Degenerate scale for multiply connected Laplace problems

The degenerate scale in the boundary integral equation (BIE) or boundary element method (BEM) solution of multiply connected problem is studied in this paper. For the mathematical analysis, we use the null-field integral equation, degenerate kernels and Fourier series to examine the solvability of BIE for multiply connected problem in the discrete system. Two treatments, the method of adding a rigid body term and CHEEF concept (Combined Helmholtz Exterior integral Equation Formulation), are applied to remedy the non-unique solution due to the critical scale. The efficiency and accuracy of the two regularizations are also addressed. For simplicity without loss of generality, the eccentric case is considered to demonstrate the occurring mechanism of degenerate scale.     

AlAs/InSe范德华异质结构的光学和可调谐电子特性

由不同二维(2D)材料相互堆叠形成异质结构已成为目前的研究热点, 使用第一性原理的计算方法探究了AlAs/ InSe异质结构的几何结构、电子性能和光学性质. 结果表明, AlAs/InSe异质结构具有典型的Type-II型能带排列并且拥有着1.28 eV的间接带隙. 通过调节层间距或施加外部电场和应变, 可以有效地改变异质结构的带隙值. 有趣的是, 当应用5 V/nm的电场时, 异质结构实现了从Type-II向Type-I的转变. 此外, 与孤立单层相比, AlAs/InSe异质结构的吸光度明显提高, 特别是在紫外区域. 表明新型的二维AlAs/InSe异质结可以作为光电材料和紫外探测器件的有力候选者.     

Two-step flux penetration in classic antiferromagnetic superconductor

The influence of antiferromagnetic order on the mixed state of a superconductor may result in creation of spin-flop domains along vortices. This may happen when an external magnetic field is strong enough to flip over magnetic moments in the vortex core from their ground state configuration. The formation of domain structure causes modification of the surface energy barrier, and creation of the new state in which magnetic flux density is independent of the applied field. The modified surface energy barrier has been calculated for parameters of the antiferromagnetic superconductor DyMo₆S₈. The prediction of two-step flux penetration process has been verified by precise magnetization measurements performed on the single crystal of DyMo₆S₈ at milikelvin temperatures. A characteristic plateau on the virgin curve B(H ₀) has been found and attributed to the modified surface energy barrier. The end of the plateau determines the critical field, which we call the second critical field for flux penetration. Received 16 August 2002 / Received in final form 22 October 2002 Published online 29 November 2002     

Two-phase regime in the magnetic field–temperature phase diagram of a type-II superconductor

The magnetic field and temperature dependencies of the magnetic moments of superconducting crystals of V₃Si have been studied. In a constant magnetic field and at temperatures somewhat below the superconducting transition temperature, the moments are hysteretic in temperature. However, the magnetic moment–magnetic field isotherms are reversible and exhibit features that formally resemble the pressure–volume isotherms of the liquid–gas transition. This suggests the existence of a first-order phase transition, a two-phase regime, and a critical point in the superconducting phase diagram. The two phases are disordered vortex configurations with the same magnetization, but with different vortex densities. The entropy change, determined from the data using the Clausius–Clapeyron equation, is consistent with estimates based on the difference in the vortex densities of the two phases.     

An expansion theorem for an eigenvalue problem of an arbitrary multiply connected domain with an eigenparameter in a general type of boundary conditions

The object of this paper is to establish an expansion theorem for a regular right-definite eigenvalue problem with an eigenvalue parameter which is contained in the Schrödinger partial differential equation and in a general type of boundary conditions on the boundary of an arbitrary multiply connected bounded domain inR ⁿ (n2). We associate with this problem an essentially self-adjoint operator in a suitably defined Hilbert space and then we develop an associated eigenfunction expansion theorem.     

多电荷离子的电子动量分布和电子剥离截面的数值研究

计算了多电荷离子的电子动量分布和多电荷离子与中性原子碰撞的电子剥离截面。     

General Tricomi-Rassias problem and oblique derivative problem for generalized Chaplygin equations

Many authors have discussed the Tricomi problem for some second order equations of mixed type, which has important applications in gas dynamics. In particular, Bers proposed the Tricomi problem for Chaplygin equations in multiply connected domains [L. Bers, Mathematical Aspects of Subsonic and Transonic Gas Dynamics, Wiley, New York, 1958]. And Rassias proposed the exterior Tricomi problem for mixed equations in a doubly connected domain and proved the uniqueness of solutions for the problem [J.M. Rassias, Lecture Notes on Mixed Type Partial Differential Equations, World Scientific, Singapore, 1990]. In the present paper, we discuss the general Tricomi-Rassias problem for generalized Chaplygin equations. This is one general oblique derivative problem that includes the exterior Tricomi problem as a special case. We first give the representation of solutions of the general Tricomi-Rassias problem, and then prove the uniqueness and existence of solutions for the problem by a new method. In this paper, we shall also discuss another general oblique derivative problem for generalized Chaplygin equations.     

A combinatorial approach to doubly transitive permutation groups

Let G be a doubly but not triply transitive group on a set X. We give an algorithm to construct the orbits of G acting on X×X×X by combining those of its stabilizer H of a point of X If the group H is given first, we compute the orbits of its transitive extension G, if it exists. We apply our algorithm to G=PSL(m,q) and Sp(2m,2), m3, successfully. We go forward to compute the transitive extension of G itself. In our construction we use a superscheme defined by the orbits of H on X×X×X and do not use group elements.     

Fast conformal mapping of multiply connected regions

An iterative method is presented which constructs for an unbounded region G with m holes and sufficiently smooth boundary a circular region H and a conformal mapping Φ from H to G. With the usual normalization both H and Φ are uniquely determined by G. With a few modifications the method can also be applied to a bounded region G with m holes. The canonical region H is then the unit disc with m circular holes. The proposed method also determines the centers and radii of the boundary circles of H and requires, at each iterative step, the solution of a Riemann–Hilbert (RH) problem, which has a unique solution. Numerically, the RH problem can be treated efficiently by the method of successive conjugation using the fast Fourier transform (FFT). The iteration for the solution of the RH problem converges linearly. The conformal mapping method converges quadratically. The results of some test calculations exemplify the performance of the method.     

Atomically smooth interfaces of type-II InAs/GaSb superlattice on metamorphic GaSb buffer grown in 2D mode on GaAs substrate using MBE

In the paper, the comparative analysis of type-II InAs/GaSb SLs deposited on three types of GaSb buffers: homoepitaxial, metamorphic and one grown using the interfacial misfit (IMF) array technique has been presented. The buffer layers as well as superlattices were grown under nominally identical technological conditions. HRXRD investigations proved better crystal quality of the metamorphic material than the IMF-GaSb. FWHM_RC were equal to 156 arcsec and 196 arcsec, respectively. The surface roughness of about 1?ML and 4?MLs was obtained using the atomic force microscope for 4.0?μm–metamorphic GaSb and 1.5?μm-IMF-GaSb layers, respectively. The etch pits density for both buffers was similar, 1–2?×?10⁷?cm^?2. Superlattice with 500 periods deposited on the homoepitaxial buffer was used as a reference of the best crystal quality. HRTEM images revealed straight InAs/GaSb interfaces with 1?ML thicknesses in this sample. The interfaces in SL deposited on IMF-GaSb buffer were undulated and smeared over 3?MLs. The use of the metamorphic buffer resulted in 1–2?ML straight InAs/GaSb interfaces. The main reason for this is the roughness of IMF-GaSb buffer with mounds on the surface. Based on the obtained results we have demonstrated the advantage of metamorphic approach over IMF growth mode in GaSb/GaAs material system. A two times thicker buffer could be the price worth paying for high quality structures, even when working in the production mode.