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.     

Particle motion in a photon gas: friction matters

The motion of a particle in the Tolman metric generated by a photon gas source is discussed. Both the case of geodesic motion and motion with nonzero friction, due to photon scattering effects, are analyzed. In the Minkowski limit, the particle moves along a straight line segment with a decelerated motion, reaching the endpoint at zero speed. The curved case shows a qualitatively different behavior; the geodesic motion consists of periodic orbits, confined within a specific radial interval. Under the effect of frictional drag, this radial interval closes up in time and in all our numerical simulations the particle ends up in the singularity at the center.     

Role of friction in tunnelling motion

One of the most interesting recent topics in condensed matter physics concerns the quantum tunnelling phenomena at low temperatures in the presence of dissipation. Such studies can be made of the motion of light interstitials (μ⁺ or H, for instance) in metals, with the aid of muon spin rotation and neutron scattering techniques. In this paper, the present status of the subject will be reviewed. Next, the utility of Mossbauer spectroscopy in analyzing a similar situation, viz. the motion of a reaction coordinate coupled to a dissipative bath, as in biological molecules, will be indicated.     

Fracture and friction: Stick-slip motion

We discuss the stick-slip motion of an elastic block sliding along a rigid substrate. We argue that for a given external shear stress this system shows a discontinuous nonequilibrium transition from a uniform stick state to uniform sliding at some critical stress which is nothing but the Griffith threshold for crack propagation. An inhomogeneous mode of sliding occurs when the driving velocity is prescribed instead of the external stress. A transition to homogeneous sliding occurs at a critical velocity, which is related to the critical stress. We solve the elastic problem for a steady-state motion of a periodic stick-slip pattern and derive equations of motion for the tip and resticking end of the slip pulses. In the slip regions we use the linear friction law and do not assume any intrinsic instabilities even at small sliding velocities. We find that, as in many other pattern forming system, the steady-state analysis itself does not select uniquely all the internal parameters of the pattern, especially the primary wavelength. Using some plausible analogy to first-order phase transitions we discuss a soft selection mechanism. This allows to estimate internal parameters such as crack velocities, primary wavelength and relative fraction of the slip phase as functions of the driving velocity. The relevance of our results to recent experiments is discussed.     

Quantum Brownian motion with large friction

Quantum Brownian motion in the strong friction limit is studied based on the exact path integral formulation of dissipative systems. In this limit the time-nonlocal reduced dynamics can be cast into an effective equation of motion, the quantum Smoluchowski equation. For strongly condensed phase environments it plays a similar role as master equations in the weak coupling range. Applications for chemical, mesoscopic, and soft matter systems are discussed and reveal the substantial role of quantum fluctuations.     

Brownian motion friction parameter of an ion near a metal surface

We derive and evaluate a pertubative expression for the friction parameter of a Brownian motion formalism. Our model system consists of a single massive ion near the surface of an electron gas. The relation of this friction parameter to recently calculated dynamical corrections to the image potential is clarified.     

Nonlinear dynamics of a rub-impact micro-rotor system with scale-dependent friction model

Scale effects in dry friction at microscale and the coefficients of friction due to adhesion force and two- and three-body deformations are considered. A rub-impact micro-rotor model with scaling nonlinear rub-impact force is presented and the nonlinear dynamic characteristics of the system in micro-electro-mechanical systems (MEMS) are investigated when the rotating speed, imbalance, damping coefficient, scale length and fractal dimension are regarded as the control parameters. Effects of scale length, fractal dimension, velocity-dependent impact factor and contact form on the coefficients of dry friction are investigated and discussed, and used to study the nonlinear behavior of rub-related vibrations with a large number of numerical simulations. The effects of rotating speed, imbalance, damping coefficient, and friction coefficient on the micro-rotor system responses are studied. It is indicated that the rub-impact micro-rotor system with the scale effects in friction alternates among the periodic, quasi-periodic and chaotic motions as the system parameters change. The results can be effectively used to diagnose the rub-impact fault, reduce the failure and improve the characteristics of a micro-rotor system, and optimize the design of micro-rotating machinery in MEMS.     

Instability criteria for a motion of a vortex subject to a non-linear friction force

Here we study the instability of the vortex motion caused by non-monotonous dependence of the friction force on the vortex velocity in the presence of a gyroforce. The analysis is done within the frameworks of “minimal” model for the elastic string subject to friction force and gyroforce. We demonstrate that even a weak gyroforce renders the condition for onset of instability more strict than for a vortex not subject to gyroforce: either the friction force must exceed a threshold, or its non-monotonic velocity dependence must be a rather steep function.     

Multiscaling of lattice curvature on friction surfaces of metallic materials as a basis of their wear mechanism

A comprehensive structural study has been performed to explore deformation and wear debris formation on friction surfaces of metallic materials. A hierarchy of structural scales of plastic deformation and failure during wear has been established. The nanoscale plays the major role in the hierarchical self-organization of multiscale debris formation processes. On this scale, bifurcational interstitial states arise in zones of local lattice curvature, with plastic distortion and motion of nonequilibrium point defects which determine the nonlinear dynamics of structure formation and wear of surface layers. Nonequilibrium vacancies on lattice sites form microporosity through the coalescence mechanism under plastic distortion. The microporosity is a precursor of meso- and macroscale plastic shearing that defines wear debris formation.     

On the effect of friction on tidal motion

Summary The effects of linear and nonlinear friction on the seiche's motion in the Adriatic sea have been studied trought a perturbative and numerical method. A roughness has been introduced to study the interaction with nonlinear friction term.

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Riassunto Si sono studiati in modo analitico e numerico gli effetti di attrito lineare e non lineare sulle oscillazioni periodiche del mar Adriatico. Si è particolarmente studiato l'effetto di una rugosità del fondo.

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Резюме Аналитически и численно исследуется влияние линейного и нелинейного трения на периодические осцилляции Адриатического моря. В частности, исследуется влияние морщинистости дна.

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Work supported by a grant CNR, Progetto Finalizzato Oceanografia.     

Quantization of motion with friction quadratic in velocity

The motion of a point object through a viscous field is considered. The friction is assumed to depend quadratically on velocity of the particle. The inverse problem of the variational calculus is solved and the Weyl quantization procedure is employed to write a Schrödinger equation. The solution of this equation shows that the quantum mechanical wave function is oscillatory for small values of the friction. Contrarily, for large values of the friction, the wave function resembles the solution of von Neumann shock problem.     

Friction coefficients and directed motion of asymmetric test particles

The behavior of a test particle in a rarefied gas of classical particles is investigated. considering different interaction mechanisms (specular and diffuse reflection, respectively). For large mass ratio between test and gas particles, analytical expressions for the linear friction coefficient are derived. Moreover, the existence of directed motion of asymmetric test particles with distinct initial conditions (but in the absence of any gradients) is shown. The analytical results are supported by a numerical simulation technique applicable to systems with any mass ratio, which is described here in detail.     

A Brownian motion version of the directed polymer problem

Consider a Brownian particle in three dimensions in a random environment. The environment is determined by a potential random in space and time. It is shown that at small noise the large-time behavior of the particle is diffusive. The diffusion constant depends on the environment. This work generalizes previous results for random walk in a random environment. In these results the diffusion constant does not depend on the environment.     

声子摩擦能量耗散机理研究

以界面摩擦为研究对象,分析了黏滑过程中的能量积累和耗散问题.基于晶格热动力学理论,通过分析界面原子在周期性势场中跳跃前后的势能差,推导了界面原子温升公式.理论表明,界面温升与摩擦系统的接触状态和材料特性有关,界面交互势能是其中影响较大的因素之一.在滑动阶段初期,由于界面原子处于非热平衡状态,晶格的热振动将通过激发出新声子而耗散能量,从而使得非热平衡向平衡状态转变.通过引入量子力学和热力学理论,分析了界面摩擦能量的耗散规律.结果表明,当声子振动频率较大时,黏着阶段存储于界面振子上的弹性势能在滑动阶段就很快完全耗散,耗散时间远小于滑动阶段的时间. 关键词： 界面摩擦 黏滑 声子 温升     

Nonlinear dynamics of a flexible mechanism with impact

The nonlinear dynamics of a slider-crank mechanism with a flexible rod is considered in this study. The flexible rod is modeled with lumped masses and periodically impacted by an external flexible sphere. The impact is modeled using a kinematic coefficient of restitution. Nonlinear dynamics tools are applied to analyze the simulated data captured from the connecting rod of the mechanism. The chaotic behavior of the system is analyzed. The stability of the motion is studied using the Lyapunov exponents. The dependence between the Lyapunov exponents and the corresponding angular velocity of the driver link of the mechanism is investigated.     

A dislocation mechanism of friction between a nanoprobe and solid surface

A dislocation mechanism of friction between an atomic-force microscope (AFM) probe and an atomically smooth solid surface is put forward. In this mechanism, the contact region is represented by an edge dislocation. The triboacoustic emission measured with an AFM shows the dislocation nature of friction. The friction force is calculated for a parabolic tip.     

Low-temperature motion of dislocations as a possible mechanism of formation of one-dimensional electronic structures in semiconductor crystals

A new mechanism is proposed for the formation of one-dimensional electronic structures in semiconductor crystals. The mechanism is based on controllable low-temperature glide of dislocations. Moving dislocations generate associations of intrinsic point defects in the form of one-dimensional chains, and the decay of the associations is impeded by low temperature. Experimental results and numerical estimates are presented for cadmium sulfide crystals. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 10, 639–644 (25 November 1997)