lequeux, ESPCI) and researchers from mechanics and computational mechanics (Patrick Le Tallec, Ecole polytechnique).
Solving numerically PDEs in highly heterogeneous media is a problem encountered in many situations, such as the transport of pollutants or the design of oil extraction strategies in geological undergrounds. When such problems are discretized by standard numerical methods the number of degrees of freedom may become prohibitive in practice, whence the need for other strategies.
Numerical solution methods inspired by asymptotic analysis are among the very few feasible alternatives, and started fifteen years ago with the contributions of Hou and Wu , Arbogast etc. We refer to , , for a recent state of the art. Numerical homogenization methods usually amount to looking for the solution of the problem () in the form
Relying on our quantitative insight in stochastic homogenization, a first task consists in addressing the three following prototypical academic examples: periodic, quasi-periodic, and stationary ergodic coefficients with short range dependence. The more ambitious challenge is to address more complex coefficients (of interest to practioners), and design adaptive and efficient algorithms for diffusion in heterogeneous media.
Our contribution to the analysis of models in laser physics is motivated by the LabEx CEMPI (Centre Européen pour les Mathématiques, la Physique et leurs Interactions, a large eight-year research and training project approved by the French government in February 2012 as a "Laboratoire d'Excellence" and an initiative of mathematicians and physicists of the Université Lille 1). For this application domain, we work in close collaboration with physicists, which ensures our direct impact on these scientific issues. We focus on two applications: optical fibers and cold atoms.
In collaboration with physicists from the PhLAM laboratory in Lille, we aim at developing new techniques for the numerical integration of a family of 1D Schrödinger-like equations modelling the propagation of laser pulses in optical fibers. The questions arising are challenging since physicists would like to have fairly fast and cheap methods for their problems, with correct qualitative and quantitative behaviors. Another point is that they are interested in methods and codes that are able to handle different physical situations, hence different terms in the NLS equation. To meet these requirements, we will have to use numerical time-integration techniques such as splitting methods or exponential Runge-Kutta methods, space discretization techniques such as finite differences and fast Fourier transforms, and absorbent boundary conditions. Our goal, together with the physicists is to be able to reproduce numerically the results of the experiments they make in actual optical fibers, and then to be able to tune parameters numerically to get more insight into the appearance of rogue waves beyond the dispersive blowup phenomenon.
Recall that the Schrödinger equation also describes Bose-Einstein condensates. A second experimental team at PhLAM projects to study questions related to Anderson localization in such condensates. In fact, they will realize the "kicked rotor" (see ), which provides a paradigm for Anderson localization, in a Bose-Einstein condensate. We plan to collaborate with them on the theoretical underpinnings of their findings, which pose many challenging questions.
Scientific results
The team obtained two striking results in 2015.
In collaboration with Felix Otto, Antoine Gloria obtained near-optimal estimates with optimal stochastic integrability in stochastic homogenization under a finite range of dependence assumption, cf. .
In collaboration with physicists at PhLAM, Stephan De Bièvre and Guillaume Dujardin, proposed in an analysis of the phenomenon of modulational instability in an optic fiber, induced by periodic modulation of the dispersion of the fiber. In particular, they characterized the frequencies at which the gain occurs and provided sharp estimates of that gain. Both numerical and physical experiments supported the analysis, cf. Figure which displays the experimental gain (above) and the numerical gain (below).
Awards
Antoine Gloria was awarded the Agathon De Potter prize in mathematics from the Académie royale de Belgique.
Functional Description
The numerical method to approximate the constitutive laws for rubber elasticity derived from polymer physics are implemented in the Inria software Modulef.
It is based on : - algorithms from stochastic geometry to generate suitable polymer networks, - Delaunay tessellation algorithms to deal with steric effects (courtesy of the Inria project-team GAMMA2), - the introduction of 1-dimensional finite elements for the polymer-chains in Modulef.
Participants: Marina Vidrascu and Antoine Gloria
Contact: Marina Vidrascu
A. Gloria, S. Neukamm (Univ. Dresden), and F. Otto (MPI for mathematics in the sciences, Leipzig) developed in a general approach to quantify ergodicity in stochastic homogenization of scalar discrete elliptic equations. Using a parabolic approach, they obtained optimal estimates on the time-decay of the so-called environment seen from the particle. This allowed them to prove optimal bounds on the corrector gradient and the corrector itself in any dimension (thus improving on ). They also obtained the first error analysis of the popular periodization method to approximate the homogenized coefficients.
In , A. Gloria and J. Nolen (Duke Univ.) proved a quantitative central limit theorem for the effective conductance on the discrete torus. In particular, they quantified the Wasserstein distance between a normal random variable and the CLT-like rescaling of the difference between the approximation of the effective conductance by periodization and the effective conductance. Their estimate is sharp and shows that the Wasserstein distance goes to zero (up to logarithmic factors) as if the energy density of the corrector was iid (which it is not). This completes and settles the analysis started in on the approximation of homogenized coefficients by periodization by characterizing the limiting law in addition to the scaling.
In , A. Gloria and F. Otto extended their results [4] , [5] on discrete elliptic equations to the continuum setting. They treated in addition the case of non-symmetric coefficients, and obtained optimal estimates in all dimensions by the elliptic approach (whereas , were suboptimal for
In , A. Gloria and D. Marahrens (MPI for mathematics in the sciences, Leipzig) extended the annealed results on the discrete Green function by D. Marahrens and F. Otto to the continuum setting. As a by-product of their result, they obtained new results in uncertainty quantification by estimating optimally the variance of the solution of an elliptic PDE whose coefficients are perturbed by some noise with short range of dependence.
In a revised version of , A. Gloria, S. Neukamm, and F. Otto developed a regularity theory for random elliptic operators inspired by the contributions of Avellaneda and Lin in the periodic setting and of S. Armstrong with C. Smart . This allowed them to consider coefficients with arbritarily slow decaying correlations in the form of a family of correlated Gaussian fields, and obtain (in the new version of this paper) a family of estimates with optimal rates and exponential-type integrability.
In , A. Gloria and F. Otto obtained the first nearly-optimal estimates with optimal stochastic integrability on the corrector for linear elliptic systems whose coefficients satisfy a finite range of dependence assumption (thus avoiding the functional inequalities they considered so far).
In , S. Armstrong, A. Gloria and T. Kuusi (Aalto University) obtained the first improvement over the thirty year-old result by Kozlov on almost periodic homogenization. In particular they introduced a class of almost periodic coefficients which are not quasi-periodic (and thus strictly contains the Kozlov class) and for which almost periodic correctors exist. Their approach combines the regularity theory developed by S. Armstrong and C. Smart in and adapted to the almost periodic setting by S. Armstrong and Z. Shen , a new quantification of almost-periodicity, and a sensitivity calculus in the spirit of .
In the mid-nineteenth century, Clausis, Mossotti and Maxwell essentially gave a first order Taylor expansion for (what is now understood as) the homogenized coefficients associated with a constant background medium perturbed by diluted spherical inclusions. Such an approach was recently used and extended by the team MATHERIALS to reduce the variance in numerical approximations of the homogenized coefficients, cf. , , . In , M. Duerinckx and A. Gloria gave the first rigorous proof of the Clausius-Mossotti formula and provided the theoretical background to analyze the methods introduced in .
In , M. de Buhan (CNRS, Univ. Paris Descartes), A. Gloria, P. Le Tallec and M. Vidrascu proposed a numerical method to produce analytical approximations (that can be used in practical nonlinear elasticity softwares) of the numerical approximations obtained in of the discrete-to-continuum energy density derived theoretically in . This numerical method is based on the parametrization of the set of polyconvex Ogden laws and on the combination of a least square method and a genetic algorithm (cf. CMA-ES, https://www.lri.fr/ hansen/cmaesintro.html).
In , M. Duerinckx and A. Gloria succeeded in relaxing one of the two unphysical assumptions made in on the growth of the energy of polymer chains. In particular, deals with the case when the energy of the polymer chain is allowed to blow up at finite deformation.
Inspired by the quantitative analysis of and , Z. Habibi (former SIMPAF post-doctoral fellow) and A. Gloria introduced in a general method to reduce the so-called resonance error in numerical homogenization, both at the levels of the approximation of the homogenized coefficients and of the correctors. This method significantly extends . The method relies on the introduction of a massive term in the corrector equation and of a systematic use of Richardson extrapolation. In the three academic examples of heterogeneous coefficients (periodic, quasiperiodic, and Poisson random inclusions), the method yields optimal theoretical and empirical convergence rates, and outperforms most of the other existing methods.
In , G. Dujardin and P. Lafitte (ECP) published a result on the asymptotic behavior of splitting schemes applied to multiscale systems which have strongly attracting equilibrium states. They proposed a definition of the asymptotic order of such schemes and proved on examples of ODEs and PDEs systems that one can achieve high asymptotic order with such schemes, provided sufficient conditions are fulfilled.
In , G. Dujardin proposed to use high order methods for the numerical simulation of rotating Bose-Einstein condensates. With his co-authors, he developed exponential Runge-Kutta methods and Lawson method for this problem and he analyzed the convergence order of these methods. In particular, they proved that one can achieve maximal order
In , S. De Bièvre, G. Dujardin, and S. Rota-Noradi, in collaboration with physicists of the PhLAM laboratory in Lille, developed an analysis of the phenomenon of modulational instability in dispersion-kicked optical fibers. They proposed a genuine analysis of the phenomenon, together with estimates on physical properties such as the gain along the fibers, and they showed that their analysis actually fits both numerical and physical experiments.
In , S. De Bièvre and G. Dujardin, in collaboration with physicists of the PhLAM laboratory in Lille, developed an analysis of the propagation along a periodically-modulated optic fiber of generalized Peregrine rogue waves. In particular, they provided a full analysis of the multiple compression points appearing in such waves.
In D. Bonheure and R. Nascimento obtained new results on the existence and qualitative properties of waveguides for a mixed-diffusion NLS. They provided a full qualitative description of the waveguides when the fourth order dissipation is small.
S. De Bièvre, S. Rota Nodari, and F. Genoud (CEMPI visitor, September 2013) have explained the geometry underlying the so-called energy-momentum method for proving orbital stability in infinite dimensional Hamiltonian systems. Applications include the orbital stability of solitons of the NLS and Manakov equations. This work appeared as a chapter (120p) in the first volume of the CEMPI Lecture Notes in Mathematics, cf. .
In , Bonheure, S. Cingolani and M. Nys obtained new striking results on stationary solutions of the 3D NLS driven by an exterior magnetic field. They construct a new class of cylindrical solutions in the energy class which concentrate, in the semi-classical limit, on a circle of the plane through the equator. In contrast with the case of solutions localized around a single point, the concentration is driven by the electrical field as well as the magnetic field
S. De Bièvre and E. Soret rigorously proved the growth rate of the energy in a Markovian model for stochastic acceleration of a particle in a random medium, cf. and .
S. De Bièvre, Carlos Mejia-Monasterio (Madrid) and Paul E. Parris (Missouri) studied thermal equilibration in a two-component Lorentz gas, in which the obstacles are modeled by rotating disks. They show that a mechanism of dynamical friction leads to a fluctuation-dissipation relation that is responsible for driving the system to equilibrium.
Stephan De Bièvre, JeremyFaupin (Metz) and Schuble (Metz) studied a related model quantum mechanically. Here a quantum particle moves through a field of quantized bose fields, modeling membranes that exchange energy and momentum with the particle. They establish a number of spectral properties of this model, that will be essential to study the time-asymptotic behavior of the system.
In A. Benoit proved that for linear hyperbolic systems of equations in the quarter space a violent instability can be caused by the accumulation of an arbitrary large number of weak instabilities. The proof of this result is based on the construction of the WKB expansions for hyperbolic corner problems with self-interacting phases and is a continuiation of .
In , C. Cancès, T. Gallouët, and L. Monsaingeon gave a gradient flow interpretation for incompressible immiscible two-phase flows in porous media. With C. Chainais-Hillairet, T. Gallouët characterized the pseudo-stationary state for a corrosion model in .
In , D. Bonheure, E. Moreira dos Santos, M. Ramos and H. Tavares construct least energy nodal solutions of Hamiltonian elliptic systems. The construct is tricky since the functional associated to Hamiltonian elliptic systems is strongly indefinite. The proof uses a dual variational argument and an approximation scheme with some ideas of Gama-convergence type.
In , D. Bonheure, P. D’Avenia and A. Pomponio aim to derive rigorously the PDE formulation of the Born-Infeld model in the electrostatic case. This nonlinear model of electromagnetism was introduced by Born and Infeld who proposed a new Lagrangian which theoretically assumes the existence of a maximal field intensity, likewise Einstein’s Lagragian of special relativity opposed to Newton’s Lagrangian of classical mechanics. The paper contains new results and new insights on the model. It covers several relevant particular cases but we are still far from the full understanding of the problem.
In and , D. Bonheure and coauthors study patterns and phase transitions in a fourth order extension of the famous Allen-Cahn model. In , some rigidity results à la Gibbons are proved while concerns qualitative properties of positive patterns with Navier boundary conditions. A conjecture related to De Giorgi’s famous one concerning the one dimensionality of monotone phase transition in the classical Allen Cahn model is proposed in .
In , D. Bonheure and collaborators study multi-layer solutions of the Lin-Ni-Takagi model, which comes from the Keller-Segel model of chemotaxis in a specific case. A remarkable feature of the results is that the layers do not accumulate to the boundary of the domain but satisfy an optimal partition problem contrary to the previous type of solutions constructed for this model.
In , M. Duerinckx proved a new mean-field limit result for the gradient flow evolution of particle systems with pairwise Riesz interactions, in dimensions 1 and 2, in cases for which this problem was still open. The proof is based on a method introduced by Serfaty in the context of the Ginzburg-Landau vortices, using regularity and stability properties of the limiting equation.
G. Dujardin and I. Lacroix are members of the ANR BECASIM project (http://
Title: Simulation numérique avancée pour les condensats de Bose-Einstein.
Type: Modèles Numériques - 2012
ANR reference: ANR-12-MONU-0007
Coordinator: Ionut DANAILA, Université de Rouen.
Duration: January 2013 - December 2016.
Partners: Université Lille 1, UPMC, Ecole des Ponts ParisTech, Inria-Nancy Grand-Est, Université Montpellier 2, Université Toulouse 3.
Title: Centre Européen pour les Mathématiques, la Physique et leurs interactions
Coordinator: Stephan De Bièvre.
Duration: January 2012 - December 2019.
Partners: Laboratoire Paul Painlevé and Laser physics department (PhLAM), Université Lille 1.
The “Laboratoire d'Excellence” Centre Européen pour les Mathématiques, la Physique et leurs interactions (CEMPI), a project of the Laboratoire de Mathématiques Paul Painlevé and the Laboratoire de Physique des Lasers, Atomes et Molécules (PhLAM), was created in the context of the "Programme d'Investissements d'Avenir" in February 2012.
The association Painlevé-PhLAM creates in Lille a research unit for fundamental and applied research and for training and technological development that covers a wide spectrum of knowledge stretching from pure and applied mathematics to experimental and applied physics.
One of the three focus areas of CEMPI research is the interface between mathematics and physics. This focus area encompasses three themes. The first is concerned with key problems of a mathematical, physical and technological nature coming from the study of complex behaviour in cold atoms physics and non-linear optics, in particular fibre optics. The two other themes deal with fields of mathematics such as algebraic geometry, modular forms, operator algebras, harmonic analysis and quantum groups that have promising interactions with several branches of theoretical physics.
Incentive Grant for Scientific Research (MIS) of the Fonds National de la Recherche Scientifique (Belgium)
Title: Patterns, Phase Transitions, 4NLS & BIon.
Coordinator: Denis Bonheure.
Duration: January 2014 - December 2016.
Partner: Université libre de Bruxelles.
Research Project (PDR) of the Fonds National de la Recherche Scientifique (Belgium).
D. Bonheure is co-investigator of this PDR.
Title: Asymptotic properties of semilinear systems.
Coordinator: Christophe Troestler (UMons).
Duration: July 2014 - June 2018.
Partner: Université de Mons, Université catholique de Louvain, Université libre de Bruxelles.
Title: Quantitative methods in stochastic homogenization
Programm: FP7
Duration: February 2014 - January 2019
Coordinator: Unibersité Libre de Bruxelles (Belgium)
Partner: Inria
Inria contact: Antoine Gloria
'This proposal deals with the development of quantitative tools in stochastic homogenization, and their applications to materials science. Three main challenges will be addressed. First, a complete quantitative theory of stochastic homogenization of linear elliptic equations will be developed starting from results I recently obtained on the subject combining tools originally introduced for statistical physics, such as spectral gap and logarithmic Sobolev inequalities, with elliptic regularity theory. The ultimate goal is to prove a central limit theorem for solutions to elliptic PDEs with random coefficients. The second challenge consists in developing an adaptive multiscale numerical method for diffusion in inhomogeneous media. Many powerful numerical methods were introduced in the last few years, and analyzed in the case of periodic coefficients. Relying on my recent results on quantitative stochastic homogenization, I have made a sharp numerical analysis of these methods, and introduced more efficient variants, so that the three academic examples of periodic, quasi-periodic, and random stationary diffusion coefficients can be dealt with efficiently. The emphasis of this challenge is put on the adaptivity with respect to the local structure of the diffusion coefficients, in order to deal with more complex examples of interest to practitioners. The last and larger objective is to make a rigorous connection between the continuum theory of nonlinear elastic materials and polymer-chain physics through stochastic homogenization of nonlinear problems and random graphs. Analytic and numerical preliminary results show the potential of this approach. I plan to derive explicit constitutive laws for rubber from polymer chain properties, using the insight of the first two challenges. This requires a good understanding of polymer physics in addition to qualitative and quantitative stochastic homogenization.'
Felix Otto's group at Max Planck Institute for Mathematics in the Sciences.
Louis Huguet, MA1 internship from ENS Cachan, 3 months.
Denis Bonheure was awarded a "Mission scientifique du FNRS" (sabbatical).
Denis Bonheure was visiting professor (in the frame of his sabbatical year) at
USP Sao Carlos, ICMC, Departamento de matematica
Karlsruher Institut fuer Technologie (KIT), Institut fuer Analysis
Pontificia Universidad Católica de Chile, Facultad de Matemáticas
Instituto Superior Tecnico de Lisboa, Departamento de Matemática
Université Aix-Marseille, Laboratoire d'Analyse, Topologie et Probabilités
Universidad de Buenos Aires, Departamento de Matemática
Università degli studi di Torino, Dipartimento di Matematica
Antoine Gloria spent two months at IHES (February–March 2015), as a guest of the Schlumberger chair of Felix Otto.
Christopher Shirley was invited by Pr. Nariyuki Minami and Pr. Fumihiko Nakano to Japan, from Nov. 26 to Dec. 13.
Denis Bonheure was General chair of the committee of the workshop in nonlinear PDEs in Brussels from Sept. 7 to 11 2015.
Antoine Gloria and Scott Armstrong organized a minisymposium on stochastic homogenization at the EQUADIFF'15 conference held in Lyon in July.
D. Bonheure and A. Gloria organize a PDE and analysis seminar at Brussels (http://
D. Bonheure is associate editor at the Bulletin of the Belgian Mathematical Society - Simon Stevin (http://
Antoine Gloria is editor at the Northwestern European Journal of Mathematics.
The members of the team review articles for many journals on a regular basis.
Denis Bonheure was invited speaker at
1st Joint Meeting Brazil-Spain in Mathematics, Universidade Federal do Ceara, Brazil, December
Variational and Topological methods in the study of nonlinear problems, Besançon, June
Unplugged in PDE’s, Sapienza di Roma, June
AMS-EMS-SPM International Meeting in Porto, June
Workshop in PDE’s, Calais, May
Nonlinear elliptic PDEs at the End of the World Congress, Universidad de Magallanes, Punta Arenas - Chile, March
Xth Americas Conference on Differential Equations and Nonlinear Analysis, Universidad de Buenos Aires, February
Karlsruhe, seminar of Nonlinear PDE, October
Karlsruhe, Colloquium of the Collaborative Research Centre on wave phenomena, October
Santiago de Chile, Seminar of the Center for Analysis and Partial Differential Equations, October
Instituto Superior Tecnico de Lisboa, Departamento de Matematica, June
TU Delft, Analysis seminar, June
Université de Lorraine, Séminaire d’Analyse et EDP de l’Institut Elie Cartan, June
Université de Aix-Marseilles, Séminaire d’Analyse Appliqué du Laboratoire d’Analyse,Topologie, Probabilités UMR 7353, May
Lille 1, Séminaire Analyse Numérique - Equations aux Dérivées Partielles, January
Stephan De Bièvre was invited speaker at
Colloquium bisontin sur les EDPs dispersives et problèmes liés, Besançon, January.
Mitia Duerinckx was invited speaker at
Numerical analysis and PDE seminar at the Université Lille 1, March
Minisymposium on Stochastic Homogenization at the conference EquaDiff 2015 in Lyon, July.
Antoine Gloria was invited speaker at
BelPRO conference on probability, Liège, January;
PDE seminar, Université de Nice, March;
AMS-EMS-SPM international meeting in Porto, June;
Workshop on stochastic homogenization, Banff research center, August;
Workshop on the calculus of variations, Lille, October;
Séminaire EDP-Proba, IHP, Paris, December.
Christopher Shirley was invited speaker at
Workshop on Spectra of Random Operators and Related Topics, Keio University, Yokohama.
Denis Bonheure is member of the Executive board of the Belgian Mathematical Society.
Stephan De Bièvre is
the scientific coordinator of the CEMPI,
member of the drafting committee of the IDEX UDL, and of the delegation that presented the pre-project to the jury in Paris (April 2015),
member of the Executive Committee of International Association of Mathematical Physics (since 2012).
Denis Bonheure is a member of the European Science Foundation panel elected by the Fundação para a Ciência e a Tecnologia for the evaluation of the research centers in Portugal for the period 2015-2020.
Guillaume Dujardin is an elected member of the Commission d'Evaluation of Inria (since 2015).
Licence
Guillaume Dujardin, Integral and differential calculus, 60h, L2 (mathematics & physics), Université Libre de Bruxelles
Stephan De Bièvre, Probability, 15h, L2 (physics), Université Lille 1
Stephan De Bièvre, Applied mathematics, 30h, L2 (physics), Université Lille 1
Stephan De Bièvre, Probability, 50h, L3 (mathematics), Université Lille 1
Master
Antoine Gloria, Elliptic regularity theory, 30h, M2, Université Libre de Bruxelles
Doctorat
Christopher Shirley, Decorrelation estimates for random operators, 4h, Gakushuin University, Tokyo
PhD supervision in the team:
PhD : Emilie Soret, Stochastic acceleration in an inelastic Lorentz gaz, Université Lille 1, June 30th 2015, Stephan De Bièvre & Thomas Simon (Lille 1)
PhD in progress : Mitia Duerinckx, Qualitative and quantitative aspects in stochastic homogenization of some PDEs, September 2014, Antoine Gloria & Sylvia Serfaty (Paris 6)
PhD supervision outside the team:
PhD : Manon Nys, Schrödinger equations with an external magnetic field: spectral problems & semiclassical states, Université Libre de Bruxelles and Università di Milano-Bicocca, September 11th 2015, Denis Bonheure (ULB) & Susanna Terracini (Torino)
PhD : Isabel Coelho, Boundary Value Problems for Some Curvature Operators, Université Libre de Bruxelles, June 20th 2015, Denis Bonheure (ULB)
Denis Bonheure was member of the jury of the PhD defence of Thuy Lien Nguyen (Université de Toulouse III - Paul Sabatier).
Antoine Gloria was in the jury of the PhD defences of Emilie Soret and Manon Nys.
Stephan De Bièvre was in the HDR jury of Dominique Spehner (April 2015, Institut Fourier, Grenoble).