Videolibrary
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
Video Library
Archive
Most viewed videos

Search
RSS
New in collection






International Conference "Analytic Theory of Differential and Difference Equations" Dedicated to the Memory of Andrey Bolibrukh
February 1, 2021 20:00, online, Moscow
 


Application of Painlevé 3 equations to dynamical systems on 2-torus modeling Josephson junction

Yulia Bibilo

University of Toronto
Video records:
MP4 248.7 Mb
Materials:
Adobe PDF 3.1 Mb

Number of views:
This page:79
Video files:16
Materials:8


Видео не загружается в Ваш браузер:
  1. Проверьте с Вашим администратором, что из Вашей сети разрешены исходящие соединения на порт 8080
  2. Сообщите администратору портала о данной ошибке

Abstract: We consider a family of dynamical systems modeling overdamped Josephson junction in superconductivity. We focus on the family's rotation number as a function of parameters. Those level sets of the rotation number function that have non-empty interiors are called the phase-lock areas. It is known that each phase-lock area is an infinite garland of domains going to infinity in the vertical direction and separated by points. Those separation points that do not lie on the abscissa axis are called constrictions.
The model can be equivalently described via a family of linear systems (Josephson type systems) on the Riemann sphere. In the talk we will discuss isomonodromic deformations of the Josephson type systems – they are derived by Painlevé 3 equations. As an application of this approach, we present two new geometric results about the constrictions of the phase-lock areas solving two conjectures about them. We also present some open problems.
The talk is based on a joint work with A. A. Glutsyuk.

Materials: bolibr2021_2.pdf (3.1 Mb)

Language: English

SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru
 
Contact us:
 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021