Events
Department of Mathematics and Statistics
Texas Tech University
 | Wednesday
Apr. 8
|
| Algebra and Number Theory
No Seminar
|
Umbrella matrices are important structures that simultaneously exhibit both transformational and stochastic properties through the row-sum-one condition. This feature preserves the centroid of the space, enabling balanced transformations and opening a broad range of applications - from multidimensional geometry and kinematic modeling to inconsistency analysis in decision theory. The presentation reviews the existing research on umbrella matrices and outlines potential directions for future investigation.
US CDT is UTC-5. This Differential Geometry, PDE and Mathematical Physics seminar is available over zoom.
Abstract: The Euler equations of inviscid compressible flow have an underlying (Lie-Poisson) Hamiltonian formulation, with extensions to viscous flow given by various related metriplectic formulations. These formulations are at the heart of many fundamental properties, such as conservation laws, involution constraints and thermodynamics. However, despite this importantance, they have been largely unexplored for numerical modeling of compressible flow, especially when momentum is predicted instead of velocity. In this talk I will discuss progress in this area, based on discrete exterior calculus, a type of structure-preserving numerical discretization. Unlike most other compressible flow schemes, the proposed approach predicts entropy density instead of total energy density; does not use Riemann solvers; and stabilizes the scheme through a novel thermodynamically compatible viscous regularization that conserves energy while generating entropy around shocks. This allows direct control of the entropy generation, instead of it being implicit in the numerics. Additionally, extensions to related models such as MHD and compressible Euler-Maxwell are straightforward since the Lie-Poisson formulation is easily generalized.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math Basement)
ZOOM details:
- Choice #1: use this
Direct Link that embeds meeting and ID and passcode.
- Choice #2: Log into zoom, then join by manually entering the meeting ID and passcode ...
* Meeting ID: 949 9288 2213
* Passcode: Applied
TTU Math Circle Spring Flyer 6:30-7:30 PM Thursdays in the basement of Math, room 010
