We construct a coupled set of nonlinear reaction-diffusion equations which are exactly solvable. The model generalizes both the Burger equation and a Boltzman reaction equation recently introduced by Th. W. Ruijgrok and T. T. Wu. Key-Words : non-linear dynamics, reaction-diffusion, solvable model. October 1993 CPT-93/P.2956 anonymous ftp or gopher: cpt.univ-mrs.fr ∗Bibos and Fakultät für Physik...

We investigate low temperature (T ) properties of three classical quantum statistics models: (I) the Fermi-Dirac equation, (II) the Boltzman equation, and (III) the Bose-Einstein equation. It is widely assumed that each of these equations is valid for all T > 0. For each equation we prove that this assumption leads to erroneous predictions as T → 0. Our approach to correct these errors gives ne...

We present a method for constructing equilibrium disks with net angular momentum in general relativity. The method solves the relativistic Vlasov equation coupled to Einstein’s equations for the gravitational field. We apply the method to construct disks that are relativistic versions of Newtonian Kalnajs disks. In Newtonian gravity these disks are analytic, and are stable against ring formatio...

The freeze out of particles from a layer of finite thickness is discussed in a phenomenological kinetic model. The proposed model, based on the Modified Boltzman Transport Equation, is Lorentz invariant and can be applied equally well for the freeze out layers with space-like and time-like normal vectors. It leads to non-equilibrated post freeze out distributions. The dependence of the resultin...

Gradient expansions in quantum transport equations of a Kadanoff–Baym form have been reexamined. We have realized that in a consistent approach the expansion should be performed also inside of the self–energy in the scattering integrals of these equations. In the first perturbation order this internal expansion gives new correction terms to the generalized Boltzman equation. These correction te...

We examine the constraints imposed by the requirement of successful nucleosynthesis on models with one large extra hidden space dimension and a single bulk neutrino residing in this dimension. We first use naive out of equilibrium conditions to constrain the size of the extra dimensions and the mixing between the active and the bulk neutrino. We then use the solution of the Boltzman kinetic equ...

Graphene membranes act as highly sensitive transducers in nanoelectromechanical devices due to their ultimate thinness. Previously, the piezoresistive effect has been experimentally verified in graphene using uniaxial strain in graphene. Here, we report experimental and theoretical data on the uni- and biaxial piezoresistive properties of suspended graphene membranes applied to piezoresistive p...