A numerical study on stick-slip motion of a brake pad in steady sliding

A numerical model for an elastic brake pad sliding under constant load and with constant velocity over a rigid surface is investigated by finite element analysis. The geometry is taken to be two-dimensional, the contact is assumed to follow the laws of continuum mechanics and temporal and spatial resolution are such that dynamical effects localized at the interface are resolved. It turns out that at the contact interface localized slip events occur either in the form of long-lasting slip pulses, or in the form of brief local relaxations. Macroscopically steady sliding, macroscopic stick-slip motion or slip-separation dynamics occurs, depending on the macroscopic relative velocity. While structural oscillations of the brake pad do not seem to play a significant role during steady sliding at least one structural oscillation mode becomes synchronized with the interfacial dynamics during stick-slip or slip-separation motion. Assuming a given friction law for the interface, the macroscopically observed friction coefficient depends considerably on the underlying dynamics on the interface.     

Self-healing slip pulses along a gel/glass interface

We present experimental evidence of self-healing shear cracks at a gel/glass interface. This system exhibits two dynamical regimes depending on the driving velocity: steady sliding at high velocity (>V(c) approximately 100--125 microm/s), characterized by a shear-thinning rheology, and periodic stick-slip dynamics at low velocity. In this last regime, slip occurs by propagation of pulses that restick via a "healing instability" occurring when the local sliding velocity reaches the macroscopic transition velocity V(c). At driving velocities close below V(c), the system exhibits complex spatiotemporal behavior.     

Activated drift motion of a classical particle with a dynamical pinning effect

A one dimensional trap model for a thermally activated classical particle is introduced to simulate driven dynamics in presence of “ageing” effects. The depth of each trap increases with the time elapsed since the particle has fallen into it. The consequences of this dynamical pinning are studied, and velocity-force characteristics are numerically obtained. A special attention is paid to the situation where the particle is pulled with a spring to ensure a finite average velocity. In the low velocity regime, the presence of a broad distribution of trapping times leads to suppression of linear response, replaced by a threshold or by sublinear dynamics. A regime of strong fluctuations is obtained when the particle is driven at intermediate velocities. Received: 12 December 1997 / Accepted: 25 February 1998     

Non-linear dynamics of a driven two-level tunnelling defect

With increasing external-field amplitude the dynamics of a driven two-level system shows a cross-over from the weak-coupling or linear-response behaviour to a non-linear regime which is characterised by the appearance of Rabi oscillations, a field-dependent dynamical susceptibility, saturation of energy dissipation and additional frequencies in the correlation function. The system any initial distribution will relax towards a stationary state with a time-dependent polarisation vector. These features are derived from the propagator of the two-level system which is calculated using a perturbative scheme with a well-defined small parameter; the roatating-wave approximation of the Bloch equations is avoided. the dynamical behaviour is discussed by means of correlation and response functions.     

Simulation of Dynamics in Two-Dimensional Vortex Systems in Random Media

Dynamics in two-dimensional vortex systems with random pinning centres is investigated using molecular dynamical simulations. The driving force and temperature dependences of vortex velocity are investigated. Below the critical depinning force Fc, a creep motion of vortex is found at low temperature. At forces slightly above Fc, a part of vortices flow in winding channels at zero temperature. In the vortex channel flow region, we observe the abnormal behaviour of vortex dynamics： the velocity is roughly independent of temperature or even decreases with temperature at low temperatures. A phase diagram that describes different dynamics of vortices is presented.     

Elements for a comparison between the Tyrrhenian and Ligurian coastal currents during spring

Summary Hydrological and current measurements effected along the western Italian coasts permit to compare the main dynamical peculiarities of the coastal circulation of the Ligurian and Tyrrhenian basins, evidencing in particular their different response to atmospheric fluctuations. While the Ligurian currents show a great energy that depends essentially on the large-scale circulation, the Tyrrhenian shelf dynamics is characterized by a low thermohaline driven velocity, largely influenced by the local wind. Paper presented at the 1° Congresso del Gruppo Nazionale per la Fisica dell' Atmosfera e dell'Oceano, Rome, June 19–22, 1984.     

Reconstruction of bowing point friction force in a bowed string

A method is presented for reconstructing the friction force and the velocity at the bowing point of a string excited by a rosined bow sliding transverse to the string. Two versions of the method of reconstruction are presented, each approximate in different ways, but both capable of sufficient accuracy to allow useful application to problems of understanding frictional interactions in this dynamical system. The method is illustrated with simulated data to verify its accuracy, and results are shown for two contrasting cases of observed stick-slip string motion. As has been found in other investigations, the friction force during sliding is not determined by the instantaneous sliding speed. The results seem to be compatible with a thermally based model of rosin friction.     

Dynamics of a mobile system with an internal acceleration-controlled mass in a resistive medium

The dynamics of a mobile system with a movable internal mass is investigated in this paper. Due to the periodic motion of the internal acceleration-controlled mass as well as the anisotropy of the external resistance, the system can move in a resistive medium. Major attention is given to the steady-state motion and stick-slip effect of the system as a whole. For anisotropic Coulomb's dry friction, in light of the non-smooth factors in both the internal control mode and external resistance, method of averaging is adopted to obtain an approximate expression of the average steady-state velocity when the stick-slip motion is absent. Optimizing the parameters of the internal controlled mass enables one to realize a maximal average steady-state velocity of the system. In view of the stick-slip effect, the steady-state motion of the system is classified into eight types, and the characteristics of each type are analyzed. Stick-slip motion is of our interest and receives extra attention. Two strategies of control are put forward based on the characteristics of stick-slip motion. Making use of these two control strategies, directed motions of the system are possible and the direction of the motion can be simply controlled by modifying the values of internal accelerations. To achieve an always forward motion with higher average steady-state velocity, further optimization is carried out. For anisotropic linear resistance, the approximate expression of average steady-state velocity can be also obtained by the method of averaging. No stick-slip motion may occur in this instance. All the analytical results are numerically simulated in order to verify their correctness.     

Fermi acceleration and its suppression in a time-dependent Lorentz gas

Some dynamical properties for a Lorentz gas were studied considering both static and time-dependent boundaries. For the static case, it was confirmed that the system has a chaotic component characterized with a positive Lyapunov exponent. For the time-dependent perturbation, the model was described using a four-dimensional nonlinear map. The behaviour of the average velocity is considered in two different situations: (i) non-dissipative and (ii) dissipative dynamics. Our results confirm that unlimited energy growth is observed for the non-dissipative case. However, and totally new for this model, when dissipation via inelastic collisions is introduced, the scenario changes and the unlimited energy growth is suppressed, thus leading to a phase transition from unlimited to limited energy growth. The behaviour of the average velocity is described using scaling arguments.     

Dynamics of a tethered polymer in shear flow

The dynamics of a single polymer tethered to a solid surface in a shear flow was observed using fluorescently labeled DNA chains. Dramatic shear enhanced temporal fluctuations in the chain extension were observed. The rate of these fluctuations initially decreased for increasing shear rate gamma; and increased above a critical gamma;. Simulations revealed that these anomalous dynamics arise from a continual recirculating motion of the chain or cyclic dynamics. These dynamics arise from a coupling of the chain velocity in the flow direction to thermally driven fluctuations of the chain in the shear gradient direction.     

Nonlinear spring model for frictional stick-slip motion

Frictional stick-slip dynamics is discussed using a model of one oscillator pulled by a nonlinear spring force. We focus our attention on the nonlinear spring parameter k₀. The dynamics of the model is carefully studied, both numerically and analytically. Our numerical investigation, which involves bifurcation diagrams, shows a rich spectrum of dynamical behavior including periodic, quasi-periodic and chaotic states. On the other hand, and for a good selection of parameters , the motion of the particle involves periodic stick-slip, erratic and intermittent motions, characterized by force fluctuations, and sliding. This study suggests that the transition between each of motion strongly depends on the nonlinear parameter k₀. The system also displays resonance at fractional frequencies of the oscillator.     

Peptide friction in water nanofilm on mica surface

Peptide frictions in water nanofilms of various thicknesses on a mica surface are studied via molecular dynamics simulations. We find that the forced lateral motion of the peptide exhibits stick-slip behaviour at low water coverage; in contrast, the smooth gliding motion is observed at higher water coverage. The adsorbed peptide can form direct peptide-surface hydrogen bonds as well as indirect peptide-water-surface hydrogen bonds with the substrate. We propose that the stick-slip phenomenon is attributed to the overall effects of direct and indirect hydrogen bonds formed between the surface and the peptide.     

In-flight and collisional dissipation as a mechanism to suppress Fermi acceleration in a breathing Lorentz gas

Some dynamical properties for a time dependent Lorentz gas considering both the dissipative and non dissipative dynamics are studied. The model is described by using a four-dimensional nonlinear mapping. For the conservative dynamics, scaling laws are obtained for the behavior of the average velocity for an ensemble of non interacting particles and the unlimited energy growth is confirmed. For the dissipative case, four different kinds of damping forces are considered namely: (i) restitution coefficient which makes the particle experiences a loss of energy upon collisions; and in-flight dissipation given by (ii) F=-ηV(2); (iii) F=-ηV(μ) with μ≠1 and μ≠2 and; (iv) F=-ηV, where η is the dissipation parameter. Extensive numerical simulations were made and our results confirm that the unlimited energy growth, observed for the conservative dynamics, is suppressed for the dissipative case. The behaviour of the average velocity is described using scaling arguments and classes of universalities are defined.     

Dynamical Large Deviations for a Boundary Driven Stochastic Lattice Gas Model with Many Conserved Quantities

We prove the dynamical large deviations for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles at the boundary: this is the so-called boundary driven process. The dynamics we considered consists of a weakly asymmetric simple exclusion process with collision among particles having different velocities.     

Nonlinear mobility of a driven system: Temperature and disorder effects

We consider the dissipative nonlinear dynamics of a model of interacting atoms driven over a substrate potential. The substrate parameters can be suitably tuned in order to introduce disorder effects starting from two geometrically opposed ideal cases: commensurate and incommensurate interfaces. The role of temperature is also investigated through the inclusion of a stochastic force via a Langevin molecular dynamics approach. Here, we focus on the most interesting tribological case of underdamped sliding dynamics. For different values of the chain stiffness, we evaluate the static friction threshold and consider the depinning transition mechanisms as a function of the applied driving force. As experimentally observed in QCM frictional measurements of adsorbed layers, we find that disorder operates differently depending on the starting geometrical configuration. For commensurate interfaces, randomness lowers considerably the chain depinning threshold. On the contrary, for incommensurate mating contacts, disorder favors static pinning destroying the possible frictionless (superlubric) sliding states. Interestingly, thermal and disorder effects strongly influence also the occurrence of parametric resonances inside the chain, capable of converting the kinetic energy of the center-of-mass motion into internal vibrational excitations. We comment on the nature of the different dynamical states and hysteresis (due to system bi-stability) observed at different increasing and decreasing strengths of the external force.     

Numerical study of nanoscale lubrication and friction at solid interfaces

This study investigates lubrication and related frictional phenomena on the nanoscale using numerical simulations. Two models of lubrication, a two-layer and a three-layer, are considered, and for the three-layer model, a lubricant layer is introduced between the two solids. The kinetic frictional force shows resonance behaviour caused by multi-phonon excitations at the interface. It is found that these frictional effects cause a peculiar stick-slip motion of the driven plate and lubricants.     

Origin of dynamic heterogeneities in miscible polymer blends: A quasielastic neutron scattering study

In order to investigate the origin of the often invoked nanoheterogeneities in miscible polymer blends, we have performed quasielastic neutron scattering experiments on the component dynamics within the miscible polymer blend polyisoprene/polyvinyl ether including the pure components as a reference. We find that the apparent local heterogeneities observed by spectroscopic techniques originate from the chain specific crossover properties between entropy driven and local chain dynamics and are, thus, a purely dynamical phenomenon.     

Effective temperature scaled dynamics of a flexible polymer in an active bath

Langevin dynamics simulations are employed to study the dynamical properties of a flexible polymer in an active bath. The diffusion of the centre of mass and end-to-end distance fluctuation are particularly analysed. We modulate both active force and active particle size to probe the activity-induced facilitation of polymer dynamics. Results indicate diffusivity and chain relaxation time can be well scaled by the effective temperature of the active bath. In addition, diffusion dynamics demonstrates an anomalous superdiffusive behaviour in short time scales, which becomes more prominent with increasing active particle size. Lastly, we extract the effective viscosity experienced by the probed chain, showing a sharp decrease with increment of effective temperature. The attenuation of effective viscosity due to activity might be responsible for the facilitated polymer dynamics.