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» Conférences d’après mars 2011 : nouveau site


Colloque Promenade dans la physique d’aujourd’hui / A Stroll through Today’s Physics

Organisé par : Basile Audoly (CNRS) et Martine Ben Amar (ENS) et Etienne Guyon (ESPCI) et Vincent Hakim (CNRS) et Éric Pérez (CNRS)

Colloque en l’honneur d’Yves Pomeau
Qu’y a-t-il de commun entre les modèles théorie cinétique puis de gaz sur réseau, le papier froissé, la dispersion dans les milieux poreux, les instabilités de convection ou de digitation et l’intermittence, les superfluides, et d’autres sujets tout aussi divers et dignes, semblerait il d’un inventaire à la Prévert ?
Réponse : Yves Pomeau
et son immense curiosité qui a motivé de nombreuses collaborations entre expérimentateurs et théoriciens, créé des ponts entre la physique et les mathématiques et entre la physique et la mécanique. Yves Pomeau, atteint par la limite d’âge, prend sa retraite du laboratoire. Nous souhaitons marquer ce départ en organisant à l’École normale supérieure un colloque portant sur les multiples aspects de son activité qui mobilisent les efforts de nombreux chercheurs de par le monde et constituent des enjeux majeurs pour la physique actuelle.
Les thèmes :
- Mécanique statistique
- Fluides quantiques et classiques
- Instabilités
- Chaos et turbulence
- Elasticité et singularités

Comité scientifique : B. Audoly (LMM, Paris VI), M. Ben Amar (LPS, ENS), P. Clavin (IRPHE, Marseille), P. Coullet, E. Guyon (PMMH, ESPCI), V. Hakim (LPS, ENS), P. Manneville (Ladhyx, Polytechnique), E. Perez (LPS, ENS)

This conference is organized in honor of Yves Pomeau on the occasion of his 65th birthday. Numerous scientists, friends and collaborators of Yves, will present recent developments in the very active fields of physics, mathematics and mechanics where Yves has made key contributions.

Ressources en ligne

  • Noisy traveling waves in models of evolution (le 28 juin 2007) — Bernard Derrida
    (in collaboration with E. Brunet, A. Mueller and S. Munier)
    The Fisher-KPP equation is known to have a one-parameter family of solutions indexed by the velocity of the traveling waves. In presence of noise, due to the underlying dynamics, one solution is selected, the velocity of which converges, in the limit of a weak noise, to the minimal velocity of the K-KPP equation. This talk will review some recent theoretical results obtained on the effect of a weak noise on the velocity and on the diffusion constant of these noisy traveling waves. I will also discuss some models of evolution which, in presence of selection, can be formulated as noisy traveling waves equations. The exact solution of a special case reveals statistical properties of genealogical trees which are quantitatively identical to those of spin glasses, as predicted by the Parisi theory.
  • From lattice gases to lattice Boltzmann’s equation (le 28 juin 2007) — Dominique D’Humières

  • Localisation par la nonlinéarité dans les dystèmes discrets (le 28 juin 2007) — Serge Aubry
    La théorie des « Breathers Discrets » dans les systèmes Hamiltoniens nonlinéaires sur réseau, sera brièvement présentée. A la différence des solitons des systèmes intégrables, les Breathers Discrets sont des solutions spatialement localisées robustes et universelles qui ne nécessitent pas de propriétés exceptionnelles pour l’Hamiltonien du système. Nous décrirons simplement les conditions pour leur existence, quelques unes de leurs propriétés et comment elles se peuvent se manifester spontanément dans des situations physiquement réalistes.
    Nous expliquerons pourquoi ce nouveau concept intrinsèquement nonlinéaire ouvre des nouvelles perspectives pour comprendre de nombreux phénomènes de la physique, de la chimie et de la biophysique mal élucidés à ce jour.
  • Growth direction and morphology of crystalline dendrites in directional solidification (le 28 juin 2007) — Alain Pocheau
    Growth direction and morphology of crystalline dendrites in directional solidification: the mesoscopic implications of anisotropy in a growth system
    The solidification of a material from a melt usually involves the growth of dendritic interfaces. In directional solidification, two directions compete for setting the growth direction of their dendrites: the heat flow direction and a preferred crystalline orientation. As the growth velocity increases, it appears that dendrite growth directions turn from the former direction to the latter direction. Meanwhile, the dendrite morphology changes with important implications regarding the formation of microstructures in the resulting solid. After having exhaustively documented these issues experimentally, we show evidence of an internal symmetry in the date base from which the form of the evolution of dendrite growth directions with parameters can be selected. This reveals an unexpected universality of the implications of anisotropy at mesoscopic scales in this growth system.
  • Can a species keep pace with a shifting climate? (le 28 juin 2007) — Henri Berestycki
    We introduce a reaction-diffusion model of the KPP type to describe the dynamics of a biological population facing a climate shift. In this context, global warming is interpreted as a Northward shift of the favourable zone for a given species. In terms of the various parameters, the question is to know whether a species is able to keep track with the climate change and how the latter affects the population size and distribution. The reaction-diffusion model sheds a new light on these questions. This is joint work with Odo Diekman, Kees Nagelkerke and Paul Zegeling (Netherlands). I will also present extensions to higher dimensions, reporting on a joint work with Luca Rossi. These involve nonlinear elliptic and parabolic equations in unbounded domains and generalized principal eigenvalues of elliptic operators. Lastly, I will mention a work with Alain Roques and Lionel Roques about the effects of geographical constraints when an Allee effect is involved.
  • The Early and Late-Stage Coalescence of Small Droplets sitting on a Plate (le 28 juin 2007) — Daniel Beysens
    (in collaboration with R.D. Narhe and Y. Pomeau)
    We investigate the early stage coalescence of two small sessile drops (diethylene glycol) on silicon wafer. Coalescence is induced either by vapor condensation or syringe deposition. The description of the early stage of the coalescence process of sessile drops implies to describe properly two singularities: one is concerned with the contact point of the merging drops and the other is the solid-liquid-vapor contact line. We find that the bridge evolution between the two coalescing drops can be characterized by only two stages of evolution, an early stage where the capillary number is large and where a dynamic bridge drying is observed with power law evolutions and a late stage where the capillary number is small and the bridge section relax exponentally, with a typical time 10 times larger than for bulk hydrodynamics. In addition to this late stage, a very late stage relaxation – that can be described by a quasi-static approximation – is still present where the composite drop relaxes to a spherical cup with a typical time 6 orders of magnitude larger than what hydrodynamics predict due to high dissipation in the contact line vicinity.
  • Adhesion and friction issues in everyday life (le 28 juin 2007) — Jacob Israelachvili

  • Life at High Péclet Numbers (le 28 juin 2007) — Raymond E. Goldstein
    Some of the most challenging and interesting issues in biology concern the emergence of multicellular organisms from unicellular individuals. The accompanying differentiation from totipotent single cells to multicellular species with cells specialized into reproductive and vegetative functions implies both costs and benefits. Not surprisingly for microscopic life in water, many of the issues surrounding these transitions involving the physics of diffusion and mixing, for the efficient exchange of nutrients and wastes with the environment is among the most basic factors affecting the fitness of organisms. In this talk, I will discuss recent experiments and theoretical work on a lineage of organisms, colonial algae, which serve as a model for understanding the transition to multicellularity. Techniques from cell biology, experimental fluid mechanics, and asymptotic methods for advection-diffusion equations help provide an answer to the basic question: What is the advantage of increasing size ?
  • From the question of the Maxwell point in non-equilibrium system to the problem of storage of information in patterns and spatial chaos (le 28 juin 2007) — Pierre Coullet

  • Vortices in the Ginzburg-Landau model in the large kappa limit (le 28 juin 2007) — Sylvia Serfaty
    In a joint work with Etienne Sandier (appeared in the book "Vortices in the magnetic Ginzburg-Landau model", Birkhauser, 2007), we studied the mathematics of the Ginzburg-Landau energy of superconductivity in 2 dimensions, in the limit where the Ginzburg-Landau parameter kappa goes to infinity. We derived rigorously the values of critical fields for which vortices appear, characterized optimal vortex locations and vortex-densities in energy-minimizers via limiting problems in various regimes of applied fields, and showed the existence of various branches of stable solutions.
  • Slow degassing in porous media (le 28 juin 2007) — Stéphane Zaleski
    Oil production and volcanic eruptions arise through a similar process: gas dissolved at very high pressure is drawn out of solution by the decrease of outside pressure. The modelling of the process involves a string of fascinating physical phenomena: contact angle dynamics of growing bubbles at nucleation sites, fractal growth of bubble “ganglia”, various types of shock formation in the Darcy equations, percolation mechanisms. In particular, a new fully analitic theory in the limit of very slow degassing will be shown.
  • Envelopes of inhomogeneous patterns in hydrodynamic instabilities (le 28 juin 2007) — Jose-Eduardo Weisfreid

  • Inclined to exchange: shocking gravity currents (le 28 juin 2007) — John Hinch
    Experiments at Laboratoire FAST have studied the flow which ensues in an inclined pipe which starts with the upper half-length filled with a heavy liquid and the lower half-length filled with a light fluid. This talks aims at providing a little theory for the special regime of slow flows in a nearly horizontal pipe. In a viscous gravity current, the light fluid spreads up along the pipe occupying the upper half of the cross-section while the heavy fluid moves down in a counter current. This viscous spreading is described by a nonlinear advection-diffusion equation for the dependence along the pipe of the height of the flat horizontal interface in the cross-section, very similar to the spreading of a viscous drop on a flat plane. Curiously, the solution of the diffusion equation involves matching a shock wave to a rarefaction wave.
  • Snail balls and more (le 29 juin 2007) — William R. Young
    I’ll consider the dynamics of a magic trick, the snail ball, which is marketed with the explanation: “A small metallic gold ball just over 2 cm in diameter ... the ball does roll, but does so incredibly slowly. To an audience it seems baffling... inside the ball, which is actually hollow, there is a viscous liquid and a smaller ball which is is the smaller heavier ball which determines the pace and this is slow because of the viscous liquid ”.
    I’ll consider an experimental cylindrical analog consisting of a hollow cylindrical shell, a nested solid cylinder, and a gap filled with viscous fluid. This apparatus advances slowly and irregularly down an inclined plane. For small slopes the speed is constant on average.
    A mathematical model is compared with simple experiments and the disagreement between theory and experiment indicates that the size of contact asperities plays a crucial role in determining the average rolling speed. This hypothesis is supported by coating the inner cylinder with sandpaper of different grades, which changes the rolling speed. Time and circumstances permitting, I’ll show other toys, involving granular materials, which roll slowly on inclined planes.
  • Super Free Fall (le 29 juin 2007) — Emmanuel Villermaux
    Can an object, solely subjected to the force of gravity, fall faster than the free fall? The answer and its consequences on some natural phenomena will be illustrated by an original experiment, and discussed by simple arguments.
  • Tetrad models of turbulence (le 29 juin 2007) — Alain Pumir

  • The soliton as a "vacuum cleaner" and electron transport (le 29 juin 2007) — Manuel G. Velarde

  • Forme et dynamique de quelques systèmes biologiques (le 29 juin 2007) — Jacques Prost
    Je montrerai comment des constructions théoriques relativement simples permettent de décrire la forme et la dynamique d’objects comme les cils de l’oreille interne, les boutons synaptiques ou les lamellipodes.
  • Patterns and symmetries in the visual cortex (le 29 juin 2007) — Mehran Kardar
    Neurons in the visual cortex respond to lines of given orientation. This preferred orientation varies continuously across most of the cortex, but also has vortex-like singularities. To describe these patterns, it is useful to understand the effect of rotations: oriented segments in natural images tend to be collinear; neurons are more likely to be connected if their preferred orientations are aligned to their topographic separation. The appropriate symmetry thus involves joint rotations of orientation preference and the underlying topography. This is verified by direct statistical tests in both natural images and in cortical maps.
  • Evolution of antibiotic resistance (le 29 juin 2007) — Eric Siggia

  • Manipulating thin-film flows: from patterned substrates to evaporating systems (le 29 juin 2007) — Howard Stone
    It is well known that fluid flow in thin films occurs in a wide range of applications. Here we describe two variants of the standard kind of problem. First, we describe the spreading of mostly wetting liquid droplets on microdecorated surfaces, i.e. assemblies of micron-size cylindrical posts arranged on square or hexagonal arrays. We obtain a variety of deterministic final shapes of the spreading droplets, including octagons, squares, hexagons and circles. Dynamic consideration provide a “shape” diagram that summarizes our observations and suggests rules for a designer’s tool box, which thus offer opportunities for control of the spreading patterns.
    Second, we consider evaporation of volatile liquids on substrates with arbitrary thermal conductivity. Using experiments and theory we show how the sense of the internal circulation depends on the ratio of the liquid and substrate conductivities.
    These results help rationalize previous studies of similar problems.
  • Close packing of elastic structures (le 29 juin 2007) — Mokhtar Adda-Bedia
    The folding of leaves in buds, the wing folding of insects in cocoons, DNA packaging in viral capsids or crumpling a piece of paper are different examples of close packed objects. Can we describe these systems using an elastic approach and can we determine their statistical properties?
  • Eigenproblem of large powers of the Laplacian in bounded domains (le 29 juin 2007) — Alfred Ramani
    We present a method for computing the spectrum of large powers N of the Laplacian in a bounded domain restricting ourselves to the one- and three-dimensional cases. Since it does not seem possible to obtain information on the eigenvalues directly from the transcendental equation that gives the spectrum, we introduce a Wallis-inspired method. We obtain the expansion of the eigenfunction and the eigenvalues in power series where l/N plays the role of the small parameter. We compare these eigenvalues to the ones obtained through a simple variational approach and remark that the latter offers an excellent approximation to the exact result.
  • Crumpling a paper or a soft tissue (le 29 juin 2007) — Martine Ben Amar
    (in collaboration with Julien Dervaux)
    Ten years ago, Yves Pomeau and I investigated the existence of singularities in the solutions of Foppl-Von Karman equations of plates. We showed that the variationnal character of elasticity selects developable surfaces, the developable conic points and folds being the most commonly encountered in experiments. The Foppl-Von Karman equations include geometric non-linearities but maintain the linear hookean elasticity, an assumption which may be questionable for soft or living tissues. The first question we have considered concerns the validity of these equations for soft tissues and arbitrary elasticity. It is known that living tissues have non trivial behaviour to loadings due to nonlinear elastic response It turns out that the only hypothesis of small thickness compared to lateral size (the plate geometry) is sufficient to recover the standard Foppl-Von Karman equations. We extend this formalism to incorporate a growth process and show that growth may induce non trivial shapes which can been seen in nature like leaves and flowers.
  • The elasticity of knots (le 29 juin 2007) — Basile Audoly
    Knots are present in everyday life and they can certainly be annoying. They can be very useful too for climbing, sailing, or simply for tying one’s shoes. In science, the topology of knots and braids has been studied quite extensively; mathematicians have proposed a number of invariants to help discriminating between various types of knots. More recently, biologists and physicists and have become interested in knots, which are found in long polymers, such as DNA. In this talk, I shall first shortly review these results. In a second part, I investigate the mechanics of knots, and show that one can explicitly calculate the shape of knotted elastic rods, which are minimizers of the Kirchhoff energy for elastic rods subject to topological constraints.
  • Soft hydraulics: physics and physiology (le 29 juin 2007) — L. Mahadevan
    Hydraulics (from the Greek word ....) is the study of fluid movements and fluid power. I will discuss the dynamics of water movements in soft fluid infiltrated solids such as gels, cells and tissues, with implications for the slow settling, bending and breaking of gels, the dynamics of nuclear and cell swelling and motility, and the water powered slow and rapid movements of tissues.
  • Statistical mechanics of a gravitational plasma (le 30 juin 2007) — Yves Pomeau
    Statistical mechanics was developed under the assumption that particles interact with short range forces. It was pointed out early on that the general methods of this theory cannot apply to systems of particles interacting with gravitation. However such gravitational plasmas are actually present in our Galaxy in the form of local clusters of millions of stars.
    I shall explain the mean-field theory valid for ‘short time scales’ of the order of the orbital period of a star in the mean field of the cluster. A ‘microscopic’ approach yields equation of equilibrium for this system thanks to the separation of time scales, the irreversibility entering at small correction to the dominant mean field dynamics.
  • Supersolid rotation and sphere packing problem (le 30 juin 2007) — Amandine Aftalion
    We use the model proposed by Josserand, Pomeau, Rica (PRL 2007) to prove properties on the ground state of a supersolid crystal and relate it to a sphere packing problem. This allows us to find, in the limit of small rotation, an approximate theoretical value for the reduction of the moment of inertia of a supersolid set in rotation, with respect to its classical value.
  • Coherent structures and patterns formations in Hamiltonian systems (le 30 juin 2007) — Christophe Josserand
    Following a conjecture done by Pomeau and Zakharov in the early 90’, I will show how coherent structures form in a family of Hamiltonian systems, the nonlinear Schrodinger equations. In particular I will present how solitons form in a 1D focusing case and how a classical version of the Bose-Einstein condensation can be observed in discrete systems.
    Finally, I will discuss some recent results on supersolids models.
  • Depinning Pomeau fronts (le 30 juin 2007) — Len Pismen
    Pomeau’s idea of fronts between a pattern and a homogeneous state being pinned on the pattern’s own structure was a deep insight into unexplored frontier between the Continuous and Discrete. Going further on this path, I consider dynamics of depinning, its modification in 2D, and imitation of patterns in continuo by dynamic Ising-like models.
  • A journey to the theory of superfluidity (le 30 juin 2007) — Sergio Rica
    I will review the principal ideas behind the theory of superfluidity of Bose-Einstein condensates, liquid and solid helium, in the frame of the Gross-Pitaevskii or Nonlinear Schrödinger equations.
  • Solitons as quantum objects (le 30 juin 2007) — Martine Le Berre
    In most physical situations solitons in optical fibers behave like classical (non quantum) objects because they are made of a large number of photons. Nevertheless there exist quantum effects without classical counterpart, like the tunneling under a potential barrier.
    We investigate one possible realization of such a quantum tunneling with solitons as basic entities. Specifically, we consider a soliton propagating in two linearly coupled fibers that are assumed identical. It has been known for some time that, at small enough coupling, asymetric soliton only can propagate and be stable. The amplitude of such an asymmetric soliton is predominantly in either fiber and remains on the same side forever classically.
    This makes, for a given energy, two possible states obtained by permutation of the two fibers. In the quantum version of the same problem, these two solitons merge into a single quantum state sharing a quantum amplitude spread between the two fibers, because of the possibility of (emph/quantum)tunneling from one fiber to the other. Orders of magnitude relevant for a possible physical application are given.
  • Wave turbulence: a story far from over (le 30 juin 2007) — Alan Newell
    Wave turbulence is the study of the long time statistical behavior of solutions to weakly nonlinear dispersive wave systems. Because it has a closed kinetic equation whose solutions capture both the equipartition and finite flux Kolmogorov solutions, the subject has often been consigned to the dustbin of solved problems. Story over, right? Wrong ! Wave turbulence is alive and well and has still lots of intellectual challenges. One set arises from the fact that wave turbulence is almost never uniformly valid over all scales. Another set of challenges arises from the anomolous way in which the Kolmogorov-Zakharov spectra are realized. I will briefly discuss these challenges.



Basile Audoly (CNRS)

Institut de mécanique d’Alembert, Université Paris 6

Martine_Ben Amar

Martine Ben Amar (ENS)

UMR 8550 Laboratoire de physique statistiques de l’ENS (LPS-ENS)


Etienne Guyon (ESPCI)

professeur émérite à l’université Paris XI, chercheur à l’ESPCI et au Centre Cavaillès
ancien directeur de l'ENS


Vincent Hakim (CNRS)

Laboratoire de physique statistique du Département de physique de l’ENS


Éric Pérez (CNRS)

UMR 8550 Laboratoire de physique statistiques de l’ENS (LPS-ENS)

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