[Landau ITP Seminars] [ITP Staff] Friday 05.06.2020

[Serge Krashakov]

Уважаемые сотрудники ИТФ,

На заседании Ученого совета ИТФ в пятницу 5 июня в режиме онлайн будет 
заслушан доклад:


04.06.2020 19:30, alexpro пишет:
>
>
> _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
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