Noise Effect on Ice Surface Softening During Friction

Financial Crimes in the Fiscal Sphere as a Threat to the Economic Security of Ukraine

“…Аналіз останніх досліджень і публікацій. Питання попередження, виявлення, розкриття та розслідування податкових злочинів, ефективність діяльності податкової міліції досліджували такі науковці, як: П. Цимбал [2], В. Хоменко [3]. Проблеми здійснення фінансових розслідувань у сфері протидії легалізації злочинних доходів в Україні висвітлювали у своїх працях С. Чернявський, О. Користін, В. Некрасов, Л. Герасименко, О. Тихонова, А. Чубенко, В. Мельник [4], Д. Долбнєва [5].…”

Time series analysis of friction force at self-affine mode of ice surface softening

“…In figure 1, the time dependencies of frictional force are depicted, which are built on the basis of approximation 𝐹 (𝑡) = 𝐴𝐺 𝜀 |𝜀(𝑡)| in accordance with [18,20]. Therein, we have shown that 𝐹 (𝑡) corresponds to the experiments described in [11][12][13][14][15][16][17] for the following quantities: 1) the strain relaxation time 𝜏 𝜀 ≈ 0.1 − 5 s; 2) the contact area 𝐴 ≈ 10 −6 − 10 −1 m 2 that is typical of friction of a polymer (poly(methyl methacrylate) PMMA), rubber and steel on ice [11,16,17] as well as for polycrystalline freshwater and saline ice over itself [12][13][14][15]; 3) the shear modulus of ice 𝐺 𝜀 ≈ 0.1 − 10 MPa, i.e., yield stress [11].…”

“…It should be noted that the formation of two-mode friction force distributions is actually observed in experiments [5,6,29]. In addition, one of the authors proposed a theory of the formation of a two-mode rubbing force distribution, based on a stochastic approach [18,20]. In these models, small and large friction were formally considered as different types of surface structures.…”

“…Experimental data and calculations [11][12][13][14][15][16][17] have shown that intermittent (stick-slip) friction can be a stochastic regime in which the static and kinetic friction forces change randomly in time. Therefore, the previously obtained transition model was supplemented by taking into account Gaussian fluctuations that play the role of external forces and lead to stick-slip friction [18]. In the basic equations, the intensities of shear strain 𝜀 and stress 𝜎, and temperature 𝑇 noises 𝐼 𝜀 , 𝐼 𝜎 , and 𝐼 𝑇 were introduced.…”

“…The case 𝜀 ≠ 0 meets its softening. The 𝜀 ≠ 0 appears at temperature 𝑇 𝑒 above critical 𝑇 𝑐0 = 1 + 𝑔 −1 , but at small 𝑇 𝑒 𝑇 𝑐0 , the ice solidifies [10,18,20].…”