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DTSTART;TZID=America/Los_Angeles:20261116T160000
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SUMMARY:AM Seminar: Heat Transport and Scalar Dissipation in Turbulent Flows: A Constructive Approach
DESCRIPTION:Presenter: Anuj Kumar\, Assistant Professor\, UC Davis \nDescription: Turbulent flows can transport heat and momentum much more efficiently than pure molecular diffusion alone. What flow structures enable this efficient transport and how can they sustain dissipation when diffusivity or viscosity is small? These questions are fundamental to understanding turbulence and have important applications in engineering. In this talk\, I will discuss a constructive approach to these questions through explicitly designed incompressible flows. We will first consider heat transport between walls held at different temperatures. Under a constraint on the power supply\, I will present a three dimensional branching construction that achieves the optimal heat transport scaling. By examining these designs carefully\, we will identify the physical mechanisms responsible for efficient heat transfer and discuss potential applications\, including the pressing problems of cooling in AI data centers. We will then turn to scalar turbulence. I will introduce a universal incompressible flow built from a carefully organized hierarchy of shear flows and explain how these constructions approach the sharp Obukhov–Corrsin regularity threshold for scalar dissipation. These constructions also exhibit eddy-diffusivity effect: advection mimics diffusion of order one even in the transport equation\, where molecular diffusion is entirely absent. Together\, these examples illustrate how the process of constructing flows that achieve sharp scaling laws can also reveal the mechanisms underlying enhanced transport and dissipation\, which are two key features of turbulence. \nAbout the speaker: Anuj Kumar is an Assistant Professor in the Department of Mathematics at the University of California Davis. His research lies at the intersection of fluid dynamics\, partial differential equations (PDEs) and applied mathematics\, combining computational\, mathematical analysis and theoretical approaches. Prior to joining UC Davis\, he was a Visiting Assistant Professor in the Department of Mathematics at the University of California Berkeley. He earned my Ph.D. in Applied Mathematics from the University of California Santa Cruz in 2023. \nThis seminar is hosted by Professor Pascale Garaud.
URL:https://events.ucsc.edu/event/am-seminar-heat-transport-and-scalar-dissipation-in-turbulent-flows-a-constructive-approach/
LOCATION:Jack Baskin Engineering\, Baskin Engineering 1156 High Street\, Santa Cruz\, CA\, 95064
CATEGORIES:Lectures & Presentations,Seminars
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SUMMARY:Bondar\, G. (AM) - Geometric and Graph Structured Optimal Transport for Learning and Control
DESCRIPTION:We motivate\, formulate\, and solve several structured optimal transportation (OT) problems for learning and control. The field of OT had its inception in 1781\, when Gaspard Monge sought the optimal map to transport mass from a given initial distribution to a desired terminal distribution. Both OT and its entropy-regularized variant\, the Schrödinger bridge problem (SBP)\, have catalyzed significant developments across mathematics. More recently\, theoretical and algorithmic developments in OT and SBP have found myriad applications in stochastic optimal control and generative AI. \nThe connecting theme across the problems studied in this dissertation is the presence of structure which can be exploited in their solution — for our work\, this structure arises from geometry underlying a solution space or from a graph capturing a correlation structure between distributional data. Our original contributions begin with automated verification and discovery of OT regularity\, followed by stochastic learning and control for resource allocation and scheduling in multi-core real-time systems\, where the problem has a natural graph structure. We also formulate and solve the problem of finding an optimal graph structure in a distribution-valued dataset where none is present. \nWhile graph-structured OT is a natural fit for data-driven stochastic learning problems\, the knowledge of system dynamics can impose geometric structure to the problem. In this dissertation\, we establish the equivalence between the stochastic optimal control and path space formulations of SBP over a compact connected Lie group. Additionally\, we develop\, analyze\, and validate a novel numerical solution scheme for the SBP with control-affine dynamics. Finally\, we investigate the application of Gromov-Wasserstein (GW) OT — a variant of the problem allowing for transport between incomparable spaces — for spatial proteomics. We show throughout our work how careful considerations of the underlying geometry and graph-structures can enable bespoke solutions for practical learning and control problems through optimal transport. \nEvent Host: Georgiy Bondar\, Ph.D. Candidate\, Applied Mathematics  \nAdvisor: Abhishek Halder \nZoom: https://ucsc.zoom.us/j/96361886043?pwd=U73TbafhzI7kgS7MYAFko3YEPVIxTb.1 \nPasscode: 564490
URL:https://events.ucsc.edu/event/bondar-g-am-geometric-and-graph-structured-optimal-transport-for-learning-and-control/
LOCATION:Engineering 2\, Engineering 2 1156 High Street\, Santa Cruz\, CA\, 95064
CATEGORIES:Ph.D. Presentations
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