Nonlinear friction as a mechanism of directed motion

A simple model (ratchet model) of occurrence of directed motion under the action of a zero-mean fluctuating force is proposed. The motion arises when the symmetry in the velocity space is violated by nonlinear friction. The mechanism of the directed motion is discussed qualitatively. Existence conditions of the motion are derived. The efficiency of conversion of the fluctuating random force to the directed motion is estimated.     

Directed motion of domain walls in biaxial ferromagnets under the influence of periodic external magnetic fields

Directed motion of domain walls (DWs) in a classical biaxial ferromagnet placed under the influence of periodic unbiased external magnetic fields is investigated. Using the symmetry approach developed in this article the necessary conditions for the directed DW motion are found. This motion turns out to be possible if the magnetic field is applied along the easiest axis. The symmetry approach prohibits the directed DW motion if the magnetic field is applied along any of the hard axes. With the help of the soliton perturbation theory and numerical simulations, the average DW velocity as a function of different system parameters such as damping constant, amplitude, and frequency of the external field, is computed.     

Ratchet motion and current reversal of coupled Brownian motors in pulsating symmetric potentials

In this study, we investigate the collective directed transport of coupled Brownian particles in spatially symmetric periodic potentials under time-periodic pulsating modulations. We find that the coupling between two particles can induce symmetry breaking and consequently collective directed motion. Moreover, the direction of motion can be reversed under certain conditions. The dependence of directed current on various parameters is systematically studied. reverse motion can be achieved by modulating the coupling free length and the phase shift of the pulsating potential. The dynamical mechanism of these transport properties is understood in terms of the effective-potential theory and the space-time transformation invariance. The directed transport of coupled Brownian motors can be manipulated and optimized by adjusting the coupling strength, pulsating frequency, or noise intensity.     

离散变质量完整系统的Noether对称性与Mei对称性

本文研究离散变质量完整系统的Noether对称性与Mei对称性.首先用差分离散变分的方法,建立起离散变质量完整系统的运动方程和能量演化方程.然后给出该系统的Noether对称性和Mei对称性的定义及离散Noether守恒量的形式.得到系统的Noether对称性与Mei对称性导致离散Noether守恒量的条件.最后举例说明结果的应用.     

Supersymmetric ratchets

The overdamped Brownian motion in a periodic potential under far from equilibrium conditions is considered. A large class of systems with an intrinsic asymmetry, called supersymmetric ratchets, is identified for which the occurrence of directed transport can be ruled out without any fine-tuning of parameters.     

变质量完整力学系统的非Noether守恒量

利用时间不变的无限小变换下的Lie对称性,研究变质量完整力学系统的一类新的守恒量.给出系统的运动微分方程,研究时间不变的无限小变换下的Lie对称性确定方程,将Hojman定理推广并应用于这类系统 关键词： 变质量系统 完整约束 确定方程 非Noether守恒量     

单面非Chetaev型非完整约束系统的非Noether守恒量

研究单面非Chetaev型非完整约束力学系统的对称性与非Noether守恒量.建立了系统的运动微分方程；给出了系统的Lie对称性和Mei对称性的定义和判据；对于单面非Chetaev型非完整系统，证明了在一定条件下，由系统的Lie对称性可直接导致一类新守恒量——Hojman守恒量，由系统的Mei对称性可直接导致一类新守恒量——Mei守恒量；研究了对称性和新守恒量之间的相互关系.文末，举例说明结果的应用. 关键词： 分析力学 单面约束 非完整系统 对称性 Hojman守恒量 Mei守恒量     

准坐标下完整力学系统的非Noether守恒量——Hojman定理的推广

利用时间不变的无限小变换下的Lie对称性，研究准坐标下完整力学系统的一类新守恒量.建立系统的运动微分方程，给出无限小变换下的Lie对称性确定方程.将Hojman定理推广，并举例说明结果的应用. 关键词： 准坐标 完整力学系统 Lie对称性 非Noether守恒量 Hojman定理     

相对论性变质量非完整可控力学系统的非Noether守恒量

在时间不变的特殊无限小变换下,研究相对论性变质量非完整可控力学系统的非Noether守恒量——Hojamn守恒量.建立了系统的运动微分方程, 给出了系统在特殊无限小变换下的形式不变性(Mei对称性)的定义和判据以及系统的形式不变性是Lie对称性的充分必要条件.得到了系统形式不变性导致非Noether守恒量的条件和具体形式.举例说明结果的应用. 关键词： 相对论 非完整可控力学系统 变质量 非Noether守恒量     

Bose-Einstein condensation and the glassy state

The distinction between a classical glass and a classical liquid is difficult, since both are disordered. The difference is in the fact that a glass is frozen while the liquid is not. In this Letter an equilibrium measure is suggested that distinguishes between a glass and a liquid. The choice of this measure is based on the idea that in a system which is not frozen symmetry under permutation of particles is physically relevant, because particles can be permuted by actual physical motion. This is not the case in a frozen system. In this Letter it is shown how to generalize naturally the quantum mechanical concept of Bose condensed fraction to classical systems in order to distinguish between the glass and the liquid. It is finite in the liquid and zero in the frozen state. The actual value of the condensed fraction in the liquid may serve also as a measure of the glassiness in the liquid.     

Symmetry relations in chemical kinetics arising from microscopic reversibility

It is shown that the kinetics of time-reversible chemical reactions having the same equilibrium constant but different initial conditions are closely related to one another by a directly measurable symmetry relation analogous to chemical detailed balance. In contrast to detailed balance, however, this relation does not require knowledge of the elementary steps that underlie the reaction, and remains valid in regimes where the concept of rate constants is ill defined, such as at very short times and in the presence of low activation barriers. Numerical simulations of a model of isomerization in solution are provided to illustrate the symmetry under such conditions, and potential applications in protein folding or unfolding are pointed out.     

Hidden symmetries and Killing tensors

Just as a Killing vector of the kinetic energy metric of a classical mechanical system can generate a symmetry of the system (an “obvious” symmetry), and thus a constant of the motion, so can a Killing tensor generate a symmetry and a constant of the motion. In the latter case the symmetry is “hidden”: for example the well-known hidden symmetries for a single particle moving under an inverse-square central force, and for the harmonic oscillator, arise in this way.     

El-Nabulsi动力学模型下非Chetaev型非完整系统的精确不变量与绝热不变量

研究El-Nabulsi动力学模型下非Chetaev型非完整系统精确不变量与绝热不变量问题. 首先, 导出El-Nabulsi-d'Alembert-Lagrange原理并建立系统的运动微分方程. 其次, 建立El-Nabulsi模型下未受扰动的非Chetaev 型非完整系统的Noether对称性与Noether对称性导致的精确不变量之间的关系; 再次, 引入力学系统的绝热不变量概念, 研究受小扰动作用下非Chetaev型非完整系统Noether对称性的摄动导致绝热不变量问题, 给出了绝热不变量存在的条件及其形式. 作为特例, 本文讨论了El-Nabulsi模型下Chetaev型非完整系统的精确不变量与绝热不变量问题. 最后分别给出非Chetaev型和Chetaev型两种约束下的算例以说明结果的应用.     

准坐标下一般完整系统的统一对称性

研究准坐标下完整力学系统在时间不变的无限小变换下的统一对称性. 列出系统的运动微分方程, 给出系统的统一对称性的定义和判据, 由系统的统一对称性导出Noether守恒量、Hojman守恒量和一类新型守恒量. 举例说明结果的应用. 关键词： 准坐标 完整系统 统一对称性 守恒量     

3D numerical model of the electrostatic coating process with moving objects using a moving mesh

In this paper, a full three dimensional FLUENT numerical model of the electrostatic coating process with the embedded moving mesh capability and piecewise linear type target motion is presented. The model includes target geometries that do not exhibit symmetry. All the dominant mechanical and electrical phenomena are taken into account. Mechanical phenomena include shaping air effects, downdraft effects and the motion of the polydispersed particles. Electrical phenomena include the particle space charge distribution, corona discharge and the electrohydrodynamic flow effects. It was demonstrated that the numerical model can accurately mimic the type of the motion used in real world applications.     

Dynamics of money

We present a dynamical many-body theory of money in which the value of money is a time dependent "strategic variable" that is chosen by the individual agents. The value of money in equilibrium is not fixed by the equations, and thus represents a continuous symmetry. The dynamics breaks this continuous symmetry by fixating the value of money at a level which depends on initial conditions. The fluctuations around the equilibrium, for instance in the presence of noise, are governed by the "Goldstone modes" associated with the broken symmetry. The idea is illustrated by a simple network model of monopolistic vendors and buyers.     

Asymmetry of the shape of surroundings as a mechanism for generating directed motion

A mechanism for generating a directed motion of a Brownian particle in an asymmetric channel under the action of a varying force field is considered. The setup implementing such a mechanism resembles typical Brownian motors using asymmetry of the energy potential (ratchet effect). It is shown that under certain conditions, the asymmetry of the shape may ensure the maximal level of rectification for a large intensity of the external field drawing the system from equilibrium. The main question formulated here is the dependence of the rectifying ability of such a mechanism on the external action parameters and, above all, on the form of the time dependence. The results obtained here for a sine signal and an aperiodic train of pulses are compared with the previous results obtained by the authors for bipolar rectangular pulses. General estimates obtained for pulses of an arbitrary shape determine its influence on the velocity of directed motion. Analysis of the proposed mechanism is based of the combination of analytic calculations for a strong external field with simulation by the method of Brownian dynamics for arbitrary parameters.     

Introduction to the physics of Brownian motors

A detailed introduction to directed transport in Brownian motors occurring in spatially periodic systems far from equilibrium is presented. We elucidate the prominent physical concepts and novel phenomena with a representative dissipative Brownian motor dynamics. Its main ingredient is a thermal noise with time-dependent temperature modulations that drive the system out of thermal equilibrium in a spatially asymmetric (ratchet-) potential. Yet, this asymmetric setup does not exhibit a concomitant obvious bias into one or the other direction of motion. Symmetry conditions for the appearance (or not) of directed current, its reversal upon variation of certain parameters, and various other generic features and applications are discussed. In addition, we provide a systematic classification scheme for Brownian motor models and review historical landmark contributions to the field. Received: 9 November 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Lattice dynamics of hcp metals

A lattice dynamical model for hcp metals has been developed which considers ion-ion interaction as a five-neighbour central pair potential and electron-ion interaction in a modified form of Bhatia's model. Complete account of the equilibrium of the hcp lattice including the effect of electron pressure has been considered and as a consequence two equilibrium conditions, necessary for the hcp structure, have been obtained and used in the study. Phonon dispersion curves for four hcp metals, Be, Mg, Y and Ho have been computed for two symmetry directions and a good agreement has been obtained with the neutron data. The results have also been compared with the use of the same model but with a single condition, reported earlier and show in general a significant improvement.     

Nonequilibrium Relaxation of Bose-Einstein Condensates: Real-Time Equations of Motion and Ward Identities

We present a field-theoretical method to obtain consistently the equations of motion for small amplitude condensate perturbations in a homogeneous Bose-condensed gas directly in real time. It is based on a linear response and combines the Schwinger-Keldysh formulation of nonequilibrium quantum field theory with the Nambu-Gor'kov formalism of quasiparticle excitations in the condensed phase and the tadpole method in quantum field theory. This method leads to causal equations of motion that allow us to study the nonequilibrium evolution as an initial value problem. It also allows us to extract directly the Ward identities, which are a consequence of the underlying gauge symmetry and which in equilibrium lead to the Hugenholtz-Pines theorem. An explicit one-loop calculation of the equations of motion beyond the Hartree-Fock-Bogoliubov approximation reveals that the nonlocal, absorptive contributions to the self-energies corresponding to the Beliaev and Landau damping processes are necessary to fulfill the Ward identities in or out of equilibrium. It is argued that a consistent implementation at low temperatures must be based on the loop expansion, which is shown to fulfill the Ward identities order by order in perturbation theory.