Finite-N fluctuation formulas for random matrices

For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic Σ _j ^N =1 (x _j ? 〈x〉) is computed exactly and shown to satisfy a central limit theorem asN → ∞. For the circular random matrix ensemble the p.d.f.’s for the statistics ½Σ _j ^N =1 (θ _j ?π) and ? Σ _j ^N =1 log 2 |sinθ _j/2| are calculated exactly by using a constant term identity from the theory of the Selberg integral, and are also shown to satisfy a central limit theorem asN → ∞.     

An analysis of reverberation fluctuation by mean square derivation

A method for evaluating the fluctuation of the reverberation envelope is proposed and examined through simulation and real data in this paper.This method is different from the coefficient of variation which is only a function of the first and second order moment of the reverberation statistical model.By using the standard variance of the mean square derivate(MSD) of the reverberation envelope,the paper shows that the reverberation fluctuation is a function of the bandwidth of the emitted signal,and that a large value of the square variance means little fluctuation of the reverberation envelope.Theoretical studies show that the standard variance is proportional to the bandwidth of the emitted signal,so we conclude that less time width or larger bandwidth of the transmitted signal produces less fluctuation.Simulation and real active sonar data processing are used to verify this conclusion.     

Analytical formulas for calculating photoelectric attenuation coefficients

Photoelectric absorption is an interaction in which an incoming gamma ray virtually transfers all of its energy to an atomic electron, usually the most tightly bound K-shell electron of an atom. This paper uses the Win XCOM computer code as a reference base. We found analytical photoelectric attenuation coefficients for researchers using the Monte Carlo simulation program for Z∈ [1; 100] and E∈[10 keV; 3 MeV]. We define a photoelectric effect operator and coefficient operators and a series for photoelectric absorption. We have calculated two polynomial coefficient operators for use with XCOM for photoelectric absorption. We determined 14 energies and atomic number limits for elements, and we find that they are accurate limits of photoelectric absorption for fitting with XCOM.     

多普勒效应公式的简便推导

基于把多普勒效应理解为波频率的坐标变换,由洛伦兹变换推导出适用于任何波的多普勒效应公式。     

Microscopic derivation of kinetic equations for interacting optical two-level systems

Kinetic equations are derived for optical two-level atoms interacting with a molecular subsystem treated as a thermostat. It is assumed that the kinetics is determined by the electric dipole interaction perturbed by the thermal motion. Dynamic parts of the kinetic equations coincide with the corresponding terms of optical Bloch equations, whereas nonlinear relaxation and shift terms have the specific form and are absent in the phenomenological generalized Bloch equations. It is shown that the relaxation kinetics can be substantially different from the exponential one and depends on the initial state of the system. In particular, the inversion relaxation is frozen at small deviations from the equilibrium. The possibility of observation of the optical bistability is discussed.     

Microscopic derivation of a quantum hamiltonian for adiabatic collective motion

The generalized density matrix method is applied to the microscopic derivation of the adiabatic collective hamiltonian. By way of construction, the hamiltonian obtained is the quantum operator in the collective variable space. For the calculation of the hamiltonian parameters, the combination of the density matrix equations of motion and the collective motion saturation principle is used. The constraint (driving force) in the equations of motion is determined self-consistently. For illustrative purposes two simple solvable models are considered.     

POD-based wall boundary conditions for the numerical simulation of turbulent channel flows

Simulation of turbulent wall-bounded flows requires a high spatial resolution in the wall region, which limits the range of Reynolds numbers which can be effectively reached. In previous work, we proposed proper orthogonal decomposition (POD) based wall boundary conditions to bypass the simulation of the inner wall region. Tests were carried out for direct numerical simulation at a low Reynolds number Re_τ = 180. The boundary condition is based on the POD spatial eigenfunctions which are determined a priori in the full channel. It consists of a three-component velocity field on the plane y⁺ = 50 which is reconstructed at each instant from a combination of selected eigenfunctions. The coefficients of the combination are estimated from the simulation in the reduced domain using the threshold-based reconstruction method described in Podvin et al. The study is now extended to large-eddy simulation at higher Reynolds numbers Re_τ = 295 and Re_τ = 590. Two versions of the reconstruction method are considered. In the first version, both the phases and the moduli of the coefficients are allowed to vary. In the second version, only the phases are adjusted. We find that the latter method is associated with improved statistics and is relatively robust with respect to the reconstruction threshold. However, it is sensitive to the details of the numerical simulation, unlike the former method, which is associated with less accurate statistics and is more dependent on the reconstruction threshold.     

Lattice Boltzmann simulation of solid particles suspended in fluid

The lattice Boltzmann method, an alternative approach to solving a fluid flow system, is used to analyze the dynamics of particles suspended in fluid. The interaction rule between the fluid and the suspended particles is developed for real suspensions where the particle boundaries are treated as no-slip impermeable surfaces. This method correctly and accurately determines the dynamics of single particles and multi-particles suspended in the fluid. With this method, computational time scales linearly with the number of suspensions,N, a significant advantage over other computational techniques which solve the continuum mechanics equations, where the computational time scales asN ³. Also, this method solves the full momentum equations, including the inertia terms, and therefore is not limited to low particle Reynolds number.     

一种气象观测数据求导的新方法

气象观测数据不可避免地带有观测误差,而对带有误差的离散数据求导是一个不适定的反问题.为了解决这一长期困扰气象工作者的问题,利用吉洪诺夫正则化思想,提出了矩形区域内观测数据的二维一阶偏导数重构算法.通过系列模拟观测数据试验检验了该算法的性能,表明该算法有效且计算精度高.另外,应用该算法对气象观测资料进行客观分析,结果表明：该算法作为一种新的客观分析方法是可行的,并且还能提高小尺度天气系统的识别能力. 关键词： 数值微分 吉洪诺夫正则化 客观分析     

Inflow conditions for spatial direct numerical simulation of turbulent boundary layers

The inflow conditions for spatial direct numerical simulation (SDNS) of turbulent boundary layers should reflect the characteristics of upstream turbulence, which is a puzzle. In this paper a new method is suggested, in which the flow field obtained by using temporal direct numerical simulation (TDNS) for fully developed turbulent flow (only flow field for a single moment is sufficient) can be used as the inflow of SDNS with a proper transformation. The calculation results confirm that this method is feasible and effective. It is also found that, under a proper time-space transformation, all statistics of the fully developed turbulence obtained by both temporal mode and spatial mode DNS are in excellent agreement with each other, not only qualitatively, but also quantitatively. The normal-wise distributions of mean flow profile, turbulent Mach number and the root mean square (RMS) of the fluctuations of various variables, as well as the Reynolds stresses of the fully developed turbulence obtained by using SDNS, bear similarity in nature. Supported by the National Natural Science Foundation of China (Grant No. 90205021), the China Postdoctoral Science Foundation (Grant No. 20060400707), and the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200328), and partially supported by Liu-Hui Center of Applied Mathematics, Nankai University and Tianjin University     

Investigating the temperature dependence of elastic constants by thermal fluctuation formula

The differences between the calculated values of elastic constants of materials and the experimental data are consistently restricting the application of thermal fluctuation formula to the mechanical properties of materials. In this work, the temperature dependence of elastic constants of many-body potentials is studied by thermal fluctuation formula. The differences between the calculated values and the experimental data are investigated in detail. Our studies show that the differences come from the thermal expansion of the materials: the calculated zero-stress states are bigger than the experimental zero-stress states of the materials, and this deviation makes Born terms of the thermal fluctuation formula decrease sharply as the temperature increases, while the fluctuation terms and the kinetic terms change little. As a result, the elastic constants, which are the sum of these three terms, decrease faster than the experimental data as the temperature increases. Our studies show that when the experimental zero-stress states are used as the reference states in constant volume and constant energy (NVE) simulations, the elastic constants calculated by thermal fluctuation formula are in good agreement with the experimental values.     

Sensitivity of approximate formulas for determining optical constants of thin films

The sensitivity of approximate formulas for determining the optical constants of thin films using measurement of reflectancesR and transmittancesT at normal incidence have been investigated theoretically. The ranges of refractive indexn, absorption indexk,2nk (=₂) andn ²–k ²(=₁) within relative errors of 5%, 10%, and 20% may be obtained. Selected signs of (₁)⁺ or (₁)^– have been determined. Validity of the condition n₀ A=n _s A has been also evaluated (A=1–R –T andA=1–R–T).     

Microscopic derivation of non-Markovian thermalization of a Brownian particle

In this paper, the first microscopic approach to Brownian motion is developed in the case where the mass density of the suspending bath is of the same order of magnitude as that of the Brownian (B) particle. Starting from an extended Boltzmann equation, which describes correctly the interaction with the fluid, we derive systematically via multiple-time-scale analysis a reduced equation controlling the thermalization of the B particle, i.e., the relaxation toward the Maxwell distribution in velocity space. In contradistinction to the Fokker-Planck equation, the derived new evolution equation is nonlocal both in time and in velocity space, owing to correlated recollision events between the fluid and particle B. In the long-time limit, it describes a non-Markovian generalized Ornstein-Uhlenbeck process. However, in spite of this complex dynamical behavior, the Stokes-Einstein law relating the friction and diffusion coefficients is shown to remain valid. A microscopic expression for the friction coefficient is derived, which acquires the form of the Stokes law in the limit where the meanfree path in the gas is small compared to the radius of particle B.Knowing the interest of Matthieu Ernst in the subtle and fundamental problems of kinetic theory, we have the pleasure to dedicate this study to him.     

Analytical formulas for calculating the blocking probability of a dynamic star network

For a dynamic routing and wavelength assignment (RWA) a star topology is shown to be more efficient in comparison with a ring topology. Analytical formulas for a dynamic RWA in a star network are presented and verified with virtual simulation.     

基于Rudin-Osher-Fatemi模型的图像除模糊和除噪音新模型

介绍一种依赖时间的新模型来解决图像除噪音和除模糊问题.分别使用逆反射、中值两种边界条件的数值试验比较本文新模型和Rudin-Osher-Fatemi模型.试验结果表明中值边界条件的误差比逆反射边界条件误差小.     

一种获取双原子分子的转动常数的方法

本文给出了对于任何双原子分子或双原子自由基分子,由其振动常数结合RKR方程、结合从头计算,获得势能曲线及其转动常数的方法.并对CN的基态和激发态进行了计算,结果与实验值符合得非常一致.A     

Microscopic theory of second-order and third-order elastic constants for an NaCl crystal

Relations between the second-order and third-order symmetry-independent elastic constants and the energy of interatomic interactions dependent on the mutual arrangement of pairs and triplets of atoms are obtained for crystals belonging to the crystal class O _h. The derived relations and experimental data on the elastic constants are used to calculate four third-order elastic constants and the temperature dependence of the elastic anisotropy factor a(T) for an NaCl crystal. The calculated dependence a(T) is in qualitative agreement with the experimental dependence a _exp(T).     

A completely iterative method for the infinite domain electrostatic problem with nonlinear dielectric media

We present an iterative method for the solution of the exterior all-space electrostatic problem for nonlinear dielectric media. The electric potential is specified on interior boundaries and the electric field decays at infinity. Our approach uses a natural variational formulation based on the total energy of the nonlinear dielectric medium subject to boundary conditions. The problem is decomposed into an exterior calculation and an interior calculation with the boundary-specified electric potentials imposed as constraints between them. Together, these enable an iterative method that is based on the variational formulation. In contrast to direct solution of the electrostatic problems, we avoid the construction, storage and solution of dense and large linear systems. This provides important advantages for multiphysics problems that couple the linear electrostatic Poisson problem to nonlinear physics: the latter necessarily involves iterative approaches, and our approach replaces a large number of direct solves for the electrostatics with an iterative algorithm that can be coupled to the iterations of the nonlinear problem. We present examples applying the method to inhomogeneous, anisotropic nonlinear dielectrics. A key advantage of our variational formulation is that we require only the free-space, isotropic, homogeneous Greens function for all these settings.     

Prediction of complex dielectric constants of polymer-clay nanocomposites

In this Letter, simple theoretical models are presented to predict the influence of aspect ratio, orientation, distribution, and interphase of layered silicates on the dielectric properties of polymer-clay nanocomposites. The predictions are in good agreement with experimental data. The results show that the morphology of the clay fillers and the thickness and dielectric properties of the interphases play an important role in determining the dielectric properties of polymer-clay nanocomposites.