风沙稳定输运中起跳沙粒运动状态分布函数

本文用气固二相流模型模拟了风沙稳定输运过程。若起跳沙粒运动状态分布函数采用由实验得到的正态分布函数形式时,计算出的水平质量流量通量随高度的变化规律与实验结果不同。经深入分析,本文提出一新的起跳沙粒运动状态分布函数形式。其中初始起跳角的分布仍采用正态分布函数形式,而对初始起跳速度则采用指数函数和正态分布函数的分段函数形式。计算结果表明本文提出的起跳沙粒运动状态分布函数与实际情况吻合较好。     

Obtaining non-negative quantum mechanical distribution function

The distribution function obtained by smoothing the original Wigner function with a weighting function, is shown to be positive everywhere, if the weighting function itself is a Wigner transform of any normalised function. The marginal distribution is recovered with a special choice of this function.     

Numerical simulation of intense helical electron beams with the calculation of the velocity distribution functions

The method of calculation of intense helical electron beams which allows to find the distribution function of electrons with respect to their transverse (oscillatory) and longitudinal velocities is developed. The initial velocity distribution function can be arbitrary. The data obtained in numerical simulation and experimental measurements for beams with various topologies are compared. The evolution of the transverse velocity distribution function with the beam current growth is traced. It is found that the transformation of the velocity distribution function may indicate a possible instability in a real beam.     

Nonexistence of Kirkwood's instability in a uniform fluid

Kirkwood's instability in the theory of fluid-solid transitions is proved to be impossible. Fluctuation of the one-particle distribution function in the first equation of the BGY hierarchy is investigated beyond Kunkin and Frisch's treatment. The second equation of the BGY hierarchy is utilized to eliminate the three-particle distribution function left in the Kunkin-Frisch result. The final expression for the first-order fluctuation of the one-particle distribution function under the presence of an external field is written in a form including only the pair correlation function and agrees identically with the one obtained from the direct expansion of the oneparticle distribution function in terms of the external field.     

Modeling dislocation — segment length distributions

The influence of intermolecular interaction between point defects, which are moving pinning points for dislocations, on the length distribution of dislocation segments is discussed. The distribution function is analyzed by Monte Carlo numerical modeling. It is shown that a length distribution can be described in the absence of external stresses by an exponential function that may differ from the Köhler function at high defect concentrations. Intermolecular interaction of defects changes the distribution function, which, with time, also becomes nearly exponential, but with different values of the parameters.     

The triplet distribution function in a fluid of hard spheres

The distribution functions of a fluid can be expressed as a series in powers, of the density. The coefficient of the fourth power of the density in the expansion of the triplet distribution function is obtained as a function of the separations of the molecules for a fluid of hard spheres. The coefficient is negative. It is used to estimate the amount by which the true triplet distribution function is less than the value attributed to it by the superposition approximation.     

Estimating the molecular weight distribution of a polymer using acoustic relaxation spectra

An approach to estimating the molecular weight distribution function of a polymer in a solution using acoustic spectroscopy data is presented. The estimation function is based on the relationship between relaxation spectra and the molecular weight distribution function, along with the relationship between the relaxation spectra and the frequency distribution of a polymer’s loss modulus.     

一类相空间中的准几率分布函数系

定义了一类相空间中的准几率分布函数系，这个准几率分布函数系直接建立在具有更加广泛意义的量子相空间Schr?dinger方程解的基础之上，其中定义_α=αp-i?q和_α=(1-α)q+i?p.发现了两个有趣的关系.(1)建立的量子相空间Schr?dinger方程的解实际上是对函数φ(λ)exp［i(1-α)qp］做窗口Fourier变换.(2)这个窗口函数g(λ)起着选择窗口形式的作用，而且不同的窗口对应着不同的分布函数.当g(λ)是一个代表Gauss窗的Gauss函数的时候，准几率分布函数就是一个类似于Husimi的分布函数f^HL_α(q,p)；当g(λ)是一个表示椭圆的复函数时，准几率分布函数就是一个椭圆分布函数f^E_α(q,p)；再在g(λ)为复函数的基础上附加α=0，就可得到标准序分布函数f^S(q,p)、反标准序分布函数f^AS(q,p)和Wigner分布函数f^W(q,p)，此时g(λ)表示高度为1/12π?而长度为λ的矩形窗. 关键词： 窗口Fourier变换 相空间 Wigner分布函数     

Distribution function of the intensity of optical waves in random systems

Statistics of coherent radiation propagating in a random medium is analyzed in the framework of diagram technique. The distribution function for radiation intensity is calculated and it is shown, that only for small values of the argument the distribution function is a simple exponential, as predicted by Rayleigh statistics. For larger values of intensity the distribution function differs drastically from the simple exponential, and the asymptotical behavior is a stretched exponential. The results obtained are confirmed by numerical simulations.     

Cooling kinetics of a granular gas of viscoelastic particles

The evolution of a granular gas of viscoelastic particles in the homogeneous cooling state is studied. The velocity distribution function of granular particles and the time dependence of the mean kinetic energy of particles (granular temperature) are found. The noticeable deviation of the distribution function from the Maxwell distribution and its non-monotonous evolution are established. The perturbation theory with respect to the small dispersion parameter is elaborated and the analytical expressions for the asymptotic time dependence of the velocity distribution function and the granular gas temperature are derived.     

加性噪声对激光一级相变类比的影响

从单模激光场的增益－噪声模型出发,导出了激光场定态强度分布函数,研究了定态分布函数的极值点随加性噪声、乘性噪声和注入信号的变化情况。结果表明,乘性噪声是使激光系统出现一级相变类比的关键因素,注入信号使相变行为减弱,而加性噪声却使得定态分布中极值点的数量和位置出现来回跳跃式变化。     

Distribution function of an electron beam in a focusing magnetic field

The distribution function of electrons moving in an axially symmetric focusing magnetic field is constructed. The macromotion and self-field of the beam are taken into account. The nonrelativistic and relativistic limits are discussed. Upon switching off the magnetic field the distribution functions obtained change into the Maxwell-Boltzmann distribution. The motion of charged particles in a focusing magnetic field is the simplest model for investigation of a beam of particles, for example, electrons, in storage or accelerator rings. In accordance with the well-known theorem of N. Bohr, a magnetic field has no effect on the distribution function for a one-dimensional distribution of electrons with respect to the momenta. However, the situation is altered if macromotion occurs in a static system, for example, the revolution of electrons in storage or accelerator rings. Maintaining the focusing of the beam in an equilibrium orbit, the magnetic field thereby affects the electron distribution function. For an actual electron beam the distribution function is determined by the initial conditions of formation of the beam; however, as a result of scattering processes it will approach some steady-state equilibrium distribution function. We will discuss the problem of finding such a distribution function in the nonrelativistic and relativistic cases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 35–40, July, 1978.The author thanks Professor I. M. Ternov of Moscow University for his constant interest in this research and Professor V. G. Bagrov of Tomsk University for help in the research.     

不同模式耦合下偏振模色散几率分布的研究

研究了偏振模色散的统计特性,在不同模式耦合条件下,应用蒙特-卡罗方法模拟偏振模色散矢量的几率分布,并对模拟结果进行了函数拟合。发现随着耦合次数增加差分群时延的几率分布从一个类似δ函数分布逐渐过渡到麦克斯韦分布;在一定的耦合下,几率分布可以呈现高斯分布。对偏振模矢量的两个方向余弦进行统计分析,发现随着耦合次数的增加,偏振模矢量两个方向余弦函数的分布从高斯分布和δ函数分布都变为均匀分布。     

Third adiabatic invariant and the collisionless distribution function of particles in a tokamak

It has been shown that the distribution function of an ensemble of particles with a given energy in a collisionless regime in a tokamak is formed as a function primarily of the third adiabatic invariant, particularly in the near-axis region. In the periphery of the plasma column, the contribution of the toroidal component of the canonical momentum/longitudinal adiabatic invariant to the distribution function becomes noticeable. The coordinate dependence of the ensemble distribution function in the velocity space is determined predominantly by the trajectories of charged particles.     

铝漫反射板200～300 nm相对双向反射分布函数的实验研究

选择了合适的测量方式．建立了铝漫反射板的相对双向反射向反射分布函数的测量装置。通过实验研究铝漫反射板的相对双向反射分布函数在不同情况下的性质表明：不同表面粗糙度的铝漫反射板相对双向反射分布函数随入射角度的变化趋势有所不同;表面镀A1 MgF2膜反射率可增大约1．5到3倍;相对双向反射分布函数在200～280nm之间不随波长改变,波长大于280nm时,随波长略有增加,最大13％。根据实验数据绘出的二维等值线图反映了光辐射以不同角度入射、观测角度固定情况下的铝漫反射板的相对双向反射分布函数的变化,对实验数据拟合得到在该情况下的铝漫反射板的相对双向反射分布函数的较精确的数学表达式。     

Hot-electron distribution functions in a subpicosecond laser interaction with solid targets of varying initial gradient scale lengths

We have studied the distribution function of the hot electrons produced during the interaction of a 120-fs, 60-mJ, 800-nm wavelength and a p-polarized laser pulse with bilayered Al/Fe targets. The main pulse interacts with a preformed plasma, obtained with a controlled prepulse, whose density gradient scale length has been measured. The electron distribution function is characterized by means of the Kalpha emission of the two materials of the target as a function of the Al-layer thickness. The low-energy region (<50 keV) of the hot-electron distribution function shows no dependency in shape on the gradient scale length, but only a variation in the total number of the generated electrons. The comparison between the experimental results and the particle-in-cell and Monte Carlo calculations of the electron distribution function and the Kalpha emission is gratifying.     

The distribution function for a subsystem experiencing temperature fluctuations

A nonlinear generalization of the Landau-Lifshitz theory of hydrodynamic fluctuations for the simplest case in which only energy flux and temperature fluctuations are observed is used to derive the distribution function for a subsystem with a fluctuating temperature, which coincides with the Levy distribution taken to be one of the main results of the so-called Tsallis’s nonextensive statistics. It is demonstrated that the same distribution function is obtained from the principle of maximum of information entropy if the latter is provided by Renyi’s entropy, which is an extensive quantity. The obtained distribution function is to be used instead of the Gibbs distribution in constructing the thermodynamics of systems with significant temperature fluctuations.     

Floating Sheath Potentials in Non-Maxwellian Plasmas

The floating sheath potential in a plasma having a Maxwellian electron distribution function is e?>s = -kTe 1n (a/b)/2 where Te is the electron temperature, a is the ratio of electron temperature to ion temperature, and b is the ratio of electron mass to ion mass. This expression is derived by equating the flux of electrons and ions to a surface in the plasma. Only electrons initially having an energy greater than -e?s flow to the surface. These electrons are in the tail of the distribution, a region that differs significantly from a Maxwellian in many plasmas. An analysis is performed where the sheath potential is solved for using a two-temperature model for the electron distribution function. The two-temperature model accurately describes the distortion from a Maxwellian in the tail of the distribution function. The magnitude of the sheath potential calculated with the two-temperature distribution is significantly smaller than that obtained using a Maxwellian distribution, a result of the reduction in the relative abundance of energetic electrons in the tail of the distribution.     

Distribution of Orientations in Fibre Suspension Flowing in a Turbulent Boundary Layer

The equation of probability distribution function for mean fibre orientation in a turbulent boundary layer is derived, in which the correlation terms of the fluctuating velocity, fluctuating angular velocity with the fluctuating probability distribution function are related to the gradient of mean probability distribution function and the dispersion coefficients in order to make the equation be solvable. The finite-difference method is used to solve the equation numerically. The results show that the fibres tend to align with the streamline, which is in agreement qualitatively with the experimental result given by visualization. The fibre aspect-ratio has a significant effect on the orientation distribution of fibres, while the effect of the distance from the wall is negligible.     

微粒特征分布函数测量理论和方法的进一步研究

运用微粒散射形体微扰理论对任意形体微粒的研究结果,根据光敏区光强的Gauss分布特征和微粒穿越位置的随机性,建立了相关模型和数学方程并求得了任意位置的微粒形体影响因子分布函数的数值解,讨论了大变化区的非线性影响.其次,根据微粒数分布离散性的特征,建立了微粒粒度分布函数的反演矩阵及其实验方法.最后进行了实验验证.