Integrability and Solutions of the(2+1)-dimensional Hunter–Saxton Equation

In this paper,the(2+1)-dimensional Hunter-Saxton equation is proposed and studied.It is shown that the(2+1)-dimensional Hunter–Saxton equation can be transformed to the Calogero–Bogoyavlenskii–Schiff equation by reciprocal transformations.Based on the Lax-pair of the Calogero–Bogoyavlenskii–Schiff equation,a non-isospectral Lax-pair of the(2+1)-dimensional Hunter–Saxton equation is derived.In addition,exact singular solutions with a finite number of corners are obtained.Furthermore,the(2+1)-dimensional μ-Hunter–Saxton equation is presented,and its exact peaked traveling wave solutions are derived.     

Van der Waals状态方程可压缩多流体流动的PPM方法

基于流体体积分数的混合型多流体数值模型,将Piecewise Parabolic Method（PPM）方法应用于可压缩多流体流动的数值模拟,采用双波近似求解多流体van der Waals状态方程的Riemann问题．模拟高密度比且含有激波的可压缩多流体流动,典型的纯界面平移问题模拟结果表明,在接触间断的界面附近,压力和速度没有任何的振荡且界面数值耗散都被控制在2—3个网格之内;一维和二维算例表明,该数值方法可以有效地处理接触间断、激波和多维滑移线等物理问题,并能够比其它多流体数值方法更精细地模拟多流体交界面．     

A high order energy preserving scheme for the strongly coupled nonlinear Schrōdinger system

A high order energy preserving scheme for a strongly coupled nonlinear Schrōdinger system is roposed by using the average vector field method. The high order energy preserving scheme is applied to simulate the soliton evolution of the strongly coupled Schrōdinger system. Numerical results show that the high order energy preserving scheme can well simulate the soliton evolution, moreover, it preserves the discrete energy of the strongly coupled nonlinear Schrōdinger system exactly.     

A particular solution of Heun equation for Hulthen and Woods‐Saxon potentials

In this article a particular solution of Heun equation is derived by making use of the Nikiforov‐Uvarov (NU) method which provides exact solutions for general hypergeometric equation and eigenvalues together with eigenfunctions of the Heun equation for this particular solution are obtained. One to one correspondence (isomorphism) of the aforesaid equation with the radial Schrödinger equation is emphasized and also physical counterparts of the parameters in this equation are put forward by introducing solutions for two different potential functions (Hulthen and Woods‐Saxon potentials).

     

电磁驱动45钢准等熵压缩的实验研究

在已有的众多准等熵加载技术中,磁驱动准等熵加载技术具有准等熵程度高、压力范围大、实验材料种类多、效费比高等特点。利用中物院流体物理研究所建成的磁驱动准等熵压缩和高速飞片实验装置CQ-1.5(最高加载压力为50GPa),成功开展了45钢的准等熵压缩实验,对装置的主要参数进行了介绍;利用激光干涉测试系统DPS获得了45钢飞片的自由面速度历史,通过反积分处理给出了材料准等熵压缩的p-V关系。通过分析实验数据,获得了45钢3种形式的等熵方程的参数。实验获得的最高等熵压力为47.5GPa。     

Anomalous transport in fluid field with random waiting time depending on the preceding jump length

Anomalous (or non-Fickian) transport behaviors of particles have been widely observed in complex porous media. To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields, in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced, and the corresponding master equation in Fourier-Laplace space for the distribution of particles is derived. As examples, two generalized advection-dispersion equations for Gaussian distribution and lévy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation.     

A type of conserved quantity of Mei symmetry of Nielsen equations for a holonomic system

A type of structural equation and conserved quantity which are directly induced by Mei symmetry of Nielsen equations for a holonomic system are studied.Under the infinitesimal transformation of the groups,from the definition and the criterion of Mei symmetry,a type of structural equation and conserved quantity for the system by proposition 2 are obtained,and the inferences in two special cases are given.Finally,an example is given to illustrate the application of the results.     

Edge states at the interface between monolayer and bilayer graphene

The electronic properties for monolayer-bilayer hybrid graphene with zigzag interface are studied by both the Dirac equation and numerical calculation in zero field and in a magnetic field. Basically there are two types of zigzag interface dependent on the way of lattice stacking at the edge. Our study shows they have different locations of the localized edge states. Accordingly, the energy-momentum dispersion and local density of states behave quit differently along the interface near the Fermi energy EF=0.