Knudsen Layer for Gas Mixtures

The Knudsen layer in rarefied gas dynamics is essentially described by a half-space boundary-value problem of the linearized Boltzmann equation, in which the incoming data are specified on the boundary and the solution is assumed to be bounded at infinity (Milne problem). This problem is considered for a binary mixture of hard-sphere gases, and the existence and uniqueness of the solution, as well as some asymptotic properties, are proved. The proof is an extension of that of the corresponding theorem for a single-component gas given by Bardos, Caflisch, and Nicolaenko [Comm. Pure Appl. Math. 39:323 (1986)]. Some estimates on the convergence of the solution in a finite slab to the solution of the Milne problem are also obtained.     

A Two-Surface Problem of the Electron Flow in a Semiconductor on the Basis of Kinetic Theory

A steady flow of electrons in a semiconductor between two parallel plane Ohmic contacts is studied on the basis of the semiconductor Boltzmann equation, assuming a relaxation-time collision term, and the Poisson equation for the electrostatic potential. A systematic asymptotic analysis of the Boltzmann–Poisson system for small Knudsen numbers (scaled mean free paths) is carried out in the case where the Debye length is of the same order as the distance between the contacts and where the applied potential is of the same order as the thermal potential. A system of drift-diffusion-type equations and their boundary conditions is obtained up to second order in the Knudsen number. A numerical comparison is made between the obtained system and the original Boltzmann–Poisson system.     

基于Boltzmann模型方程的气体运动论HPF并行算法

从修正的BGK-Blotzmann模型方程出发，引入离散速度坐标技术对气体分子速度分量进行离散降维，基于非定常时间分裂数值计算方法和无波动、无自由参数的NND耗散差分格式，发展直接求解气体分子速度分布函数的气体运动论有限差分数值格式，提出了一套能有效模拟各流域三维绕流问题的气体运动论统一算法，在分析研究气体运动论数值算法内在并行度的基础上，开展各流域三维绕流问题统一算法的HPF（高性能FORTRAN）并行化程度设计，建立一套能有效模拟各流域复杂外形体绕流的HPF并行算法软件，并进行了不同Knudsen(克努森）数下三维球体绕流及类“神舟号”返回舱外形体绕流的初步数值实验，将计算结果与过渡区有关实验数据及各流域气体绕流现象进行比较分析，证实了发展的气体运动论HPF并行算法在求解稀薄流到连续流不同流域复杂绕流问题方面的可行性。     

The Kinetic Theory of Simple Reacting Spheres: I. Global Existence Result in a Dilute-Gas Case

Existence of global-in-time, spatially inhomogeneous, and L ¹-renormalized solutions is proven for the model of simple reacting spheres under the assumptions that initially the system has a finite total mass, energy, and entropy.     

固-液界面热整流现象的气体运动论分析

本文采用非平衡态分子动力学模拟方法,研究了固-液界面体系中的热整流现象。系统的两端为固体,而流体处于中间夹层,两端固-液界面的势能参数不同。模拟计算结果表明,此系统实现热整流的原因是左右两端固体壁面对流体分子吸附特性的不对称性。基于气体运动论的分析表明,高低温固体壁面所吸附流体分子数、温度协调系数和系统压强在正反向传热过程中均存在一定差异,从而形成了热整流效应;并且两端固-液界面差异性越大,热整流现象越明显。     

Second law of thermodynamics in volume diffusion hydrodynamics in multicomponent gas mixtures

We presented the thermodynamic structure of a new continuum flow model for multicomponent gas mixtures. The continuum model is based on a volume diffusion concept involving specific species. It is independent of the observer?s reference frame and enables a straightforward tracking of a selected species within a mixture composed of a large number of constituents. A method to derive the second law and constitutive equations accompanying the model is presented. Using the configuration of a rotating fluid we illustrated an example of non-classical flow physics predicted by new contributions in the entropy and constitutive equations.     

Long-Time-Tail Effects on Lyapunov Exponents of a Random, Two-Dimensional Field-Driven Lorentz Gas

We study the Lyapunov exponents for a moving, charged particle in a two-dimensional Lorentz gas with randomly placed, nonoverlapping hard-disk scatterers in a thermostatted electric field, . The low-density values of the Lyapunov exponents have been calculated with the use of an extended Lorentz–Boltzmann equation. In this paper we develop a method to extend theses results to higher density, using the BBGKY hierarchy equations and extending them to include the additional variables needed for calculation of the Lyapunov exponents. We then consider the effects of correlated collision sequences, due to the so-called ring events, on the Lyapunov exponents. For small values of the applied electric field, the ring terms lead to nonanalytic, field-dependent contributions to both the positive and negative Lyapunov exponents which are of the form ~ ²ln~, where ~ is a dimensionless parameter proportional to the strength of the applied field. We show that these nonanalytic terms can be understood as resulting from the change in the collision frequency from its equilibrium value due to the presence of the thermostatted field, and that the collision frequency also contains such nonanalytic terms.     

Theory of electromagnetic wave propagation in a plasma-filled corrugate waveguide immersed in a finite magnetized field

The linear theory of electromagnetic radiation from a high-power backward-wave-oscillator (BWO), travelling-wave-tube (TWT) with plasma-filled, sinusoidally corrugate waveguide driven by an intense relativistic electron beam (IREB) has been derived and analysed numerically. A general dispersion relation is presented for analysing a plasmafilled corrugate waveguide immersed in magnetized plasma in this paper. It is shown that the linear theory developed here is in good agreement with the previous work.     

声子色散和磁场对极性晶体中极化子自陷能的影响

利用线性组合算符和幺正变换相结合的方法,研究了声子色散和磁场对极性晶体中极化子振动频率和自陷能的影响.计及纵光学(LO)声子色散,在抛物近似下导出了极性晶体中极化子自陷能随电子-纵光学声子耦合常数、回旋共振频率和声子色散系数之间的变化关系.数值计算结果表明极化子自陷能随电子-纵光学声子耦合常数、回旋共振频率和声子色散系数的增大而增大.     

Boltzmann Limit and Quasifreeness for a Homogenous Fermi Gas in a Weakly Disordered Random Medium

We discuss some basic aspects of the dynamics of a homogenous Fermi gas in a weak random potential, under negligence of the particle pair interactions. We derive the kinetic scaling limit for the momentum distribution function with a translation invariant initial state and prove that it is determined by a linear Boltzmann equation. Moreover, we prove that if the initial state is quasifree, then the time evolved state, averaged over the randomness, has a quasifree kinetic limit. We show that the momentum distributions determined by the Gibbs states of a free fermion field are stationary solutions of the linear Boltzmann equation; this includes the limit of zero temperature.     

Nonlinear Couette Flow in a Low Density Granular Gas

A model kinetic equation is solved exactly for a special stationary state describing nonlinear Couette flow in a low density system of inelastic spheres. The hydrodynamic fields, heat and momentum fluxes, and the phase space distribution function are determined explicitly. The results apply for conditions such that viscous heating dominates collisional cooling, including large gradients far from the reference homogeneous cooling state. Explicit expressions for the generalized transport coefficients (e.g., viscosity and thermal conductivity) are obtained as nonlinear functions of the coefficient of normal restitution and the shear rate. These exact results for the model kinetic equation are also shown to be good approximations to the corresponding state for the Boltzmann equation via comparison with direct Monte Carlo simulation for the latter.     

Dispersion of electromagnetic waves in the presence of magnetic monopoles of electron mass in a uniform magnetic field

The dispersion relation of electromagnetic waves in the presence of magnetic monopoles of electron mass in a uniform magnetic field is obtained. The waves of the frequencyω in the range ω_ϱi<Ω_i<ω<Ω _e <ω_ϱa are analysed. It is shown that the monopole charges lead to observable effects. Finally, the results are applied to a typical pulsar.     

On the Diffusion in a Lattice Gas Model: Group-Theoretic Approach

Motivated by some recent results concerning the model of a noninteracting one-dimensional lattice gas with an order preservation of particles where multiple occupancy of the sites is not excluded, we give new symmetries and new reductions of the corresponding continuum nonlinear partial differential equation. Closed-form analytic solutions are found.     

Vapor Flows Along a Plane Condensed Phase with Weak Condensation in the Presence of a Noncondensable Gas

A steady flow of a vapor in a half space condensing at incidence onto a plane condensed phase is considered in the case where another gas that does not condense (the noncondensable gas) is present near the condensed phase. A systematic asymptotic analysis of the Boltzmann equation for hard-sphere molecules is performed in the case where condensation is weak, and the relation among the parameters of the vapor flow at infinity, those associated with the plane condensed phase, and the amount of the noncondensable gas is derived in an analytical form. The result supplements the numerical result for the relation for arbitrarily strong condensation obtained on the basis of a model Boltzmann equation and under the restriction that the vapor molecules are mechanically identical with the noncondensable-gas molecules [Taguchi et al., Phys. Fluids 15: 689 (2003)]. PACS numbers: 47.45.-n, 51.10.+y, 05.20.Dd, 05.60.-k     

Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation

~~Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation1. Feynman, R., There's plenty of room at the bottom, Journal of Microelectromechanical Systems, 1992, 1: 60 -66. 2. Piekos, E. S., Breuer, K. S., Numerical modeling of micromechanical devices using the direct simulation Monte Carlo method, Transactions of the ASME, Journal of Fluids Engineering, 1996, 118: 464-469. 3. Beskok, A., Karniadakis, G. E., Trimmer, W., Rarefaction and …     

Investigation of Cyber-Security and Cyber-Crimes in Oil and Gas Sectors Using the Innovative Structures of Complex Intuitionistic Fuzzy Relations

Recently, there has been enormous development due to advancements in technology. Industries and enterprises are moving towards a digital system, and the oil and gas industries are no exception. There are several threats and risks in digital systems, which are controlled through cyber-security. For the first time in the theory of fuzzy sets, this research analyzes the relationships between cyber-security and cyber-crimes in the oil and gas sectors. The novel concepts of complex intuitionistic fuzzy relations (CIFRs) are introduced. Moreover, the types of CIFRs are defined and their properties are discussed. In addition, an application is presented that uses the Hasse diagram to make a decision regarding the most suitable cyber-security techniques to implement in an industry. Furthermore, the omnipotence of the proposed methods is explained by a comparative study.     

Photoinduced Electron Transfer From Carbazole to Halomethanes in a Gas Phase

Intermolecular photoinduced electron transfer (PET) in a gas phase was studied using carbazole vapor fluorescence quenching by halomethanes (CHCl₃, CH₂Br₂, CCl₄, CHBr₃). The fluorescence quenching rate constants k _q changing from 2.3·10⁵ sec^–1·torr^–1 in mixtures with CHCl₃ to 4.6·10⁶ sec^–1·torr^–1 in mixtures with CHBr₃ at a constant temperature of 403 K were estimated. The dependence of the carbazole fluorescence decay rates in the presence of halomethanes on the free energy change G during transfer of the electron from carbazole to halomethanes is considered. It is suggested to take into account the influence of the vibrational energy of the carbazole molecule E _vib and its temperature changes in estimation of the G values. The differences between PET in the gas and liquid phases were analyzed. It is found that for mixtures with CCl₄ and CHBr₃ the negative temperature dependence of k _q is observed, when the decay rates and efficiencies of the intermolecular PET decreased with temperature increase in the range 403–573 K, i.e. these mixtures the electron transfer is not a barrier-restricted process.     

Phase Transitions in a Driven Lattice Gas with Anisotropic Interactions

The Ising lattice gas, with its well known equilibrium properties, displays a number of surprising phenomena when driven into nonequilibrium steady states. We study such a model with anisotropic interparticle interactions (J _||J ), using both Monte Carlo simulations and high temperature series techniques. Under saturation drive, the shift in the transition temperature can be both positive and negative, depending on the ratio J _||/J ! For finite drives, both first- and second-order transitions are observed. Some aspects of the phase diagram can be predicted by investigating the two-point correlation function at the first nontrivial order of a high-temperature series expansion.     

Self-Similar Solution of Spherical Shock Wave Propagation in a Mixture of a Gas and Small Solid Particles with Increasing Energy under the Influence of Gravitational Field and Monochromatic Radiation

Similarity solution for a spherical shock wave with or without gravitational field in a dusty gas is studied under the action of monochromatic radiation. It is supposed that dusty gas be a mixture of perfect gas and micro solid particles. Equilibrium flow condition is supposed to be maintained and energy is varying which is continuously supplied by inner expanding surface. It is found that similarity solution exists under the constant initial density. The comparison between the solutions obtained in gravitating and non-gravitating medium is done. It is found that the shock strength increases with an increase in gravitational parameter or ratio of the density of solid particles to the initial density of the gas, whereas an increase in the radiation parameter has decaying effect on the shock waves.