A Method of Calculating the Density Matrix for a System of Interacting Bosons in Coherent-state Basis

The time-dependent behaviour of a system of several interacting boson modes is described in coherent state basis. In the Schrödinger picture the unitary time development operator is used. The variation of the density operator for the whole system is described for arbitrary situations (even such without P-representation). The method is applied to the parametric amplification process with strong pump field.     

A Simple and Accurate Method for Calculating the Gaussian Beam Expansion Coefficients

The calculation of the diffraction field radiated from the ultrasonic transducer can be simplified by using the Gaussian beam expansion technique. The key problem of this technique is how to determine the coefficients of Gaussian functions. We present a simple and accurate optimization method to calculate the Gaussian beam expansion coefficients, Half of the coefficients are obtained by solving linear equations. The other half are derived from the Fourier series expansion. Wave field simulation results demonstrate the validity of the new method.     

The Fractional Parentage Coefficients for a Double-j Fermion System

The coefficients of fractional parentage (CFPs) for a double-j fermion system are defined. The CFPs are given when the wave functions are classified according to the group chains U(N) ⊃ U(N₁) × U(N₂) ⊃ SP(N₁)× SP(N₂) ⊃O(3₁)×O(3₂) ⊃ O(3) and U(N) ⊃ SP(N) ⊃ SP(N₁)× SP(N₂) ⊃ O(3₁)× O(3₂) ⊃ O(3). Using these CFPs many repeating calculations can be avoided.     

Invariant Solutions of a Nonlinear System of Differential Equations for Electromagnetic Field

Abstract

Solutions invariant under subalgebras of the affine algebra AIGL(3, ?) are found.     

Prediction and Refinement of High-Order Virial Coefficients for a Hard-Sphere System

The n^th virialcoefficient for a hard-sphere system is expressed as the sum of n^2 and a remainder. When n ≥ 3, the remainders of the viriaJs can be accurately expressed with Pade-type functions of n. The maximum deviations are only 0.039-0.053%, which are much better than the existing approaches. By using the predicted virials, the compressibility factors of the hard-sphere system can be predicted very accurately in the whole stable fluid region, and those in the metastable fluid region can also be well predicted up to a packing fraction of 0.545. The simulated B7 and Bl0 are found to be inconsistent with the other known virials, and thus they are refined to be 53.2467 and 105.042, respectively.     

A Direct Algorithm Maple Package of One-Dimensional Optimal System for Group Invariant Solutions

To construct the one-dimensional optimal system of finite dimensional Lie algebra automatically, we develop a new Maple package One Optimal System. Meanwhile, we propose a new method to calculate the adjoint transformation matrix and find all the invariants of Lie algebra in spite of Killing form checking possible constraints of each classification.Besides, a new conception called invariance set is raised. Moreover, this Maple package is proved to be more efficiency and precise than before by applying it to some classic examples.     

New Soliton-like Solutions and Multi-soliton Structures for Broer-Kaup System with Variable Coefficients

By using the further extended tanh method [Phys. Lett. A 307 （2003） 269; Chaos, Solitons ＆ Fractals 17 （2003） 669] to the Broer-Kaup system with variable coefficients, abundant new soliton-like solutions and multl-solitonlike solutions are derived. Based on the derived multi-soliton-like solutions which contain arbitrary functions, some interesting multi-soliton structures are revealed.     

Controllable Optical Solitons in Optical Fiber System with Distributed Coefficients

We present how to control the dynamics of optical solitons in optical fibers under nonlinearity and dispersion management, together with the fiber loss or gain. We obtain a family of exact solutions for the nonlinear Schrödinger equation, which describes the propagation of optical pulses in optical fibers, and investigate the dynamical features of solitons by analyzing the exact analytical solutions in different physical situations. The results show that under the appropriate condition, not only the group velocity dispersion and the nonlinearity, but also the loss/gain can be used to manipulate the light pulse.     

A Mixed Finite Element Method for Stationary Magneto-Heat Coupling System with Variable Coefficients

In this article, a mixed finite element method for thermally coupled, stationary incompressible MHD problems with physical parameters dependent on temperature in the Lipschitz domain is considered. Due to the variable coefficients of the MHD model, the nonlinearity of the system is increased. A stationary discrete scheme based on the coefficients dependent temperature is proposed, in which the magnetic equation is approximated by Nédélec edge elements, and the thermal and Navier–Stokes equations are approximated by the mixed finite elements. We rigorously establish the optimal error estimates for velocity, pressure, temperature, magnetic induction and Lagrange multiplier with the hypothesis of a low regularity for the exact solution. Finally, a numerical experiment is provided to illustrate the performance and convergence rates of our numerical scheme.     

Invariant operator theory for the single-photon energy in time-varying media

After the birth of quantum mechanics, the notion in physics that the frequency of light is the only factor that determines the energy of a single photon has played a fundamental role. However, under the assumption that the theory of Lewis--Riesenfeld invariants is applicable in quantum optics, it is shown in the present work that this widely accepted notion is valid only for light described by a time-independent Hamiltonian, i.e., for light in media satisfying the conditions,ε(t)=ε(0), μ(t)=μ(0), and σ(t)=0 simultaneously. The use of the Lewis--Riesenfeld invariant operator method in quantum optics leads to a marvelous result:the energy of a single photon propagating through time-varying linear media exhibits nontrivial time dependence without a change of frequency.     

The Response to a Uniform Electric Field in Calculating the Electronic Structure of Crystals with a Basis of Localized Orbitals

Physics of the Solid State - The response to the external uniform electric field is calculated for the electronic structure of crystals using the localized basis functions in the form of...     

Invariant Measures for Passive Scalars in the Small Noise Inviscid Limit

We study the singular values of the product of two coupled rectangular random matrices as a determinantal point process. Each of the two factors is given by a parameter dependent linear combination of two independent, complex Gaussian random matrices, which is equivalent to a coupling of the two factors via an Itzykson-Zuber term. We prove that the squared singular values of such a product form a biorthogonal ensemble and establish its exact solvability. The parameter dependence allows us to interpolate between the singular value statistics of the Laguerre ensemble and that of the product of two independent complex Ginibre ensembles which are both known. We give exact formulae for the correlation kernel in terms of a complex double contour integral, suitable for the subsequent asymptotic analysis. In particular, we derive a Christoffel–Darboux type formula for the correlation kernel, based on a five term recurrence relation for our biorthogonal functions. It enables us to find its scaling limit at the origin representing a hard edge. The resulting limiting kernel coincides with the universal Meijer G-kernel found by several authors in different ensembles. We show that the central limit theorem holds for the linear statistics of the singular values and give the limiting variance explicitly.     

旋转不变的非局域均值算法在磁共振图像去噪中的应用

磁共振成像（MRI）实验时常采用多次扫描累加平均提高图像信噪比（SNR）,但当扫描过程中运动引起图像变形时,简单地累加平均就无法奏效.为此,本研究组曾提出一种匹配加权平均方法（MWA）提高图像的信噪比.在此基础上,该文提出一种旋转不变的非局域均值算法（RINLM）,即选取圆形邻域区域并将其划分为一系列以中心像素为圆心的等面积圆环,再计算模式的相似性.RINLM算法可以更好地利用图像中旋转的冗余信息、找到更多的相似结构,提高算法的去噪性能.我们把该方法应用于低信噪比图像序列的平均和去噪中,可以更好地处理旋转的局部运动.与非局域均值算法（NLM）相比,RINLM算法可以进一步提高图像的信噪比;与MWA方法相比,其与RINLM算法的结合可以进一步提高磁共振图像序列信噪比,更好的保持图像边缘信息.     

Rate Coefficients for Some Collisional Processes in High-Current Hydrogen Discharges

Rate coefficients are presented for a number of collisional processes important in high-current hydrogen discharges. The energy distribution of the plasma electrons has been assumed to be Maxwellian.     

Development of Thermospray Interfaced HPLC-FAAS System for Studies on Cadmium Speciation in Human Body Fluids

Early work on cadmium speciation of body fluids using GC-AA indicated the presence of CdCl₂, but other non-volatile Cd compounds were not detected (1). Such compounds may be detected by LC-AA.

To this end, an HPLC-Flame AA system (FAAS) has been developed using a thermospray. This device greatly increased the sensitivity of the flame AA system. Its use revealed the presence of numerous non-volatile cadmium compounds in urine and perspiration and confirmed our earlier observation that perspiration is a major process for removing cadmium from the body. Using data obtained, the half life of cadmium in the body is about 18 months rather than 20–30 years as currently believed.     

On the Existence of Invariant Measure for Lagrangian Velocity in Compressible Environments

We study transport of a passive tracer particle in a time dependent turbulent flow in the medium with positive molecular diffusivity. We show that there exists then a probability measure equivalent to the underlying physical probability, corresponding to the Eulerian velocity field, under which the particle Lagrangian velocity observations are stationary. As an application we derive the existence of the Stokes drift and the effective diffusivity—the characteristics of the long time behavior of the particle motion.