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Inspired by spring-block models, we elaborate a "minimal" physical model of earthquakes which reproduces two main empirical seismological laws, the Gutenberg-Richter law and the Omori aftershock law. Our point is to demonstrate that the simultaneous incorporation of aging of contacts in the sliding interface and of elasticity of the sliding plates constitutes the minimal ingredients to account for both laws within the same frictional model.

We introduce and investigate a multiscale model for the propagation of rupture fronts in friction. Taking advantage of the correlation length for the motion of individual contacts in elastic theory, we introduce collective contacts which can be characterized by a master equation approach. The problem of the dynamics of a chain of those effective contacts under stress is studied. We show that it can be reduced to an analog of the Frenkel-Kontorova model. In some limits this allows us to derive analytical solutions for kinks describing the rupture fronts. Numerical simulations are used to study more complex cases.

We investigate the velocity dependence of kinetic friction with a model that makes minimal assumptions on the actual mechanism of friction so that it can be applied at many scales, provided the system involves multicontact friction. Using a recently developed master equation approach, we investigate the influence of two concurrent processes. First, at a nonzero temperature, thermal fluctuations allow an activated breaking of contacts that are still below the threshold. As a result, the friction force monotonically increases with velocity. Second, the aging of contacts leads to a decrease of the friction force with velocity. Aging effects include two aspects: the delay in contact formation and aging of a contact itself, i.e., the change of its characteristics with the duration of stationary contact. All these processes are considered simultaneously with the master equation approach, giving a complete dependence of the kinetic friction force on the driving velocity and system temperature, provided the interface parameters are known.

Using molecular dynamics based on Langevin equations with a coordinate- and velocity-dependent damping coefficient, we study the frictional properties of a thin layer of "soft" lubricant (where the interaction within the lubricant is weaker than the lubricant-substrate interaction) confined between two solids. At low driving velocities the system demonstrates stick-slip motion. The lubricant may or may not be melted during sliding, thus exhibiting either the "liquid sliding" (LS) or the "layer over layer sliding" (LoLS) regimes. The LoLS regime mainly operates at low sliding velocities. We investigate the dependence of friction properties on the misfit angle between the sliding surfaces and calculate the distribution of static frictional thresholds for a contact of polycrystalline surfaces.

At the mesoscale friction occurs through the breaking and formation of local contacts. This is often described by the earthquakelike model which requires numerical studies. We show that this phenomenon can also be described by a master equation, which can be solved analytically in some cases and provides an efficient numerical solution for more general cases. We examine the effect of temperature and aging of the contacts and discuss the statistical properties of the contacts for different situations of friction and their implications, particularly regarding the existence of stick-slip.

We show that the transition from smooth sliding to stick-slip motion in a single planar frictional junction always takes place at an atomic-scale relative velocity of the substrates.

We propose a model for a one-dimensional chain of interacting particles in an external periodic potential. In this model the particles have a complex structure treated in a mean-field fashion: particle collisions are inelastic and also each particle is considered as having its own thermostat. We derived the Fokker-Planck equation for this model and demonstrated that the model has a truly equilibrium ground state. When an external dc force is applied to the atoms, the model exhibits a hysteresis even at high temperatures due to the clustering of atoms with the same velocity. Another effect of clustering is phase separation in the steady state when the system splits into regions of immobile atoms ("traffic jams") and regions of running atoms.

We propose a two-dimensional lattice-gas (2D LG) model where atoms may be in two different states: the immobile state, in which they jump as usual in the LG model, and the running state, in which the atoms always jump in the driving direction. The model demonstrates a typical behavior of "traffic-jam" models: the system splits into domains of immobile atoms (jams) and running atoms. We considered four variants of the 2D LG model, namely the multilane and truly 2D models, each with "passive" and "active" atomic jumps. The model has the steady state with a power law distribution of jam sizes characterized by a universal exponent 3/2. The phase diagram of the model shows that the mobility of the 2D system is lower than the mobility of the 1D model due to the spreading of jams in the direction transverse to the driving direction.

We study the nonlinear dc response of a two-dimensional underdamped system of interacting atoms subject to an isotropic periodic external potential with triangular symmetry. When driving force increases, the system transfers from a disorder locked state to an ordered sliding state corresponding to a moving crystal. By varying the values of the effective elastic constant, damping, and temperature, we found different scenarios and intermediate phases during the ordering transition. For a soft atomic layer, the system passes through a plastic-channel regime that appears as a steady-state regime at higher values of the damping coefficient. For high values of the effective elastic constant, when the atomic layer is stiff, the intermediate plastic phase corresponds to a traffic-jam regime with immobile islands in the sea of running atoms. At a high driving of the stiff layer, a solitonlike elastic flow of atoms has been observed.

The mobility and the diffusivity of a dimer (two atoms coupled by an elastic spring) in a periodic substrate potential under the action of the dc and ac external forces are studied. It is shown that the dimer diffusivity may be strongly enhanced due to driving.

Molecular dynamics is used to investigate the melting of a thin lubricant film confined between two crystalline surfaces. The dynamics of the film is significantly affected by the substrate, both in the solid and in the molten phases. The solid phase, able to sustain shear stress, shows, however, large diffusional motions of the atoms. The melting temperature depends strongly on the confinement. A phenomenological microscopic theory, based on the Lindemann criterion, is proposed to explain this effect.

Multiple and supersonic topological excitations (kinks) driven by an external dc force in the Frenkel-Kontorova model (a chain of atoms subjected to a periodic substrate potential) with the exponential interatomic interaction are studied with the help of numerical simulation. The simulation results are interpreted in terms of dynamics of two limiting cases, the exactly integrable sine-Gordon equation and the Toda chain. The stability of driven kinks and scenarios of their destruction are described for a wide range of model parameters.

We analyze a probability of atomic jumps for more than one lattice spacing in activated surface diffusion. First, we studied a role of coupling between the x and y degrees of freedom for the diffusion in a two-dimensional substrate potential. Simulation results show that in the underdamped limit the average jump length scales with the damping coefficient eta as proportional, variant eta(-sigma(lambda)) with 1/2

Molecular-dynamics study of a thin (one to five layers) lubricant film between two substrates in moving contact are performed using Langevin equations with an external damping coefficient depending on distance and velocity of atoms relative the substrates, motivated by microscopic configurations. They show that the minimal friction coefficient is obtained for the solid-sliding regime. A detailed analysis of the results, the comparison with other microscopic modeling approaches of friction, and the evaluation of quantities that can be compared to experiments, such as the velocity of the transition from stick slip to smooth sliding, are used to discuss the relevance of the microscopic simulations of friction.

We study the nonlinear dc response of a two-dimensional underdamped system of interacting atoms subject to an isotropic periodic external potential with triangular symmetry. We consider various values of the effective elastic constant of the system, two different atomic interaction potentials, and different concentrations of atoms. In the case of a closely packed layer, when its structure is commensurate with the substrate, there is a locked-to-running transition as a function of the driving force, whose mechanism depends on the effective elastic constant. For a low elastic constant, where the layer is weakly coupled, the transition is achieved via the creation of an avalanche of moving particles that leaves a depleted region in its wake. On increasing the effective elastic constant the depleted region becomes less marked and there is a crossover to a scenario in which an island of moving particles nucleates the transition. In the case of a partially filled atomic layer, several dynamical phase transitions between states with different atomic mobility are observed. The mobility of atoms as a function of the external force can vary nonmonotonically with increasing force. For the case of a small external damping, the system can be trapped at a large force in an immobile metastable state, thus demonstrating a "fuse-safety device" on an atomic scale.

Diffusion of a particle in the N-dimensional external potential which is periodic in one dimension and unbounded in the other N-1 dimensions is investigated. We find an analytical expression for the overdamped diffusion and study numerically the cases of moderate and low damping. We show that in the underdamped limit, the multidimensional effects lead to a reduction (compared to the one-dimensional motion) in the jump lengths between subsequent trappings of the atom at the minima of the external periodic potential. As an application, we consider the diffusion of a dimer adsorbed on the crystal surface.