Oleg Zayats | Searcharxiv

arXiv2019

Skew Brownian motion with dry friction: The Pugachev-Sveshnikov approach

The Caughey-Dieness process, also known as the Brownian motion with two valued drift, is used in theoretical physics as an advanced model of the Brownian particle velocity if the resistant force is assumed to be dry friction. This process also appears in many other fields, such as applied physics, mechanics, astrophysics, and pure mathematics. In the present paper we are concerned with a more general process, skew Brownian motion with dry friction. The probability distribution of the process itself and of its occupation time on the positive half line are studied. The approach based on the Pugachev-Sveshnikov equation is used.

math.PR↗

arXiv2017

On energy dissipation in a friction-controlled slide of a body excited by random motions of the foundation

We study a friction controlled slide of a body excited by random motions of the foundation it is placed on. Specifically, we are interested in quantities such as displacement, traveled distance, and energy loss due to friction. Assuming that the random excitation is switched off at some time, it is shown that the problem can be treated in an analytic, explicit, manner. Particularly, we derive formulas for the moments of the displacement and distance, and also for the average energy loss. To accomplish that we use the Pugachev-Sveshnikov equation for the characteristic function of a continuous random process given by a system of SDEs. This equation is solved by reduction to a parametric Riemann boundary value problem of complex analysis.

math.PR↗