Alexei V. Khomenko

Synergetic theory for a jamming transition in traffic flow.

The theory of a jamming transition is proposed for the homogeneous car-following model within the framework of the Lorenz scheme. We represent a jamming transition as a result of the spontaneous deviations of headway and velocity that is caused by the acceleration/braking rate to be higher than the critical value. The stationary values of headway and velocity deviations and time of acceleration/braking are derived as functions of control parameter (time needed for car to take the characteristic velocity).

MULTIFRACTAL ANALYSIS OF STRESS TIME SERIES DURING ULTRATHIN LUBRICANT FILM MELTING

Melting of an ultrathin lubricant film confined between two atomically flat surfaces is studied using the rheological model for viscoelastic matter approximation. Phase diagram with domains, corresponding to sliding, dry, and two types of stick-slip friction regimes has been built taking into account additive noises of stress, strain, and temperature of the lubricant. The stress time series have been obtained for all regimes of friction using the Stratonovich interpretation. It has been shown that self-similar regime of lubricant melting is observed when intensity of temperature noise is much larger than intensities of strain and stress noises. This regime is defined by homogenous distribution, at which characteristic stress scale is absent. We study stress time series obtained for all friction regimes using multifractal detrended fluctuation analysis. It has been shown that multifractality of these series is caused by different correlations that are present in the system and also by a power-law distribution. Since the power-law distribution is related to small stresses, this case corresponds to self-similar solid-like lubricant.

Hysteresis phenomena at ultrathin lubricant film melting in the case of first-order phase transition

Within the framework of Lorentz model for description of viscoelastic medium the influence of deformational defect of the shear modulus is studied on melting of ultrathin lubricant film confined between the atomically flat solid surfaces. The possibility of jump-like and continuous melting is shown. Three modes of lubricant behavior are found, which correspond to the zero shear stress, the Hooke section of loading diagram, and the domain of plastic flow. Transition between these modes can take place according to mechanisms of first-order and second-order phase transformations. Hysteresis of dependencies of stationary stresses on strain and friction surfaces temperature is described. Phase kinetics of the system is investigated. It is shown that ratio of the relaxation times for the studied quantities influences qualitatively on the character of the stationary mode setting.

PHASE DYNAMICS AND KINETICS OF THIN LUBRICANT FILM DRIVEN BY CORRELATED TEMPERATURE FLUCTUATIONS

The melting of an ultrathin lubricant film is studied at friction between atomically flat surfaces. We take into account fluctuations of lubricant temperature, which are defined by the Ornstein-Uhlenbeck process. Phase diagrams and portraits are calculated for second- and first-order transitions (the melting of an amorphous and that of a crystalline lubricants, respectively). It is shown that, in the former case, a stick-slip friction domain, separating the regions of dry and sliding friction, appears. In the latter case, three domains of stick-slip friction arise, which are characterized by the transitions between dry, metastable and stable sliding friction. The increase in the correlation time of lubricant temperature fluctuations leads to increasing in the rubbing-surface temperature needed for realization of sliding friction. The stationary states, corresponding to dry, stable and metastable sliding friction, are reached as a result of damped oscillations.

Noise influence on solid¿liquid transition of ultrathin lubricant film

The melting of ultrathin lubricant film by friction between atomically flat surfaces is studied. The additive noises of the elastic shear stress and strain, and the temperature are introduced for building the phase diagrams with the domains of sliding, stick-slip, and dry friction. It is shown that increase of the strain noise intensity causes the lubricant film melting even at low temperatures of the friction surfaces.

Self-organized criticality within fractional Lorenz scheme

The theory of a flux steady-state related to avalanche formation is presented for the simplest model of a sand pile within the framework of the Lorenz approach. The stationary values of sand velocity and sand pile slope are derived as functions of a control parameter (driven sand pile slope). The additive noise of above values are introduced for building a phase diagram, where the noise intensities determine both avalanche and non-avalanche domains, as well as mixed one. Corresponding to the SOC regime, the last domain is crucial to affect of the noise intensity of the vertical component of sand velocity and especially sand pile slope. To address to a self-similar behavior, a fractional feedback is used as an efficient ingredient of the modified Lorenz system. In the spirit of Edwards paradigm, an effective thermodynamics is introduced to determine a distribution over an avalanche ensemble with negative temperature. Steady-state behavior of the moving grains number, as well as non-extensive values of entropy and energy is studied in detail. The power law distribution over the avalanche size is described within a fractional Lorenz scheme, where the energy noise plays a crucial role. This distribution is shown to be a solution of both fractional and nonlinear Fokker–Planck equation. As a result, we obtain new relations between the exponent of the size distribution, fractal dimension of phase space, characteristic exponent of multiplicative noise, number of governing equations, dynamical exponents and non-extensivity parameter.

Study of friction of Ag and Ni nanoparticles: an atomistic approach

Manipulation of metal nanoparticles using atomic force microscopy is a promising new technique for probing tribological properties at the nanoscale. In spite of some advancements in experimental investigations, there is no unambiguous theoretical treatment of processes accompanying the movement of metallic nanoislands adsorbed on a flat surface, and additional research is required. In this paper, we describe computer experiments based on classical molecular dynamics in which the behavior of silver and nickel nanoparticles interacting with a graphene sheet and sheared with constant force is studied. Frictional force acting on the nanoislands is measured as a function of their size. It is shown that its average value grows approximately linearly with contact area, and slopes of linear fits are close to the experimentally observable ones. The dependence of the friction force value and of the shape of the measured friction curves on the type of metal atom is revealed, and its possible reasons originating from atomistic background are discussed.

Hysteresis Behavior in the Stick–Slip Mode at the Boundary Friction

A tribological system is considered that consists of two atomically smooth solid surfaces separated by an ultrathin lubricant film. A thermodynamic model based on the Landau theory of phase transitions is built that describes the behavior of this system in the boundary friction mode. The free energy density for an ultrathin lubricant film is given in the form of expansion in series in terms of the powers of order parameter that is reduced to the shear modulus of the lubricant. The kinetics of the system is studied on the basis of a model describing first-order phase transitions between kinetic modes of friction. It is shown that in the presence of spring between the external drive and block the width of temperature hysteresis increases versus fixed coupling.

Explosive crystallization mechanism of ultradisperse amorphous films

The explosive crystallization of germanium ultradisperse amorphous films has been studied experimentally. We show that crystallization may be initiated by local heating at the small film thickness but is realized spontaneously at large thickness. The fractal pattern of the crystallization phase is discovered to be inherent in the phenomena of diffusion-limited aggregation. It is shown that in contrast to the ordinary crystallization mode, the explosive one is connected with the instability which is caused by self-heating. A transition from the first mechanism to the second one is modelled by the Lorenz system. The process of explosive crystallization is represented on the basis of the self-organized criticality conception. The front movement is described as the effective diffusion in the ultrametric space of hierarchically subordinated avalanches, corresponding to the explosive crystallization of elementary volumes of ultradisperse powder. The expressions for the stationary crystallization heat distribution and the steady-state heat current are obtained. The heat needed for initiation of the explosive crystallization is obtained as a function of the thermometric conductivity. The time dependence of the spontaneous crystallization probability in a thin film is examined.