稀相气固悬浮体越过沿平面匀速运动激波后的流动结构*

本文给出气固悬浮体中激波感生边界层的渐近数值分析,其中计及了作用于固体粒子的Saf-fman升力.研究结果表明粒子横越边界层的迁移导致了粒子轨道的交叉,因此对目前通用的含灰气体模型应做相应的修正.本文利用匹配渐近展开方法得到了匀速运动激波后方的两相侧壁边界层方程,详细描述了在Lagrange坐标下计算颗粒相流动参数的方法,并给出了粒子浓度很低情况下的数值结果.     

Ballistic motion of a tracer particle coupled to a Bose gas

We study the motion of a heavy tracer particle weakly coupled to a dense interacting Bose gas exhibiting Bose–Einstein condensation. In the so-called mean-field limit, the dynamics of this system approaches one determined by nonlinear Hamiltonian evolution equations. We derive the effective dynamics of the tracer particle, which is described by a non-linear integro-differential equation with memory, and prove that if the initial speed of the tracer particle is below the speed of sound in the Bose gas the motion of the particle approaches an inertial motion at constant velocity at large times.     

Hamiltonian Dynamics of a Particle Interacting with a Wave Field

We study the Hamiltonian equations of motion of a heavy tracer particle interacting with a dense weakly interacting Bose-Einstein condensate in the classical (mean-field) limit. Solutions describing ballistic subsonic motion of the particle through the condensate are constructed. We establish asymptotic stability of ballistic subsonic motion.     

Numerical modeling of the movement of a rigid particle in viscous fluid

Modeling the movement of a rigid particle in viscous fluid is a problem physicists and smathematicians have tried to solve since the beginning of this century. A general model for an ellipsoidal particle was first published by Jeffery in the twenties. We exploit the fact that Jeffery was concerned with formulae which can be used to compute numerically the velocity field in the neighborhood of the particle during his derivation of equations of motion of the particle. This is our principal contribution to the subject. After a thorough check of Jeffery's formulae, we coded software for modeling the flow around a rigid particle based on these equations. Examples of its applications are given in conclusion. A practical example is concerned with the simulation of sigmoidal inclusion trails in porphyroblast.     

Equation of motion for a radiating charged particle in classical electrodynamics

We propose classical equations of motion for charged particles in an electromagnetic field. These are general formulas for the particle acceleration that take the radiation-induced deceleration into account and contain no second derivatives of the particle velocity. In several particular cases considered, the new equations yield results coinciding with those known in the literature and experimentally verified. We show that in the range of ultrahigh energies, classical electrodynamics does not lead to inherent inconsistencies and in principle allows particle motion with energies exceeding the Pomeranchuk limit.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 143, No. 1, pp. 112–130, April, 2005.     

The macroscopic system of Einstein-Maxwell equations for a system of interacting particles

We derive the macroscopic Einstein—Maxwell equations up to the second-order terms, in the interaction for systems with dominating electromagnetic interactions between particles (e.g., radiation-dominated cosmological plasma in the expanding Universe before the recombination moment). The ensemble averaging of the microscopic Einstein and Maxwell equations and of the Liouville equations for the random functions of each type of particle leads to a closed system of equations consisting of the macroscopic Einstein and Maxwell equations and the kinetic equations for one-particle distribution functions for each type of particle. The macroscopic Einstein equations for a system of electromagnetically and gravitationally interacting particles differ from the classical Einstein equations in having additional terms in the lefthand side due to the interaction. These terms are given by a symmetric rank-two traceless tensor with zero divergence. Explicitly, these terms are represented as momentum-space integrals of the expressions containing one-particle distribution functions for each type of particle and have much in common with similar terms in the left-hand side of the macroscopic Einstein equations previously obtained for a system of self-gravitating particles. The macroscopic Maxwell equations for a system of electromagnetically and gravitationally interacting particles also differ from the classical Maxwell equations in having additional terms in the left-hand side due to simultaneous effects described by general relativity and the interaction effects. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 125, No. 1, pp. 107–131, October, 2000.     

On existence of solutions for a system of Boltzmann transport equations

We consider a linear system of Boltzmann transport equations. The system models charged particle transport in tissue, for example. Although only one species of particles, say photons, is invasing these particles mobilize electrons and positrons. Hence in realistic modelling of particle transport one needs a coupled system of three Boltzmann transport equations. The solution of this system must satisfy the inflow boundary condition. We show existence and uniqueness result of the solution applying coercitivity of the underlying linear operator and its adjoint operator. In addition, we consider existence of continuous solutions by iterative methods. Copyright © 2008 John Wiley & Sons, Ltd.     

Can the Kerr Solution Be Found by the Einstein–Infeld–Hoffmann Method?

We present expansions of the Kerr metric in harmonic coordinates for the values of the radial coordinate r at which the dimensionless parameters m/r and a/r (m and a are parameters used in the Kerr solution) are of the respective second and first orders of smallness. We show that it is impossible to obtain these expansions uniquely using the Einstein–Infeld–Hoffmann method. We conclude that we must normalize the Kerr metric expansions for the expressions obtained in deriving the equations of translational motion of particle singularities and the evolution equations of their spins in the post-Newtonian and higher-order approximations.     

Emission of Cherenkov radiation as a mechanism for Hamiltonian friction

We study the motion of a heavy tracer particle weakly coupled to a dense, weakly interacting Bose gas exhibiting Bose–Einstein condensation. In the so-called mean-field limit, the dynamics of this system approaches one determined by nonlinear Hamiltonian evolution equations. We prove that if the initial speed of the tracer particle is above the speed of sound in the Bose gas, and for a suitable class of initial states of the Bose gas, the particle decelerates due to emission of Cherenkov radiation of sound waves, and its motion approaches a uniform motion at the speed of sound, as time t tends to ∞.     

平面射流中纳米粒子积聚的矩方法

应用大涡模拟方法求解平面湍射流场,矩方法求解纳米粒子的一般动力学方程．通过对每种情况3 000个时间步的平均,得到了Schmidt数和Damkohler数对纳米粒子动力学特性的影响．结果发现, 当气体参数不变时,Schmidt数的变化只对直径小于1 nm的颗粒数密度的分布产生影响．直径小的颗粒其颗粒数密度沿流动方向下降迅速,而具有大Schmidt数的颗粒,沿横向的分布较窄．较小的颗粒容易发生积聚和扩散,并且体积增长较快,因而颗粒多分散性较为明显．小的颗粒积聚时间尺度能增强颗粒的碰撞和积聚频率,导致颗粒尺寸迅速增大．Damkohler数越大,颗粒的多分散也越明显．     

Continuity of Solutions of a Class of Fractional Equations

In practice many problems related to space/time fractional equations depend on fractional parameters. But these fractional parameters are not known a priori in modelling problems. Hence continuity of the solutions with respect to these parameters is important for modelling purposes. In this paper we will study the continuity of the solutions of a class of equations including the Abel equations of the first and second kind, and time fractional diffusion type equations. We consider continuity with respect to the fractional parameters as well as the initial value.     

Uniform convergence of a finite difference scheme for a system of coupledreaction‐diffusion equations

We study a system of coupled reaction‐diffusion equations. The equations have diffusion parameters of different magnitudes associated with them. Near each boundary, their solution exhibit two overlapping layers. A difference scheme on layer‐adapted piecewise uniform meshes is used to solve the system numerically. We show that the scheme is almost second‐order convergent, uniformly in both perturbation parameters, thus improving previous results [3].     

Reflected pulses from a refractive random medium at grazing incidence

A problem of acoustic pulse reflection by a one-dimensionalrefractive random medium is considered in the case of grazingangle incidence. The material parameters of the medium are assumedto vary with a random microscale and a deterministic macroscale.A system of stochastic equations for random scattering variablesis derived based upon the random modelling of three separatescales of variations. The statistical properties of the reflectedpulses are characterized by an asymptotic diffusion limit theoremof stochastic differential equations with multiple scales. Thetransport equations governing the limiting stochastic distributionsof the random reflection coefficient are obtained in the propagatingregime, which leads to the power spectral densities of the reflectedpressure and particle velocity fields.     

两相流中柱状固粒对流体湍动特性影响的研究

对含柱状固粒的两相流场,建立了包含柱状固粒对流场影响的流体脉动速度方程,在求解脉动速度方程的基础上,经平均得到流体的湍流强度和雷诺应力.将该方法用于槽流湍流场的求解,并与单相流实验结果进行了比较.计算中变化柱状固粒的参数,给出了固粒的体积分数、长径比、松驰时间对流场湍动特性的影响,说明粒子对流场的湍动特性起着抑制作用,其抑制的程度与粒子的体积分数、长径比成正比,与粒子的松弛时间成反比.     

Mode-coupling approximation in a fractional-power generalization: Particle dynamics in supercooled liquids and glasses

We describe the particle dynamics in supercooled liquids in the mode-coupling approximation in a fractional-power generalization, where the kinetic integro-differential equations are exactly derived from the equations of motion of the dynamical variables by projection operator methods. We show that in the case of separated time scales in the particle dynamics and with the nonlinear interaction between the stochastic and translation motion modes taken into account, the solution of the equations gives a well-defined picture of singularities of the one-particle dynamics of supercooled liquids and glasses. Comparison with the data for the metal alloy Fe ₅₀ Cr ₅₀ atomic dynamics simulation demonstrates a good agreement in the entire temperature range corresponding to the supercooled liquid and glass phases.     

Equation for the Complex Energy of a Bound Particle in a Laser Radiation Field in the Presence of Strong Constant Electromagnetic Fields

We construct exact solutions of the Schrodinger and Pauli equations for charged particles in the external field of the Redmond generalized configuration. We calculate the Green's functions of scalar and spinning particles in this field. Using them, we calculate the equations for the complex quasienergy of a bound particle (bound by a short-range potential) two different ways. In the example of an external constant electric field, we discuss the applicability domain of the obtained equations and the differences between their solutions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 2, pp. 198–211, November, 2005.     

Particle methods for multi-group pedestrian flow

We consider a multi-group microscopic model for pedestrian flow describing the behaviour of large groups. It is based on an interacting particle system coupled to an eikonal equation. Hydrodynamic multi-group models are derived from the underlying particle system as well as scalar multi-group models. The eikonal equation is used to compute optimal paths for the pedestrians. Particle methods are used to solve the equations on all levels of the hierarchy. Numerical test cases are investigated and the models and, in particular, the resulting evacuation times are compared for a wide range of different parameters.     

An optimal homotopy analysis method based on particle swarm optimization: application to fractional-order differential equation

This paper describes a new problem-solving mentality of finding optimal parameters in optimal homotopy analysis method (optimal HAM). We use particle swarm optimization (PSO) to minimize the exact square residual error in optimal HAM. All optimal convergence-control parameters can be found concurrently. This method can deal with optimal HAM which has finite convergence-control parameters. Two nonlinear fractional-order differential equations are given to illustrate the proposed algorithm. The comparison reveals that optimal HAM combined with PSO is effective and reliable. Meanwhile, we give a sufficient condition for convergence of the optimal HAM for solving fractional-order equation, and try to put forward a new calculation method for the residual error.     

On a practical implementation of particle methods

This paper is devoted to a practical implementation of deterministic particle methods for solving transport equations with discontinuous coefficients and/or initial data, and related problems. In such methods, the solution is sought in the form of a linear combination of the delta-functions, whose positions and coefficients represent locations and weights of the particles, respectively. The locations and weights of the particles are then evolved in time according to a system of ODEs, obtained from the weak formulation of the transport PDEs.The major theoretical difficulty in solving the resulting system of ODEs is the lack of smoothness of its right-hand side. While the existence of a generalized solution is guaranteed by the theory of Filippov, the uniqueness can only be obtained via a proper regularization. Another difficulty one may encounter is related to an interpretation of the computed solution, whose point values are to be recovered from its particle distribution. We demonstrate that some of known recovering procedures, suitable for smooth functions, may fail to produce reasonable results in the nonsmooth case, and discuss several successful strategies which may be useful in practice. Different approaches are illustrated in a number of numerical examples, including one- and two-dimensional transport equations and the reactive Euler equations of gas dynamics.     

Closure method for spatially averaged dynamics of particle chains

We study the closure problem for continuum balance equations that model the mesoscale dynamics of large ODE systems. The underlying microscale model consists of classical Newton equations of particle dynamics. As a mesoscale model we use the balance equations for spatial averages obtained earlier by a number of authors: Murdoch and Bedeaux, Hardy, Noll and others. The momentum balance equation contains a flux (stress), which is given by an exact function of particle positions and velocities. We propose a method for approximating this function by a sequence of operators applied to the average density and momentum. The resulting approximate mesoscopic models are systems in closed form. The closed form property allows one to work directly with the mesoscale equations without the need to calculate the underlying particle trajectories, which is useful for the modeling and simulation of large particle systems. The proposed closure method utilizes the theory of ill-posed problems, in particular iterative regularization methods for solving first order linear integral equations. The closed form approximations are obtained in two steps. First, we use Landweber regularization to (approximately) reconstruct the interpolants of the relevant microscale quantities from the average density and momentum. Second, these reconstructions are substituted into the exact formulas for stress. The developed general theory is then applied to non-linear oscillator chains. We conduct a detailed study of the simplest zero-order approximation, and show numerically that it works well as long as the fluctuations of velocity are nearly constant.