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Seminar
FIELD Mathematics
DATE August 19 (Thu), 2021
TIME 18:00-19:00
PLACE Online
SPEAKER 심우주
HOST Kim, Doheon
INSTITUTE 서울대학교
TITLE Euler-type discretization of thermodynamic Cucker-smale model on complete Riemannian manifolds
ABSTRACT

In this talk, we discuss an Euler-type discretization of second order ODE models on connected, complete and smooth Riemannian manifolds, and study its application to thermodynamic Cucker-smale(TCS) model. Our proposed discrete model is expressed in terms of an exponential map on a tangent bundle endowed with the Sasaki metric. Compared to projection-based discretization on manifolds, it is embedding free and enjoys the same structural properties as the corresponding continuous models. For the proposed model, we provide a sufficient framework leading to asymptotic velocity alignment of TCS particles. For the unit-d sphere (Sd), we provide explicit representations of the Sasaki metric and the corresponding geodesics on TSd, and show that the TCS model exhibits a dichotomy in asymptotic spatial patterns.

zoom link: https://us02web.zoom.us/j/88624015514?pwd=UnA1UW5RWCtQTEEwNWJVOGRobnZ3UT09

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