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)
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