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。     

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.     

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.     

On the relation between the wave aberration function and the phase transfer function for an incoherent imaging system with circular pupil

The consideration is carried out in its general formulation: the wave aberration function is represented in terms of classical aberrations (the Zernike polynomials), the phase transfer function (argument of the complex optical transfer function) is defined by a chain of transformations originating from the generalized pupil function. Quasi-analytical quadrature formulas are derived that link the optical transfer function and the phase transfer function with the aberration terms. It is shown that the phase transfer function contains information on the odd-order aberrations, which can be retrieved from coefficients to the Taylor expansion of the derived quadrature relation. Received 16 June 2001     

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.     

Extracting the Green's function from measurements of the energy flux

Existing methods for Green's function extraction give the Green's function from the correlation of field fluctuations recorded at those points. In this work it is shown that the Green's function for acoustic waves can be retrieved from measurements of the integrated energy flux through a closed surface taken from three experiments where two time-harmonic sources first operate separately, and then simultaneously. This makes it possible to infer the Green's function in acoustics from measurements of the energy flux through an arbitrary closed surface surrounding both sources. The theory is also applicable to quantum mechanics where the Green's function can be retrieved from measurement of the flux of scattered particles through a closed surface.     

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.     

A generalized RPA theory of the nuclear response function

A new method of calculating the response function is proposed. The new method gives the response which is explicitly a generalization of the RPA response in a perturbative sense.When we calculate the transition amplitude of a one-body operator from the ground state to a particle-hole (p-h) state, the new response function provides all the second-order effects in addition to the first-order ones which can be obtained in the RPA theory. The new response function is obtained by the following procedure. Firstly, we consider the second RPA theory which is a generalization of the usual RPA theory. It is found that the second RPA misses some of the second-order effects. Secondly, we formulate a modified second RPA equation from the equation of motion of the operators, and then derive the p-h response function from it. It is found that the newly derived p-h response function is obtained by adding new terms to the self-energy of the p-h response function derived from the second RPA theory. Lastly, we introducd vertex functions which take into account the transitions from a particle (hole) state to a particle (hole) state. Note that the p-h response function deals with only the transition amplitudes from a particle (hole) state to a hole (particle) state.     

Relation between phase function and Green's function

A relation is established between the phase of the wave function and Green's function of onedimensional motion. On the basis of this relation, a series of accurate equations are obtained, including a formula for obtaining the Green's function at different one-dimensional coordinates from its form at coinciding one-dimensional coordinates.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 20–24, November, 1979.It remains to thank V. L. Bonch-Bruevich for useful discussions.     

A comment on the smoothed Wigner function

The Wigner function is one possible choice, from many, of correspondence between density matrices and quasi-distribution functions on phase space. For pure states, smoothing by convolution with any one of a set of kernels, renders only the Wigner function, from a large set of these quasi-distributions, positive.     

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.     

改进的单次散射相函数解析表达式

单次散射相函数对电磁辐射传输模拟过程的准确性和计算效率有重要的影响.基于电磁散射与辐射传输中的基本理论,对单次散射相函数的解析表达式进行了研究,提出了一种新的单次散射相函数解析表达式.比较了单个粒子的Henyey-Greenstein相函数、Henyey-Greenstein*相函数与新的相函数随角度的分布,发现新的散射相函数提高了后向散射峰值,可以更合理地描述单个粒子的散射特性.按三种气溶胶粒子谱分布模式计算了Henyey-Greenstein*相函数和新的相函数对应的数值结果,并与多分散系Mie散射相函数进行对比,发现新的相函数提高了与多分散系Mie散射相函数的符合程度.研究表明,对于大角度(大于90°)后向散射,新的相函数与Mie散射相函数均方根差较小的占73.3%,高于Henyey-Greenstein*相函数的26.7%,证明了新的相函数可以显著提高后向散射峰值.新的相函数对准确模拟辐射传输过程具有重要意义.     

Determining the complex point-spread function of a scanning differential heterodyne microscope

For a scanning differential heterodyne microscope, the two-dimensional point spread function and the pupil function are determined from experimental measurements of the intensity distribution of a probing beam. The phase components of these functions were restored from the measured distributions using the Gerchberg-Saxton algorithm. Based on the two-dimensional pupil function, the three-dimensional point-spread function is determined in the scalar approximation using the Debye integral. The aberration function of the microscope is analyzed from the viewpoint of the composition of aberrations and method of their balancing. The focusing adjustment criterion of the microscope for an object under study by the phase response from the test structure is considered.     

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.     

Partition function zeros for the two-dimensional Ising model

The distribution of complex temperature zeros of the partition function of the two-dimensional Ising model in the absence of a magnetic field is investigated. For anisotropic square and triangular lattices the distribution function is two-dimensional and satisfies a partial differential equation derived from a generalized scaling theory. Corresponding results for the isotropic square, triangular and honeycomb lattices are also presented.     

On the wave function of the universe

A discussion of the wave function for an isotropic universe is given. In order to alleviate that wave function from some of the quantum gravity difficulties, a logarithmic factor $\text{1 ? ln(}\text{R}\text{R}{}_0\text{)}$ is introduced in the gravitational action integral. The discussion is extended to the primordial Coleman-Weinberg scenario.     

On the method for calculating the reflection function

We consider the problem of calculating the reflection function for the case of radio-wave propagation in a stratified inhomogeneous absorbing ionosphere. A stable method for calculating the reflection function is proposed. Examples of calculations by the proposed method are shown for symmetric and parabolic ionospheric layers. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 9, pp. 766–772, September 2007.     

On reducing interface curvature computation errors in the height function technique

A detailed analysis of the errors involved in computing the interface curvature from volume fraction distributions using a height function technique is presented. An improved version of the height function technique is proposed, based on introducing a correction of the height function discretization error estimated from the local osculating spheres at interface points. By using this error correction and an appropriate discretization of the partial derivatives of the height function, a substantial improvement in the accuracy of the interface curvature computation can be efficiently achieved.