Derivation of a hydrodynamic equation for Ginzburg-Landau models in an external field

The lattice approximation to a time-dependent Ginzburg-Landau equation is investigated in the presence of a small external field. The evolution law conserves the spin, but is not reversible. A nonlinear diffusion equation of divergence type is obtained in the hydrodynamic limit. The proof extends to certain stochastically perturbed Hamiltonian systems.     

Real-time fractal signal processing in the time domain

Fractal analysis has proven useful for the quantitative characterization of complex time series by scale-free statistical measures in various applications. The analysis has commonly been done offline with the signal being resident in memory in full length, and the processing carried out in several distinct passes. However, in many relevant applications, such as monitoring or forecasting, algorithms are needed to capture changes in the fractal measure real-time. Here we introduce real-time variants of the Detrended Fluctuation Analysis (DFA) and the closely related Signal Summation Conversion (SSC) methods, which are suitable to estimate the fractal exponent in one pass. Compared to offline algorithms, the precision is the same, the memory requirement is significantly lower, and the execution time depends on the same factors but with different rates. Our tests show that dynamic changes in the fractal parameter can be efficiently detected. We demonstrate the applicability of our real-time methods on signals of cerebral hemodynamics acquired during open-heart surgery.     

史瓦西时空中自由粒子的运动方程

直接求解史瓦西时空中自由粒子的测地线方程,得出粒子运动方程的一般常见形式.此方法与一般教材中根据史瓦西度规的静态球对称性以及四速归一条件得出的运动方程完全相同.此方法物理意义更清晰、明确,同时对理解弯曲时空中的测地线方程具有重要意义.     

Motion of spiral waves in the complex Ginzburg-Landau equation

Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered. For parameters close to the vortex limit, and for a system of spiral waves with well-separated centres, laws of motion of the centres are found which vary depending on the order of magnitude of the separation of the centres. In particular, the direction of the interaction changes from along the line of centres to perpendicular to the line of centres as the separation increases, with the strength of the interaction algebraic at small separations and exponentially small at large separations. The corresponding asymptotic wavenumber and frequency are determined. These depend on the positions of the centres of the spirals, and so evolve slowly as the spirals move.     

The onset of superconductivity in the time dependent Ginzburg-Landau theory

The fluctuations of the local order parameter above the superconducting transition temperature give rise to singularities in the electrical conductivity and the diamagnetic susceptibility. Using the time dependent Ginzburg-Landau equation the fluctuation of the current density is calculated. By means of the fluctuation-dissipation theorem and a dispersion relation the electromagnetic response function is then determined for small frequencies and wave-numbers. The dynamical conductivity for bulk material, thin films, and thin wires shows an increasing peak at zero frequency the width of which decreases as the transition temperature is approached. This structure should be observable in microwave experiments.     

基于复Ginzburg-Landau方程的双核光纤中调制不稳定性的仿真研究

在双核光纤光学系统中,应用复Ginzburg-Landau方程,研究了连续波的不稳定性问题.双核光纤光学系统是由一个非线性离散主核和一个线性附核构成的.研究发现,在线性微扰下存在调制不稳定性.系统仿真结果表明：如果充分考虑调制不稳定性,则该系统将产生规则或者不规则的脉冲序列.反之,如果不考虑调制不稳定性它将产生一连串具有连续增长振幅的离散峰.这表明在反常群速度色散情况下,一串归零脉冲的峰值或者单一归零脉冲峰值仍然是增强的.在光纤中产生归零序列脉冲源,这一研究结果对全光纤通信有一定的价值,对光纤光学及物理学 关键词： 光孤子 复Ginzburg-Landau方程 双核光纤 调制不稳定性     

The solutions of the generalized classical and quantum harmonic oscillators with time dependent mass, frequency, two-photon parameter and external force: The squeezing effects

The exact analytical solutions of a generalized classical harmonic oscillator with time dependent mass, frequency, two-photon parameter and external forces are obtained. By using the invariance property of the scaled Wronskian, these solutions are used to obtain the solutions of the quantum mechanical counterpart of the oscillator under Heisenberg picture. In order to discuss the applications of these solutions of the quantum mechanical oscillator, we calculate the exact analytical expressions for the second order variances of both the canonically conjugate quadratures in terms of the time dependent mass, frequency and two-photon parameter. However, these variances calculated in terms of the initial coherent state do not depend on the time dependent driven terms. We argued that the time dependent frequency is on the way of the exact analytical solutions and hence it is kept constant throughout the investigation. We, however, discuss few situations of physical interest where the mass is varying in time. The special circumstance where all the parameters are time independent is used to discuss the squeezing effect in both the quadratures. It is seen that the parameter g involving the two-photon interaction term produces squeezing effects. With the increase of interaction time, the squeezing in both the quadrature components exhibit collapse and revival phenomena for g < ω (frequency of the oscillator). The squeezing of X-quadrature is completely ruled out for g > ω. However, the squeezing for P-quadrature is possible for small interaction time. The squeezing patterns of the X and P-quadratures are also discussed for pulsating mass, and for mass increasing with time. The squeezing is also discussed when the mass is increasing exponentially in time. It is envisage that the solutions could be used in the investigation of quantum statistical properties of the radiation field coupled to the said oscillator.     

A collective variable approach for optical solitons in the cubic-quintic complex Ginzburg-Landau equation with third-order dispersion

Considering the theory of electromagnetic, especially from the Maxwell equations, a basic equation modeling the propagation of ultrashort optical solitons in optical fibers is derived, namely a cubic-quintic complex Ginzburg-Landau equation (CQGLE) with third-order dispersion (TOD). Considering this one-dimensional CQGLE, we derive the equations of motion of pulse parameters called collective variables (CVs), of a pulse propagating in dispersion-managed (DM) fiber optic-links. Equations obtained are investigated numerically in order to view the evolution of pulse parameters along the propagation distance. A fully numerical simulation of the CQGLE finally tests the results of the CV theory. It appears chaotic pulses, attenuate pulses and stable pulses under some parameter values.     

Space time fractional KdV Burgers equation for dust acoustic shock waves in dusty plasma with non-thermal ions

The KdV–Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly charged nonthermal ions, and hot and cold dust species is derived using the reductive perturbation method. The Boltzmann distribution is used for electrons in the presence of the cold(hot) dust viscosity coefficients. The semi-inverse method and Agrawal variational technique are applied to formulate the space–time fractional KdV–Burgers equation which is solved using the fractional sub-equation method. The effect of the fractional parameter on the behavior of the dust acoustic shock waves in the dusty plasma is investigated.     

The study of fractal correlation method in the displacement measurement and its application

The classical digital speckle, or digital image, correlation method of deformation measurement is based on gray level correlation between unformed and deformed digital images. The pattern of artificial random speckles and the natural textures on some object's surfaces have fractal characteristics, and their fractal dimensions represent both gray and morph information. Furthermore, the fractal dimensions are stable feature parameters of the patterns. The digitized images of the patterns are confirmed to be also fractals. By this fact, a new method of displacement measurement is developed in the paper, based on the fractal dimensions correlation. The in-plane displacement fields of a body can be acquired. In order to verify the validity of the new method, an experiment has been designed and the results have been compared with those obtained from the classical digital image correlation method. The validity of the new method is not less than that of classical method. Further discussions about the traits and the developing vista of the method are given at the end.     

The improved fractional sub-equation method and its applications to the space-time fractional differential equations in fluid mechanics

By introducing a new general ansätz, the improved fractional sub-equation method is proposed to construct analytical solutions of nonlinear evolution equations involving Jumarie?s modified Riemann-Liouville derivative. By means of this method, the space-time fractional Whitham-Broer-Kaup and generalized Hirota-Satsuma coupled KdV equations are successfully solved. The obtained results show that the proposed method is quite effective, promising and convenient for solving nonlinear fractional differential equations.     

The forms of three-order Lagrangian equation in relative motion

In this paper, the general expressions of three-order Lagrangian equations in a motional coordinate system are obtained. In coordinate systems with some specific forms of motion, the expressions corresponding to these equations are also presented.     

Intensity‐dependent ultrafast dynamics of injection currents in unbiased GaAs quantum wells

The intensity dependence of optically‐induced injection currents in unbiased GaAs semiconductor quantum wells grown in [110] direction is investigated theoretically for a number of well widths. Our microscopic analysis is based on a 14 × 14 band k · p method in combination with the multisubband semiconductor Bloch equations. An oscillatory dependence of the injection current transients as function of intensity and time is predicted and explained. It is demonstrated that optical excitations involving different subbands and Rabi flopping are responsible for this complex dynamics. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Application of Extended Tanh-Function Approach in Toda Lattice Equations

In this paper, we generalize the extended tanh-function approach, which used to find new exact travelling wave solutions of nonlinear partial differential equations (NPDES) or coupled nonlinear partial differential equations, to nonlinear differential-difference equations (NDDES). As illustration, we discuss some Toda lattice equations, and solitary wave and periodic wave solutions of these Toda lattice equations are obtained by means of the extended tanh-function approach. PACS numbers: 05.45.Yv, 02.30.Jr, 02.30.Ik.     

The superposition method in seeking the solitary wave solutions to the KdV-Burgers equation

In this paper, starting from the careful analysis on the characteristics of the Burgers equation and the KdV equation as well as the KdV-Burgers equation, the superposition method is put forward for constructing the solitary wave solutions of the KdV-Burgers equation from those of the Burgers equation and the KdV equation. The solitary wave solutions for the KdV-Burgers equation are presented successfully by means of this method.     

非结构混合网格上的NS方程求解方法

提出了一套较为通用的,完全自动化的非结构混合网格生成方法.在物面粘性作用区,采用一种改进的推进层方法生成三棱柱形和金字塔形网格;在其他流动区域采用阵面推进方法生成四面体网格.采用一种改进精度的格心有限体积法对三维NS方程进行了求解,在加速收敛措施方面,提出了一种新的当地时间步长取定方法来减小质量较差的网格单元对流场计算稳定性和收敛速度的不利影响.以M6机翼和DLR/F4翼身组合体外形的粘性流场作为数值算例,验证了上述网格生成和流场求解方法的正确性和实用性.     

周期场时间导数Ornstein-Uhlenbeck噪声Fokker-Planck方程的小参数展开求解

通过引入变量,周期场中内部时间导数Ornstein-Uhlenbeck噪声驱动的布朗运动可用高维Fokker-Planck方程来描述. 上述系统不能直接应用通常的小参数展开和势谷中心展开近似求解. 用一种变通的小参数展开方法近似求解了系统的Fokker-Planck方程,结果适用于小势垒高度、中等关联时间和较大的相空间区域,近似解析解可获得系统的改进. 关键词： Fokker-Planck方程 周期势 时间导数Ornstein-Uhlenbeck噪声 小参数展开     

The spectral order of accuracy: A new unified tool in the design methodology of excitation-adaptive wave equation FDTD schemes

We define a new concept, termed the spectral order of accuracy (SOoA), which is the spectral domain analogue of the familiar order of accuracy (OoA). The SOoA is pivotal in a refined version of a recently-introduced methodology for formulating excitation-adaptive wave equation FDTD (WE-FDTD) schemes, described below. This concept is the basis for a unified classification for both existing and new schemes. Both one- and two-dimensional cases are presented for boundless, source free, homogeneous, isotropic and lossless media. The 1-D and 2-D cases are developed in detail for the (3, 2M + 1) (temporal, spatial) and (3, 3) 2-D stencils, respectively. Stability analysis is built into the methodology in terms of either analytical conditions or “stability maps” defined herein. The methodology is seen as a generalization of many existing schemes that also provides a unified tool for a systematical design of WE-FDTD schemes subject to specific requirements in terms of the spectral content of the excitation. The computational efficiency for all schemes remains the same for a given stencil, since the core of the FDTD code is unchanged between schemes, the difference being only in the values of scheme coefficients.     

The B(3) Field from Curved Spacetime Embedded in the Irreducible Representation of the Einstein Group

The details of this paper build on the previous work of M. Sachs and M. Evans that describe an enhanced form of general relativity which contains an inherently non-abelian field tensor. We focus on a particular field arising from the non-abelian form of electrodynamics. In particular, the form of this field will be demonstrated in a first-order perturbation approach within the context of a simple manifold, and also the leading order contribution to this field due to the presence of matter. The enhanced form of general relativity, as detailed in [1], is that of antisymmetrized general relativity which relies on the irreducible representation of the Einstein translation group. We also discuss the possibility of an inherent energy induced by curvature.