SIMULATION OF GAS DYNAMICS IN PLASMA REACTOR FOR CARBON DIOXIDE CONVERSION

Numerical simulation of a bulk-type plasma reactor for carbon dioxide conversion with distributed gas injection and pumping has been performed in hydrodynamic approximation by solution of Navier-Stokes equation using the mathematical package COMSOL. It is shown that the geometry of gas injection and pumping, which determines the trajectories of the particles and their residence time in reactor, can significantly affect the energy efficiency of the conversion. Different particles on their way from inlet to pumping hole move along different trajectories and spend different times inside the reactor. If the residence time of the gas in the reactor is less than optimal, the gas conversion will be incomplete. If this time is more than optimal, then an excessive amount of energy will be applied to the already converted gas. It is shown that the reactor height affects significantly the energy efficiency of plasma conversion of carbon dioxide.

Energy loss by fast-travelling charged particles traversing two-dimensional materials

We consider the problem of the radiation losses by fast-traveling particles traversing two-dimensional (2d) materials or thin films. After review¬ing the screening of electromagnetic fields by two dimensional conducting ma¬terials, we obtain the energy loss by a fast particle traversing such a material or film. In particular, we discuss the pattern of radiation emitted by monolayer graphene treated within a hydrodynamic approximation. These results are com¬pared with recent published results using similar approximations and, having in mind a potential application to particle detection, we briefly discuss how one can improve on the signals obtained by using other two-dimensional materials.

Application of A-analytic Functions to the Investigation of the Cauchy Problem for a Stationary Poroelasticity System

In a reversible hydrodynamic approximation, a closed system of second-order dynamic equations with respect to the displacement vector of an elastic porous body and pore pressure has been obtained. The Cauchy problem for the obtained system of poroelasticity equations in the stationary case is considered. The Carleman formula for the Cauchy problem under consideration has been constructed.

Uniformly accurate machine learning-based hydrodynamic models for kinetic equations

A framework is introduced for constructing interpretable and truly reliable reduced models for multiscale problems in situations without scale separation. Hydrodynamic approximation to the kinetic equation is used as an example to illustrate the main steps and issues involved. To this end, a set of generalized moments are constructed first to optimally represent the underlying velocity distribution. The well-known closure problem is then solved with the aim of best capturing the associated dynamics of the kinetic equation. The issue of physical constraints such as Galilean invariance is addressed and an active-learning procedure is introduced to help ensure that the dataset used is representative enough. The reduced system takes the form of a conventional moment system and works regardless of the numerical discretization used. Numerical results are presented for the BGK (Bhatnagar–Gross–Krook) model and binary collision of Maxwell molecules. We demonstrate that the reduced model achieves a uniform accuracy in a wide range of Knudsen numbers spanning from the hydrodynamic limit to free molecular flow.

Дестабилизация внедрения высокоскоростной струи в хрупких материалах

The results of penetration of a high-speed metal jet (with a velocity of 3–7 km/s) into brittle materials (ceramics and glass) have been analyzed. The data on jet destabilization as a result of the response of the brittle material to the high-speed penetration are presented. The generalized dependence of the high-speed jet absorption efficiency on the bending strength of the brittle material has been constructed in the hydrodynamic approximation.

Электрические токи, индуцированные в плазме ионно-звуковыми солитонами: учет захваченных электронов

The currents induced by ion-acoustic solitons have been studied in a two-component magnetic–hydrodynamic approximation (MHD model) taking into account the trapped electrons. The solitons have been shown to excite unipolar nonpolar pulses of the ion and electron currents, and the established mechanisms of their excitation are. The spatiotemporal characteristics of the current pulses have been calculated, and the requirements for the spatiotemporal resolution of the experimental equipment necessary for detection of plasma currents induced by solitons have been determined. It has been shown that the solitons are the effective mechanism of plasma current generation.

Incompressible hydrodynamic approximation with viscous heating to the Boltzmann equation

The incompressible Navier–Stokes–Fourier (INSF) system with viscous heating was first derived from the Boltzmann equation in the form of the diffusive scaling by Bardos–Levermore–Ukai–Yang [Kinetic equations: Fluid dynamical limits and viscous heating, Bull. Inst. Math. Acad. Sin.[Formula: see text] 3 (2008) 1–49]. The purpose of this paper is to justify such an incompressible hydrodynamic approximation to the Boltzmann equation in [Formula: see text] setting in a periodic box. Based on an odd–even expansion of the solution with respect to the microscopic velocity, the diffusive coefficients are determined by the INSF system with viscous heating and the super-Burnett functions. More importantly, the remainder of the expansion is proven to decay exponentially in time via an [Formula: see text] approach on the condition that the initial data satisfies the mass, momentum and energy conversation laws.