Ground State and Single Vortex for Bose-Einstein Condensates in Anisotropic Traps

For Bose-Einstein condensation of neutral atoms in anisotropic traps at zero temperature, we present simple analytical methods for computing the properties of ground state and single vortex of Bose-Einstein condensates, and compare those results to extensive numerical simulations. The critical angular velocity for production of vortices is calculated for both positive and negative scattering lengths a, and find an analytical expression for the large-N limit of the vortex critical angular velocity for a 〉0, and the critical number for condensate population approaches the point of collapse for a 〈 0, by using approximate variational method.     

Generalized Riccati equation expansion method and its application to the Bogoyavlenskii's generalized breaking soliton equation

Based on the computerized symbolic system Maple and a Riccati equation, a Riccati equation expansion method is presented by a general ansatz. Compared with most of the existing tanh methods, the extended tanh-function method, the modified extended tanh-function method and generalized hyperbolic-function method, the proposed method is more powerful. By use of the method, we not only can successfully recover the previously known formal solutions but also construct new and more general formal solutions for some nonlinear differential equations. Making use of the method, we study the Bogoyavlenskii's generalized breaking soliton equation and obtain rich new families of the exact solutions, including the non-travelling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions.     

Directed Motion of a Molecular Motor Based on the Four-State Model with Unequal Substeps

A periodic one-dimensional four-state hopping model is proposed. In the model, the substeps betweenarbitrary adjacent states are unequal, and an explicit solution of the master equation is first obtained for the probabilitydistribution as a function of the time and position for any initial distribution with all the transients included. Next, thetransient behaviors in the initial period of time and the characteristic time to reach the steady state for the molecularmotor are discussed. Finally, we compare the steady state results to experiments and illustrate qualitatively the kineticbehaviors of a molecular motor under external load F.     

Variable Separation and Derivative-Dependent Functional Separable Solutions to Generalized KdV Equations

Using the generalized conditional symmetry approach, a complete list of canonicalforms for the Kortewegde-Vries type equations with which possessing derivative-dependent functional separable solutions (DDFSSs) is obtained.The exact DDFSSs of the resulting equations are explicitly exhibited.     

Braiding structures on formal Poisson groups and classical solutions of the QYBE

If is a quasitriangular Lie bialgebra, the formal Poisson group can be given a braiding structure. This was achieved by Weinstein and Xu using purely geometrical means, and independently by the authors by means of quantum groups. In this paper we compare these two approaches. First, we show that the braidings they produce share several similar properties (in particular, the construction is functorial); secondly, in the simplest case (G=SL₂) they do coincide. The question then rises of whether they are always the same this is positively answered in a separate paper.     

变截面微小通道传热特性的研究

为研究变截面微小通道的流动和传热特性,设计了9种不同微小尺度的变截面通道。采用实验研究的方法,得出了流体在变截面微小通道中的传热特性以及与常规尺度通道的差异。分别比较了通道的进出口宽度比、通道的高宽比对变截面、微小尺度通道传热特性的影响。根据实验结果,得到了描述水在变截面微小通道中的流动及传热特性的无量纲关联式。     

宇宙常数的Bulk流形的起源

关于宇宙常数问题是个至今没有解决的问题, 它的来源至今还没有一个共识. 从额外维的流形出发, 给出了宇宙常数的,bulk,流形起源的理论, 得到了不同情况下宇宙常数的取值和宇宙常数随时间演化的函数, 并且得到了可拟合现代天文观测的宇宙常数.     

共轭梯度法求解多宗量瞬态热传导反问题

提出瞬态热传导反问题中热物性参数和边界条件多宗量反演的一般数值求解模式,导出了敏度计算公式,并用共轭梯度法求解,探讨了测点数目、测量误差和变量初值对反演结果的影响,并进行了数值验证.     

三维位势问题边界元法中几乎奇异积分的正则化

采用一种半解析正则化算法,计算了三维位势问题边界元法中近边界点的几乎强奇异和几乎超奇异面积分.该算法适用于三角形线性等参元.对高次单元将其细分为几个三节点三角形单元即可应用该算法.由于几乎奇异性,与内点邻近的单元上的积分,采用半解析正则化积分算法计算;而远处单元的积分仍保持常规高斯积分.对三维热传导算例,计算了近边界点的温度和热流.数值结果证明了该算法的有效性和精确性.     

稳态问题混合边界积分方程的高精度求积法与分裂外推

提出了求积法解稳态问题的混合边界积分方程,它拥有高精度,低复杂度.通过并行地解粗网格上的离散方程,根据误差的多参数渐近展开,应用分裂外推算法得到高精度的近似解,同时获得后验误差估计.