Current layers and filaments in a semiconductor model with an impact ionization induced instability

Dissipative structures associated with an instability in a semiconductor far from equilibrium are studied. A generation-recombination mechanism, which effects anS-shaped current-voltage characteristics, is coupled to diffusion and drift of the electrons. The spectrum of linear recombination-diffusion modes is computed for the homogeneous steady state with negative differential conductivity. The obtained soft mode instability gives rise to the bifurcation of a family of transversally modulated inhomogeneous steady states and longitudinal travelling waves. The inhomogeneous steady states are calculated from the full nonlinear transport equations for plane and cylindrical geometries. They correspond to oscillatory and solitary concentration profiles, including depletion and accumulation layers and cylindrical filaments. Conditions for the formation of kink-shaped coexistence profiles are established in terms of equal area rules. The current-voltage characteristics are extended to include inhomogeneous current states. Nonequilibrium phase transitions between various branches of these characteristics are associated with switching through filamentation.     

Nonequilibrium MHD plasma flow in a high-interaction disk generator

Nonequilibrium MHD plasma flow in a high-interaction disk-type MHD generator is examined by numerical simulations based on the two-temperature model equations. The simulations are performed for the generators driven by working gases: He-Cs and He-K. Homogeneous and inhomogeneous plasma behavior is observed with change of the load resistance, and it is found that the structures of the inhomogeneous plasma differ for different seed materials. The plasma structures associated with both the partial ionization instability and the magnetoacoustic instability are discussed for both plasmas     

反应性RM不稳定混合特性研究: 反应活性与介质不均匀性的影响

预混火焰界面的RM（Richtmyer-Meshkov）不稳定现象在自然界和工程实践中十分常见,但目前关于反应性RM不稳定的研究主要集中于均匀介质的情况,而实际中的预混气体往往是非均匀的,因此开展非均匀介质中火焰界面演化和混合特性的研究十分必要。采用带单步化学反应的Navier-Stokes方程和高精度数值格式,研究了预混火焰界面在入射激波及反射激波作用下的RM不稳定过程,考察了化学反应活性以及介质非均匀性对RM不稳定过程中火焰界面混合特性的变化规律的影响。结果表明,在入射激波作用后的阶段,在均匀介质中的火焰界面形态呈现典型的"钉-帽-泡"结构,化学反应活性越强,界面的"泡"结构和"钉-帽"结构增长越快;而在非均匀介质中,火焰界面形态则呈现"钉-钉"结构,界面在流向速度差的诱导下被更大程度地拉伸。在第一次反射激波作用后的阶段,混合区的增长速率不依赖于反应活性和均匀性,仅与流动特性有关。时间尺度的研究表明,大尺度流动是反应性RM不稳定的主导因素,其次是化学反应,最后是小尺度混合,化学反应的强化会抑制大尺度流动,非均匀性会强化大尺度流动。      

Kinetic boundary layers in gas mixtures: Systems described by nonlinearly coupled kinetic and hydrodynamic equations and applications to droplet condensation and evaporation

We consider a mixture of heavy vapor molecules and a light carrier gas surrounding a liquid droplet. The vapor is described by a variant of the Klein-Kramers equation, a kinetic equation for Brownian particles moving in a spatially inhomogeneous background; the gas is described by the Navier-Stokes equations; the droplet acts as a heat source due to the released heat of condensation. The exchange of momentum and energy between the constituents of the mixture is taken into account by force terms in the kinetic equation and source terms in the Navier-Stokes equations. These are chosen to obtain maximal agreement with the irreversible thermodynamics of a gas mixture. The structure of the kinetic boundary layer around the sphere is then determined from the self-consistent solution of this set of coupled equations with appropriate boundary conditions at the surface of the sphere. For this purpose the kinetic equation is rewritten as a set of coupled moment equations. A complete set of solutions of these moment equations is constructed by numerical integration inward from the region far away from the droplet, where the background inhomogeneities are small. A technique developed in an earlier paper is used to deal with the severe numerical instability of the moment equations. The solutions so obtained for given temperature and pressure profiles in the gas are then combined linearly in such a way that they obey the boundary conditions at the droplet surface; from this solution source terms for the Navier-Stokes equation of the gas are constructed and used to determine improved temperature and pressure profiles for the background gas. For not too large temperature differences between the droplet and the gas at infinity, self-consistency is reached after a few iterations. The method is applied to the condensation of droplets from a supersaturated vapor, where small but significant corrections to an earlier, not fully consistent version of the theory are found, as well as to strong evaporation of droplets under the influence of an external heat source, where corrections of up to 40 % are obtained.     

Ordering kinetics in bcc alloys with allowance for diffusion processes

The kinetics of inhomogeneous ordering in binary bcc substitution alloys of arbitrary stoichiometry is considered with the account for for diffusion processes. A system of kinetic equations describing the joint evolution of the occupancies of two sublattices of a bcc lattice is derived using a phenomenological approach. It is shown that, even within the mean-field approximation, this approach allows one to describe simultaneously the processes of establishment of the long-range order and diffusion of the alloy components. Numerical analysis of the obtained system of equations showed that quick onset of long-range order first occurs, which is followed by slow diffusion of the alloy components.     

Structural evolution of the Tropical Pacific climate network

An attempt is made to develop an equilibrium kinetic equation for a weakly non ideal inhomogeneous gravitational system utilizing the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations. It is shown that the pair correlational function explicitly depends upon the nature of binary interaction between particles. The corresponding kinetic equation containing pair correlation corrections is devoid of the degeneracy present in the collisionless Boltzmann equation with respect to the nature of the two particle interactions, unlike the Vlasov equation that cannot recognize the nature of two particle interaction. A net effect of the particle correlations can be realized only if the spatial symmetry of the correlation interaction is broken due to a spatial inhomogeneity. Such an inhomogeneity is inherently present in a bulk gravitational system in view of the unshielded long range nature of the two-particle interactions. In a finite gravitational system, the effects of pair correlations in the first order kinetic equation can be expressed in terms of the macroscopic gravitational potential to obtain a modified Boltzmann distribution that includes the effects of correlations.     

Spinodal decomposition of an ABv model alloy: Patterns at unstable surfaces

We develop mean-field kinetic equations for a lattice gas model of a binary alloy with vacancies (ABv model) in which diffusion takes place by a vacancy mechanism. These equations are applied to the study of phase separation of finite portions of an unstable mixture immersed in a stable vapor. Due to a larger mobility of surface atoms, the most unstable modes of spinodal decomposition are localized at the vapor-mixture interface. Simulations show checkerboard-like structures at the surface or surface-directed spinodal waves. We determine the growth rates of bulk and surface modes by a linear stability analysis and deduce the relation between the parameters of the model and the structure and length scale of the surface patterns. The thickness of the surface patterns is related to the concentration fluctuations in the initial state. Received 28 October 1998     

Green's function equations of motion for a many-fermion system: II. Inhomogeneous system at finite temperature

The equations of motion for many-time causal Green's functions are extended to an inhomogeneous many-fermion system at finite temperature. The boundary condition that the perturbation vanishes in the remote past and distant future (adiabatic hypothesis) is used to determine the unperturbed propagator. The temperature enters the theory only as a parameter. Thus there is no need for analytic continuations in the complex temperature-time plane. The theory is used to derive thermal Hartree-Fock theory and Wick's theorem at finite temperature. A linked cluster perturbation expansion at finite temperature is obtained by iterating the equations of motion, without unlinked disconnected diagrams even appearing. After integration over frequency, the present theory gives the perturbation theory rules in terms of global propagators that Baym and Sessler obtained from the imaginary-time theory.     

The discrete coagulation-fragmentation equations: Existence,uniqueness, and density conservation

The discrete coagulation-fragmentation equation describes the kinetics of cluster growth in which clusters can coagulate via binary interactions to form larger clusters or fragment to form smaller ones. These models have many applications in pure and applied science ranging from cluster formation in galaxies to the kinetics of phase transformations in binary alloys. Our results relate to existence, uniqueness, density conservation and continuous dependence and they generalise the corresponding results in [ref. 2] for the Becker-Doring equations for which the processes are restricted to clusters gaining or shedding one particle. Examples are given which illustrate the role of the assumptions on the kinetic coefficients and show the rich set of analytic phenomena supported by the general discrete coagulation-fragmentation equations.     

非均匀磁场中的动力论漂移迴旋损失锥不稳定性

本文从解析和数值计算两种途径仔细研究了磁场非均匀性漂移共振的动力论效应对于漂移迴旋损失锥不稳定性(DCLC)的影响。发现在高β等离子体中,磁场非均匀效应是非常重要的,磁漂移共振对于负能的模起耗散作用,从而使原有的DCLC不稳定性加强,而且不稳定性的参数区域大大扩展了。有限β值效应并没有象流体近似理论所预言的那样使DCLC模稳定。 关键词：     

Stochastic statistical theory of nucleation and evolution of nano-sized precipitates in alloys with application to precipitation of copper in iron

A consistent and computationally efficient stochastic statistical approach (SSA) is developed to study the kinetics of nucleation and evolution of nano-sized precipitates in alloys. To increase the accuracy of the method, many refinements of the previous simplified versions of this approach have been made. We consider a realistic vacancy-mediated exchange kinetics rather than the simplified direct-atomic-exchange model; use quantitative, cluster statistical methods rather than simple mean-field-type approximations; allow strong concentration and temperature dependences of generalized mobilities in the resulting kinetic equations; consider realistic alloy models based on first-principle calculations, and so on. We also introduce the “maximum thermodynamic gain” principle to determine the key kinetic parameter of the SSA, the characteristic length of local equilibrium in the course of the nucleation process. For several realistic models of iron-copper alloys studied, the results of the SSA-based simulations of precipitation kinetics made in this work agree well with the kinetic Monte Carlo simulation results for all main characteristics of the microstructure. The approach developed is also used to study the kinetics of nucleation and changes in microstructural evolution under variations of temperature or concentration.     

Linear and nonlinear fluctuations of electron-temperature-gradient driven mode and electron acoustic mode in a two-electron temperature nonthermal magnetized plasma

Nonlinear vortical structures and soliton formation are investigated for electron temperature gradient instability in a two-electron temperature non-Maxwellian magnetoplasma. The inhomogeneity in magnetic field is also considered. A new set of nonlinear equations, using transport equations of Braginskii”s model, are formulated to study the nonlinear structures. A modified linear dispersion relation of coupled electron temperature gradient (ETG) mode and electron acoustic wave is derived. The ETG instability is found to increase with increase in η_ec value that increases with sharp density gradients. The results are applied to auroral region of earth's magnetosphere and the calculated values of the nonlinear electric field of fast solitary waves are found to be in agreement with the Viking satellite observations.     

Quantum Boltzmann equations for binary interactions between identical particles

The inhomogeneous master equation obtained in a previous paper (by Van Vliet) is employed to obtain as first-moment equation two quantum mechanical Boltzmann equations (diagonal) for systems of weakly interacting identical particles. The interactions considered are of a binary nature: fermion-fermion or boson-boson. The resulting equations have the same structure as before. The total Boltzmann equation (diagonal and nondiagonal part) is also derived.     

Nonequilibrium fluctuations in the Rayleigh-Bénard problem for binary fluid mixtures

We have employed a simple Galerkin-approximation scheme to calculate nonequilibrium temperature and concentration fluctuations in a binary fluid subjected to a temperature gradient with realistic boundary conditions. When a fluid mixture is driven outside thermal equilibrium, there are two instability mechanisms, namely a Rayleigh (stationary) and a Hopf (oscillatory) instability, causing long-ranged fluctuations. The competition of these two mechanisms causes the structure factor associated with the temperature fluctuations to exhibit two maxima as a function of the wave number q of the fluctuations, in particular, close to the convective instability. In the presence of thermally conducting but impermeable walls the intensity of the temperature fluctuations vanishes as q goes to zero, while the intensity of the concentration fluctuations remains finite in the limit of vanishing q. Finally, we propose a simpler small-Lewis-number approximation scheme, which is useful to represent nonequilibrium concentration fluctuations for mixtures with positive separation ratio, even close to (but below) the convective instability.     

Enskog-like kinetic models for vehicular traffic

In the present paper a general criticism of kinetic equations for vehicular traffic is given. The necessity of introducing an Enskog-type correction into these equations is shown. An Enskog-like kinetic traffic flow equation is presented and fluid dynamic equations are derived. This derivation yields new coefficients for the standard fluid dynamic equations of vehicular traffic. Numerical simulations for inhomogeneous traffic flow situations are shown together with a comparison between kinetic and fluid dynamic models.     

The formation of quasi-crystalline structures in a dislocation cluster

The formation of inhomogeneous dislocation structures is investigated within a model taking into account correlation interaction between screw dislocations. This interaction is found to give rise to an instability of the homogeneous state of the system. It is shown that when the critical nonequilibrium conditions for this instability are attained in a local volume, an inhomogeneous dislocation structure is formed spontaneously. As the degree of instability of the system increases further, this structure is transformed into a cellular quasi-crystalline structure.