Bloch equations and completely positive maps

Abstract

The phenomenological dissipation of the Bloch equations is re-examined in the context of completely positive maps. Such maps occur if the dissipation arises from a reduction of a unitary evolution of a system coupled to a reservoir. In such a case the reduced dynamics for the system alone will always yield completely positive maps of the density operator. We show that, for Markovian Bloch maps, the requirement of complete positivity imposes some Bloch inequalities on the phenomenological damping constants. For non-Markovian Bloch maps some kind of Bloch inequalities involving eigenvalues of the damping basis can be established as well. As an illustration of these general properties we use the depolarizing channel with white and coloured stochastic noise.     

Free energy functional and Bogolubov equations

By using a functional integral formulation of the theory of superconductivity, we derive a generalization of the Ginsburg-Landau free energy functional valid at all temperatures. It reduces to it near the critical temperature. By minimization of this new functional we get the usual Bogolubov self-consistent equations for superconductors.     

中国折叠炕桌案折叠机巧研究

目的 通过对折叠炕桌案的形成、发展和榫卯结构进行研究,探索折叠家具中承载的熠熠生辉的科技含量和创新成果,为现代设计和创新提供源泉。方法 用文献考证、田野考查、总结归纳等方法,并通过对考古出土、传世家具进行结构复原、测绘扫描、三维展示等方式来对折叠炕桌案进行研究分析。总结出存世折叠炕桌案的折叠结构和固定结构,并对四种不同的榫卯组合进行了深入的分析和研究。 结论 中国折叠家具通过榫卯组合来实现折叠、拆卸、插接和转动等结构,使家具完成造型变化和高度调整,满足礼仪等级、功能转换、存储存放和搬运移动等需求。折叠家具的产生可以溯源至战国两汉墓出土的矮型折叠家具,发展到明清时期后形成了更为丰富复杂的折叠结构,展现中国古代科学严谨的工匠精神和创新精神。     

基于折页模式与折页单元组配关系的折页机工作效能分析方法

分析了折页模式的描述格式,根据印张折痕的位置关系及变向特性对折页模式进行了分解,将复杂折页模式分解为了一系列平行折的顺次组合。结合平行折研究了折页模式与折页单元之间的组配关系,归纳了折页模式与折页单元的组配规则。以JDF定义的85种常用折页模式为参照,提出了一种基于折页模式与折页单元组配的折页机工作效能分析方法。     

Hot working behavior of 2205 austenite-ferrite duplex stainless steel characterized by constitutive equations and processing maps

The hot deformation characteristics of the 2205 duplex stainless steel were analyzed using constitutive equations and processing maps. The hot compression tests were performed at temperature range of 950-1200 °C and strain rate of 0.001-1 s⁻¹. Flow stress was modeled by the constitutive equation of hyperbolic sine function. However, the stress exponent and strain rate sensitivity were different at low and high deformation temperatures where austenite and ferrite are dominant, respectively. It was recognized that strain at the peak point of flow curve increases with the Zener-Hollomon parameter, Z, at low temperature deformation while at high temperature deformation it actually decreases with Z. The power dissipation map, instability map and processing map were developed for the typical strain of 0.3. It was realized that dynamic restoration mechanisms could efficiently hinder the occurrence of flow instability at low and medium strain rates. Otherwise, the increase in strain rate at low and high temperatures could increase the risk of flow instability.     

折叠式集成化光学相关器

利用超短光路结构和空间折叠光路结构,研制出一种小型多功能光学相关器,它能高速处理256×256像素图像。光学相关器易上下拆卸,并方便地实现Vander Lugt相关和联合变换相关之间的互换。实验结果证实了该系统具有较好的相关性能。     

折叠式纸盒质量分析及控制

随着包装印刷的不断发展,折叠式的纸盒越来越多地投入到市场。不少的产品包装盒由原来的塑料,木材等改为折叠式的纸包装盒。选用纸质材料印刷的包装盒产品,其造型可以突破以往的包装局限性,充分发挥纸的良好物理性与印刷的适用性等优势。通过纸张的物理性及印刷的适应性,我们可以设计出精美的图案及造型,经过印刷企业的各种加工成型工艺方法得到实现。     

一类具阻尼项的三阶非线性中立型泛函微分方程的振动性和渐近性

研究一类具阻尼项的三阶非线性中立型连续分布时滞泛函微分方程解的振动性和渐近性,利用广义Riccati变换、积分平均技巧和一些分析技巧,对α≠β的情况,建立了一组保证该方程每一解振动或者收敛到零的充分条件,所得结果改进和推广了最新文献中的一些熟知的准则.     

On the method of functional equations and the performance of desingularized boundary element methods

A correspondence is made between the reciprocal relation for linear elliptic partial differential equations and the Riesz integral representation. The former relates the boundary distributions and appropriate normal fluxes of two arbitrary solutions, and the latter expresses a continuous linear functional in terms of an integral involving a representing function. When sufficient regularity conditions are met, the representing function is identified with the unknown boundary distribution. In principle, the representing function may be expressed in terms of the images of a complete set of orthonormal basis functions with known normal fluxes, as suggested by Kupradze [Kupradze VD. On the approximate solution of problems in mathematical physics. Russ Math Surv 1967; 22: 59–107]; in practice, the representing function is computed by solving integral equations using boundary element methods. The basic procedure involves expressing the representing function in terms of finite-element or other basis functions, and requiring the satisfaction of the reciprocal relationship with a suitable set of test functions such as Green's functions and their dipoles. When the singular points are placed at the boundary, we obtain the standard boundary integral equation method. When the singular points are placed outside the domain of solution, we obtain a system of functional equations and associated class of desingularized boundary integral methods. When sufficient regularity conditions are met and the test functions comprise a complete set, then in the limit of infinite discretization the numerical solution converges to the unknown boundary distribution. An overview of formulations is presented with reference to Laplace's equation in two dimensions. Numerical experimentation shows that, in general, the solution obtained by desingularized methods becomes increasingly less accurate as the singular points of Green's functions move farther away from the boundary, but the loss of accuracy is significant only when the exact solution shows pronounced variations. Exceptions occur when the integral equation does not have a unique solution. In contrast, and in agreement with previous findings, the condition number of the linear system increases rapidly with the distance of the singular points from the boundary, to the extent that a dependable solution cannot be obtained when the singularities are located even a moderate distance away from the boundary. The desingularized formulation based on Green's function dipoles is superior in accuracy and reliability to the one that uses Green functions. The implementation of the method to the equations of elastostatics and Stokes flow are also discussed.     

Folding mirror schlieren diffraction interferometer

We demonstrate the use of a mirror as a viewing diaphragm to generate a built-in diffracted reference beam in schlieren diffraction interferometry (SDI). The use of a mirror edge as a diffracting element instead of a conventional knife edge considerably enhances the contrast of the schlieren pattern, and it is shown to be equal to that of a phase knife edge. This increase in contrast is due to the fact that the otherwise unutilized diffracted beam in SDI is recombined in the described folding mirror geometry.     

折叠自行车设计研究

简述了自行车的发展及现状,分析了在我国发展折叠自行车的可行性及重要性.基于对国内外自行车发展趋势的理解和认识,介绍了一款人性化、合理化的折叠自行车的设计方案.     

Folding in power-law viscous multi-layers

We study high-amplitude folding in layered rocks with two-dimensional numerical simulations. We employ the finite-element method to model shortening of an incompressible multi-layer with power-law viscous rheology. The Lagrangian numerical mesh is deformed and re-meshed to accurately follow the layer interfaces. Three settings are considered: (i) pure shearing of a confined multi-layer, (ii) simple shearing of a multi-layer above a detachment, and (iii) slump folding owing to gravity sliding. In our pure shear simulations, finite-amplitude folds always develop despite confinement and thin weak interlayers. The fold shapes can be significantly irregular, resulting from initial geometrical heterogeneities that are perturbations of the layer interfaces and differences in layer thickness. The bulk normal viscosity of the multi-layer decreases significantly with progressive folding. This structural softening decreases the bulk normal viscosities by a factor of 2-20. For simple shear, the multi-layer does not develop asymmetric fold shapes significantly. Fold axial planes in the multi-layer are mostly curved and not parallel. For slump folding, fold shapes can be significantly asymmetric exhibiting strongly curved fold axial planes and overturned fold limbs. The rheology of the competent layers has a major impact on the fold shapes for gravity-driven multi-layer folding.     

现代建筑中的折叠结构

可展与折叠结构是一类可以自由地大尺度改变几何构形的结构。它们可以从体积较小的闭合或者收缩状态变换到开启或者展开状态。相对于传统结构而言,可展与折叠结构具有建造速度快、施工方便等优点,而且便于运输和存储,可反复使用,因而在民用、军事、航天等领域被广泛应用。针对可展与折叠结构的共性问题及关键技术,采用理论分析、数值模拟、物理模型实验相结合的研究手段,对多种新型可展与折叠结构的几何构成、运动过程以及受力性能等进行了深入的研究。     

Localized Deformation in Compression and Folding of Paperboard

The localized deformation patterns developed during in‐plane compression and folding of paperboard have been studied in this work. X‐ray post‐mortem images reveal that cellulose fibres have been reoriented along localized bands in both the compression and folding tests. In folding, the paperboard typically fails on the side where the compressive stresses exists and wrinkles are formed. The in‐plane compression test is however difficult to perform because of the slender geometry of the paperboard. A common technique to determine the compression strength is to use the so‐called short‐span compression test (SCT). In the SCT, a paperboard with a free length of 0.7 mm is compressed. Another technique to measure the compression strength is the long edge test where the motion of the paperboard is constrained on the top and bottom to prevent buckling. A continuum model that previously has been proposed by the authors is further developed and utilized to predict the occurrence of the localized bands. It is shown that the in‐plane strength in compression for paperboard can be correlated to the mechanical behaviour in folding. By tuning the in‐plane yield parameters to the SCT response, it is shown that the global response in folding can be predicted. The simulations are able to predict the formation of wrinkles, and the deformation field is in agreement with the measured deformation pattern. The model predicts an unstable material response associated with localized deformation into bands in both the SCT and folding. Copyright © 2016 John Wiley & Sons, Ltd.     

Folding and cutting DNA into reconfigurable topological nanostructures

Topology is the mathematical study of the spatial properties that are preserved through the deformation, twisting and stretching of objects. Topological architectures are common in nature and can be seen, for example, in DNA molecules that condense and relax during cellular events. Synthetic topological nanostructures, such as catenanes and rotaxanes, have been engineered using supramolecular chemistry, but the fabrication of complex and reconfigurable structures remains challenging. Here, we show that DNA origami can be used to assemble a M?bius strip, a topological ribbon-like structure that has only one side. In addition, we show that the DNA M?bius strip can be reconfigured through strand displacement to create topological objects such as supercoiled ring and catenane structures. This DNA fold-and-cut strategy, analogous to Japanese kirigami, may be used to create and reconfigure programmable topological structures that are unprecedented in molecular engineering.     

Construction of the exact solution of the ring-plate problem by solving functional equations

This paper presents a method of constructing the exact solution of the ring-plate problem. The method is based on the general solution formula (nonseries form) of the biharmonic equation. The method changes solving the boundary-value problems of the ring plate into solving three functional equations and computing the coefficients of a simple Fourier series, or only solving four functional equations. The method is believed to be new. The simpler formulas of the solutions of all cases of the ring-plate boundary-value problems without any free boundary are obtained. Several examples are given.     

具连续分布滞量的非线性抛物型偏微分方程的振动准则

考虑一类具连续分布滞量的非线性抛物型偏微分方程的振动性，借助Green定理将多维振动问题转化为关于某一类具连续分布滞量的非线性微分不等式的一维问题，给出了该类方程在Robin，Dirichlet边值条件下所有解振动的若干充分判据。所得结论充分地表明，振动是由时滞量引起的。     

标签裹包折标机构设计

目的设计一套标签裹包折标机构。方法基于机构设计理论与方法,将解析法与Auto CAD辅助作图法相结合,对裹包折标执行机构进行参数设计;利用Solid Works软件的建模工具,对裹包折标机构进行局部结构建模设计。结果针对矩形纸板标签及特定裹包要求,设计提出了标签裹包折标的系统机构原理,以最小传动角理论对关键折标机构完成了参数化设计,并设计了结构模型,理论上验证了设计的标签裹包折标机构的可行性。结论设计的标签裹包折标机构适用于刚性或柔性物体包装,为标签裹包系统设计及技术应用提供了理论参考。