A new approach to solve the one-dimensional Schrödinger equation using a wavefunction potential

A new approach to find exact solutions to one–dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. We recover known solutions as well as to get new ones for both free and interacting particles with wavefunctions having vanishing and non–vanishing Bohm potentials. For most of the potentials, no solutions to the Schrödinger equation produce a vanishing Bohm potential. A (large but) restricted family of potentials allows the existence of particular solutions for which the Bohm potential vanishes. This family of potentials is determined, and several examples are presented. It is shown that some quantum, such as accelerated Airy wavefunctions, are due to the presence of non–vanishing Bohm potentials. New examples of this kind are found and discussed.     

纵横载荷作用下功能梯度梁的弯曲和过屈曲

基于一阶非线性梁理论和物理中面概念,导出了纵横向载荷作用下功能梯度材料(FGM)梁非线性弯曲和过屈曲问题的控制方程,并获得了该问题的精确解;据此解研究了梯度材料性质、外载荷、横向剪切变形以及边界条件等因素对功能梯度材料梁非线性力学行为的影响,分析中假设功能梯度材料性质只沿梁厚度方向,并按成分含量的幂指数函数形式变化。结果表明:纵横载荷共同作用下,功能梯度梁的弯曲构形将有无限多个;随着梯度指数的增大,梁的变形减小,临界载荷升高;随着长高比的增大,横向剪切变形的影响减小。     

Spin Dynamics and Dirac Nodes in a Kagome Lattice

Herein, the spin dynamics for various magnetic configurations arranged on a Kagome lattice is investigated. Using a Holstein–Primakoff expansion of the isotropic Heisenberg Hamiltonian with multiple exchange parameters, the development and evolution of magnetic Dirac nodes with both anisotropy and magnetic field are examined. From the classical energies, the phase diagrams for the ferromagnetic (FM), antiferrimagnetic (AfM), and the 120°  phases are shown as functions of J₁, J₂, J₃, and anisotropy. Furthermore, the production of bosonic Dirac and Weyl nodes in the spin-wave spectra is shown. Through frustration of the magnetic geometry, a connection to the asymmetric properties of the Kagome lattice and the various antiferromagnetic configurations is discerned. Most interesting is the 120°  phase, which does not have Dirac nodes when considering only J₁ due to the formation of an analogous antiferromagnetic honeycomb lattice, but gains Dirac symmetry with next-nearest neighbor interactions. Additionally, the presence of flat modes that are characteristic of cluster excitations is shown. Further study of external frustrations from a magnetic field and anisotropy reveals a tunability of the exchange interactions and nodal points.     

Hybrid and multi-field variational principles for geometrically exact three-dimensional beams

This paper addresses the development of several alternative novel hybrid/multi-field variational formulations of the geometrically exact three-dimensional elastostatic beam boundary-value problem. In the framework of the complementary energy-based formulations, a Legendre transformation is used to introduce the complementary energy density in the variational statements as a function of stresses only. The corresponding variational principles are shown to feature stationarity within the framework of the boundary-value problem. Both weak and linearized weak forms of the principles are presented. The main features of the principles are highlighted, giving special emphasis to their relationships from both theoretical and computational standpoints.     

火试金法配料过程自动化的探索和应用

火试金法中配料方式采用的是传统的人工配料,针对人工配料方式的不足,设计了一款自动化程度较高的自动配料机,通过对配料机的准确性、效率及可靠性实验,结果表明配料机检测称量误差在±0.2 g以内,效率为人工配料的2~3倍,检测结果与人工配料的相一致。与此同时,应用此设备改善了工作环境,避免了人为失误造成的检测质量问题,降低了复检率,为企业降低了成本,提高了效益,在业内具有广泛应用前景。     

再生核空间W_2~1[a,b]中线性微分方程组初值问题的数值求解

再生核方法在某些方程(组)解的表示和逼近中具有独特的优势,用一种新的再生核讨论线性微分方程组初值问题解的精确表示与近似计算.较之以往的同类文章,对一些重要定理进行了更简单有效的证明.另外本文的再生核由于其结构简单,易于算法实现.最后的算例充分的显示了基于的再生核方法的有效性.     

一个改进的SQP型算法

本文建立非线性等式和不等式约束规划问题的一个序列二次规划(SQP)型算法.算法的每次迭代只需解一个确实可解的二次规划，然后对其解进行简单的显式校正，便可产生关于罚函数是下降的搜索方向，克服Maratos效应.在适当的假设条件下，还论证了算法的全局收敛性和超级收敛性.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

Speeding up the FMMR perfect sampling algorithm: A case study revisited

In a previous paper by the second author, two Markov chain Monte Carlo perfect sampling algorithms—one called coupling from the past (CFTP) and the other (FMMR) based on rejection sampling—are compared using as a case study the move‐to‐front (MTF) self‐organizing list chain. Here we revisit that case study and, in particular, exploit the dependence of FMMR on the user‐chosen initial state. We give a stochastic monotonicity result for the running time of FMMR applied to MTF and thus identify the initial state that gives the stochastically smallest running time; by contrast, the initial state used in the previous study gives the stochastically largest running time. By changing from worst choice to best choice of initial state we achieve remarkable speedup of FMMR for MTF; for example, we reduce the running time (as measured in Markov chain steps) from exponential in the length n of the list nearly down to n when the items in the list are requested according to a geometric distribution. For this same example, the running time for CFTP grows exponentially in n. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2003     

基于增广Lagrange函数的RQP方法

Recursive quadratic programming is a family of techniques developd by Bartholomew-Biggs and other authors for solving nonlinear programming problems.This paperdescribes a new method for constrained optimization which obtains its search di-rections from a quadratic programming subproblem based on the well-known aug-mented Lagrangian function.It avoids the penalty parameter to tend to infinity.We employ the Fletcher‘s exact penalty function as a merit function and the use of an approximate directional derivative of the function that avoids the need toevaluate the second order derivatives of the problem functions.We prove that thealgorithm possesses global and superlinear convergence properties.At the sametime, numerical results are reported.