Structure and evolution of magnetohydrodynamic solitary waves with Hall and finite Larmor radius effects.

Nonlinear and low-frequency solitary waves are investigated in the framework of the one-dimensional Hall-magnetohydrodynamic model with finite Larmor effects and two different closure models for the pressures. For a double adiabatic pressure model, the organization of these localized structures in terms of the propagation angle with respect to the ambient magnetic field θ and the propagation velocity C is discussed. There are three types of regions in the θ-C plane that correspond to domains where either solitary waves cannot exist, are organized in branches, or have a continuous spectrum.

Quasicollapse of oblique solitons of the weakly dissipative derivative nonlinear Schrödinger equation.

Numerical integrations of the derivative nonlinear Schrödinger equation for Alfvén waves, supplemented by a weak dissipative term (originating from diffusion or Landau damping), with initial conditions in the form of a bright soliton with nonvanishing conditions at infinity (oblique soliton), reveal an interesting phenomenon of "quasicollapse": as the dissipation parameter is reduced, larger amplitudes are reached and smaller scales are created, but on an increasing time scale. This process involves an early bifurcation of the initial soliton toward a breather that is analyzed by means of a numerical inverse scattering technique. This evolution leads to the formation of persistent dark solitons that are only weakly affected when crossed by the decaying breather which has the form of either a localized structure or an extended wave packet.

Dynamical model for nonlinear mirror modes near threshold.

Using a reductive perturbative expansion of the Vlasov-Maxwell (VM) equations for magnetized plasmas, a pseudodifferential equation of gradient type is derived for the nonlinear dynamics of mirror modes near the instability threshold. This model, where kinetic effects arise at a linear level only, develops a finite-time singularity, indicating the existence of a subcritical bifurcation. A saturation mechanism based on the local variations of the ion Larmor radius, is then phenomenologically supplemented.

Hydrodynamics of bacterial colonies: phase diagrams.

We present numerical simulations of a recent hydrodynamic model describing the growth of bacterial colonies on agar plates. We show that this model is able to qualitatively reproduce experimentally observed phase diagrams, which relate a colony shape to the initial quantity of nutrients on the plate and the initial wetness of the agar. We also discuss the principal features resulting from the interplay between hydrodynamic motions and colony growth, as described by our model.

Hydrodynamics of bacterial colonies: a model.

We propose a hydrodynamic model for the evolution of bacterial colonies growing on soft agar plates. This model consists of reaction-diffusion equations for the concentrations of nutrients, water, and bacteria, coupled to a single hydrodynamic equation for the velocity field of the bacteria-water mixture. It captures the dynamics inside the colony as well as on its boundary and allows us to identify a mechanism for collective motion towards fresh nutrients, which, in its modeling aspects, is similar to classical chemotaxis.