MIT Free English Class is for international students, sholars, spouses. Twenty seven years ago we created a community to welcome the nations to MIT and assist with language and friendship. Join our Tuesday/Thursday conversation classes around tables inside W11-190.

The Chaplains invite you to take a brief pause for refreshments and conversation as you cross campus this month. Find us in the Stata Street on Tuesday afternoons. Look for the rocking chairs!

Speaker: Kyle McKeeTitle: Circulation and Transport in Hele-Shaw FlowsAbstract:Viscously-dominated flow between two closely-spaced plates is described by two-dimensional potential flow according to the standard Hele-Shaw approximation. When driven exclusively by pressure, the class of realizable potential flows is highly restricted: only flows with exactly zero circulation are possible. For example, the Hele-Shaw experiments presented in Van Dyke's famous Album of Fluid Motion clearly illustrate this zero-circulation restriction. In the present work, we demonstrate how the Hele-Shaw cell can be used to capture flows with circulation - by using a conducting fluid and applying a constant magnetic field normal to the plates. We describe the physical picture and experimentally re-create canonical Hele-Shaw flows from Album of Fluid Motion now with arbitrary amounts of circulation induced by electromagnetic effects. The experimental flows are well described by our accompanying theoretical model. In the second part of this talk, I will segue into a related investigation of transport (advection-diffusion) in multiply-connected potential flows. By constructing a suitable conformal mapping, which is computed using recently developed methods (the AAA algorithm), we simplify the governing equations. We then formulate a boundary-integral solution to the governing equations in the mapped domain, where the exact Green's function is known. Distinct scalings for the rate of transport (Nusselt number) under various boundary conditions are revealed.

Ten minutes for your mind@2:50 every day at 2:50 pm in multiple time zones:Europa@2:50, EET, Athens, Helsinki (UTC+2) (7:50 am EST) https://us02web.zoom.us/j/88298032734Atlantica@2:50, EST, New York, Toronto (UTC-4) https://us02web.zoom.us/j/85349851047Pacifica@2:50, PST, Los Angeles, Vancouver (UTC=7) (5:50 pm EST) https://us02web.zoom.us/j/85743543699Almost everything works better again if you unplug it for a bit, including your mind. Stop by and unplug. Get the benefits of mindfulness without the fuss.@2:50 meets at the same time every single day for ten minutes of quiet together.No pre-requisite, no registration needed.Visit the website to view all @2:50 time zones each day.at250.org or at250.mit.edu

Speaker: Yoon-Joo Kim (Columbia University)Title: The Néron model of a Lagrangian fibrationAbstract:Singular fibers in minimal elliptic fibrations were classified by Kodaira and Néron in the 1960s. In his proof, Néron constructed and systematically used a special group scheme acting on an elliptic fibration. This group scheme is now called the Néron model. A Lagrangian fibration is a higher-dimensional generalization of an elliptic fibration. Néron’s theory is restricted to 1-dimensional bases, so one cannot use Néron’s original approach to study higher-dimensional Lagrangian fibrations. The higher-dimensional analog of Néron’s definition was recently proposed by David Holmes. Quite unfortunately, Holmes also showed that such a generalized Néron model often fails to exist, even in simple cases. In this talk, we show that Holmes’s generalized Néron model does exist for an arbitrary projective Lagrangian fibration of a smooth symplectic variety, under a single assumption that the Lagrangian fibration has no fully-nonreduced fibers. This generalizes Néron’s result to many higher-dimensional Lagrangian fibrations. Such a construction has several applications. First, it extends Ngô's results on Hitchin fibrations to many Lagrangian fibrations. Second, it allows Lagrangian fibrations to be considered as a minimal model-compactification of a smooth commutative group scheme-torsor. Third, it provides a tool to study birational behaviors of Lagrangian fibrations. Finally, the notion of a Tate-Shafarevich twist can be understood via the Néron model.

Speakers: Jared Speck (Vanderbilt University)Title: The Einstein-Euler Free Boundary Problem in Spherical SymmetryAbstract: I will discuss my forthcoming paper with M. Disconzi on spherically symmetric solutions to the Einstein–Euler equations. The main result is local well-posedness for a class of initial data satisfying the physical vacuum condition. Our work provides the first rigorous existence result for a model of a dynamic, self-gravitating relativistic gaseous star with compact spatial support.