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Texas A&M University

Events for 03/22/2023 from all calendars

Numerical Analysis Seminar

iCal  iCal

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Dr Francis Aznaran, University of Oxford

Title: Finite element methods for the Stokes–Onsager–Stefan–Maxwell equations of multicomponent flow

Abstract: The Onsager framework for linear irreversible thermodynamics provides a thermodynamically consistent model of mass transport in a phase consisting of multiple species, via the Stefan–Maxwell equations, but a complete description of the overall transport problem necessitates also solving the momentum equations for the flow velocity of the medium. We derive a novel nonlinear variational formulation of this coupling, called the (Navier–)Stokes–Onsager–Stefan–Maxwell system, which governs molecular diffusion and convection within a non-ideal, single-phase fluid composed of multiple species, in the regime of low Reynolds number in the steady state. We propose an appropriate Picard linearisation posed in a novel Sobolev space relating to the diffusional driving forces, and prove convergence of a structure-preserving finite element discretisation. This represents some of the first rigorous numerics for the coupling of multicomponent molecular diffusion with compressible convective flow. The broad applicability of our theory is illustrated with simulations of the centrifugal separation of noble gases and the microfluidic mixing of hydrocarbons.

Topology Seminar

iCal  iCal

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Lei Chen, University of Maryland

Title: Mapping class groups of circle bundles over a surface

Abstract: In this talk, we study the algebraic structure of mapping class group Mod(M) of 3-manifolds M that fiber as a circle bundle over a surface S1 → M → Sg. We prove an exact sequence 1 → H1(Sg) → Mod(M) → Mod(Sg) → 1, relate this to the Birman exact sequence, and determine when this sequence splits. This is joint work with Bena Tshishiku.


iCal  iCal

Time: 6:00PM - 7:00PM

Location: BLOC 306

Speaker: Matthias Maier, Texas A&M University

Title: Mathematical Modeling, Fluids, and Airplanes that Shouldn't Fly

Abstract: Flight has fascinated mankind for millennia. It was not until the beginning of the 20th century that "lift" could be used for the first heavier-than-air flight. Even though airplanes are nowadays a central tool of transportation, the notion of flight remains a fascinating topic with a number of questions still unresolved today. In this talk we will examine a classical theory of flight based on "potential flows." These are flows that can be described (in 2D) as a complex-valued function defined on the complex number plane. Based on this representation we will derive two fundamental theorems for potential flow, Blasius' Thorem and the Kutta-Joukowsky Theorem, that describe the "lift" of a body in potential flow.