Events
Department of Mathematics and Statistics
Texas Tech University
 | Monday
Feb. 12
|
| Algebra and Number Theory
No Seminar
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We examine how stationary solutions to Galerkin approximations of the Navier--Stokes equations behave in the limit as the Grashof number $G$ tends to $\infty$. An appropriate scaling is used to place the Grashof number as a new coefficient of the nonlinear term, while the body force is fixed. A new type of asymptotic expansion, as $G\to\infty$, for a family of solutions is introduced. Relations among the terms in the expansion are obtained by following a procedure that compares and totally orders positive sequences generated by the expansion. The same methodology applies to the case of perturbed body forces and similar results are obtained. We demonstrate with a class of forces and solutions that have convergent asymptotic expansions in $G$. All the results hold in both two and three dimensions, as well as for both no-slip and periodic boundary conditions.
In this talk, I will indicate how the sheaf topos of smooth sets serves as a sufficiently powerful and convenient context to host classical (bosonic) Lagrangian field theory. As motivation, I will recall the textbook description of variational Lagrangian field theory, and list desiderata for an ambient category in which this can rigorously be phrased. I will then explain how sheaves over Cartesian spaces naturally satisfy all the desiderata, and furthermore allow to rigorously formalize several more field theoretic concepts. Time permitting, I will indicate how the setting naturally generalizes to include the description of (perturbative) infinitesimal structure, fermionic fields, and (gauge) fields with internal symmetries. This is based on joint work with Hisham Sati. Please email the seminar organizer for Zoom meeting details.
Abstract. Sparse grids is a common strategy for mitigating the curse of dimensionality for problems with moderate number of dimensions. First developed in the contest of multidimensional quadrature, the approach has been very successful when handling problems of interpolation, regression and finding the solutions to partial differential equations. We will look at sparse grid interpolation and the theoretical results that guarantee convergence for different classes of problems, and we will then consider the challenges in extending the approach to a context of approximating discontinuous functions. Finally, we will conclude with some of our latest results in extending sparse grids to finite element and discontinuous Galerkin settings.
When: 4:00 pm (Lubbock's local time is GMT -6)
Where: room MATH 011 (basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link
Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 944 4492 2197
* Passcode: applied
 | Thursday
Feb. 15
6:30 PM
MA 108
|
| Mathematics Education
Math Circle
Aaron Tyrrell
Mathematics and Statistics, Texas Tech University
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Math Circle spring poster
abstract noon CST (UT-6)