Elastic Scattering of Ultracold 133Cs and 85Rb Atoms in Triplet State

Elastic scattering properties of the ultracold interaction for the triplet state of 133Cs and 85Rb atoms are studied using two kinds of potentials by the same phase Φ. One is the interpolation potential, and another is Lennard-Jones potential (L J12,6). The radial Schr(o)dinger equation is also solved using two computational methods, the semiclassical method (WKB), and the Numerov method. Our results are found to be in an excellent agreement with the more recent theoretical values. It shows that the two potentials and methods are applicable for studying ultracold collisions between the mixing alkali atoms.     

一种新型双势和周期势模型的构造及其精确解

提出了一种构造并精确求解新型势函数的方法.采用这种方法.讨论了一维二次型函数的通解,将这种二次型函数分段连接构造出一种新型一维双势阱模型和新型一维周期势模型,在此基础上得出了这两种新型势模型的精确解.     

气体放电等离子体特性测量I-V曲线不对称性的研究

利用气体放电双探针法研究了等离子体的I-V曲线中的电流I相对于电压V轴交点的不对称性,并提出2种可能的解释:一认为是由于两探针表面积不同引起的;二认为是由于探针所在处等离子体电位不等引起的.本文利用仪器的工艺误差和调换放电管电压的方法,对提出的2种可能原因分别进行验证,并指出第二种解释的合理性,并对其进行了理论分析.     

THE QUARK CLUSTER MODEL OF NUCLEAR FORCE:(Ⅱ) QUARK CONFINEMENT POTEPNTIAL AND COLOR VAN DER WAALS FORCE

The color-analog Van der Waals force between two hadrons is studied by the coupling channel resonating group method in the framework of the Gaussian-type quark confinement potential. The problem of the boundary values for the two channel coupling differential equations is changed to the problem of the initial values. The equations are solved numerically by the Gill method. The calculated results show that there is no color Van der Waals force between hadrons in the confinement potential model. This indicates that the confinement potential model not only can describe the internal structure of hadrons but also can be used to calculate the hadron-hadron interactions.     

Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method

The Dirac equation for Eckart potential and trigonometric Manning Rosen potential with exact spin symmetry is obtained using an asymptotic iteration method. The combination of the two potentials is substituted into the Dirac equation,then the variables are separated into radial and angular parts. The Dirac equation is solved by using an asymptotic iteration method that can reduce the second order differential equation into a differential equation with substitution variables of hypergeometry type. The relativistic energy is calculated using Matlab 2011. This study is limited to the case of spin symmetry. With the asymptotic iteration method, the energy spectra of the relativistic equations and equations of orbital quantum number l can be obtained, where both are interrelated between quantum numbers. The energy spectrum is also numerically solved using the Matlab software, where the increase in the radial quantum number nr causes the energy to decrease. The radial part and the angular part of the wave function are defined as hypergeometry functions and visualized with Matlab 2011. The results show that the disturbance of a combination of the Eckart potential and trigonometric Manning Rosen potential can change the radial part and the angular part of the wave function.     

Numerical solution of the linearized Boltzmann equation for an arbitrary intermolecular potential

A numerical procedure to solve the linearized Boltzmann equation with an arbitrary intermolecular potential by the discrete velocity method is elaborated. The equation is written in terms of the kernel, which contains the differential cross section and represents a singularity. As an example, the Lennard-Jones potential is used and the corresponding differential cross section is calculated and tabulated. Then, the kernel is calculated so that to overcome its singularity. Once, the kernel is known and stored it can be used for many kinds of gas flows. In order to test the method, the transport coefficients, i.e. thermal conductivity and viscosity for all noble gases, are calculated and compared with those obtained by the variational method using the Sonine polynomials expansion. The fine agreement between the results obtained by the two different methods shows the feasibility of application of the proposed technique to calculate rarefied gas flows over the whole range of the Knudsen number.     

Parameter estimation of the FitzHugh-Nagumo model using noisy measurements for membrane potential

This paper proposes an identification method to estimate the parameters of the FitzHugh-Nagumo (FHN) model for a neuron using noisy measurements available from a voltage-clamp experiment. By eliminating an unmeasurable recovery variable from the FHN model, a parametric second order ordinary differential equation for the only measurable membrane potential variable can be obtained. In the presence of the measurement noise, a simple least squares method is employed to estimate the associated parameters involved in the FHN model. Although the available measurements for the membrane potential are contaminated with noises, the proposed identification method aided by wavelet denoising can also give the FHN model parameters with satisfactory accuracy. Finally, two simulation examples demonstrate the effectiveness of the proposed method.     

Application of an inverse-scattering method to determine the effective interaction between composite particles

An inverse-scattering method developed recently by Münchow and Scheid is used to determine the effective potential between two α-particles. The α-α scattering phase shifts from a microscopic calculation using the generator coordinate method are employed with the inversescattering technique to obtain a unique, energy-dependent optical potential. A comparison of this potential with the direct (or folded) potential clearly reveals the Pauli exchange effects arising from the inclusion of nuclear exchange between the two a-particles. It is shown that the inverse-scattering approach is accurate for the α-α system even at low energies and should be applicable to heavy-ion systems.     

Controlling the collision between two solitons in the condensates by a double-barrier potential

We present an analytical solution of two solitons of Bose-Einstein condensates trapped in a double-barrier potential by using a multiple-scale method.In the linear case,we find that the stable spots of the soliton formation are at the top of the barrier potential and at the region of barrier potential absence.For weak nonlinearity,it is shown that the height of the barrier potential has an important effect on the dark soliton dynamical properties.Especially,in the case of regarding a double-barrier potential as the output source of the solitons,the collision spots between two dark solitons can be controlled by the height of the barrier potential.     

Possibility of propagation of dissipative solitons in ac-driven superlattice

The renormalization equation for nonlinear electromagnetic wave propagating in ac-driven superlattice with dissipation has been derived by averaging method. The expression for dissipative soliton potential is obtained. The values of high-frequency field amplitudes allowing for two types of dissipative soliton are found. The shape and type of such solitons are shown to be regulated by changing the high-frequency field amplitude. The chaotic behavior of electrons in superlattice is investigated by the Melnikov method.     

用直接方法和希耳伯变换计算二维瞬态势及其梯度

本文用直接方法和希耳伯变换给出了计算二维瞬态势及其梯度的新方法.这种方法可以计算复杂度从传统的O(N_t²)降低到O(N_t).在计算势及其梯度时,该方法的直接计算中所用的权重因子不随时间变化,因此它们只需在第一个时间步长时计算一次.所以,当用于二维瞬态散射的时间推进算法中时,该方法可节省大量的CPU时间.数值结果表明该方法的精度非常高.     

Thomas-Fermi description of nuclear systems including spin-orbit interactions

The Thomas-Fermi statistical method is generalized to include spin-orbit interactions. The momentum distributions are given by toroids, different for two particle spin orientations. A system of two coupled differential equations is derived by a variational procedure for the densities of the two populations. From these equations the polarization at the surface of nuclear matter is calculated, as well as the change of the nuclear surface tension due to spin-orbit coupling. Within the statistical framework the coupling strength of the spin-orbit potential is found to be in reasonable agreement with experiment by using only the experimental single-particle level order of the shell model which implies an excess of states with spin parallel to the orbital angular momentum.     

Effective coupling between two Brownian particles

We use the system-plus-reservoir approach to study the dynamics of a system composed of two independent Brownian particles. We present an extension of the well-known model of a bath of oscillators which is capable of inducing an effective coupling between the two particles depending on the choice made for the spectral function of the bath oscillators. The coupling is nonlinear in the variables of interest, and an exponential dependence on these variables is imposed in order to guarantee the translational invariance of the model if the two particles are not subject to any external potential. The effective equations of motion for the particles are obtained by the Laplace transform method, and, besides recovering all the local dynamical properties for each particle, we end up with an effective interaction potential between them. We explicitly analyze one of its possible forms.     

一维和二维多势阱能谱的Bsplines计算

用Bsplines函数基计算了一维多势阱和二维Henon Heiles势的能谱,得到了精度较高的结果.将这一结果与采用高斯基函数计算的结果进行比较,结果表明:Bsplines函数基用于研究一维束缚态问题比高斯函数基方法更方便,具有灵活、可塑性强、效率高等优点,适用于不同形式势作用下的系统的变分求解.     

Rational polynomial approximants and scattering amplitude for long range potentials

Rational approximants are introduced for expansions in orthogonal polynomials. They are proposed as a method to obtain fast convergent approximations. We investigate this possibility, by summing the partial wave expansion of the scattering amplitude in two cases, for which the exact phase shifts may be determined. In the first case, we consider the repulsive inverse square potential, as an example of the long range interactions usual in atomic collision processes. The results show, that when using this approximants, the knowledge of a few phase shifts is enough to obtain a degree of accuracy that requires several hundreds of them, when partial sums are used for the calculations. In the second case, we have considered the delta shell potential. Here the two approaches give similar results.     

Exchange interactions in rare-earth iron garnets

Exchange parameters previously reported for YbIG, ErIG and EuIG are compared. One of the three possible sets of parameters found for ErIG is shown to agree fairly well with the EuIG parameters and can also be fitted using an exchange potential. Tentative exchange potential parameters associated with the two types of superexchange pathways which couple the rare-earth ion to neighboring iron ions are obtained. A new method for calculating the YbIG exchange parameters is described and the parameters are compared with those reported previously.     

基于变分方法的有限区域风场分解与重构I: 理论框架和仿真实验

众所周知, 风场分解与重构最有效的方法就是引入速度势和流函数, 其一般通过求解两个Poisson 方程得到. 由于速度势和流函数在边界上的耦合性质,有限区域风场分解是不唯一的, 这对风场分解带来了很大困难. 本文采用变分伴随结合正则化方法来克服风场分解的不唯一性, 其核心是把速度势和流函数的边值作为控制变量来反演. 目标泛函由两部分组成, 一是衡量重构风场误差大小的观测项; 二是保证风场分解问题适定的正则化项, 其目的在于寻求具有气象意义的稳定正则化解. 数值试验结果表明, 在正确选取正则化参数后, 利用变分伴随结合正则化方法进行有限区域风场分解与重构是有效可行的.     

Linear differential equations for the one‐dimensional scattering problem

The transmission and reflection amplitudes of an electron moving in a one dimensional potential of arbitrary form are obtained using the transfer matrix method. It is shown that the one‐dimensional scattering problem, in its most general form, can be reduced to Cauchy problem for a set of two linear differential equations.     

Depletion interactions in binary mixtures of repulsive colloids

Acceptance ratio method, which has been used to calculate the depletion potential in binary hard-sphere mixtures, is extended to the computation of the depletion potential of non-rigid particle systems. The repulsive part of the Lennard-Jones pair potential is used as the direct pair potential between the non-rigid particles. The depletion potential between two big spheres immersed in a suspension of small spheres is determined with the acceptance ratio method through the application of Monte Carlo simulation. In order to check the validity of this method, our results are compared with those obtained by the Asakura-Oosawa approximation, and by Varial expansion approach, and by molecular dynamics simulation. The total effective potential and the depth of its potential well are computed for various softness parameters of the direct pair potential.     

反应N(2D)+H2→NH+H和N(2D)+D2→ND+D的立体动力学理论研究.

基于Ho等人的精确势能面(J. Chem. Phys. 119, 3063(2003))研究,运用准经典轨线方法计算了21.3 kJ/mol碰撞能下反应N(²D)+H₂→NH+H和N(²D)+D₂→ND+D的产物与反应物之间的矢量相关．发现两个反应的产物角分布都是前向和后向呈现峰值分布,产物的转动角动量矢量j′不仅是取向的,而且是在y轴负方向上定向的．两个反应显示出的同位素效应主要归因于同位素质量的差别．