Solving the initial condition of the string relaxation equation of the string model for glass transition: part-I

The string model for the glass transition can quantitatively describe the universal α-relaxation in glassformers,including the average relaxation time,the distribution function of the relaxation time,and the relaxation strength as functions of temperature.The string relaxation equation(SRE) of the model,at high enough temperatures,simplifies to the well-known single particle mean-field Debye relaxation equation,and at low enough temperatures to the well-known Rouse-Zimm relaxation equation that describes the relaxation dynamics of linear macromolecules.However,its initial condition,necessary to the further model predictions of glassy dynamics,has not been solved.In this paper,the special initial condition(SIC) of the SRE,i.e.for straight strings and the dielectric spectrum technique that is one of the most common methods to measure the glassy dynamics,was solved exactly.It should be expected that the obtained SIC would benefit the solution of the general initial condition of the SRE of the string model,i.e.for stochastically spatially configurating strings,as will be described in separate publications.     

Simulations of the flipping images and microparameters of molecular orientations in liquids according to the molecule string model

The relaxation dynamics of liquids is one of the fundamental problems in liquid physics,and it is also one of the key issues to understand the glass transition mechanism.It will undoubtedly provide enlightenment on understanding and calculating the relaxation dynamics if the molecular orientation flipping images and relevant microparameters of liquids are studied.In this paper,we first give five microparameters to describe the individual molecular string(MS) relaxation based on the dynamical Hamiltonian of the MS model,and then simulate the images of individual MS ensemble,and at the same time calculate the parameters of the equilibrium state.The results show that the main molecular orientation flipping image in liquids(including supercooled liquid) is similar to the random walk.In addition,two pairs of the parameters are equal,and one can be ignored compared with the other.This conclusion will effectively reduce the difficulties in calculating the individual MS relaxation based on the single-molecule orientation flipping rate of the general Glauber type,and the computer simulation time of interaction MS relaxation.Moreover,the conclusion is of reference significance for solving and simulating the multi-state MS model.     

Decoupling multimode vibrational relaxations in multi-component gas mixtures: Analysis of sound relaxational absorption spectra

Decoupling the complicated vibrational-vibrational (V-V) coupling of a multimode vibrational relaxation remains a challenge for analyzing the sound relaxational absorption in multi-component gas mixtures. In our previous work [Acta Phys. Sin. 61 174301 (2012)], an analytical model to predict the sound absorption from vibrational relaxation in a gas medium is proposed. In this paper, we develop the model to decouple the V-V coupled energy to each vibrational- translational deexcitation path, and analyze how the multimode relaxations form the peaks of sound absorption spectra in gas mixtures. We prove that a multimode relaxation is the sum of its decoupled single-relaxation processes, and only the decoupled process with a significant isochoric-molar-heat can be observed as an absorption peak. The decoupling model clarifies the essential processes behind the peaks in spectra arising from the multimode relaxations in multi-component gas mixtures. The simulation validates the proposed decoupling model.     

Response of thermal source in a transversely isotropic thermoelastic half-space with mass diffusion by using a finite element method

The two-dimensional problem of generalized thermoelastic diffusion material with thermal and diffusion relaxation times is investigated in the context of the Lord-Shulman theory.As an application of the problem,a particular type of thermal source is considered and the problem is solved numerically by using a finite element method.The components of displacement,stress,temperature distribution,chemical potential,and mass concentration are obtained.The resulting quantities are depicted graphically for a special model.An appreciable effect of relaxation times is observed on various resulting quantities.     

Entanglement sudden death induced by the Dzialoshinskii--Moriya interaction

In this paper, we study the entanglement dynamics of two-spin Heisenberg XYZ model with the Dzialoshinskii--Moriya (DM) interaction. The system is initially prepared in the Werner state. The effects of purity of the initial state and DM coupling parameter on the evolution of entanglement are investigated. The necessary and sufficient condition for the appearance of the entanglement sudden death (ESD) phenomenon has been deduced. The result shows that the ESD always occurs if the initial state is sufficiently impure for the given coupling parameter or the DM interaction is sufficiently strong for the given initial state. Moreover, the critical values of them are calculated.     

Baecklund Transformations for the Initial Problems of Nizhnich and Nizhnich－Novikov－Veselov Equations

The homogeneous balance method is a method for solving genera/partial differential equations (PDEs). In this paper we solve a kind of initial problems of the PDEs by using the special Baecklund transformations of the initial problem. The basic Fourier transformation method and some variable-separation skill are used as auxiliaries. Two initial problems of Nizlmich and the Nizlanich-Novikov-Veselov equations are solved by using this approach.     

Calculation of Free Energy of the Integrable Landau—Lifshitz model

The generalized Bethe-ansatz method of thermodynamic analysis of integrable systems was employed to compute the free energy of a classical integrable model,i.e.the Landau-Lifshitz model.Using the action-angle variables of the model and by imposing a periodic boundary condition.we derive a phase-shifted density of states for the excitations of the system.The free energy,in the thermodynamic limit,can be expressed analytic in terms of two coupled nonlinear integral equations of the finie temperature excited energy for effective phonons and kinks (antikinks).we solve these equations iteratively for a special case that the model is in the limit of anisotropic strong yz coupling.     

Spatial pattern formation of a ratio-dependent predator-prey model

This paper presents a theoretical analysis of evolutionary process that involves organisms distribution and their interaction of spatially distributed population with diffusion in a Holling-III ratio-dependent predator-prey model, the sufficient conditions for diffusion-driven instability with Neumann boundary conditions are obtained. Furthermore, it presents novel numerical evidence of time evolution of patterns controlled by diffusion in the model, and finds that the model dynamics exhibits complex pattern replication, and the pattern formation depends on the choice of the initial conditions. The ideas in this paper may provide a better understanding of the pattern formation in ecosystems.     

Solutions of the modification heating conduction equations of a kind of laser thermal effect

This paper has solved the Chester modified heat conduction equation of the different relaxation time Υ value under different temperature conditions, different boundary conditions and the different initial conditions by different means of methods. These solutions can help to obtain temperature field of laser thermal effects.     

玻璃化转变的分子串模型中分子串弛豫模式的计算机模拟

基于玻璃化转变的分子串模型的哈密顿量(Hamiltonian),提出了模拟分子串第一和第二弛豫模式的蒙特卡罗(Monte Carlo)模拟方案.模拟得出的第一和第二弛豫模式的弛豫时间,与分子串模型中分子串弛豫方程所预言的结果完全一致,即理论预期和模拟结果相互印证.这不仅说明了分子串模型的分子串弛豫方程、至少是第一和第二弛豫模式的理论预言的正确性,同时也表明了本文所提出的模拟方法的有效性,并进一步明晰了分子串中分子的随机涨落和跃迁运动的图像,也为三态甚至是多态的分子串弛豫动力学研究,以及对进一步模拟分子串之 关键词： 弛豫动力学 蒙特卡罗模拟 分子串     

Bianchi type IX string cosmological model in general relativity

We have investigated Bianchi type IX string cosmological models in general relativity. To get a determinate solution, we have assumed a condition ρ=λ i.e. rest energy density for a cloud of strings is equal to the string tension density. The various physical and geometrical aspects of the models are also discussed.     

String cosmology in LRS Bianchi type-II dusty Universe with time-decaying vacuum energy density Λ

A model of a cloud formed by massive strings is used as a source of LRS Bianchi type-II with time-decaying vacuum energy density Λ. To construct string cosmological models, we have used the energy–momentum tensor for such strings as formulated by Letelier (1983). The high nonlinear field equations have been solved for two types of strings: (i) massive string and (ii) Nambu string. The expansion θ in the model is assumed to be proportional to the shear σ. This condition leads to A = βB ^m , where A and B are the metric coefficients, m is a constant and β is an integrating constant. Our models are in accelerating phase which is consistent with the recent observations of supernovae type-Ia. The physical and geometrical behaviour of these models are also discussed.     

Gravitational waves as string vacua II

Classical propagation of (super)strings through gravitational shock waves is analyzed. The exact classical solutions are used for quantization and for the identification of the exact quantumS-matrix describing string scattering by the wave. ThisS-matrix coincides with theS-matrix of the string-string scattering in theflat space-time for particular profile of the shock wave! This is interpreted as the generation of curved geometry from the flat space-time string theory. The quantum consistence of (super)string motion in gravitational plane wave backgrounds is then studied. It turns out that for the standard dimensionsD=26 (D=10) the vanishing of the Ricci tensor for the plane wave is sufficient condition for vanishing of the Weyl (superWeyl) anomaly. Thus, plane wave solutions of the Einstein equations are automatically the classical (super)string vacua. For particular plane waves the anomaly can be evaluated even nonperturbatively.This is the second part of the review based on the PhD thesis of the author defended in 1989 at SISSA, Trieste.     

分子串模型中空间弛豫模式的弛豫动力学的蒙特卡罗模拟

基于玻璃化转变的分子串模型的分子串弛豫方程,提出了更为精确的模拟分子串中所有空间弛豫模式(SRM)的蒙特卡罗模拟方案. 模拟得出各个SRM的弛豫时间随温度和分子串长度的变化结果与分子串模型中分子串弛豫方程的预言完全一致,即理论预期和模拟结果相互印证. 应当指出,分子串能否作为液态中集体单元的必要条件是在考虑到分子串之间的不均匀随机相互作用后,分子串的所有SRM的定性特征是不能改变的,这就需要对不同分子串的SRM之间的耦合进行研究. 但是迄今为止,仍未发现相关的严格解,仅有近似的自洽弛豫平均场方法. 由此可知,所提出的模拟方案为研究不同分子串的SRM之间的耦合(包括上述自洽场的可行性)提供了必要的基础. 关键词： 玻璃化转变 弛豫动力学 蒙特卡罗模拟 分子串     

Rosette motion and string scattering of 20 MeV electrons in MgO single crystals

Analytical estimates and computer simulations were undertaken to perceive the motion of negative particles through a lattice structure, the interaction being classical binary scattering. Three distinct modes of particle motion along atomic strings were found depending on the magnitude of the transverse energy and the angular momentum L of the particle with regard to the string axis. At small and large L increased scattering on the strings as compared with random penetration dominates. At medium L and negative transverse energy (bound state particles in the attractive potential) a rosette motion along the string occurs. In this case small impact parameters to the string atoms are avoided and thus an increased penetrability of the negative particles results. The influence of thermal lattice vibrations on these motions was studied.

Experimentally, the negative particle motion modes manifested themselves in the penetration profiles of 20 MeV electrons through an 8 μm MgO single crystal.     

Black string perturbations in RS1 model

Keywords We present a general formalism for black string perturbations in the Randall-Sundrum 1 model (RS1). First, we derive the master equation for the electric part of the Weyl tensor E _μν. Solving the master equation using the gradient expansion method, we give the effective Teukolsky equation on the brane at low energy. It is useful to estimate gravitational waves emitted by perturbed rotating black strings. We also argue on the effect of the Gregory-Laflamme instability on the brane using our formalism.     

Stochastic finite element analysis of a vibrating string

The response of a vibrating string subjected to spatial white noise excitation is analyzed by using the finite element (Galerkin) method. The discretization is achieved by using basis functions in the spatial and random spaces. The continuous time finite element equations are then integrated in time by using the central difference algorithm. It is shown that when the string is divided into N segments, the Galerkin approach leads to N(N?1) degrees of freedom which are governed by N subsets of equations. The subsets are similar in form. Furthermore, for a uniform string, they are governed by the same operator as that which governs the system of (N?1) degrees of freedom arising from the corresponding deterministic problem. Random initial conditions can also be treated by the same method, and the analysis of strings with initial conditions described by the standard Brownian process is carried out. Numerical results are given to illustrate the stochastic response.