相空间中非保守系统的Herglotz广义变分原理及其Noether定理

与经典变分原理相比,基于由微分方程定义的作用量的Herglotz广义变分原理给出了非保守动力学系统的一个变分描述,它不仅能够描述所有采用经典变分原理能够描述的动力学过程,而且能够应用于经典变分原理不能适用的非保守或耗散系统.将Herglotz广义变分原理拓展到相空间,研究相空间中非保守力学系统的Herglotz广义变分原理与Noether定理及其逆定理.首先,提出相空间中Herglotz广义变分原理,给出相空间中非保守系统的变分描述,导出相应的Hamilton正则方程;其次,基于非等时变分与等时变分之间的关系,导出相空间中Hamilton-Herglotz作用量变分的两个基本公式;再次,给出Noether对称变换的定义和判据,提出并证明相空间中非保守系统基于Herglotz变分问题的Noether定理及其逆定理,揭示了相空间中力学系统的Noether对称性与守恒量之间的内在联系.在经典条件下,Herglotz广义变分原理退化为经典变分原理,与之相应的相空间中的Noether定理退化为经典Hamilton系统的Noether定理.文末以著名的Emden方程和平方阻尼振子为例说明上述方法和结果的有效性.     

含裂纹梁参数的谐响应识别

主要研究含裂纹梁在简谐激励作用下的动力特性,提出一种依据幅值变化对裂纹参数进行识别的新方法。首先,在振动过程中考虑裂纹的呼吸特性,以悬臂梁为例建立含裂纹梁的二维有限元模型,指出在一般激励频率下,其对应的幅值均是明显信号,可用来描述裂纹梁的动力特性。其次,当激励频率分别取无裂纹梁一阶频率的1/4和二阶频率的1/4时,幅值随裂纹参数的变化明显不同,可依据响应幅值的变化对裂纹参数进行识别。然后,利用曲面拟合技术绘出幅值变化曲面,对未知参数的裂纹进行识别,验证了该方法的有效性,并归纳出利用幅值变化对任意裂纹参数进行识别的基本步骤。最后,针对无裂纹梁频率计算可能存在误差的情况,分析识别方法的鲁棒性,结果显示即使最大误差为10%,该方法也能对裂纹参数进行准确识别。     

Skin formation in drying a film of soft matter solutions:Application of solute based Lagrangian scheme

When a film of soft matter solutions is being dried, a skin layer often forms at its surface, which is a gel-like elastic phase made of concentrated soft matter solutions. We study the dynamics of this process by using the solute based Lagrangian scheme which was proposed by us recently. In this scheme, the process of the gelation(i.e., the change from sol to gel) can be naturally incorporated in the diffusion equation. Effects of the elasticity of the skin phase, the evaporation rate of the solvents, and the initial concentration of the solutions are discussed. Moreover, the condition for the skin formation is provided.     

Quantum Measurement of Two-Qubit System in Damping Noise Environment

It is known that the inevitable interaction of the entangled qubits with their environments may result in the degradation of quantum correlation.We study the decoherence of two remote qubits under general local single-and two-sided amplitude-damping channel(ADC).By using concurrence,quantum discord and Clauser-Horne-ShimonyHolt(CHSH)inequality,we find that the relation between the residual quantum correlations and the initial ones are different.Recently,Wang et al.[Int.J.Theor.Phys.54(2015)5]showed that there exist a set of partially entangled states that are more robust than maximally entangled states in terms of the residual quantum correlation measured by concurrence,fully entangled fraction and quantum discord,respectively.Here we find that both in single-and two-sided ADC,only the evolution of CHSH inequality with the initial parameter is proportional to that of the initial nonlocality.That means the initial state with maximally nonlocality will retain its role in the evolution.It implies that the evolution of nonlocality may reveal the characteristics of quantum state better.Furthermore,we discuss the evolutions of the three different quantum measurements with the initial parameter under generalized amplitude damping channel(GADC)and find that they are all proportional to that of the initial state.     

Nonlinear Saturation Amplitude in Classical Planar Richtmyer–Meshkov Instability

The classical planar Richtmyer–Meshkov instability(RMI) at a fluid interface supported by a constant pressure is investigated by a formal perturbation expansion up to the third order,and then according to definition of nonlinear saturation amplitude(NSA) in Rayleigh–Taylor instability(RTI),the NSA in planar RMI is obtained explicitly.It is found that the NSA in planar RMI is affected by the initial perturbation wavelength and the initial amplitude of the interface,while the effect of the initial amplitude of the interface on the NSA is less than that of the initial perturbation wavelength.Without marginal influence of the initial amplitude,the NSA increases linearly with wavelength.The NSA normalized by the wavelength in planar RMI is about 0.11,larger than that corresponding to RTI.     

First principle study of LiXS_2(X=Ga,In) as cathode materials for Li ion batteries

From first principle calculations, we demonstrate that LiXS_2(X = Ga, In) compounds have potential applications as cathode materials for Li ion batteries. It is shown that Li can be extracted from the LiXS_2 lattice with relatively small volume change and the XS_4 tetrahedron structure framework remains stable upon delithiation. The theoretical capacity and average intercalation potential of the LiGaS_2(LiInS_2) cathode are 190.4(144._2) m Ah/g and 3.50 V(3.53 V). The electronic structures of the LiXS_2 are insulating with band gaps of _2.88 eV and 1.99 eV for X = Ga and In, respectively.However, Li vacancies, which are formed through delithiation, change the electronic structure substantially from insulating to metallic structure, indicating that the electrical conductivities of the LiXS_2 compounds should be good during cycling.Li ion migration energy barriers are also calculated, and the results show that Li ion diffusions in the LiXS_2 compounds can be as good as those in the currently widely used electrode materials.     

大学物理实验教学应突出原理性

大学物理实验是理工科大学教学当中最基本、最重要的教学环节,为了巩固基本理论知识,促进理论教学,培养理论联系实际的能力而开设的。在大学物理实验教学中,不是简单的技能培训。因而实验教学要将实验原理和实验操作并重,实验设计应以原理透明化,突出加强。在真正懂得原理的前提下才能达到锻炼操作能力和理解理论知识的目的,并为创新型人才培养真正起到奠定基础的作用。     

基于“慕课”的物理类微课程设计探索

“慕课”起步,微课程先行!鉴于目前微课程设计缺乏规范模式,本文旨在对此进行深入探讨．在微课程设计缺乏充分的理论基础支持的前提下,本文首先利用文献综述法归纳得出微课程的基本特征,据此确定微课程设计原则;其次以此原则为指导,借鉴远程开放教育的设计模式,类比探索出微课程设计的基本模式;最后将这种微课程设计模式应用于物理类课程,并结合物理类课程特点进行实证分析,成功实现了物理类微课程设计．教学实践活动进一步检验了本文构建的微课程设计模式切实可行、效果良好．     

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.