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The self-affine mode of ice softening during friction is investigated within the rheological model for viscoelastic medium approximation. The different modes of ice rubbing, determined by formation of surface liquid-like layer, are studied. The analysis of time series of friction force is carried out, namely Fourier analysis, construction of autocorrelation and difference autocorrelation functions. The spectral power law is detected for modes of crystalline ice as well as of a mixture of stable ice and metastable softening. The self-similarity and aperiodic character of corresponding time series of friction force are proved., Comment: 10 pages, 4 figures

This article is a continuation of our previous studies of the frictional anisotropy of metal nanoparticles on the surface of a graphene substrate for other temperature conditions. The friction force acting on palladium nanoparticles on a graphene sheet in various lateral directions is investigated using classical molecular dynamics modelling. Anisotropy is studied at high sliding speeds of nanoparticles consisting of 10000 atoms on the surface of graphene. The effect of incommensurability and short-range order of the contact surfaces of nanoparticles, as well as the graphene deformation lead to the absence of an expressed angular dependence of the friction force., Comment: 6 pages, 4 figures

The ice surface softening during friction is shown as a result of spontaneous appearance of shear strain caused by external supercritical heating. This transformation is described by the Kelvin-Voigt equation for viscoelastic medium, by the relaxation equations of Landau-Khalatnikov-type and for heat conductivity. The study reveals that the above-named equations formally coincide with the synergetic Lorenz system, where the order parameter is reduced to shear strain, stress acts as the conjugate field, and temperature plays the role of a control parameter. Using the adiabatic approximation, the stationary values of these quantities are derived. The examination of dependence of the relaxed shear modulus on strain explains the ice surface softening according to the first-order transition mechanism. The critical heating rate is proportional to the relaxed value of the ice shear modulus and inversely proportional to its typical value., Comment: 10 pages, 3 figures

The approach of nonequilibrium evolution thermodynamics earlier offered is developed. It helps to describe the processes of defect formation within the adiabatic approximation. The basic equations system depends on the initial defects distribution (dislocations and grain boundaries). The phase diagram is determined with the domains of the realization of different limiting structure types. The interaction effect of several defect types on the formation of a limiting structure is investigated in terms of the internal energy. The conditions of the formation of two limiting structures are found. The kinetics of the steady-state values establishment of the defects density is investigated within the scope of the adiabatic approximation. The dislocations density change follows the evolution of the grain boundaries density in this approach. It is shown that grain sizes, in limiting structures, decrease with an increase of the elastic strains., Comment: 14 pages, 6 figures

In this note we prove that each weak solution for the 3D Navier-Stokes system satisfies Leray-Hopf property. Moreover, each weak solution is rightly continuous in the standard phase space $H$ endowed with the strong convergence topology., Comment: Find a mistake

Friction force acting on silver and nickel nanoparticles sheared on a graphene sheet in different lateral directions is investigated using classical molecular dynamics simulations. The results reveal the existence of frictional anisotropy for both metals. In most cases, the maximum value of the friction force is about two times larger than the minimum one. The form of dependencies of instantaneous values of the friction force components on the corresponding lateral components of the position of the centre of mass of the nanoislands strongly depends on sliding direction, varying between the sawtooth and the irregular one. A qualitative explanation of the results based on the "patch" model is proposed., Comment: 13 pages, 8 figures, PDFLaTeX

We present classical molecular dynamics calculations of the behavior of copper and gold nanoparticles on a graphene sheet, sheared with a constant applied force $F_{\rm a}$. The force $F_{\rm s}$ acting on the particle from the substrate depends on the material of the nanoparticles (Au or Cu), and exhibits a sawtooth dependency on time, which we attribute to local commensurability between the metal nanoparticle surface atomic positions with the graphene lattice. The time-averaged value of $F_{\rm s}$ (the friction force) acting on Au nanoparticles increases linearly with the contact area, having slopes close to the experimentally observable ones. A qualitative model is proposed to explain the observed results., Comment: 8 pages, 7 figures

The formation of an adatom adsorption structure in dynamic force microscopy experiment is shown as a result of the spontaneous appearance of shear strain caused by external supercritical heating. This transition is described by the Kelvin-Voigt equation for a viscoelastic medium, the relaxation Landau-Khalatnikov equation for shear stress, and the relaxation equation for temperature. It is shown that these equations formally coincide with the synergetic Lorenz system, where the shear strain acts as the order parameter, the conjugate field is reduced to the stress, and the temperature is the control parameter. Within the adiabatic approximation, the steady-state values of these quantities are found. Taking into account the sample shear modulus vs strain dependence, the formation of the adatom adsorption configuration is described as the first-order transition. The critical temperature of the tip linearly increases with the growth of the effective value of the sample shear modulus and decreases with the growth of its typical value., Comment: 10 pages, 3 figures

We present results of the study of chromospheric and photospheric line-of-sight velocity fields in the young active region NOAA 11024. Multi-layer, multi-wavelength observational data were used for the analysis of the emerging flux in this active region. Spectropolarimetric observations were carried out with the telescope THEMIS on Tenerife (Canary Islands) on 4 July 2009. In addition, space-borne data from SOHO/MDI, STEREO and GOES were also considered. The combination of data from ground- and space-based telescopes allowed us to study the dynamics of the lower atmosphere of the active region with high spatial, spectral, and temporal resolutions. THEMIS spectra show strong temporal variations of the velocity in the chromosphere and photosphere for different activity features: two pores, active and quiet plage regions, and two surges. The range of variations of the chromospheric line-of-sight velocity at the heights of formation of the H-alpha core was extremely large. Both upward and downward motions were observed in these layers. In particular, a surge with upward velocities up to -73 km/s were detected. In the photosphere, predominantly upward motions were found, varying from -3.1 km/s upflows to 1.4 km/s downflows in different structures. The velocity variations at different levels in the lower atmosphere are compatible with magnetic flux emergence., Comment: 17 pages, 8 figures; accepted for publication in Solar Physics

A deterministic theory describing the melting of an ultrathin lubricant film between two atomically smooth solid surfaces has been developed. The lubricant state is described by introducing a parameter of excess volume that arises owing to the solid structure chaotization at its melting. The thermodynamic and shear kinds of melting are described consistently. The dependences of the stationary friction force on the lubricant temperature and the shear velocity of rubbing surfaces that move with respect to each other with a constant velocity have been analyzed. In the framework of a simple tribological model, the stick-slip mode of friction, when the lubricant periodically melts and solidifies, has been described. The influence of velocity, temperature, and load on the stick-slip friction has been analyzed. A qualitative comparison between the results obtained and experimental data has been carried out., Comment: 9 pages, 6 figures, 40 references

Manipulation of metal nanoparticles using atomic force microscope 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., Comment: 23 pages, 9 figures

Mechanical exfoliation of a graphite surface with an adhesive nanoasperity is studied under different temperatures ranging from 298 K to 2 K using classical molecular dynamics. Two types of the interlayer interaction are investigated. For a pairwise Lennard-Jones potential the complete removal of the upper graphene layer during the retraction of the nanoasperity occurs in the whole range of the temperatures considered. The results obtained using registry dependent potential, which takes into account electronic delocalization contribution besides the van der Waals one, exhibit more pronounced temperature dependence. In this case the exfoliation takes place for temperatures higher than 16 K, but beginning from 8 K down to 2 K the system behavior manifests qualitative changes with the absence of cleavage of the sample. Analytical estimates combined with the results of the simulations reveal that the contribution of the overlap of pi orbitals of carbon atoms plays an important role in the exfoliation of graphite., Comment: 24 pages, 16 figures

Computer experiments concerning interactions between a graphite surface and the rigid pyramidal nanoasperity of a friction force microscope tip when it is brought close to and retracted from the graphitic sample are presented. Covalent atomic bonds in graphene layers are described using a Brenner potential and tip-carbon forces are derived from the Lennard-Jones potential. For interlayer interactions a registry-dependent potential with local normals is used. The behavior of the system is investigated under conditions of different magnitudes of tip-sample interaction and indentation rates. Strong forces between the nanoasperity and carbon atoms facilitate the cleavage of the graphite surface. Exfoliation, i. e. total removal of the upper graphitic layer, is observed when a highly adhesive tip is moved relative to the surface at low rates, while high rates cause the formation of a small flake attached to the tip. The results obtained may be valuable for enhancing our understanding of the superlubricity of graphite., Comment: 16 pages, 11 figures

Melting of an ultrathin lubricant film confined between two atomically flat surfaces is we 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., Comment: 22 pages, 10 figures, 41 references

A deterministic theory describing the behavior of an ultrathin lubricant film between two atomically-smooth solid surfaces is proposed. For the description of lubricant state the parameter of excess volume arising due to chaotization of solid medium structure in the course of melting is introduced. Thermodynamic and shear melting is described consistently. Dependences of friction force on temperature of lubricant, shear velocity of rubbing surfaces, and pressure upon surfaces are analyzed. Within the framework of a simple tribological model the stick-slip mode of friction, when the lubricant periodically melts and solidifies, is described. The obtained results are qualitatively compared with the experimental data., Comment: 14 pages, 6 figures, 33 references

The thermodynamic model of ultrathin lubricant film melting, confined between two atomically-flat solid surfaces, is built using the Landau phase transition approach. Non-equilibrium entropy is introduced describing the part of thermal motion conditioned by non-equilibrium and non-homogeneous character of the thermal distribution. The equilibrium entropy changes during the time of transition of non-equilibrium entropy to the equilibrium subsystem. To describe the condition of melting, the variable of the excess volume (disorder parameter) is introduced which arises due to chaotization of a solid structure in the course of melting. The thermodynamic and shear melting is described consistently. The stick-slip mode of melting, which is observed in experiments, are described. It is shown that with growth of shear velocity, the frequency of stiction spikes in the irregular mode increases at first, then it decreases, and the sliding mode comes further characterized by the constant value of friction force. Comparison of the obtained results with experimental data is carried out., Comment: 11 pages, 4 figures

Molecular dynamics simulations of ultrathin water film confined between atomically flat rigid diamond plates are described. Films with thickness of one and two molecular diameters are concerned and TIP4P model is used for water molecules. Dynamical and equilibrium characteristics of the system for different values of the external load and shear force are investigated. An increase of the external load causes the transition of the film to a solidlike state. This is manifested in the decreasing of the diffusion constant and in the ordering of the liquid molecules into quasidiscrete layers. For two-layer film under high loads molecules also become ordered parallel to the surfaces. Time dependencies of the friction force and the changes of its average value with the load are obtained. In general, the behaviour of the studied model is consistent with the experimental results obtained for simple liquids with spherical molecules., Comment: 10 pages, 9 figures, PDFLaTeX

The reliability of quiet Sun magnetic field diagnostics based on the \ion{Fe}{1} lines at 6302 \AA has been questioned by recent work. We present here the results of a thorough study of high-resolution multi-line observations taken with the new spectro-polarimeter SPINOR, comprising the 5250 and 6302 \AA spectral domains. The observations were analyzed using several inversion algorithms, including Milne-Eddington, LTE with 1 and 2 components, and MISMA codes. We find that the line-ratio technique applied to the 5250 \AA lines is not sufficiently reliable to provide a direct magnetic diagnostic in the presence of thermal fluctuations and variable line broadening. In general, one needs to resort to inversion algorithms, ideally with realistic magneto-hydrodynamical constrains. When this is done, the 5250 \AA lines do not seem to provide any significant advantage over those at 6302 \AA . In fact, our results point towards a better performance with the latter (in the presence of turbulent line broadening). In any case, for very weak flux concentrations, neither spectral region alone provides sufficient constraints to fully disentangle the intrinsic field strengths. Instead, we advocate for a combined analysis of both spectral ranges, which yields a better determination of the quiet Sun magnetic properties. Finally, we propose the use of two other \ion{Fe}{1} lines (at 4122 and 9000 \AA) with identical line opacities that seem to work much better than the others., Comment: ApJ, in press

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 transitions. Hysteresis of dependences 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., Comment: 13 pages, 6 figures, LaTeX

The melting of ultrathin lubricant film is studied by friction between atomically flat surfaces. The fluctuations of lubricant temperature are taken into account defined by Ornstein-Uhlenbeck process. The phase diagrams and portraits are calculated for the cases of second-order and first-order transitions -- the melting of amorphous and crystalline lubricants. It is shown that in the first case the stick-slip friction domain appears, dividing the regions of dry and sliding friction. In the second case the three stick-slip friction domains arise characterized by transitions between dry, metastable and stable sliding friction. The increase of correlation time of the lubricant temperature fluctuations leads to increasing of the frictional surfaces temperature needed for realization of sliding friction. The singular point, meeting the mode of dry friction, has complex character of stability. The stationary states, corresponding to the stable and metastable sliding friction, are presented by the focus-type singular points., Comment: 9 pages, 6 figures, REVTeX

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 a phase diagram 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., Comment: 10 pages, 2 figures, LaTeX

Jamming transition in traffic flow (between free and jammed traffic) for homogeneous car following model has been investigated taking into account fluctuations of characteristic acceleration/braking time. These fluctuations are defined by Ornstein-Uhlenbeck process. The behaviour of the most probable deviation of headway from its optimal value has been studied and phase diagram of the system has been calculated for supercritical and subcritical regimes of jam formation. It has been found that for the first regime the fluctuations of characteristic acceleration/braking time result in coexistence of free moving and jammed traffic, that is typical for the first-order phase transition, and in appearance of two steady states for the second mode. These states correspond to non-zero values of headway deviation at which the formation of jam and congested traffic are possible. Using phase-plain portraits method the kinetics of the system transitions has been analyzed for different domains of the phase diagram for both regimes., Comment: 12 pages, 6 figures, LaTeX

The theory of a flux steady-state related to avalanche formation is presented for the simplest model of a sand pile within framework of the Lorenz approach. The stationary values of sand velocity and sand pile slope are derived as functions of control parameter (driven sand pile slope). The additive noises of above values are introduced to build the phase diagram, where the noise intensities determine both avalanche and non-avalanche domains, as well as mixed one. Being corresponded to the SOC regime, the last domain is crucial to affect of the noise intensities of vertical component of sand velocity and sand pile slope especially. To address to a self-similar behavior, a fractional feedback is used as efficient ingredient of the modified Lorenz system. In a spirit of Edwards paradigm, an effective thermodynamics is introduced to determine a distribution over avalanche ensemble with negative temperature. Steady-state behavior of the moving grains number, as well as nonextensive values of entropy and energy is studied in detail. The power-law distribution over avalanche sizes is described within a fractional Lorenz scheme, where noise of the energy plays a crucial role. This distribution is shown to be solution of both fractional Fokker-Planck equation and nonlinear one. As a result, we obtain new relations between exponent of the size distribution, fractal dimension of phase space, characteristic exponent of multiplicative noise, number of governing equations, dynamical exponents and nonextensivity parameter., Comment: 26 pages, 13 figures, RevTeX

Self-organizing system is studied whose behavior is governed by field of an order parameter, a fluctuation amplitude of conjugate field and a couple of Grassmannian conjugated fields that define the entropy as a control parameter. Within the framework of self-consistent approach the dependencies of macro- and microscopic susceptibilities as well as memory and nonergodicity parameters are determined as a functions of the intensities of thermal and quenched disorders. Making use of the sandpile model shows that proposed scheme determines the conditions of avalanches formation in self-organized criticality phenomena., Comment: 17 pages, 6 figures, REVTeX

The theory of a jamming transition is proposed for the homogeneous car-following model within the framework of 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)., Comment: 10 pages, 2 figures, LaTeX

The explosive crystallization of germanium ultradisperse amorphous films is studied experimentally. We show that crystallization may be initiated by local heating at the small film thickness but it realizes spontaneously at the large ones. The fractal pattern of the crystallized phase is discovered that is 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 the self-heating. A transition from the first mechanism to the second one is modelled by 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 films is examined., Comment: 22 pages, 5 figures, LaTeX