Birkhoff系统的时间积分定理

研究Birkhoff系统的时间积分定理.建立Birkhoff系统的时间积分等式，由此等式导出系统的类功率方程，Pfaff-Birkhoff积分变分原理以及Pfaff-Birkhoff-d′Alembert微分变分原理. 关键词： Birkhoff系统 时间积分等式 类功率方程 变分原理     

有耗孤子的最小作用量原理及其在二维光子带隙结构中的应用

采用变分方法对于二维矩形光子带隙结构中X点孤子的耗散以及相干作用进行了动力学分析.通过对由作用量原理得到的孤子参量联立方程组的分析可知，除了耗散作用导致孤子的幅度衰减，并引起孤子横向的展宽以外，同向孤子的相互作用负势函数为耗散作用所减弱，从而使得孤子在x方向的束缚态被削弱.孤子中心间距随x的增加呈现出增幅变化且波动周期增大，当纵向距离增大到一定值后，孤子中心间距将一直增大下去.     

Investigation of Heisenberg algebra for a modified anti-de Sitter and modified antiSnyder models

In this paper,we consider a possible modification of the de Sitter and anti-de Sitter space for the extended uncertainty principle.For the modified anti-de Sitter model we discuss the representation and wave functions of the momentum operator for a one-dimensional box problem.Also,we consider modified Snyder and anti-Snyder models for the generalized uncertainty principle.Then,we assume the Hamiltonian with different potential and solve the Heisenberg algebra for the modified(anti)-de Sitter and(anti)-Snyder models in both position and in the momentum space.     

Correlation functions from a unified variational principle: Trial Lie groups

Time-dependent expectation values and correlation functions for many-body quantum systems are evaluated by means of a unified variational principle. It optimizes a generating functional depending on sources associated with the observables of interest. It is built by imposing through Lagrange multipliers constraints that account for the initial state (at equilibrium or off equilibrium) and for the backward Heisenberg evolution of the observables. The trial objects are respectively akin to a density operator and to an operator involving the observables of interest and the sources. We work out here the case where trial spaces constitute Lie groups. This choice reduces the original degrees of freedom to those of the underlying Lie algebra, consisting of simple observables; the resulting objects are labeled by the indices of a basis of this algebra. Explicit results are obtained by expanding in powers of the sources. Zeroth and first orders provide thermodynamic quantities and expectation values in the form of mean-field approximations, with dynamical equations having a classical Lie–Poisson structure. At second order, the variational expression for two-time correlation functions separates–as does its exact counterpart–the approximate dynamics of the observables from the approximate correlations in the initial state. Two building blocks are involved: (i) a commutation matrix which stems from the structure constants of the Lie algebra; and (ii) the second-derivative matrix of a free-energy function. The diagonalization of both matrices, required for practical calculations, is worked out, in a way analogous to the standard RPA. The ensuing structure of the variational formulae is the same as for a system of non-interacting bosons (or of harmonic oscillators) plus, at non-zero temperature, classical Gaussian variables. This property is explained by mapping the original Lie algebra onto a simpler Lie algebra. The results, valid for any trial Lie group, fulfill consistency properties and encompass several special cases: linear responses, static and time-dependent fluctuations, zero- and high-temperature limits, static and dynamic stability of small deviations.     

有限变形的三维粘弹性本构模型(英文)

遗传积分形式与弹性元件和粘壶串并联表示的微分形式可以描述高聚物小变形情况下的粘弹性特性.文章以这些小变形的本构模型为起点,推出有限变形下的本构模型.一个有限变形过程分解成一系列微小变形子过程.小变形子过程中,应力的转动变化由弹性本构方程确定,主应力的变化由弹性元件和粘壶串并联结构的模型确定,这样提出了一个满足客观性原理的有限变形的粘弹性本构模型.模型材料参数随应变率而变,所以模型适合于从准静态到冲击载荷的较宽应变率范围.作为应用,计算了简单剪切有限变形,就建议的模型与现有的模型进行了比较,结果表明建议的模型能够描述高聚物有限变形情况下的粘弹性性质.     

相空间中的Noether定理及其应用

从修改的哈密顿变分原理出发导出相空间的 Noether 定理,对正则拉氏量系统,分析该系统在相空间中的对称性质,可导出其相应的守恒量,而这种相空间中的对称性质在位形空间中常常又是不呈现出来的.对奇异拉氏量系统,该系统具有 Dirac约束,我们分析了约束系统的对称性质,讨论了 Dirac 猜想是否有效.     

电磁波在左右手介质界面折射与反射特性的研究

研究了电磁波在左右手介质界面折射与反射的特性,给出了折射系数和反射系数,从另外一个方面探讨了最小作用量原理在左手材料中的适用性;从电动力学和最小作用量原理证明了Snell定律,验证了Snell定律在左手材料中的适用性,并且得到Fresnell公式在左右手材料中的一致性.     

Possible Critical Orientations of Interacting Composite Particles

We obtain possibly valuable information about the phase diagram linked to the critical orientations for composite matter subjected to interactions at high fermion as well as boson number density but low temperature, which is not easily accessible to experiments. Our results qualitatively resemble those proposed before by using other theories once we can calibrate our results by tuning the critical orientation and the rarefaction measure (relevant to the temperature).     

双棱镜干涉实验中的参量取值研究

本文从理论上推导出双棱镜干涉实验中各参量的取值范围,并通过实验研究找到测量误差小于1%时各参量的取值,这为减小实验误差提供了理论和实验依据.     

求任意形状截面无限长直载流螺线管磁场的一种方法

在电磁学中,无限长直载流螺线管的磁场是一个基本与核心的问题,为了得到这一系统的磁场,通常的做法是：先就圆截面情况计算,然后把截面为任意形状无限长直螺线管看成是由无数大大小小的圆截面螺线管叠加而成,由此得到螺线管内的磁场均匀而管外磁场为零的一般结论.这里给出了一种推导截面为任意形状无限长直螺线管内外磁场的直接方法.先计算螺线管表面一窄条的磁场,再算总磁场.这种方法物理图像清楚,数学过程简单,可以在教学中加以应用.