[Landau ITP Seminars] Friday 05.06.2020

[alexpro]

Уважаемые сотрудники ИТФ,

На заседании Ученого совета ИТФ в пятницу 29 мая в режиме онлайн будет
заслушан доклад:


Nikolay Stepanov, Mikhail Skvortsov

Inverted pendulum driven by a horizontal random force: statistics of the 
non-falling trajectory and supersymmetry

We study stochastic dynamics of an inverted pendulum subject to a random 
force in the horizontal direction. Considered at the entire time axis, 
the problem admits a unique solution which always remains in the upper 
half plane. We develop a new technique for treating statistical 
properties of this unique non-falling trajectory. In our approach based 
on the supersymmetric formalism of Parisi and Sourlas, statistics of the 
non-falling trajectory is expressed in terms of the zero mode of a 
corresponding transfer-matrix Hamiltonian. The emerging mathematical 
structure is similar to that of the Fokker-Planck equation, but it is 
rather written for the «square root» of the distribution function.
We derive the specific boundary conditions that correspond to the 
non-falling trajectory. Our results for the distribution function of the 
angle and its velocity at the non-falling trajectory are in perfect 
agreement with direct numerical simulations of the stochastic pendulum 
equation. In the limit of very strong noise, an exact analytical 
solution is obtained.


Ссылка для подключения к семинару - http://bbb2.itp.ac.ru/b/a-o-ytc-2k3