共查询到20条相似文献,搜索用时 15 毫秒
1.
按分布函数的定义不同,描述高能带电粒子在等离子体中输运的-Planck方程有不同的形式。从数值计算的观点出发对两种不同形式的Fokker-Planck方程作了比较和评价,并指出Fokker-Planck碰撞项可解释为速度空间的对流扩散项。在此基础上用有限差分方法求解二维(速度一维,几何一维)含时Fokker-Planck方程,编制了计算程序CAPT,并将其应用于α粒子的输运研究。最后计算了典型的Tokamak D-T聚变堆参数下α粒子的损失,并给出了堆内α粒子的分布及损失α粒子的速度分布。 相似文献
2.
Ballistic annihilation with continuous initial velocity distributions is investigated in the framework of the Boltzmann equation. The particle density and the rms velocity decay as c approximately t(-alpha) and velocity approximately t(-beta), with the exponents depending on the initial velocity distribution and the spatial dimension d. For instance, in one dimension for the uniform initial velocity distribution beta = 0.230 472ellipsis. In the opposite extreme d-->infinity, the dynamics is universal and beta-->(1-2(-1/2))d(-1). We also solve the Boltzmann equation for Maxwell particles and very hard particles in arbitrary spatial dimension. These solvable cases provide bounds for the decay exponents of the hard sphere gas. 相似文献
3.
Summary The present paper describes a direct method of obtaining are expression of the distribution function of charged particles
which diffuse in a plasma. The distribution function in velocity, angle and time is presented starting from the Fokker-Planck
equation. Temperature, average velocity and energy of charged particles (electron or ions) have also been calculated as functions
of time.
The authors of this paper have agreed to not receive the proofs for correction. 相似文献
4.
We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of
sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a size-dependent terminal
velocity. They are either allowed to merge whenever they cross or there is a size ratio criterion enforced to account for
collision efficiency. Such a system may be described, in mean field approximation, by the Smoluchowski kinetic equation with
a differential sedimentation kernel. We obtain self-similar steady-state and time-dependent solutions to the kinetic equation,
using methods borrowed from weak turbulence theory. Analytical results are compared with direct numerical simulations (DNS)
of moving and merging particles, and a good agreement is found. 相似文献
5.
鉴于试验观察淤泥絮凝结构的技术难度,本文尝试以布朗动力学为基础,采用蒙特卡洛方法动态模拟电离作用下颗粒成长为絮团的过程.为结合实际情况,泥沙颗粒初始位置由颗粒粒径和淤泥密度决定,颗粒初始速度按照相应条件下高斯随机分布给定.边界条件用和实际符合较好的循环边界.在模拟数据分析的基础上,讨论并比较了颗粒粒径和淤泥密度对絮凝时间以及絮团开放程度的影响.另一方面,讨论了电离作用后颗粒电荷量对絮团生长的影响.解释了泥沙颗粒表面电荷密度变化对絮凝过程和絮团结构的影响,模拟结果和实际情况较为一致. 相似文献
6.
Summary The Fokker-Planck equation describing a beam of charged particles entering a homogeneous medium is solved here for a stationary
case. Interactions are taken into account through Coulomb cross-section. Starting from the charged-particle distribution as
a function of velocity and penetration depth, some important kinetic quantities are calculated, like mean velocity, range
and the loss of energy per unit space. In such quantities the energy straggling is taken into account. This phenomenon is
not considered in the continuous slowing-down approximation that is commonly used to obtain the range and the stopping power.
Finally the well-known Bohr or Bethe formula is found as a first-order approximation of the Fokker-Planck equation.
The authors of this paper have agreed to not receive the proofs for correction. 相似文献
7.
The problem is to establish the correct diffusion equation in a medium that is inhomogeneous and whose temperature also varies in space. As a special model we study particles whose phase space distribution obeys Kramers' equation with a generalized collision operator. In the usual limit of strong collisions a diffusion equation is obtained. This equation contains additional drift terms, which depend on the form of the collision operator. They cannot be expressed as a mobility and a diffusion coefficient, unless the decay law of the velocity happens to be linear. Conclusion: no universal form of the diffusion equation exists, but each system has to be studied individually.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday 相似文献
8.
Toshiya Ohtsuki 《Physica A》1982,110(3):606-616
The self-diffusion process of Brownian particles is theoretically investigated for concentrated systems in the presence of strong potential interactions between particles. Starting from an N-particle diffusion equation, a formalism is developed to calculate the self-diffusion coefficient and the velocity autocorrelation function on the basis of the superposition approximation for the three-particle distribution function of non-equilibrium states. Explicit calculations are carried out for model systems of hard spheres with a screened Coulomb potential. Calculated time-dependent self-diffusion coefficients are compared with available data of the Brownian dynamics. Without introducing any phenomenological or adjustable parameters, quantitative agreement is achieved. 相似文献
9.
S. O. Gladkov 《Technical Physics》2000,45(7):854-857
The dependence of the mean size of dispersed phase particles on the physical parameters of a system (temperature, density, and sound velocity in a substance) was found. The generalized Fokker-Planck equation was used to calculate the particle size distribution. The obtained binary distribution function was proved to adequately describe a large array of experimental data in actual physical conditions. It was shown rigorously that the fine-grain phase (powder) results when the viscocrystalline phase is subjected to shear loads. The shape of the distribution turned out to be independent of external actions, i.e., remained the same both on sedimentation and at pressure drop. 相似文献
10.
We investigate the settling of heavy particles in a steady, two-dimensional random velocity field, and find instances in which particle suspension occurs. This leads to a bimodal velocity distribution that may explain some apparently conflicting results reported in the literature. The bimodal distribution is typically smeared out by a time dependence of the ambient flow but, if the time variation is slow, the settling rates of some particles will be as well. The resulting broadbanded velocity distribution of the settling particles will have significance for processes such as rain drop formation, in which the spread of particle velocities affects the statistics of particle collisions. 相似文献
11.
J. Piasecki 《Journal of statistical physics》1984,35(5-6):635-643
The motion of a charged hard rod, accelerated by a constant and uniform external field, in a fluid of mechanically identical neutral particles is studied. The system, initially at rest, is excited through collisions with the accelerated particle. A class of initial configurations is found for which recollisions between the charged rod and the excitation caused by it (a moving particle) never occur. The evolution of the velocity distribution of the test particle is analyzed in this case. The possibility of obtaining from microscopic dynamics a kinetic equation is discussed. The dependence of the current on the external field is shown to agree with that predicted by the Boltzmann equation. 相似文献
12.
The distribution function in position and velocity space for the Brownian motion of particles in an external field is determined by the Kramers equation, i.e., by a two variable Fokker-Planck equation. By expanding the distribution function in Hermite functions (velocity part) and in another complete set satisfying boundary conditions (position part) the Laplace transform of the initial value problem is obtained in terms of matrix continued fractions. An inverse friction expansion of the matrix continued fractions is used to show that the first Hermite expansion coefficient may be determined by a generalized Smoluchowski equation. The first terms of the inverse friction expansion of this generalized Smoluchowski operator and of the memory kernel are given explicitly. The inverse friction expansion of the equation determining the eigenvalues and eigenfunctions is also given and the connection with the result of Titulaer is discussed. 相似文献
13.
We prove the existence and uniqueness of an equilibrium state with unit mass to the dissipative linear Boltzmann equation with hard-spheres collision kernel describing inelastic interactions of a gas particles with a fixed background. The equilibrium state is a universal Maxwellian distribution function with the same velocity as field particles and with a non-zero temperature lower than the background one. Moreover thanks to the H-Theorem we prove strong convergence of the solution to the Boltzmann equation towards the equilibrium. 相似文献
14.
A. Ya. Silenko 《Journal of Experimental and Theoretical Physics》1998,87(2):246-250
The Dirac-Pauli equation is used to obtain the exact equation of spin motion for spin-1/2 particles with an anomalous magnetic
moment in a constant and uniform magnetic field. Exact formulas are established for the angular velocity of the revolution
of such particles along circular orbits and the rotation of the particle spin with respect to momentum. Finally, a quantum
mechanical equation for the motion of the particles in a strong magnetic field is derived.
Zh. éksp. Teor. Fiz. 114, 448–457 (August 1998) 相似文献
15.
The rotational motion and orientational distribution of ellipsoidal particles in turbulent flows are of significance in environmental and engineering applications. Whereas the translational motion of an ellipsoidal particle is controlled by the turbulent motions at large scales, its rotational motion is determined by the fluid velocity gradient tensor at small scales, which raises a challenge when predicting the rotational dispersion of ellipsoidal particles using large eddy simulation (LES) method due to the lack of subgrid scale (SGS) fluid motions. We report the effects of the SGS fluid motions on the orientational and rotational statistics, such as the alignment between the long axis of ellipsoidal particles and the vorticity, the mean rotational energy at various aspect ratios against those obtained with direct numerical simulation (DNS) and filtered DNS. The performances of a stochastic differential equation (SDE) model for the SGS velocity gradient seen by the particles and the approximate deconvolution method (ADM) for LES are investigated. It is found that the missing SGS fluid motions in LES flow fields have significant effects on the rotational statistics of ellipsoidal particles. Alignment between the particles and the vorticity is weakened; and the rotational energy of the particles is reduced in LES. The SGS-SDE model leads to a large error in predicting the alignment between the particles and the vorticity and over-predicts the rotational energy of rod-like particles. The ADM significantly improves the rotational energy prediction of particles in LES. 相似文献
16.
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption phenomenon. For sake of simplicity, the analysis is performed by considering a sample in the shape of a slab limited by two perfectly blocking surfaces, in such a manner that the problem is one-dimensional in the space. Two cases are investigated. In the former, the initial distribution of the diffusing particles is assumed of gaussian type, centered around the symmetry surface in the middle of the sample. In the latter, the initial distribution is localized close to the limiting surfaces. In both cases, we show that the evolution toward to the equilibrium distribution is not monotonic. In particular, close to the limiting surfaces the bulk density of diffusing particles present maxima and minima related to the finite velocity of the diffusion process connected to the second order time derivative in the partial differential equation describing the evolution of the bulk density in the sample. 相似文献
17.
H. Dekker 《Physics letters. A》1982,88(1):21-25
The markovian Boltzmann equation for a newtonian gas consisting of two kinds of particles (test and host species) is evaluated analytically by means of systematic scaling methods for the one-dimensional system in the Rayleigh limit of heavy test particles. In the spatially uniform situation the velocity autocorrelation function of the test particles obeys a remarkably simple differential-integral equation. Elementary Laplace analysis reveals an exact t-3 long-time tail. 相似文献
18.
废旧橡胶制品颗粒与砂土颗粒混合物作为建筑填充材料具有环保、轻质、减震效果好等特点.软硬组分的混合比例可以调制体系力学性能从而实现兼顾材料柔韧性与强度的需求,但细观层面上材料性能改变的原因尚不明确.本文主要研究玻璃-橡胶混合颗粒体系的弹性行为及其微观机制.利用飞行时间法测量混合材料等效动弹性模量,发现随着橡胶颗粒增加,体系逐渐从类玻璃刚性行为转变为类橡胶柔性行为.离散元模拟结果与实验结果类似.此外,模拟显示低橡胶颗粒占比样品内主要由玻璃颗粒构成主力链结构,而橡胶颗粒基本不参与强力链的构成.当橡胶颗粒占比较大时,玻璃颗粒和橡胶颗粒共同构成主力链网络结构,但颗粒间法向接触力分布相对更为均匀,可视为玻璃颗粒悬浮于橡胶颗粒中.基于上述结果,提出了改进的等效介质理论,用于描述混合颗粒体系的弹性行为.研究认为:橡胶颗粒占比较小时内部颗粒的变形相对均匀,材料近似满足等应变假设,视为并联弹簧模型;橡胶颗粒占比较大时混合材料近似满足等应力假设,视为串联弹簧模型.两种模型得到的结果与模拟结果一致.上述结果有利于从微观角度揭示混合颗粒材料弹性行为的变化机制. 相似文献
19.
The objective of this paper is to present a model for predicting clustering of aerosol particles in uniformly sheared turbulent flows laden with small heavy particles. The background of the model for predicting clustering is based on a kinetic equation for the two-point probability density function of the relative velocity distribution of two particles. The effect of clustering of particles in homogeneous turbulent shear flows is demonstrated and compared with known results of direct numerical simulations. It is shown that the universality of the clustering process can take place if the characteristic cluster size is smaller than the shear scale. 相似文献
20.
P. H. Chavanis 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,52(1):61-82
We study the relaxation of a test particle immersed
in a bath of field particles interacting via weak long-range
forces. To order 1/N in the N→+∞ limit, the
velocity distribution of the test particle satisfies a
Fokker-Planck equation whose form is related to the Landau and
Lenard-Balescu equations in plasma physics. We provide explicit
expressions for the diffusion coefficient and friction force in the
case where the velocity distribution of the field particles is
isotropic. We consider (i) various dimensions of space d=3,2 and
1; (ii) a discret spectrum of masses among the particles; (iii)
different distributions of the bath including the Maxwell
distribution of statistical equilibrium (thermal bath) and the step
function (water bag). Specific applications are given for
self-gravitating systems in three dimensions, Coulombian systems in
two dimensions and for the HMF model in one dimension. 相似文献