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Item A Stochastic Model of Stick-Slip Boundary Friction with Account for the Deformation Effect of the Shear Modulus of the Lubricant(Allerton Press, Inc., 2010) Хоменко, Олексій Віталійович; Хоменко, Алексей Витальевич; Khomenko, Oleksii Vitaliiovych; Ляшенко, Яків Олександрович; Ляшенко, Яков Александрович; Liashenko, Yakiv OleksandrovychThe melting of an ultrathin lubricating film during the friction of two solid atomically smooth surfaces is studied within the limits of the Lorentz model that approximates a viscoelastic medium, the deformation effect of the shear modulus being taken into account. It is shown that the action of a random force representing additive non-correlated noise results in the sustained oscillation mode that corresponds to stickslip friction. The numerical modeling of the process yields the ratios between the relaxation times at which the stick-slip mode is characterized by a high amplitude. The amplitude of stick-slip transitions is found to decrease as the shear modulus of the lubricant increases. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/18093Item Multifractal analysis of stress time series during ultrathin lubricant film melting(World Scientific Publishing Company, 2010) Хоменко, Олексій Віталійович; Хоменко, Алексей Витальевич; Khomenko, Oleksii Vitaliiovych; Ляшенко, Яків Олександрович; Ляшенко, Яков Александрович; Liashenko, Yakiv Oleksandrovych; Борисюк, Вадим Миколайович; Борисюк, Вадим Николаевич; Borysiuk, Vadym MykolaiovychMelting 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. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/18082Item Melting of ultrathin lubricant film due to dissipative heating of friction surfaces(Pleiades publishing, Ltd, 2007) Хоменко, Олексій Віталійович; Хоменко, Алексей Витальевич; Khomenko, Oleksii Vitaliiovych; Ляшенко, Яків Олександрович; Ляшенко, Яков Александрович; Liashenko, Yakiv OleksandrovychMelting of an ultrathin lubricant film during friction between atomically smooth surfaces is studied. Additive noise of shear stress and strain as well as of film temperature is introduced and the phase diagram is constructed. On the diagram, the noise intensity for this temperature and the temperature of friction surfaces determine the regions of sliding, dry, and stick-slip friction. As a result of numerical analysis of the Langevin equation for various regions of the diagram, time series of stresses are constructed, which make it possible to explain the experiment on friction, in which intermittent motion is observed. Lubricant melting due to dissipa-tive heating of friction surface is considered and the experimental time dependences of friction force are interpreted. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/16209Item Phase dynamics and kinetics of thin lubricant film driven by correlated temperature fluctuations(World scientific publishing company, 2007) Хоменко, Олексій Віталійович; Хоменко, Алексей Витальевич; Khomenko, Oleksii Vitaliiovych; Ляшенко, Яків Олександрович; Ляшенко, Яков Александрович; Liashenko, Yakiv OleksandrovychThe 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. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/16208Item Influence of temperature correlations on phase kinetics of boundary friction(Львівський університет, 2007) Хоменко, Олексій Віталійович; Хоменко, Алексей Витальевич; Khomenko, Oleksii Vitaliiovych; Ляшенко, Яків Олександрович; Ляшенко, Яков Александрович; Liashenko, Yakiv OleksandrovychUsing the Lorenz model for viscoelastic medium approximation 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 portraits are defined corresponding to the different regions of dynamic phase diagram and determining system’s kinetics. It is shown that the singular point, meeting the mode of dry friction, has indefinite character of stability. The other most probable steady-states of the system, corresponding to the stable and metastable sliding friction, are presented by the focus-type singular points in phase portraits. Consequently, the system can demonstrate damping oscillations near stable steady-states. The large extension of depicting trajectories near focuses along the axes of phase plane testifies to stability of sliding friction. Since maximums of distribution function, separated by the pronounced minimums of probability, correspond to the steady-state modes of friction, the transitions between them occur after large intervals of time. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/16203Item Stochastic theory of ultrathin lubricant film melting in stick-slip regime(Pleiades Publishing, Inc, 2005) Хоменко, Олексій Віталійович; Хоменко, Алексей Витальевич; Khomenko, Oleksii Vitaliiovych; Ляшенко, Яків Олександрович; Ляшенко, Яков Александрович; Liashenko, Yakiv OleksandrovychMelting of an ultrafhin lubricant film under friction between atomically smooth surfaces is studied in terms of the Lorentz model. Additive noise associated with shear stresses and strains, as well as with film temperature, is introduced, and a phase diagram is constructed where the noise intensity of the film temperature and the temperature of rubbing surfaces define the domains of sliding, dry, and stick-slip friction. Conditions are found under which stick-slip friction proceeds in the intermittent regime, which is characteristic of self-organized criticality. The stress self-similar distribution, which is provided by temperature fluctuations, is represented with allowance for nonlinear relaxation of stresses and fractional feedbacks in the Lorentz system. Such a fractional scheme is used to construct a phase diagram separating out different types of friction. Based on the study of the fractional Fokker-Planck equation, the conclusion is drawn that stick-slip friction corresponds to the subdiffusion process. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/16201