Nanostructured surfaces 

The stability analysis of stationary modes 
Of the ice surface softening during the friction process
Yushchenko O.V.1, Badalian A.Yu.1, 
1 Sumy State University, 2 Rimskii-Korsakov St., 40007 Sumy, Ukraine
E-mail: o.yushchenko@phe.sumdu.edu.ua

In this paper, a further study of synergetic model of ice softening during friction is carried out. The origin model describes softening of the ice surface in consequence of spontaneous appearance of shear strain due to external supercritical heating. The result is a self-organization process of the strain (order parameter), stress shear components (conjugate field) and layer temperature (control parameter). In this case, the Kelvin-Voigt equation for viscoelastic medium, equation for heat conductivity and relaxation equation of Landau-Khalatnikov-type were taken as a basis of consideration [1]. 
It is shown that the behavior of different softening modes can be described by this model. The ranges of change were found for the main parameters of the system, which set different modes. Stationary values were found during the analysis. Moreover, phase portraits are built and the kinetics of the system is described for each mode. Type of the system behavior is described in accordance with the character of stability of singular points. There are three main types of stability: steady-state, steady-focus, or saddle-focus. The increasing layer temperature enhances the system stochasticity, which can lead to the appearance of the Lorenz attractor in the phase portrait. The results obtained are in good agreement with the known experimental data.

1.	Khomenko A.V., Khomenko K.P., FalkoV.V. Nonlinear model of ice surface softening during friction // Condens. Matter Phys.-2016.-19.-P. 33002: 1–10 .