弱磁场中弱相互作用费米气体的有限粒子数效应(英文)

由弱磁场中弱相互作用费米气体的配分函数,导出有限粒子数条件下系统的配分函数G(β,N ).在此基础上,运用统计平均方法求解有限粒子数弱相互作用费米气体热力学量的解析表达式,给出各种温度条件下的热力学性质.研究结果表明,有限粒子数效应使各个热力学量都产生了一个修正项,除温度趋于0外,粒子数对化学势的修正项有直接影响,对内能和热容量的修正项并不产生直接影响.并且有限粒子数效应总是降低化学势,从而使化学势的0点向低温漂移,粒子数增大,会削弱这种效应,粒子间的相互排斥会加强这种效应.     

Bose-Einstein condensation of bouncing balls

Microscopic bouncing balls, i.e., particles confined within a positive one-half-dimensional gravitational potential, display Bose-Einstein condensation (BEC) not only in the thermodynamic limit but also in the case of a finite number of particles, and the critical temperature with a finite number of particles is higher than that in the thermodynamic limit. This system is different from the one-dimensional harmonic potential one, for which the standard result indicates that the BEC is not possible unless the number of particles is finite.     

光滑粒子流体动力学有限元法接触算法研究

 耦合光滑粒子流体动力学（SPH）方法和有限元法（FEM）,是研究冲击动力学问题的一种有效途径。为解决SPH粒子和有限单元间的接触问题,提出了SPH-FEM接触算法。该算法是在有限元节点处设置背景粒子,采用SPH接触算法的思想,计算施加在SPH粒子和有限元节点上的接触力,并且以外力的形式分别加入到SPH动量方程和有限元动力学方程中。利用SPH-FEM接触算法,对两杆撞击以及圆柱形钢弹正冲击钢板发生的冲塞破坏过程进行了三维数值模拟,靶板采用含损伤的Johnson-Cook模型和Grüneisen状态方程,模拟结果与实验结果吻合较好。     

[Russian Text Ignored]

Some aspects of the theory of fluctuating microfield in a system of charged particles are considered. The question concerning regions of validity for Holtsmark-like and Gauss-like microfield distributions in a rarefied and a dense plasma is discussed. The influence of finite dimensions of particles (test particles as well as field particles) on the microfield distribution is investigated. Expressions for a “dynamic” (two-time) generalization of the Holtsmark distribution are obtained for limiting cases. By methods of microfield theory certain formulas for the fluctuations of the electric charges within a finite volume of an electrolyte are derived too.     

The Effect of Finite Larmor Radius on Gravitational Instability of a Finitely Conducting Magnetised Hall Medium in Presence of Suspended Particles

The problem of stability of a self-gravitating, infinite homogeneous gas in the presence of suspended particles is investigated. The medium is assumed conducting and effect of external magnetic field, Hall current and finite Larmor radius corrections are also considered. The equations of the problem are linearized and from linearized equations a general dispersion relation for a dusty gas-particle medium is obtained. The dispersion relation is reduced for two special cases of wave propagations: Parallel and perpendicular to the direction of uniform magnetic field. The effect of suspended particles on the medium is investigated in both the cases. It is found that in the presence of finite Larmor radius corrections and suspended particles the condition of instability is determined by Jeans's criterion for a self gravitating finitely conducting magnetised Hall medium.     

Diffusion approximation for billiards with totally accommodating scatterers

We study the 2D motion of independent point particles colliding with a periodic array of circular obstacles. The interaction between the particles and the obstacles is described by a total accommodation reflection law. Assuming that the array of scatterers has finite horizon, the density of particles is approximated by the solution of a diffusion equation in the long-time and large-scale regime. The proof relies on a multiscale asymptotics and gives the order of approximation.     

Casimir friction force between polarizable media

This work is a continuation of our recent series of papers on Casimir friction, for a pair of particles of low relative particle velocity. Each particle is modeled as a simple harmonic oscillator. Our basic method, as before, is the use of quantum mechanical statistical mechanics, involving the Kubo formula, at finite temperature. In this work we begin by analyzing the Casimir friction between two particles polarizable in all spatial directions, this being a generalization of our study in [J.S. Høye, I. Brevik, Europhys. Lett. 91, 60003 (2010)], which was restricted to a pair of particles with longitudinal polarization only. For simplicity the particles are taken to interact via the electrostatic dipole-dipole interaction. Thereafter, we consider the Casimir friction between one particle and a dielectric half-space, and also the friction between two dielectric half-spaces. Finally, we consider general polarizabilities (beyond the simple one-oscillator form), and show how friction occurs at finite temperature when finite frequency regions of the imaginary parts of polarizabilities overlap.     

基于小关联时间两相湍流色噪声的近似模型及数值模拟

从一般高斯型色噪声模型出发,通过泛函导数,应用小关联时间,近似计算多维色噪声,得到有效Fokker-Planck方程.将其应用到两相湍流中得到颗粒相的概率密度函数输运方程,从而得到颗粒相的二阶矩模型.将颗粒应力方程简化成代数方程,建立代数应力模型.将对流扩散方程的有限分析法运用到求解两相流模型中,对壁面两相射流进行数值模拟,并将求解结果与实验结果进行对比分析.     

Finite temperature scaling theory for the collapse of Bose-Einstein condensate

We show how to apply the scaling theory in an inhomogeneous system like harmonically trapped Bose condensate at finite temperature. We calculate the temperature dependence of the critical number of particles by a scaling theory within the Hartree-Fock approximation and find that there is a dramatic increase in the critical number of particles as the condensation point is approached.     

Flows with suspended and floating particles

The evolution of the configuration of a set of particles dispersed in a flowing liquid is crucial in many applications such as sedimentation, slurry transport, rheology and structured arrays of micro- and nano-particles. Direct simulation based on what is called fictitious domain method coupled with finite element method has been used to study particulate flows and sedimentation process. Here we extend the previously proposed formulations to naturally include buoyancy force and the capillary driven attraction or repulsion of particles located at fluid interfaces. The set of differential equations is discretized using a fully implicit-fully coupled fictitious domain/finite element approach, avoiding numerical instabilities that may arise from explicit integration. The proposed formulation and implementation are validated by comparing the predictions of simple 2D flows to available numerical or analytical solutions. The method is then used to analyze the flotation of 2D particles and capillary driven aggregation at fluid interfaces.     

Solvability of linear kinetic equations with multi-energetic inelastic scattering

In this paper we shall analyse the linear Boltzmann equation describing the motion of test particles through a background of heavy field particles that can appear in several energy states. The inelastic scattering process consists in the exchange of quanta of energy between the field and test particles. The well-posedness of the problem is investigated by means of the substochastic semigroup theory and the conditions on the scattering collision frequencies are given for the evolution to keep the collision rate finite and to preserve the total number of particles.     

Effect of Conductivity on Magneto-Gravitational Instability of a Medium with Finite Larmor Radius and Suspended Particles

The self-gravitational instability of an infinite homogeneous magnetised and finitely conducting gas-particle medium is considered to include the finite Larmor radius effect in the presence of suspended particles. The equations of the problem are linearized and from linearized equations a general dispersion relation for dusty-gas is obtained. The dispersion relations are also obtained for propagation, parallel and perpendicular to the direction of uniform magnetic field. The Jeans, criterion is discussed for these two different directions of wave propagation. It is found that in the presence of finite Larmor radius corrections and suspended particles the condition of instability is determined by Jeans' criterion for a self gravitating, finitely conducting, magnetized gas-particle medium.     

Magnetic hyperfine splitting in superparamagnetic particles in external magnetic fields

The magnetic hyperfine splitting in Mössbauer spectra of superparamagnetic particles, induced by an external magnetic field, has been calculated. Numerical results have been obtained both for isolated particles with a finite value of the magnetic anisotropy energy constant and for strongly interacting particles. Moreover, analytical approximations are derived. The theoretical results are compared with results of experimental studies of supported α-Fe particles and magnetic particles in ferrofluids.     

A Review of Elastic Light Scattering Theories

Mie scattering is an important tool for diagnosing microparticles or aerosol particles in technical or natural environments. Mie theory is restricted to spherical, homogeneous, isotropic and non-magnetic particles in a non-absorbing medium. However, as microparticles are hardly ever spherical or homogeneous, there is much interest in more advanced scattering theories. During recent decades, scattering methods for non-spherical and non-homogeneous particles have been developed and even some computer codes are readily available. Extension of Mie theory covers coated spheres, stratified spheres and clustered spheres. For homogeneous non-spherical particles such as spheroids, ellipsoids and finite cylinders, surface discretization methods have been developed. Scattering by inhomogeneous particles may be computed by volume discretization methods.     

The Arrow of Time in the Equations of Motion

It is argued that time's arrow is present in all equations of motion. But it is absent in the point particle approximations commonly made. In particular, the Lorentz-Abraham-Dirac equation is time-reversal invariant only because it approximates the charged particle by a point. But since classical electrodynamics is valid only for finite size particles, the equations of motion for particles of finite size must be considered. Those equations are indeed found to lack time-reversal invariance, thus ensuring an arrow of time. Similarly, more careful considerations of the equations of motion for gravitational interactions also show an arrow of time. The existence of arrows of time in quantum dynamics is also emphasized.     

A Possible Origin of Quantum Correlations

We intend to eliminate the known conflict between relativity and quantum mechanics. We believe the “instant” correlation between entangled distant quantum particles can be explained by the fact that in a laboratory reference frame the photon traveling duration is positive and finite while its proper (in vacuum) traveling duration is equal to zero. In the latter case, any two events that are separated (in a laboratory reference frame) by an arbitrary finite distance can be considered as simultaneous ones. So, the photon nonlocal correlation turns out to be a relative property and may be explained like known twins paradox in relativity. In such a situation, any standard causal interaction between the correlated particles is absent in a laboratory reference frame; however, some specific mutual couple appears between them; this couple is strictly oscillating without some oriented energy or/and information transferring. We also motivate the basic hypothesis extension on quantum particles having nonzero masses.     

一种有限元-光滑粒子流体动力学耦合算法

介绍一种新的有限元-光滑粒子流体动力学耦合算法.通过将SPH法中的粒子固连到单元边界上实现有限元计算与SPH计算的耦合,粒子可以连接到单元边界上的任意点,且一条单元边界可以与多个粒子连接,耦合界面处粒子分布与单元分布无相互限制.应用该算法模拟应力波传播和高速冲击问题.结果表明,算法在应力波传播计算中具有良好的精度,在高速冲击问题中计算精度与SPH法相近的,而计算效率大大提高.     

Simulation of electromagnetic scattering by random discrete particles using a hybrid FE-BI-CBFM technique

A hybrid finite element–boundary integral–characteristic basis function method (FE-BI-CBFM) is proposed for an efficient simulation of electromagnetic scattering by random discrete particles. Specifically, the finite element method (FEM) is used to obtain the solution of the vector wave equation inside each particle and the boundary integral equation (BIE) using Green's functions is applied on the surfaces of all the particles as a global boundary condition. The coupling system of equations is solved by employing the characteristic basis function method (CBFM) based on the use of macro-basis functions constructed according to the Foldy–Lax multiple scattering equations. Due to the flexibility of FEM, the proposed hybrid technique can easily deal with the problems of multiple scattering by randomly distributed inhomogeneous particles that are often beyond the scope of traditional numerical methods. Some numerical examples are presented to demonstrate the validity and capability of the proposed method.     

基于波导、金和氧化锌的随机激光器的研究

通过将金属金嵌入到上下两层波导结构中,与ZnO随机粒子相结合,设计出一种新型结构的随机激光器。采用时域有限差分法(FDTD),数值模拟了该随机激光器系统的光场分布和模式频谱图,并针对金粒子和金薄膜两种情况进行对比分析。结果显示,采用金粒子作夹层时,出射激光模式数量减少,单色性较好;采用金薄膜作夹层时,出射激光光强较大。