Analysis of the equal width wave equation with the mesh-free reproducing kernel particle Ritz method

In this paper,we analyse the equal width(EW) wave equation by using the mesh-free reproducing kernel particle Ritz(kp-Ritz) method.The mesh-free kernel particle estimate is employed to approximate the displacement field.A system of discrete equations is obtained through the application of the Ritz minimization procedure to the energy expressions.The effectiveness of the kp-Ritz method for the EW wave equation is investigated by numerical examples in this paper.     

Exactly quantized dynamics of classical incommensurate sliders

We report peculiar velocity quantization phenomena in the classical motion of an idealized 1D solid lubricant, consisting of a harmonic chain interposed between two periodic sliders. The ratio upsilon(c.m.)/upsilon(ext) of the chain center-of-mass velocity to the externally imposed relative velocity of the sliders stays pinned to exact "plateau" values for wide ranges of parameters, such as slider corrugation amplitudes, external velocity, chain stiffness, and dissipation, and is strictly determined by the commensurability ratios alone. The phenomenon is explained by one slider rigidly dragging the kinks that the chain forms with the other slider. Possible consequences of these results for some real systems are discussed.     

Modeling of the dynamic contact in stick-slip microdrives using the method of reduction of dimensionality

In this work we present a new method to describe movements of stick-slip microdrives. On the microscopic scale we model the contact between actuator and slider as a dynamic tangential contact using the method of reduction of dimensionality. On the macroscopic scale simple one- and three-dimensional equations of motion are derived. An algorithm to solve these equations will be introduced. The results of the simulation will be compared qualitatively and quantitatively to experimental investigations. Even for the simplest assumed model it proves that experimental and numerical values correlate excellently.     

物理质团法:一个普适的数值方法体系

无网格方法根据分布于近邻空间各个方向的微元体物理信息构造离散方程,显著降低了空间导数计算对微元体本身及微元体之间拓扑结构的条件限制,极大提高了拉氏方法的大变形计算能力.由于不能利用微元体的完备几何信息,不容易构造符合物理的无网格算法,对那些物理参数存在间断的模型对象,难以获得稳定和准确的计算结果.本文基于对物理规律及数值模拟发展趋势的分析,提出符合物理且具有强普适性的无网格方法体系.基于该方法的一维算例表明,即使物理参数存在强烈间断,数值结果也能很好地逼近问题的真解.     

Simple functional-differential equations for the bound-state wave-function components

We present a new method of a direct derivation of differential equations for the wave-function components of identical-pariticles systems. The method generates in a simple manner all the possible variants of these equations. In some cases they are the differential equations of Faddeev of Yakubovskii. It is shown that the case of the bound states allows to formulate very simple equations for the components which are equivalent to the Schrödinger equation for the complete wave function. The components with a minimal antisymmetry are defined and the corresponding equations are derived.     

Dynamic analysis of periodic structures

The natural vibration analysis of a periodic structure with repeated identical substructures may be simplified by using some symmetrical properties of the substructure dynamic matrices, resulting in a set of linear difference equations in the displacements. These equations are readily solved for cyclic symmetric systems, simply supported systems and infinite systems. The order of the overall frequency equations is at most equal to one half of the total number of degrees of freedom retained for a single substructure regardless of the number of substructures in the system. With these natural modes, the system with general boundary conditions at end stations is analyzed by a fast converging method.     

Functional integral formulation of classical wave equations

It is shown in this paper that classical wave equations admit path integral formulations. For this, the evolution of the system is first set-up in terms of a fundamental solution or propagator. We choose this last name because it suggests a connection with functional integrals, which are exploited in this work. A functional integral in terms of non-singular functions is then proposed and shown to converge to the propagator in the appropriate limit for the case of scalar wave equations. One of the advantages of such formulation is that it provides an adequate framework for mesh-free numerical methods. This is demonstrated through a computational implementation that combines a simple second-degree polynomial local approximation of the continuous field and an approximate statement of the exact evolution equations. Numerical simulations of modal analysis and transient dynamics indicate the feasibility of the technique.     

Kink plateau dynamics in finite-size lubricant chains

We extend the study of velocity quantization phenomena recently found in the classical motion of an idealized 1D model solid lubricant - consisting of a harmonic chain interposed between two periodic sliding potentials [A. Vanossi, M. Manini, G. Divitini, G.E. Santoro, E. Tosatti, Phys. Rev. Lett. 97 (2006) 056101]. This quantization is due to one slider rigidly dragging the commensurate lattice of kinks that the chain forms with the other slider. In this follow-up work we consider finite-size chains rather than infinite chains. The finite-size (i) permits the development of robust velocity plateaus as a function of the lubricant stiffness, and (ii) allows an overall chain length re-adjustment which spontaneously promotes single-particle periodic oscillations. These periodic oscillations replace the quasi-periodic motion produced by general incommensurate periods of the sliders and the lubricant in the infinite-size model. Possible consequences of these results for some real systems are discussed.     

Application of the method of approximate integrals of the motion to Fermi and Bose systems. IV

The method of approximate integrals of the motion is used to obtain equations describing the thermodynamics of Bose and Fermi systems with more consistent allowance for interparticle correlations. Under some simplifying assumptions, these equations lead to well-known results of theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 3–5, June, 1980.     

Stair and Step Soliton Solutions of the Integrable (2+1) and (3+1)-Dimensional Boiti-Leon-Manna-Pempinelli Equations

The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of a (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Also, we extend the equation to a (3+1)-dimensional case and obtain some exact solutions for the new equation by applying the multiple exp-function method. By these applications, we obtain single-wave, double-wave and multi-wave solutions for these equations.     

Stair and Step Soliton Solutions of the Integrable (2+1) and (3+1)-Dimensional Boiti-Leon-Manna-Pempinelli Equations

The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of a (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Also, we extend the equation to a (3+1)-dimensional case and obtain some exact solutions for the new equation by applying the multiple exp-function method. By these applications, we obtain single-wave, double-wave and multi-wave solutions for these equations.     

非均匀无序系统中Anderson局域化的标度理论——实空间重整化群途径

针对大量具有空间调制的无序系统,本文提出一种实空间重整化群变换方案。这个方案保证了在空间映象下相对的空间调制结构不变,因此可用以研究非均匀无序系统Anderson局域化的临界性质。在有限晶格近似下,我们对无序金属超晶格的一个简化模型求解了RG方程,得到不动点和临界指数的近似值,并发现空间调制在一定程度上引起无序系统电子局域化性质的改变。 关键词：     

Infinite Conservation Laws,Continuous Symmetries and Invariant Solutions of Some Discrete Integrable Equations

Two new shift operators are introduced for which a few differential-difference equations are generated by applying the R-matrix method. These equations can be reduced to the standard Toda lattice equation and(1+1)-dimensional and(2+1)-dimensional Toda-type equations which have important applications in hydrodynamics, plasma physics, and so on. Based on these consequences, we deduce the Hamiltonian structures of two discrete systems. Finally,we obtain some new infinite conservation laws of two discrete equations and employ Lie-point transformation group to obtain some continuous symmetries and part of invariant solutions for the(1+1) and(2+1)-dimensional Toda-type equations.     

基于多物理场的TFC磁头热传导机理及其影响因素仿真研究

为了利用微尺度热效应的热致飞高控制(TFC)磁头技术实现磁头飞行高度的精确控制,分析了工作状态下TFC滑块在多物理场综合作用下所呈现出来的传热特性及其主要影响因素,考虑了磁头磁盘间超薄气膜的稀薄效应,建立滑块导热、空气轴承表面传热、气膜流动等模型,利用有限元法,对磁头热变形作用机理及热传导特性对滑块动力学特性影响进行了仿真研究,结果表明,建立的传热模型及对雷诺方程的修正适用于求解磁头磁盘界面气膜传热问题和磁头滑块的动力学问题;影响滑块热力学性能的因素主要可以归结为加热器高度、热生成率以及材料的传热系数;空气轴承力及工作表面热变形的双重作用决定了滑块飞行高度的改变.仿真结果为磁头滑块加热器的设计及空气轴承动力学特性分析提供了依据.     

Extension of the finite volume particle method to viscous flow

The finite volume particle method (FVPM) is a mesh-free method for fluid dynamics which allows simple and accurate implementation of boundary conditions and retains the conservation and consistency properties of classical finite volume methods. In this article, the FVPM is extended to viscous flows using a consistency-corrected smoothed particle hydrodynamics (SPH) approximation to evaluate velocity gradients. The accuracy of the viscous FVPM is improved by a higher-order discretisation of the inviscid flux combined with a second-order temporal discretisation. The higher-order inviscid FVPM is validated for a 1-D shock tube problem, in which it demonstrates an enhanced shock capturing ability. For two-dimensional simulations, a small arbitrary Lagrange–Euler correction to fully Lagrangian particle motion is beneficial in maintaining a favourable particle distribution over long simulation times. The viscous FVPM is validated for two-dimensional Poiseuille, Taylor–Green and lid-driven cavity flows, and good agreement is achieved with analytic or reference numerical solutions. These results establish the viability of FVPM as a tool for mesh-free simulation of viscous flows in engineering.     

基于椭圆偏振显微镜的纳米级磁头润滑膜观测方法

针对磁头飞行导致液体润滑膜的转移研究以及润滑膜在磁头上的动态变化特性观测问题,基于改进的垂直物镜的椭圆偏振显微镜,提出起偏器相移方法的磁头表面润滑膜厚度计算模型,实现了润滑膜厚度的测量。实验以非极性润滑剂Z03覆盖的磁头为样品对椭圆偏振显微镜进行标定,以极性润滑剂Zdol4000作为样品,对其在磁头表面的去湿现象进行观察。该方法测量精度可达0.37 nm,分辨力约0.36 μm,可为其他纳米级薄膜观测提供一定的技术参考。     

Molecular,metabolic, and genetic control: An introduction

The living cell is a miniature, self-reproducing, biochemical machine. Like all machines, it has a power supply, a set of working components that carry out its necessary tasks, and control systems that ensure the proper coordination of these tasks. In this Special Issue, we focus on the molecular regulatory systems that control cell metabolism, gene expression, environmental responses, development, and reproduction. As for the control systems in human-engineered machines, these regulatory networks can be described by nonlinear dynamical equations, for example, ordinary differential equations, reaction-diffusion equations, stochastic differential equations, or cellular automata. The articles collected here illustrate (i) a range of theoretical problems presented by modern concepts of cellular regulation, (ii) some strategies for converting molecular mechanisms into dynamical systems, (iii) some useful mathematical tools for analyzing and simulating these systems, and (iv) the sort of results that derive from serious interplay between theory and experiment. (c) 2001 American Institute of Physics.     

On the derivation of Smoluchowski equations with corrections in the classical theory of Brownian motion

Differential equations governing the time evolution of distribution functions for Brownian motion in the full phase space were first derived independently by Klein and Kramers. From these so-called Fokker-Planck equations one may derive the reduced differential equations in coordinate space known as Smoluchowski equations. Many such derivations have previously been reported, but these either involved unnecessary assumptions or approximations, or were performed incompletely. We employ an iterative reduction scheme, free of assumptions, and calculate formally exact corrections to the Smoluchowski equations for many-particle systems with and without hydrodynamic interaction, and for a single particle in an external field. In the absence of hydrodynamic interaction, the lowest order corrections have been expressed explicitly in terms of the coordinate space distribution function. An additional application of the method is made to the reduction of the stress tensor used in evaluating the intrinsic viscosity of particles in solution. Most of the present work is based on classical Brownian motion theory, but brief consideration is given in an appendix to some recent developments regarding non-Markovian equations for Brownian motion.Supported by the National Science Foundation.     

INTEGRABILITY OF LIE SYSTEMS THROUGH RICCATI EQUATIONS

Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyze a geometric method to construct integrability conditions for Riccati equations following these approaches. Our procedure provides us with a unified geometrical viewpoint that allows us to analyze some previous works on the topic and explain new properties. Moreover, this new approach can be straightforwardly generalized to describe integrability conditions for any Lie system. Finally we show the usefulness of our treatment in order to study the problem of the linearizability of Riccati equations.     

Riccati-Type Equations, Generalised WZNW Equations, and Multidimensional Toda Systems

We associate to an arbitrary ℤ-gradation of the Lie algebra of a Lie group a system of Riccati-type first order differential equations. The particular cases under consideration are the ordinary Riccati and the matrix Riccati equations. The multidimensional extension of these equations is given. The generalisation of the associated Redheffer–Reid differential systems appears in a natural way. The connection between the Toda systems and the Riccati-type equations in lower and higher dimensions is established. Within this context the integrability problem for those equations is studied. As an illustration, some examples of the integrable multidimensional Riccati-type equations related to the maximally nonabelian Toda systems are given. Received: 3 August 1998 / Accepted: 21 December 1998