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.     

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.     

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.     

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。     

Long-distance effects on the \mathrm{B}\to X_{\mathrm{s}}\gamma photon energy spectrum

We compute long-distance effects on the photon energy spectrum in inclusive radiative decays of B mesons using light-cone expansion and heavy-quark effective theory. We show that for sufficiently high photon energy, the leading nonperturbative QCD contribution is attributed to the distribution function. The distribution function is found to be universal in the sense that the same distribution function also encodes the leading nonperturbative contribution to inclusive semileptonic decays of B mesons at large momentum transfer. Some basic properties of the distribution function are deduced in QCD. Ways of extracting the distribution function directly from experiment and their implications are discussed. The theoretically clean methods for the determination of are described. Received: 7 June 1999 / Published online: 14 October 1999     

Multistability of impact, utility and threshold concepts of binary choice models

The decision making problem in the context of binary choice is considered by means of impact function, utility function and threshold model approaches. The properties of generalized impact function and utility function are examined; it is shown that these two approaches are equivalent. Their relation to the threshold model is studied and the correspondence between respective cumulative distribution functions is displayed. The stationary state corresponding to the thermodynamic equilibrium is determined within mean field approximation. Multistability of the stationary state is expressed in terms of the distribution function of the random variable of impact/utility function. The correspondence with statistical physics predictions for Ising model is discussed: logistic distribution leads to the mean-field result, i.e. Curie-Weiss approximation. Variations of the distribution functions and/or other model parameters, of social character, self-support, nonlinearity of social interactions, etc., would break the direct correspondence to statistical physics of Ising model, leading in particular cases to richer structure of the multistability.     

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.     

Angular distribution of magnetic particles in particulate tapes

The distribution functions of magnetic recording particulate tapes were studied by the measurements of magnetoremanence. For fitting distribution function, cosines series function such as Legendre polynomial has been popularly used, however, Gaussian function is found to be preferable for sharp or wide distributions. Audio metal tape has the sharpest distribution function among the seven tapes.     

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.     

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。     

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.     

光谱线型函数的四种形式及其变换关系

从理论上研究了光谱线型函数的四种形式及其关系,以多普勒展宽导致的线型函数为例,分析了光子数、能量按频率及波长分布函数的最大值和半高全宽。结果表明,光子数、能量按频率的分布函数近似相等,光子数、能量按波长的分布函数也近似相等。通过对多普勒线型函数的分析,建立了根据两条光谱线的线型函数的最大值比值求得光子数比值的方法。     

The effective Hamiltonian approach for the two-nucleon distribution function

The microscopic two-body effective Hamiltonian equation satisfied by the two-nucleon distribution function needed for two-particle transfer processes is derived. The usual approximations made in order to obtain a partial solution to this equation are discussed and compared. It is concluded that contributions to the distribution function from both core state and channel coupling terms are likely to be comparable to continuum configurations in importance. Such contributions must certainly be included if an unambiguous normalization for the distribution function is desired.     

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。     

Analysis of distribution of partially polarized light

A new method for characterization of the distribution of the partially polarized light is described. Analysis of distribution is based on three dimensional radial distribution function. The radial distribution function is useful method of determining type of the distribution of partially polarized light. For uniformity analysis of the distribution method which is based on calculation of the correlation coefficient is presented.     

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.     

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.     

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.     

Influence of metastable-metastable collisions on electron distribution function in afterglow

The time dependence of the electron distribution function in helium afterglow, for pressures of 60–260 Pa, is calculated for the case in which metastable-metastable reactions are present. The time variation of the shape of the distribution function shows that careful consideration must be made of the time derivative of the distribution function in the Boltzmann equation for the calculation of the rate constant of such reactions from experimentally determined distribution function.     

����������β¡�ֲ�����µ�ɫɢ�����о�

当同时使用离子(或电子)回旋及中性束注入方式加热等离子体时,高能量粒子的能量分布函数一般应为尾部隆起(简称尾隆)分布。这种具有正能量梯度区域的分布函数更容易激发不稳定性,同时由于分布函数尾部隆起,在色散关系中引入了新的色散函数。主要研究了这种新色散函数的计算方法,结果表明:色散函数实部是关于原点对称的奇函数;而虚部则是关于纵轴对称的偶函数。色散函数的实部有2~4个极值点且极值点的位置与尾隆分布函数的能量梯度⊿有关、虚部有1~3个极值点但极值点位置与⊿无关。当其宗量趋于无穷大时,色散函数的值趋于零。当尾隆分布趋近于麦克斯韦分布时,用该方法计算的结果与色散函数表中给出的结果非常吻合。