Split-step orthogonal spline collocation methods for nonlinear Schrödinger equations in one, two, and three dimensions

Split-step orthogonal spline collocation (OSC) methods are proposed for one-, two-, and three-dimensional nonlinear Schrödinger (NLS) equations with time-dependent potentials. Firstly, the NLS equation is split into two nonlinear equations, and one or more one-dimensional linear equations. Commonly, the nonlinear subproblems could be integrated directly and accurately, but it fails when the time-dependent potential cannot be integrated exactly. In this case, we propose three approximations by using quadrature formulae, but the split order is not reduced. Discrete-time OSC schemes are applied for the linear subproblems. In numerical experiments, many tests are carried out to prove the reliability and efficiency of the split-step OSC (SSOSC) methods. Solitons in one, two, and three dimensions are well simulated, and conservative properties and convergence rates are demonstrated. We also apply the ways of solving the nonlinear subproblems to the split-step finite difference (SSFD) methods and the time-splitting spectral (TSSP) methods, and the approximate ways still work well. Finally, we apply the SSOSC methods to solve some problems of Bose-Einstein condensates.     

The split closure of a strictly convex body

The Chvátal-Gomory closure and the split closure of a rational polyhedron are rational polyhedra. It has been recently shown that the Chvátal-Gomory closure of a strictly convex body is also a rational polytope. In this note, we show that the split closure of a strictly convex body is defined by a finite number of split disjunctions, but is not necessarily polyhedral. We also give a closed form expression in the original variable space of a split cut for full-dimensional ellipsoids.     

分子内裂分G-四链体脱氧核糖核酸酶用于Hg2+的特异性定量检测

G-四链体DNA酶是由核酸G-四链体与氯化血红素(Hemin)结合后形成的一种具有过氧化物酶活性的人工酶,利用这种DNA酶,可进行多种化学及生物传感器的设计。为提高G-四链体DNA酶类Hg2+传感器的选择性,本研究在传感器的设计过程中引入了分子内裂分G-四链体,即将形成G-四链体的富G序列拆分成两部分,分别放置在Hg2+探测序列的两端。在无Hg2+存在时,部分富G序列被包埋在某一分子内二倍体结构中,无法形成G-四链体。而在Hg2+存在下,Hg2+对T-T碱基错配的稳定能力可以促使Hg2+探测序列形成分子内二倍体结构,并伴随着原有分子间二倍体结构的破坏及分子内裂分G-四链体的生成。利用生成的裂分G-四链体与Hemin作用后检测体系酶活性的提高,实现Hg2+传感器的设计。利用该传感器,可在50～500 nmol/L及2.0～7.5μmol/L两个浓度范围内实现Hg2+的定量检测,检出限为47 nmol/L。由于裂分G-四链体DNA酶的使用强化了传感器对Hg2+的依赖性,极大地提高了设计的Hg2+传感器的选择性。对实际水样的加标回收结果显示,回收率为97.5%～104.5%,证明此传感器可以满足实际水样中痕量Hg2+的分析要求。     

A thermodynamically-consistent microplane model for shape memory alloys

In microplane theory, it is assumed that a macroscopic stress tensor is projected to the microplane stresses. It is also assumed that 1D constitutive laws are defined for associated stress and strain components on all microplanes passing through a material point. The macroscopic strain tensor is obtained by strain integration on microplanes of all orientations at a point by using a homogenization process. Traditionally, microplane formulation has been based on the Volumetric–Deviatoric–Tangential split and macroscopic strain tensor was derived using the principle of complementary virtual work. It has been shown that this formulation could violate the second law of thermodynamics in some loading conditions. The present paper focuses on modeling of shape memory alloys using microplane formulation in a thermodynamically-consistent framework. To this end, a free energy potential is defined at the microplane level. Integrating this potential over all orientations provides the macroscopic free energy. Based on this free energy, a new formulation based on Volumetric–Deviatoric split is proposed. This formulation in a thermodynamic-consistent framework captures the behavior of shape memory alloys. Using experimental results for various loading conditions, the validity of the model has been verified.     

Subregion-Adaptive Integration of Functions Having a Dominant Peak

Abstract

Many statistical multiple integration problems involve integrands that have a dominant peak. In applying numerical methods to solve these problems, statisticians have paid relatively little attention to existing quadrature methods and available software developed in the numerical analysis literature. One reason these methods have been largely overlooked, even though they are known to be more efficient than Monte Carlo for well-behaved problems of low dimensionality, may be that when applied naively they are poorly suited for peaked-integrand problems. In this article we use transformations based on “split t” distributions to allow the integrals to be efficiently computed using a subregion-adaptive numerical integration algorithm. Our split t distributions are modifications of those suggested by Geweke and may also be used to define Monte Carlo importance functions. We then compare our approach to Monte Carlo. In the several examples we examine here, we find subregion-adaptive integration to be substantially more efficient than importance sampling.     

Maritime crude oil transportation - A split pickup and split delivery problem

The maritime oil tanker routing and scheduling problem is known to the literature since before 1950. In the presented problem, oil tankers transport crude oil from supply points to demand locations around the globe. The objective is to find ship routes, load sizes, as well as port arrival and departure times, in a way that minimizes transportation costs. We introduce a path flow model where paths are ship routes. Continuous variables distribute the cargo between the different routes. Multiple products are transported by a heterogeneous fleet of tankers. Pickup and delivery requirements are not paired to cargos beforehand and arbitrary split of amounts is allowed. Small realistic test instances can be solved with route pre-generation for this model. The results indicate possible simplifications and stimulate further research.     

泡沫铝在SHPB高温动态下的变形过程研究

利用分离式Hopkinson压杆(SHPB)实验装置研究轻质泡沫铝在动态压缩下的温度相关性,重点设计了一种基于SHPB的可视化高温炉,在此基础上通过高速摄影观测泡沫铝试件在高低温且动态压缩下的变形过程。动态加载下的实验结果表明：常温下,胞壁在变形过程中易于观察到屈曲失稳、撕裂、弯曲等现象,且在压缩的过程中碎片飞溅;高温下材料软化较明显,呈现出更多的塑性弯曲现象,但是屈曲失稳与撕裂的现象并不显著,变形过程中并无碎片产生。     

Meta材料谐振行为的因果性研究

分析了横电磁波作用下开口谐振环双各向异性Meta材料,揭示了虚波数引起Meta材料谐振行为的事实.利用Floquet模将开口谐振环周期性结构的场分布展开,从电磁波传播角度得出了凋落模是引起Meta材料谐振行为的原因.对于来自主平面上的入射波,具有相同极化方式的Floquet透射模将发生谐振,并且电谐振和磁谐振将随着入射角的不同而改变.