The number of bound states of a one-particle Hamiltonian on a three-dimensional lattice

We consider the Hamiltonian , describing the motion of one quantum particle on a three-dimensional lattice in an external field. We investigate the number of eigenvalues and their arrangement depending on the value of the interaction energy for μ ≥ 0 and λ ≥ 0. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 425–443, March, 2009.     

大跨越管道油气混输压力波速及响应特性研究

基于双流体模型,利用小扰动理论,提出了油气混输大跨越管道压力波速模型.利用计算机编程对其求解,通过大跨越管道油气混输实例,得到了以下结论:压力波速的变化受气相影响较大,即使少量气体也能在较大程度上影响压力波速,随混输气量增大,压力波速减小,压力响应时间延长;混输低点气体所承受的压力较混输高点大,从而低点处气相压缩系数小,混输低点较混输高点压力波速增大,压力响应时间相应缩短;在输运管道低点处,气体受到极大压缩,压力波速的变化不明显,几乎收敛于恒定值,在混输管道高点处压力波速变化剧烈.     

Equivariant crystalline cohomology and base change

Given a perfect field of characteristic , a smooth proper -scheme , a crystal on relative to and a finite group acting on and , we show that, viewed as a virtual -module, the reduction modulo of the crystalline cohomology of is the de Rham cohomology of modulo . On the way we prove a base change theorem for the virtual -representations associated with -equivariant objects in the derived category of -modules.

     

Development of a finite-element analysis methodology for the propagation of delaminations in composite structures

Analysing the collapse of skin-stiffened structures requires capturing the critical phenomenon of skin-stiffener separation, which can be considered analogous to interlaminar cracking. This paper presents the development of a numerical approach for simulating the propagation of interlaminar cracks in composite structures. A degradation methodology was introduced in MSC.Marc, which involved the modelling of a structure with shell layers connected by user-defined multiple-point constraints (MPCs). User subroutines were written that employ the virtual crack closure technique (VCCT) to determine the onset of crack growth and modify the properties of the user-defined MPCs to simulate crack propagation. Methodologies for the release of failing MPCs are presented and are discussed with reference to the VCCT assumption of self-similar crack growth. The numerical results obtained by using the release methodologies are then compared with experimental data for a double-cantilever beam specimen. Based on this comparison, recommendations for the future development of the degradation model are made, especially with reference to developing an approach for the collapse analysis of fuselage-representative structures. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 15–42, January–February, 2007.     

基于GPU加速的几何纹理合成方法

提出了一种基于GPU加速的几何纹理合成方法,以解决几何纹理合成过程中高计算量、高存储占用和高耗时等问题.首先,对样本几何纹理数据进行子块划分,并根据子块在样本中的位置关系设计可重用样本顶点数据的数据结构,优化存储以降低内存的占用率;然后,采用GPU多线程并发技术设计并行加速算法,将串行的几何纹理合成过程并行化,从而实现快速生成任意尺寸的新的几何纹理.实验结果表明,该算法不仅占用存储较少,而且在保证合成质量的同时极大地降低了几何纹理的合成耗时.     

基于子带位平面容错算法的应用

在研究容错图像编码算法的基础上，针对图像压缩编码中复杂度较大和将图像分成多个小块而带来的图像重建中有分块痕迹等问题，在子带位平面编码（SBC）算法中加入了与图像无关的率失真优化编码并采用虚拟分块的方法，对SBC算法进行了改进，实验结果表明，在相同压缩倍数和相同误码率情况下，本算法与传统的图像压缩算法重建图像的峰值信噪比提高了1．0～1．5dB。     

Elastoplastic Analysis with Limited Plastic Deformations and Displacements*

ABSTRACT

This paper presents solution methods for elastoplastic and shakedown analysis of linearly elastic, perfectly plastic bodies for which the conventional classical formulations of these problems are completed by constraints on overall plastic deformation and elastoplastic displacement. The methods are described in terms of nonlinear mathematical programming and provide solutions when the plastic reserves of the body are not fully exhausted, and the plastic performance and the plastic deformations are controlled. Application of the method is illustrated by an example.     

中央肋对接平尾结构非对称载荷测量技术

针对中央肋对接平尾结构,使用直接测量法和提出的唯象拟合法对其非对称弯矩载荷进行测量。通过先后开展虚拟试验和地面载荷校准试验,分别建立了两种测量方法的非对称载荷模型,并对其适用性和准确性进行研究。地面试验和飞行试验结果显示,唯象拟合法能够有效地完成平尾结构的非对称载荷测量,地面试验验模误差最大值为1.57%;直接测量法由于中央对称面附近连接有对接肋和平尾接头等导致局部传力比较复杂,测量精度较差,地面试验验模误差达到8.11%。

     

Limit constructions over Riemann surfaces and their parameter spaces, and the commensurability group actions

To any compact hyperbolic Riemann surface X, we associate a new type of automorphism group — called its commensurability automorphism group, ComAut(X). The members of ComAut(X) arise from closed circuits, starting and ending at X, where the edges represent holomorphic covering maps amongst compact connected Riemann surfaces (and the vertices represent the covering surfaces). This group turns out to be the isotropy subgroup, at the point represented by X (in $ T_\infty $), for the action of the universal commensurability modular group on the universal direct limit of Teichmüller spaces, $ T_\infty $. Now, each point of $ T_\infty $ represents a complex structure on the universal hyperbolic solenoid. We notice that ComAut(X) acts by holomorphic automorphisms on that complex solenoid. Interestingly, this action turns out to be ergodic (with respect to the natural measure on the solenoid) if and only if the Fuchsian group uniformizing X is arithmetic. Furthermore, the action of the commensurability modular group, and of its isotropy subgroups, on some natural vector bundles over $ T_\infty $, are studied by us.     

Convergence analysis of virtual element methods for semilinear parabolic problems on polygonal meshes

In this article, we discuss and analyze new conforming virtual element methods (VEMs) for the approximation of semilinear parabolic problems on convex polygonal meshes in two spatial dimension. The spatial discretization is based on polynomial and suitable nonpolynomial functions, and a Euler backward scheme is employed for time discretization. The discrete formulation of both the proposed schemes—semidiscrete and fully discrete (with time discretization) is discussed in detail, and the unique solvability of the resulted schemes is discussed. A priori error estimates for the proposed schemes (semidiscrete and fully discrete) in H¹‐ and L²‐norms are derived under the assumption that the source term f is Lipschitz continuous. Some numerical experiments are conducted to illustrate the performance of the proposed scheme and to confirm the theoretical convergence rates.