Dirac-delta function approximations to the scattering phase function

Dirac-delta function approximations are used to represent the single scattering phase function of large spherical particles or voids. The phase function for a spherical particle or void can be represented by a series of Legendre polynomials; however, as the diameter is increased, forward scattering becomes dominant and the number of terms in the series becomes very large. A Dirac-delta function approximation consists of a Dirac-delta function in the forward direction plus a finite series of Legendre polynomials. The Dirac-delta function accounts for strong forward scattering. Particular attention is given to large ice spheres and spherical voids in ice. The Dirac-delta function is shown effective in reducing the number of terms needed to describe the phase function.     

随机扩散模型一种新的密度函数统计方法

引入核函数法对随机扩散方程（SDE）样本的密度分布进行统计,希望用核函数来减少统计涨落。由于SDE样本的密度随时间发展,越来越稀疏,所以核函数也应该越来越大,也就是说核函数应该随时间在变化。通过一个瞬时释放的二维扩散问题（具有解析解）,从定性和定量两个角度比较了变带宽核函数法和传统统计方法在密度分布统计中的性能差别,论述了变带宽核函数法的优缺点,变带宽核函数法在牺牲部分峰值的前提下可以很好地解决SDE样本密度分布统计涨落问题,在工程应用中值得推广。     

On the derivation of the velocity autocorrelation function in liquids from the incoherent scattering function

The derivation of the velocity autocorrelation function from a knowledge of the self-correlation function is demonstrated for a liquid rubidium model. It is argued that the method will be important in the processing of neutron scattering data from liquids.     

A new procedure for obtaining the Voigt function dependent upon the complex error function

This work proposes a new method for obtaining the differential equation of the Voigt function and, from this equation, expressing the Voigt function as dependent upon the complex error function. In addition, the integral expression of the successive derivatives of the Voigt function is given, and from this a method is generalized which permits the representation, also, of other functions depending on the complex error function. This enables us to simplify other functions which are the convolution of a Gaussian function with rational polynomial functions. Moreover, the relationship between the Lorentzian (w_L), Gaussian (w_G) and Voigt (w_V) widths at half maximum for the function is given, which is of great interest in diverse branches of physics, such as plasma spectroscopy, astrophysics, nuclear magnetic resonance, etc.     

On the theory of the work function

Starting from a definition of the work function in terms of total energies of the electron system it is shown that this work function can be obtained from the single-particle Schrödinger equations in the density-functional formalism in the way suggested by the Sommerfeld model. It is also shown that the change of the equilibrium ion positions accompanying the ionization of the crystal has no influence on the work function. A comparison is made with Koopmans' theorem. The use of several potentials for computations of the work function is critically investigated.     

Bayesian estimation of the wave function

Recently there have been many theoretical works on statistical inference in quantum systems. In the present Letter, we deal with the estimation of an unknown wave function under the assumption of a general parametric model. We propose the Bayesian estimation of a wave function and show the optimality result when we adopt the Bures distance as a loss function. We see some examples where the quantum state is better estimated by our method than by that based on the maximum-likelihood estimate.     

The differential equations of the Voigt function

The three second-order partial differential equations of the Voigt function are presented, leading to a powerful and accurate method of determining the Voigt function in the calculation of a line profile in a stellar atmosphere.     

Moments of the virtual photon structure function

The photon structure function is a useful testing ground for QCD. It is perturbatively computable apart from a contribution from what is usually called the hadronic component of the photon. There have been many proposals concerning this nonperturbative part of the real photon structure function. By studying moments of the virtual photon structure function, we explore the extent to which proposed nonperturbative contributions can be identified experimentally.     

Dielectric function of the QCD vacuum

It is shown that the inverse of the ghost form factor in the Hamilton approach to Yang-Mills theory in Coulomb gauge can be interpreted as the color dielectric function of the QCD vacuum. Furthermore, the horizon condition to the ghost form factor implies that in the infrared the QCD vacuum is a perfect color diaelectric medium and therefore a dual superconductor. The dielectric function is explicitly calculated within a previously developed variational approach, using a specific ansatz for the vacuum wave functional.     

On constructing the wave function of a quantum particle from its Wigner phase-space distribution function

For a Schrödinger wave function, the part of the phase that depends only on time disappears in the construction of the corresponding Wigner phase-space (quasi)distribution function. Despite this, it can be recovered from the Wigner function using the quantum Hamilton–Jacobi equation. This is demonstrated for three simple cases.     

Connection of the velocity autocorrelation function to the mean-square-displacement and to the memory function of generalized master equations

General connections between the velocity autocorrelation function and the mean-square-displacement for a special initial condition are established and shown to reduce in the high-temperature limit to earlier such results obtained by Scher and Lax. A simple and useful relation, which is valid in the high temperature limit, between the velocity autocorrelation function and memory functions in generalized master equations is given.     

Construction of the Green's function for the pseudoharmonical oscillator

In the present paper we have constructed the Green's function for the pseudoharmonical potential, which is considered as an intermediate potential between the harmonic and anharmonic potentials. We have used a hybrid method, by combining the Laplace transformation method and the Green's function technique. The Green's function is used for obtaining the density matrix for a quantum-statistical system, in coordinate representation. Even if this is not a new result, the method can be applied to a class of exactly solvable potentials.     

On the two-point cross-correlation function of anisotropic, spatially homogeneous ambient noise in the ocean and its relationship to the Green's function

It is well established that the free-space Green's function can be recovered from the two-point cross-correlation function of a random noise field if the noise is white and isotropic. Ambient noise in the ocean rarely satisfies either of these conditions. However, a non-uniform spectrum could be pre-whitened by the application of a suitable filter but anisotropy cannot be so readily eliminated. To investigate the effects of vertical anisotropy, three azimuthally uniform, spatially homogeneous noise fields are analyzed, two of which are idealized, while the third is representative of ambient noise in the deep ocean. In each case, the coherence function, the cross-correlation function, and the derivative of the latter with respect to the correlation delay, are derived for vertical and horizontal alignments of the sensor pair. With vertical sensors, any step-function discontinuity in the directional density function is mapped into a delta function at an appropriate time delay in the derivative (with respect to time delay) of the cross-correlation function. No such mapping occurs with horizontal sensors. In this case, only horizontally traveling noise can generate delta functions in the derivative of the cross-correlation function, and these always appear at the retarded time on either side of the origin.     

New approach for solving the Wigner function from the Husimi function in the two-mode entangled state representation

We introduce a new method to calculate the Wigner function when its corresponding Husimi function is given. A new formula is derived for calculating conveniently the Wigner function in two-mode entangled state representation. As application, we derive Wigner functions of some quantum states, such as two-mode entangled state, the electron's two-mode squeezed canonical coherent state, and the electron's coordinate eigenstate.     

A memory function model for the velocity autocorrelation function and the self-diffusion coefficient in simple dense fluids

A memory-function model is used to compute the velocity autocorrelation function and the self-diffusion coefficient of a dense Lennard-Jones fluid from the zero-time correlation functions of the molecular velocity and its first two time derivatives. It is shown that these zero-time correlation functions can be evaluated in terms of the radial distribution function and the pair potential only, i.e. without considering higher order correlation functions. Since molecular dynamics results are available for the radial distribution function as well as the velocity autocorrelation function and the self-diffusion coefficient, a rigorous test of the chosen memory function is possible. The agreement is reasonable, although generally not within the error bands of the molecular dynamics results.     

Multiferroism in the dielectric function of CuO

The multiferroic properties of bulk CuO are manifested in the dielectric function which can be triggered by an external magnetic field h and by the temperature T. Within a microscopic model and a Green's function technique we have calculated the dielectric function \varepsilon ({\bf k};T,\;h). At the magnetic phase transition temperature T_{{\rm N}2} the dielectric function offers a pronounced anomaly. This kink disappears when the magnetic field is enhanced and \varepsilon ({\bf k};T,\;h) decreases with increasing h ‐field. Both properties are indications for a strong magnetoelectric coupling in this material. The observation of multiferroism in CuO within an analytical approach is achieved by considering frustration and a linear magnetoelectric coupling. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gluon distribution function from the Berger–Block–Tan form of the structure function F 2

Physics of Atomic Nuclei - We present a set of formulas to extract the gluon distribution function from the Berger–Block–Tan form of the deep inelastic structure function F 2 and its...     

在计算机中实现三角函数的硬件解算方法

针对目标跟踪中大量存在的三角函数运算,提出在火控计算机中建立三角函数解算单元,采用硬件实现三角函数解算的设想。而三角函数解算单元是一种可以完成正弦函数解算功能的函数芯片。它的设计核心是以角度值为地址,通过硬件查表计算,可对0到90度的正弦函数值进行查表。查表精度可设计到0.001°,最大查表时间即为函数值的解算时间。余弦查表计算是采用正弦同一芯片,可以根据相位差90度的关系进行查表。实践表明三角函数的硬件解算速度快,精度高,可以替代通常方法的函数解算。因此,如果在火控系统中,设计一个地址译码器电路,就可建立多个三角函数芯片解算单元,通过计算机数据指令,实现对多个三角函数值的并行计算,从而提高系统对多个目标的快速跟踪处理能力。     

Numerical approach to the Caputo derivative of the unknown function

If a function can be explicitly expressed, then one can easily compute its Caputo derivative by the known methods. If a function cannot be explicitly expressed but it satisfies a differential equation, how to seek Caputo derivative of such a function has not yet been investigated. In this paper, we propose a numerical algorithm for computing the Caputo derivative of a function defined by a classical (integer-order) differential equation. By the properties of Caputo derivative derived in this paper, we can change the original typical differential system into an equivalent Caputo-type differential system. Numerical examples are given to support the derived numerical method.