|DATE||August 19 (Thu), 2021|
|TITLE||Euler-type discretization of thermodynamic Cucker-smale model on complete Riemannian manifolds|
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.