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  • Quantum condensed phases
    Our most recent result was to understand what happens when an obstacle is moved through a real condensate, including the layer separating it from the outside. There the critical speed we had computed before in the homogeneous case fall to zero, so that one cannot use anymore a criterion based upon a transition from elliptic to hyperbolic flow equations. We have shown that, thanks to a rescaling of the equations in the boundary layer, there is no critical speed, but only a smooth transition from a wave drag to a more classical vortex shedding problem. I plan in the near future to incorporate in this picture the effects of the quantum fluctuations to represent what I have called the quantum braking. Another issue still under investigation is the occurence of finite time singularities in the momentum distribution due to the absence of smooth momentum distribution at equilibrium.
    C. Josserand, Y. Pomeau and S. Rica Vortex shedding in a model of superflow Physica D 134 (1999)p. 111-125
    Pomeau Y. M.E. Brachet, S. Metens and S. Rica Théorie cinétique d'un gaz de Bose dilué avec condensat C.R. Ac. Sci., t. 327, série IIb, p. 791-798 (1999)
    Y. Pomeau and S. Rica Thermodynamics of a dilute Bose-Einstein gas with repulsive interactions J. of Physics A33, 691 (2000)
    Y. Pomeau and S. Rica Thermodynamics of a dilute non perfect Bose-Einstein gas Europhys. Letters 51, 20 (2000).
    Y. Pomeau, Théorie de Bogoliubov hors-équilibre C.R. Ac. Sci., t. 1, série IV, p. 91-98, (2000)
    C. Josserand and Y. Pomeau Nonlinear aspects of the theory of Bose-Einstein condensates Nonlinearity 14, R25-R62 (2001)

  • Classical hydrodynamics
    This is about one of the great unsolved problems in fluid mechanics: starting from smooth initial data with finite energy, do the solutions of the fluid equations for incompressible inviscid fluids remain smooth at any time? We have explored the various physical constraints put on self similar solutions blowing up in finite time. at the moment we have reduced the problem to the one of finding periodic solutions of transformed fluid equations that are smooth and satisfy various constraints. We hope to start the numerical problem of their solutions quite soon.
  • Capillarity
    I have been working lately on the moving contact line problem. at the moment we are on the way of formulating a consistent set of equations for macroscopic problems where the physical effects at the molecular level of the moving contact line are incorporated in various phenomenological coefficients and functions. We have developed a rather extensive program of calculation of dynamics of the contact line in the limit of slow dynamics, that is relevant for many applications. With Mahadevan and Mokhtar Adda-Bedia, we looked at the problem of the merging of three phases along a contact line. Contrary to what one could think, this merging is robust in the parameter space, not the result of some exceptional combination of physical parameters.
    L. Mahadevan and Pomeau Y. Rolling droplet Physics of Fluids, 327, Série IIb, p. 155-160 (1999)
    Pomeau Y. Représentation de la ligne de contact mobile dans les équations de la mécanique des fluides C.R. Ac. Sci., Série IIb, t. 328, p. 1-6 (2000)
    Pismen L. Pomeau Y. Disjoining potential and spreading of thin films in the diffuse interface model coupled to hydrodynamics Phys Rev E 62, 2480 (2000).
    C. Andrieu, D.A. Beysens, V.S. Nikolaev. Pomeau Y. Coalescence of sessile drops J. of Fluid Mech. 453, 427-438 (2002)
    Y. Pomeau Recent progress in the moving contact line problem : a review CR Ac. Sc. 330 (2002) 207-222.
    M. Ben Amar, L. Cummings et Y. Pomeau Points singuliers d'une ligne de contact mobile CRAS, t. 329, Série IIb, p. 277-282 (2001)
    M. Ben Amar, L. Cummings et Y. Pomeau to appear in the Physics of fluids

  • Elasticity
    We are presently finishing the writing of a book, 'Elasticity and geometry' to appear at Oxford Univ. press. This writing led us to some developements, as for instance the buckling of a spherical shell in the strongly non linear regime, the same for a plate, and more recently on various questions on the elasticity of thin rods.
    Pomeau Y., S. Rica Plaques très comprimées C.R. Ac. Sci., t. 325, Série II, p. 181-187 (1997)
    Pomeau Y. Buckling of thin plates in the weakly and strongly nonlinear regimes Philosophical Magazine B78 , 235, (1998)

  • Combustion
    This follows a previous work with Bill Young and Alain Pumir where we had shown that the effective diffusion coefficient in a pattern of rolls at large Péclet number is the geometric average of the 'turbulent' diffusion coefficient and of the molecular diffusion coefficient. We have studied the effective speed of propagation of a flame and/or a reaction-diffusion front in such a fast cellular flow. A result from the University of Chicago stated that the effective speed of propagation is at least of order Pe^(1/5) at large Péclet numbers. Applying the techniques used for the diffusion of the pasive scalar, we showed that the exact law is like Pe^(1/4). There remains to explore various limits of the coefficients of this law as the chemical reaction becomes fast.
    Pomeau Y. Dispersion at large Péclet number In " Mixing Chaos and Turbulence " ed. H. Chaté et al. NATO ASI series, series B : physics Vol 373, Kluwer New York (1999).
    B. Audoly, H.Berestycki et Y. Pomeau, Réaction diffusion en écoulement stationnaire rapide C.R. Ac. Sci., IIb, t. 328, p. 255-262, (2000)