Effective-mass Hamiltonian for abrupt heterojunctions

Recent work by Morrow and Brownstein [Phys. Rev. B 30, 678(1984)] has indicated that no derivation exists which would uniquely specify the form of the effective mass theory kinetic energy operator in the neighborhood of an abrupt heterojunction. Present work starts from a basic principle, i.e. the Lagrange equation of motions and provides such a derivation of a uniquely determined effective mass kinetic energy operator. The result is an operator introduced long ago by BenDaniel and Duke.     

An element-free Galerkin(EFG) method for numerical solution of the coupled Schrdinger-KdV equations

The present paper deals with the numerical solution of the coupled Schrdinger-KdV equations using the elementfree Galerkin(EFG) method which is based on the moving least-square approximation.Instead of traditional mesh oriented methods such as the finite difference method(FDM) and the finite element method(FEM),this method needs only scattered nodes in the domain.For this scheme,a variational method is used to obtain discrete equations and the essential boundary conditions are enforced by the penalty method.In numerical experiments,the results are presented and compared with the findings of the finite element method,the radial basis functions method,and an analytical solution to confirm the good accuracy of the presented scheme.     

The attenuation of the higher-order cross-section modes in a duct with a thin porous layer

A numerical method for sound propagation of higher-order cross-sectional modes in a duct of arbitrary cross-section and boundary conditions with nonzero, complex acoustic admittance has been considered. This method assumes that the cross-section of the duct is uniform and that the duct is of a considerable length so that the longitudinal modes can be neglected. The problem is reduced to a two-dimensional (2D) finite element (FE) solution, from which a set of cross-sectional eigen-values and eigen-functions are determined. This result is used to obtain the modal frequencies, velocities and the attenuation coefficients. The 2D FE solution is then extended to three-dimensional via the normal mode decomposition technique. The numerical solution is validated against experimental data for sound propagation in a pipe with inner walls partially covered by coarse sand or granulated rubber. The values of the eigen-frequencies calculated from the proposed numerical model are validated against those predicted by the standard analytical solution for both a circular and rectangular pipe with rigid walls. It is shown that the considered numerical method is useful for predicting the sound pressure distribution, attenuation, and eigen-frequencies in a duct with acoustically nonrigid boundary conditions. The purpose of this work is to pave the way for the development of an efficient inverse problem solution for the remote characterization of the acoustic boundary conditions in natural and artificial waveguides.     

Galerkin Finite Element Study on the Effects of Variable Thermal Conductivity and Variable Mass Diffusion Conductance on Heat and Mass Transfer

This article investigates the effects of variable thermal conductivity and variable mass diffusion coefficient on the transport of heat and mass in the flow of Casson fluid. Numerical simulations for two-dimensional flow induced by stretching surface are performed by using Galerkin finite element method (GFEM) with linear shape functions. After assembly process, nonlinear algebraic equations are linearized through Picard method and resulting linear system is solved iteratively using Gauss Seidal method with simulation tolerance 10^-8. Maximum value of independent variable η is searched through numerical experiments. Grid independent study was carried out and error analysis is performed. Simulated results are validated by comparing with already published results. Parametric study is carried out to explore the physics of the flow. The concentration increases when mass diffusion coefficient is increased. The concentration and thermal boundary layer thicknesses increase when ε₁ and ε are increased. The effect of generative chemical reaction on concentration is opposite to the effect of destructive chemical reaction on the concentration.     

静态电磁场边值问题计算方法

介绍常用的电磁场分析方法——解析法、有限差分法、有限元法.以静态电磁场边值问题为例,分别用自己编写的MATLAB有限差分程序及大型有限元分析软件ANSYS求出了数值解,并与解析法得到的精确解进行比较,得出了用数值法求解电磁场问题基本满足工程需要的结论.采用数值计算时,对如何减小计算机内存,取消冗余数据,也做了进一步的讨论.     

Renormalization of the Mass Gap

We have explicitly shown that QCD is the color gauge invariant theory at non-zero mass gap as well. It has been defined as the value of the regularized full gluon self-energy at some finite point. The mass gap is mainly generated by the nonlinear interaction of massless gluon modes. All this allows one to establish the structure of the full gluon propagator in the explicit presence of the mass gap. In this case, the two independent general types of formal solutions for the full gluon propagator as a function of the regularized mass gap have been found. The nonlinear iteration solution at which the gluons remain massless is explicitly present. The existence of the solution with an effective gluon mass is also demonstrated.     

A finite difference approach with velocity interfacial conditions for multiscale computations of crystalline solids

We propose a class of velocity interfacial conditions and formulate a finite difference approach for multiscale computations of crystalline solids with relatively strong nonlinearity and large deformation. Full atomistic computations are performed in a selected small subdomain only. With a coarse grid cast over the whole domain and the coarse scale dynamics computed by finite difference schemes, we perform a fast average of the fine scale solution in the atomistic subdomain to force agreement between scales. During each coarse scale time step, we adopt a linear wave approximation around the interface, with the wave speed updated using the coarse grid information. We then develop a class of velocity interfacial conditions with different order of accuracy. The interfacial conditions are straightforward to formulate, easy to implement, and effective for reflection reduction in crystalline solids with strong nonlinearity. The nice features are demonstrated through numerical tests.     

Numerical investigation of a coupled moving boundary model of radial flow in low-permeable stress-sensitive reservoir with threshold pressure gradient

The threshold pressure gradient and formation stress-sensitive effect as the two prominent physical phenomena in the development of a low-permeable reservoir are both considered here for building a new coupled moving boundary model of radial flow in porous medium. Moreover, the wellbore storage and skin effect are both incorporated into the inner boundary conditions in the model. It is known that the new coupled moving boundary model has strong nonlinearity. A coordinate transformation based fully implicit finite difference method is adopted to obtain its numerical solutions. The involved coordinate transformation can equivalently transform the dynamic flow region for the moving boundary model into a fixed region as a unit circle, which is very convenient for the model computation by the finite difference method on fixed spatial grids. By comparing the numerical solution obtained from other different numerical method in the existing literature, its validity can be verified. Eventually, the effects of permeability modulus, threshold pressure gradient, wellbore storage coefficient, and skin factor on the transient wellbore pressure, the derivative, and the formation pressure distribution are analyzed respectively.     

用改进的格点哈密顿量计算2+1维QCD 0++胶球质量

用改进的格点哈密顿量和截断本征方程法计算2＋1维QCD 0^ 胶球质量,结果显示较好的标度行为。     

Vorticity conditioning in the computation of two-dimensional viscous flows

The problem of evaluating the boundary values of the vorticity in the calculation of two-dimensional viscous flows is considered. It is shown that the splitting of the fourth-order equation for the stream function into two second-order problems implies specific integral conditions which fix the abstract projection of the vorticity field with respect, to the linear manifold of the harmonic functions. These conditions are a direct consequence of the boundary conditions on the velocity, and ensure satisfaction of physically essential conservation laws for the vorticity. The discrete analogue of, the projection conditions produces as many algebraic equations as the number of boundary points and requires the solution of an equal number of Dirichlet problems. In the particular case of stationary linearized equations (Stokes equations) a direct, i.e., noniterative method of solution is obtained. Steady and unsteady computational schemes relying on the projection conditions on the vorticity are introduced and extensive numerical results of finite difference calculations of the driven-cavity model problem are reported and discussed.     

Fermion Mass Mixing in Vacuum

Renormalization group procedure for effective particles is applied to a theory of fermions that interact only through mass mixing terms in their Hamiltonian. Problems with virtual pair production in vacuum are avoided by using the front form of Hamiltonian dynamics. Masses and states of physical fermions emerge at the end of a calculation that is carried out exactly irrespective of the strength of the mass mixing terms. An a priori infinite set of renormalization group equations for all momentum modes of fermion quantum fields is reduced to just one equation for a two-by-two mass matrix. In distinction from scalars, fermions never become tachyons but appear chirally rotated when the mass mixing interaction term is sufficiently strong.     

Probing the validity of average Hamiltonian theory for spin I=1, 3/2 and 5/2 nuclei by analyzing a simple two-pulse sequence

In this work, we investigate the accuracy of controlling spin I=1, 3/2 and 5/2 spin systems by average Hamiltonian theory. By way of example, we consider a simple two-pulse echo sequence and compare this perturbation scheme to a numerical solution of the Von Neumann equation. For the different values of I, we examine this precision as a function of the quadrupolar coupling as well as various experimental parameters such as the pulse spacing and pulse width. Experiments and simulations on I=3/2 and I=5/2 spin systems are presented that highlight a spectral artifact introduced due to finite pulse widths as predicted by average Hamiltonian theory. The control of these spin systems by this perturbation scheme is considered by investigating a phase cycling scheme that suppresses these artifacts to zeroth-order of the Magnus expansion.     

A High-Order Conservative Numerical Method for Gross-Pitaevskii Equation with Time-Varying Coefficients in Modeling BEC

We propose a high-order conservative method for the nonlinear Schrodinger/Gross-Pitaevskii equation with time-varying coefficients in modeling Bose-Einstein condensation(BEC). This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method.Moreover, it preserves several conservation laws well and even exactly under some specific conditions.     

使用混合网格计算非达西渗流

针对垂直裂缝井的特殊流动模式,从非达西定律出发,建立二维平面的非达西渗流方程.通过建立一组无量纲量,最终得到无量纲的渗流方程及其定解条件.假定外边界为圆形,用PEBI网格及混合网格对求解区域进行网格划分,用有限差分法对无量纲的方程进行离散,最终得到垂直裂缝井的井底压力数值解.根据此数值解并考虑井筒存储和表皮因子的影响,得到真实垂直裂缝井的井底压力.对计算结果的分析表明,使用混合网格求解非达西渗流井底压力相当准确,该方法也适用于水平井等更复杂井型及复杂边界的问题求解.     

含对流与蒸发表面的有限厚度材料的双曲型热传导分析

本文对于含有对流与蒸发表面的有限厚度材料,在遭受一脉冲表面热流作用时的双曲型热传导进行了分析,采用热势函数描述的双曲型热传导方程来描述该问题,并用有限差分法进行数值求解．同时,本文还就表面对流与蒸发对材料表面与内部瞬态温度变化的影响以及材料双曲型热传导对表面蒸发的影响进行了分析．     

Numerical simulation of the soliton solutions for a complex modified Korteweg—de Vries equation by a finite difference method

In this paper,a Crank-Nicolson-type finite difference method is proposed for computing the soliton solutions of a complex modifed Korteweg de Vries(MKdV)equation(which is equivalent to the Sasa-Satsuma equation)with the vanishing boundary condition.It is proved that such a numerical scheme has the second order accuracy both in space and time,and conserves the mass in the discrete level.Meanwhile,the resuling scheme is shown to be unconditionally stable via the von Nuemann analysis.In addition,an iterative method and the Thomas algorithm are used together to enhance the computational efficiency.In numerical experiments,this method is used to simulate the single-soliton propagation and two-soliton collisions in the complex MKdV equation.The numerical accuracy,mass conservation and linear stability are tested to assess the scheme's performance.     

On the solution of the number-projected Hartree-Fock-Bogolyubov equations

The numerical solution of the recently formulated number-projected Hartree-Fock-Bogolyubov (HFB) equations is studied in an exactly solvable cranked-deformed shell-model Hamiltonian. It is found that the solution of these number-projected equations involves similar numerical effort as that of bare HFB. We consider that this is significant progress in the mean-field studies of quantum many-body systems. The results of the projected calculations are shown to be in almost complete agreement with the exact solutions of the model Hamiltonian. The phase transition obtained in the HFB theory as a function of the rotational frequency is shown to be smeared out with the projection.     

非线性波动方程的新数值迭代方法

提出了一种新的求解非线性波动方程的数值迭代法,它是一种半解析的方法.与完全的数值计算方法扰法相比,它能够考虑各阶谐波的相互作用,且能够满足能量守恒定律.用它研究了非线性声波在液体中的传播性质,结果表明,在微扰法适用的声强范围内迭代法也适用,在微扰法不适用的一个较宽的声强范围内迭代法依然适用.     

Isometric Embeddings into the Minkowski Space and New Quasi-Local Mass

The definition of quasi-local mass for a bounded space-like region Ω in space-time is essential in several major unsettled problems in general relativity. The quasi-local mass is expected to be a type of flux integral on the boundary two-surface \({\Sigma=\partial \Omega}\) and should be independent of whichever space-like region \({\Sigma}\) bounds. An important idea which is related to the Hamiltonian formulation of general relativity is to consider a reference surface in a flat ambient space with the same first fundamental form and derive the quasi-local mass from the difference of the extrinsic geometries. This approach has been taken by Brown-York [4,5] and Liu-Yau [16,17] (see also related works [3,6,9,12,14,15,28,32]) to define such notions using the isometric embedding theorem into the Euclidean three space. However, there exist surfaces in the Minkowski space whose quasilocal mass is strictly positive [19]. It appears that the momentum information needs to be accounted for to reconcile the difference. In order to fully capture this information, we use isometric embeddings into the Minkowski space as references. In this article, we first prove an existence and uniqueness theorem for such isometric embeddings. We then solve the boundary value problem for Jang’s [13] equation as a procedure to recognize such a surface in the Minkowski space. In doing so, we discover a new expression of quasi-local mass for a large class of “admissible” surfaces (see Theorem A and Remark 1.1). The new mass is positive when the ambient space-time satisfies the dominant energy condition and vanishes on surfaces in the Minkowski space. It also has the nice asymptotic behavior at spatial infinity and null infinity. Some of these results were announced in [29].