Yves Pomeau

Condensation of Classical Nonlinear Waves

We study the formation of a large-scale coherent structure (a condensate) in classical wave equations by considering the defocusing nonlinear Schrödinger equation as a representative model. We formulate a thermodynamic description of the classical condensation process by using a wave turbulence theory with ultraviolet cutoff. In three dimensions the equilibrium state undergoes a phase transition for sufficiently low energy density, while no transition occurs in two dimensions, in complete analogy with standard Bose-Einstein condensation in quantum systems. On the basis of a modified wave turbulence theory, we show that the nonlinear interaction makes the transition to condensation subcritical. The theory is in quantitative agreement with the numerical integration of the nonlinear Schrödinger equation.

Dynamical formation of a Bose–Einstein condensate

We explain how a condensate forms in finite time by a selfsimilar blow-up of the solution of the relevant quantum Boltzmann kinetic equation for a dilute quantum Bose gas. The condensate, once it is there, keeps exchanging mass with the rest of the distribution until equilibrium is reached, as described by a version of the kinetic equation that includes the existence of this condensate.

Two hundred years of capillarity research

Two centuries after seminal work by Pierre-Simon Laplace and Thomas Young, capillarity’s modern applications arise in fields ranging from biology and oceanography to propulsion, materials science, and novel devices.

Critical Velocities and Nucleation of Vortices in a Model of Superflow

We study the superfluid flow around an obstacle and observe a transition to dissipation which is explained by the nucleation of quantized vortices. This transition between a potential flow state, dominated by sounds waves (phonons), toward a vortical state occurs at a well determined velocity threshold. We study the dependence of the critical velocity in different geometries in 2 or 3 spaces dimension. We also report a new mechanism of nucleation of a pair of vortices (vortex-antivortex) from the collision between (very short wavelength) sound waves.

Rayleigh-Bénard Convection as a Model of a Nonlinear System: A Personal View

This is a (personal) review of work done on Rayleigh-Benard instability, seen primarily as a model system generating periodic structures in space as more or less parallel convection rolls. This nonequilibrium crystallography was and still is a rich source of inspiration, as I show.