Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation

The paper is focused on justification of a statistical modelling algorithm for solution of the nonlinear kinetic Boltzmann equation on the base of a projection method. Hermite functions are used as an orthonormal basis. The error of approximation of a function by a partial sum of Hermite functions series is estimated in the L2 norm. The estimates are compared for two variants of the projection method in the case of solutions to the homogeneous gas relaxation problem with a known solution.

Anisotropic Flow in the Few Collisions Regime: Application to Bottomonia

Considering the kinetic Boltzmann equation in the limit of very few collisions, we study the evolution of the phase space distribution of bottomonia interacting with an expanding gas of massless partons. We investigate the scaling of the anisotropic flow coefficients on the initial eccentricities and the inverse Knudsen number, and compute their transverse momentum dependence.

A drift-kinetic analytical model for scrape-off layer plasma dynamics at arbitrary collisionality

A drift-kinetic model to describe the plasma dynamics in the scrape-off layer region of tokamak devices at arbitrary collisionality is derived. Our formulation is based on a gyroaveraged Lagrangian description of the charged particle motion, and the corresponding drift-kinetic Boltzmann equation that includes a full Coulomb collision operator. Using a Hermite–Laguerre velocity space decomposition of the gyroaveraged distribution function, a set of equations to evolve the coefficients of the expansion is presented. By evaluating explicitly the moments of the Coulomb collision operator, distribution functions arbitrarily far from equilibrium can be studied at arbitrary collisionalities. A fluid closure in the high-collisionality limit is presented, and the corresponding fluid equations are compared with previously derived fluid models.

Statistical modelling algorithm for solving the nonlinear Boltzmann equation based on the projection method

A statistical modelling algorithm is constructed for solution of the nonlinear kinetic Boltzmann equation based on the projection method. Hermite polynomials are used as an orthonormalized basis. The algorithm was tested on calculations for the problem of one-dimensional relaxation of gas with a known solution.

Classical Size Effects in Films of n-PbTe

Based on kinetic Boltzmann equation the boundary problem of calculating the conductivity and Seebeck coefficient for a film with a rectangular cross section is solved. Mirror- diffuse mechanism of reflection of the charge carriers from the surfaces of the film is considered. Calculations were performed for different thicknesses nondegenerate semiconductor n-PbTe. A comparison of theoretical calculations with obtained experimental data for vapor-phase condensates based on PbTe is made.

Guiding and amplification of microwave radiation in a plasma channel created in gas by intense ultraviolet laser pulse

The evolution of non-equilibrium plasma channel created in xenon by powerful KrF-femtosecond laser pulse is studied. It is demonstrated that such a plasma channel can be used as a waveguide for both transportation and amplification of the microwave radiation. The specific features of such a plasma waveguide are studied on the basis of the self-consistent solution of the kinetic Boltzmann equation for the electron energy distribution function in different spatial points of the gas media and the wave equation in slow-varying amplitude approximation for the microwave radiation guided and amplified in the channel.