V.Vasan:Markovian embedding of fractional differential eq. with application to prob. in hydrodynamic

Описание: Date: Friday, 5 September, 2025 - 15:00 to 16:00 CEST
Title : Markovian embeddings of fractional differential equations with applications to problems in hydrodynamics
Speaker: Vishal Vasan, International Centre for Theoretical Sciences, Tata Institute of Fundamental Research

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy
Organizers : Pavan Pranjivan Mehta** and Arran Fernandez***
** SISSA, International School of Advanced Studies, Italy
*** Eastern Mediterranean University, Northern Cyprus

Keywords: Numerical methods, Fractional differential equations, Fluid dynamics

Abstract

The Maxey–Riley-Gatignol equation, a fractional-differential equation, has been extensively used by the fluid dynamics community to study the dynamics of small inertial particles in fluid flow. The nonlocal behaviour in time arises from the interaction of the fluid disturbance and the particle. In this talk, I’ll summarise a perspective on the problem that leads to a Markovian system, in a larger-dimensional state space. I will then show how this perspective can be xploited to obtain a memory-efficient numerical method for systems with nonlocal behaviour in time, whenever a particular ‘spectral representation’ is available. This more general property also arises in other applications such as the Stefan problem of melting ice, hydrodynamic walkers, among others.

Biography

Vishal Vasan is a faculty member at the International Centre for Theoretical Sciences, a centre of the Tata Institute of Fundamental Research. Dr Vasan obtained a BE in Mechanical Engineering from Anna University, an MS (Mechanical Engg.) from Arizona State University and then an MS and PhD in Applied Mathematics from the Univ. of Washington. Dr Vasan was the S Chowla Research Asst. Professor in the Dept of Mathematics at Pennsylvania State University from 2012-2015 before moving to ICTS. His main interest is the theoretical and numerical analysis of partial differential equations as well as their applications, specifically inverse problems. The application domains include large-scale atmospheric and ocean dynamics, Bose-Einstein condensates and cold atoms, water waves and coastal engineering, growth and its regulation in biological tissues among others. More recently Dr Vasan has been focusing on the theory underlying the data-driven viewpoint of dynamical systems.

Bibliography

[1] S Ganga Prasath, Vishal Vasan and Rama Govindarajan. “Accurate solution method for the Maxey–Riley equation, and the effects of Basset history.” In: Journal of Fluid Mechanics 868 (2019), pp. 428–460
[2] Divya Jaganathan, Rama Govindarajan and Vishal Vasan. “Explicit integrators for nonlocal equations: The case of the Maxey-Riley-Gatignol equation.” In: Quarterly of Applied Mathematics 83.1 (2025), pp. 135–158
[3] Divya Jaganathan, and Rahil N Valani. “Markovian embedding of nonlocal equations using spectral representation.” arXiv preprint arXiv:2402.00009 (2023).