Thermoelastically coupled axisymmetric nonlinear vibration of shallow spherical and conical shells

The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied. Based on the large deflection theories of yon Ktirrntin and the theory of thermoelusticity, the whole governing equations and their simplified type are derived. The time-spatial variables are separated by Galerkin ‘ s technique, thus reducing the governing equations to a system of time-dependent nonlinear ordinary differential equation. By means of regular perturbation method and multiple-scales method, the first-order approximate analytical solution for characteristic relation of frequency vs amplitude parameters along with the decay rate of amplitude are obtained, and the effects of different geometric parameters and coupling factors us well us boundary conditions on thermoelustically coupled nonlinear vibration behaviors are discussed.     

Antiplane problem of circular ARC interfacial rigid line inclusions

The antiplane problem of circular arc rigid line inclusions under antiplane concentrated force and longitudinal shear loading was dealt with. By using RiemannSchwaz‘s symmetry principle integrated with the singularity analysis of complex functions, the general solution of the problem and the closed form solutions for some important practical problems were presented. The stress distribution in the immediate vicinity of circular arc rigid line end was examined in detail. The results show that the singular stress fields near the rigid inclusion tip possess a square-root singularity similar to that for the corresponding crack problem under antiplane shear loading, but no oscillatory character. Furthermore, the stresses are found to depend on geometrical dimension, loading conditions and materials parameters. Some practical results concluded are in agreement with the previous solutions.     

复杂非线性系统的某些动力学理论与应用

自然界和工程技术中存在大量的非线性因素和现象,非线性动力学奠定了研究非线性系统丰富多样的运动模式和演化过程的定性或定量规律的坚实理论基础．非线性动力学的研究深刻地揭示了客观世界的复杂性和多样性,它不仅对数理科学的发展有重大理论意义,而且与其他学科广泛交叉,在各个科学技术领域都有十分广阔的应用前景．     

碳纤维增强复合材料板中Ⅰ型裂纹扩展方向预测理论研究

对含裂纹碳纤维增强的复合材料层合板进行了裂纹扩展方向预测理论的研究．介绍了一种新的复合材料Z断裂理论,在裂纹尖端Z因子的定义中引入了新概念:面内平均应变,面内膨胀应变能密度因子和交互特征函数．并通过理论分析和实验测试证明了Z断裂理论的正确性．     

与非平衡问题相关的尺度效应:场与微粒

纳米技术的出现,使我们有必要更好地了解,在原子水平上材料微结构的变化是如何影响和控制着材料的宏观性能.这一挑战涉及到许多以前不曾考虑和不曾了解的现象.其中,位错理论的基础现在知道是有问题的.宏观尺度下采用的简化假设,也许不能用于微观和纳米尺度.尺度效应的含义,涉及到物理系统的非均质和非平衡特性.宏观尺度下的均匀与平衡特性,在材料的物理尺度减少到微米量级时就不再保持了.这些基本观点不能够为了方便而随意到处使用,因为这会改变预测的结果.更令人不满的是在建立物理模型时缺乏一致性.由此产生的问题是在确定制造过程中的有关参数时无能为力,导致由于成本过高而不切实际的终端产品.先进的复合材料和陶瓷材料就存在这样的问题.本文将要讨论的是在原子尺度与连续介质尺度下应用理论模型时存在的潜在问题,而不是去揭示自然的真相.主要讨论微粒,均匀连续介质或者两者的结合.尺度效应问题当前的发展趋势,趋向于在有或者没有时间效应的情况下寻找材料微结构的不同特征尺寸.从原子模拟模型中将了解到许多情况,原子模拟计算将揭示计算结果如何随着边界条件和尺度变化而不同.量子力学,连续介质力学和宇宙模型证明,没有普遍适用的方法.当前的主要兴趣也许是针对多尺度物理问题在技术上建立更高的精度,以得到一个更好的表达结果.      

Real-Time Thermal Ward-Takahashi Identity for Vectorial Current in QED and QCD

It is shown that by means of canonical operator approach the Ward-Takahashi identity (WTI) at finite temperature T and finite chemical potential μ for complete vectorial vertex and complete fermion propagator can be simply proven, rigorously for Quantum Electrodynamics, and approximately for Quantum Chromodynamics, where the ghost effect in the fermion sector is neglected. The WTI shown in the real-time thermal matrix form will give definite thermal constraints on the imaginary part of inverse complete Feynman propagator including self-energy for fermion and will play an important role in relevant physical processes. When the above inverse propagator is assumed to be real, the thermal WTI will essentially be reduced to its form at T=μ=0 thus one can use it in the latter‘s form. At this point, a practical example is indicated.     

Intensity Correlation Function of a Single-Mode Laser Driven by Two Colored Noises with Colored Cross-Correlation

By using the linear approximation method, the intensity correlation function and the intensity correlation time are calculated in a gain-noise model of a single-mode laser driven by colored cross-correlated pump noise and quantum noise, each of which is colored. We detect that, when the cross-correlation between both noises is negative, the behavior of the intensity correlation function C(t) versus time t, in addition to decreasing monotonously, also exhibits several other cases, such as one maximum, one minimum, and two extrema (one maximum and one minimum), i.e., some parameters of the noises can greatly change the dependence of the intensity correlation function upon time. Moreover, we find that there is a minimum Tmin in the curve of the intensity correlation time versus the pump noise intensity, and the depth and position of Train strongly depend on the quantum noise self-correlation time T2 and cross-correlation time T3.     

Full Quantum Theory of Transient-State Electromagnetically Induced Transparency

We develop a full quantum theory of transient-state electromagnetically induced transparency (EIT) in the vapor of three-level A-type atoms interacting with probe and coupling lasers. As applications of the full quantum theory, we show that transient-state EIT medium exhibits normal dispersion and find that group velocities of both coupling and probe lasers are greatly reduced. It is shown that the group velocity of the probe laser in the transient-state EIT case is equal to that in the adiabatic EIT case and that the coupling laser group velocity in the transient-state EIT is generally less than that in the adiabatic EIT.     

Radiative lifetimes of Rydberg 6pnd J=2 states of Pb I by multichannel quantum defect theory

Energy levels of the odd-parity 6pnd J=2 Rydberg states of Pb I are analysed by the multichannel quantum defect theory (MQDT) in the frame of a five-channel three-limit calculation model. With optimal MQDT parameters, channel admixture coefficients are obtained and used to calculate the theoretical lifetimes of the levels by comparing to the previously measured lifetimes. The predicted lifetimes for higher-lying Rydberg states are given and discussed. These predicted lifetimes are very different from those obtained by the four-channel two-limit model pl:eviously used, which means that introduction of the additional interacting channel is important for studying the 6pnd J=2 Rydberg states of Pb I.     

Atomic dynamics in the mode－mode competition system

The atomic dynamical properties in the system with competing k-photon and l-photon transitions are studied fully by means of quantum theory. We discuss the influences of the mode－mode competition, the relative competing strengths of the atom and the two-mode field, and the initial state of the system on the atomic dynamics. We show that the presence of the mode－mode competition can result in quite a periodical collapses-revivals of the atomic inversion and the increase of the initial photons of the system can lead to the collapse－revival phenomenon and prolong the revival time of the atomic inversion.