Applied Math Seminar
I am co-coordinating the Applied Math Seminar with Dr. Chuntian Wang at The University of Alabama in Spring 2024.
Time: Friday at 11:00am - 11:50am (unless otherwise noted).
Format: either virtually or in person at Gordon Palmer Hall 346.
Time: Friday at 11:00am - 11:50am (unless otherwise noted).
Format: either virtually or in person at Gordon Palmer Hall 346.
Schedule
Time | Location | Speaker | Title |
---|---|---|---|
Jan 19, 11am | GP 346 | Ihsan Topaloglu | A Variational model involving nonlocal interactions of Wasserstein type |
Feb 16, 11am | GP 346 | Yalchin Efendiev | Multicontinuum homogenization and applications |
Feb 27, 11am | GP 346 | Lynn Schreyer | Compartment models with memory |
Mar 8, 11am | GP 346 | Patrick Guidotti | Connecting the dots |
Mar 29, 11am | GP 346 | Jiuyi Zhu | Bounds of nodal sets of eigenfunctions |
Apr 22, 11am | GP 346 | Miloud Sadkane | On the stability radius for linear time-delay systems |
Abstracts
- Jan 19, 2024
Ihsan Topaloglu
Title: A Variational model involving nonlocal interactions of Wasserstein type
Abstract: In this talk I will consider a variational problem which appears in models of bilayer membranes. After introducing and deriving the model I will establish the existence of volume-constrained minimizers where the energy functional consists of two competing terms: a surface energy term penalizing transitions between sets and a nonlocal energy involving the Wasserstein distance between equal volume sets. In the second part of the talk I will consider the maximization of the minimum Wasserstein distance between two given sets, and show that this maximum is obtained by a micella. These results are drawn from joint works with Almut Burchard, Davide Carazzato, Michael Novack, and Raghavendra Venkatraman. - Feb 16, 2024
Yalchin Efendiev
Title: Multicontinuum homogenization and applications
Abstract: In this talk, I will talk about general approaches for multiscale modeling (closely related to porous media applications). I will mainly focus on numerical approaches, where multiscale finite element basis functions are constructed and used in approximating the solution. In these approaches, macroscopic equations are formed via some variational formulations of the problem. I will discuss how these approaches are used in deriving, so called upscaling techniques and the relation to well known upscaling methods. The concepts discussed in the talk are used for linear and nonlinear problems. I will discuss some applications. - Feb 27, 2024
Lynn Schreyer
Title: Compartment Models with Memory
Abstract: The beauty and simplicity of compartment modeling makes it a useful approach for simulating dynamics in an amazingly wide range of applications, including pharmacokinetics (where e.g. a liver is considered a compartment), global carbon cycling (different depths of soils are considered compartments), and epidemiology (SIR models!) and population dynamics. These contexts, however, often involve compartment-to-compartment flows that are physically incongruent with the conventional assumption of complete mixing that results in exponential residence times in linear models. Here we detail a general method for assigning any desired residence time distribution to a given intercompartmental flow, extending compartment modeling capability to transport operations, power-law residence times, diffusions, etc., without resorting to composite compartments, fractional calculus, or partial differential equations (PDEs) for diffusive transport. This is achieved by writing the mass exchange rate coefficients as functions of age-in-compartment as done in one of the first compartment models (epidemiology!) in 1917, at the cost of converting the usual ordinary differential equations to a system of first-order PDEs. Example calculations demonstrate incorporation of advective lags, advective-dispersive transport, power-law residence time distributions, or diffusive domains in compartment models. We also provide simulations of the generalized SIR model presented by Kissler et al. (2020) 11 compartment-model for the COVID epidemic. - Mar 8, 2024
Patrick Guidotti
Title: Connecting the dots
Abstract: We revisit the well-known kernel method of interpolation and, by taking a slightly unusual point view, show how it can be used (and modified in a natural way) for the purpose of gaining insight into the (geometric) structure of scattered data points such as point clouds. One of the advantages of the method is that it is global and does not require any direct explicit understanding of data points neighborhoods. - Mar 29, 2024
Jiuyi Zhu
Title: Bounds of nodal sets of eigenfunctions
Abstract: Motivated by Yau's conjecture, the study of the measure (sizes) of nodal sets (zero-level sets) of eigenfunctions has been attracting much attention. We investigate the nodal sets of Steklov eigenfunctions, Neumann eigenfunctions, and Dirichlet eigenfunctions in the domain and on the boundary of the domain. For the analytic domain, we show the sharp upper bounds of interior nodal sets for Steklov eigenfunctions, and the sharp upper bounds of the intersections of nodal sets with the boundary for Neumann and Dirichlet eigenfunctions. Furthermore, we will discuss the unified way to obtain the sharp upper bounds of nodal sets for eigenfunctions of bi-Laplace equations. - Apr 22, 2024
Miloud Sadkane
Title: On the stability radius for linear time-delay systems
Abstract: In this talk, an algorithm is proposed to compute the stability radius of a linear time-delay differential system. The exponential factor in the characteristic equation is replaced by its Padé approximant. This reduces the computation to that of imaginary eigenvalues of special matrix polynomials. A bisection method is then used to compute lower and upper bounds of the stability radius. The algorithmic aspects are discussed and illustrated numerically.