Upcoming talks
Speaker: Shuang Liu, Department of Mathematics, UNT
Date: Monday, November 13, 2023
Time/location: GAB 461 @ 4pm
Title: Computational Moving Boundary Problems
Abstract:
Moving boundary (or often called "free boundary") problems are ubiquitous in nature and technology. A computational perspective of moving boundary problems can provide insight into the "invisible" properties of complex dynamics systems, advance the design of novel technologies, and improve the understanding of biological and chemical phenomena. However, challenges lie in the numerical study of moving boundary problems. Examples include difficulties in solving PDEs in irregular domains, handling moving boundaries efficiently and accurately, as well as computing efficiency difficulties. In this talk, I will discuss three specific topics of moving boundary problems, with applications to ecology (population dynamics), plasma physics (ITER tokamak machine design), and cell biology (cell movement). In addition, some techniques of scientific computing will be discussed.
Speaker: TBA
Date: Monday, November 27, 2023
Time/location: GAB 461 @ 4pm
Title: TBA
Abstract: TBA
Speaker: TBA
Date: Monday, December 4, 2023
Time/location: GAB 461 @ 4pm
Title: TBA
Abstract: TBA
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Past talks
Speaker: Paco Villarroya, Department of Applied Mathematics, Santa Clara University
Date: Wednesday, September 6, 2023
Time/location: GAB 461 @ 4pm
Title: A characterization of compactness for singular integral operators
Abstract: pdf
Speaker: Tamara Kucherenko, CUNY
Date: Monday, September 18, 2023
Time/location: GAB 461 @ 4pm
Title: Ergodic theory on coded shifts
Abstract: We discuss ergodic properties of coded shift spaces. A coded shift is defined as a closure of all bi-infinite concatenations of words from a fixed countable generating set. It turns out that many well-known classes of shifts are coded including transitive subshifts of finite type, S-gap shifts, generalized gap shifts, transitive Sofic shifts, Beta shifts, and many more. We derive sufficient conditions for the uniqueness of measures of maximal entropy based on the partition of the coded shift into its sequential set (sequences that are concatenations of generating words) and its residual set (sequences added under the closure). We will also outline some flexibility results for the entropy on the sequential and the residual set. (Joint work with M. Schmoll and C. Wolf)
Speaker: Natasha Sharma, Department of Mathematical Sciences, UT El Paso
Date: Monday, October 9, 2023
Time/location: GAB 461 @ 4pm
Title: Unconditional Energy Stability and Solvability for a C0 Interior Penalty Method for a Sixth-Order Cahn-Hilliard type equation modeling microemulsions
Abstract: Microemulsions are thermodynamically stable, transparent, isotropic single-phase mixtures of two immiscible liquids stabilized primarily by surfactants. Recently, microemulsion systems have emerged as an effective tool in capturing the static properties of ternary oil-water-surfactant systems with widespread applications such as enhanced oil recovery processes, the development of environmentally-friendly solvents, consumer and commercial cleaning product formulations, and drug delivery systems. Despite its applications, a major challenge impeding the use of these equations has been, and continues to be, a lack of understanding of these complex systems. Microemulsions can be modeled by means of an initial-boundary value problem for a sixth-order Cahn-Hilliard equation. In this talk, we present a numerical scheme for approximating the solutions to these sixth-order equations. To numerically approximate this sixth-order evolutionary equation, we introduce the chemical potential as a dual variable and consider a Ciarlet-Raviart-type mixed formulation consisting of a linear second-order parabolic equation and a nonlinear fourth-order elliptic equation. Here, the spatial discretization relies on a continuous interior penalty Galerkin finite element method while for the temporal discretization, we propose a first-order accurate time-stepping scheme. Theoretical properties of convergence, unique solvability, and unconditional stability of the proposed scheme will be discussed and through extensive numerical experiments, we will demonstrate the performance of the proposed scheme.
Speaker: Wesley Perkins, Lyon College
Date: Monday, October 23, 2023
Time/location: GAB 461 @ 2:30pm
Title: Modulational and Subharmonic Dynamics of Periodic Waves
Abstract: In this talk, we will explore some of the modern techniques used to study the stability and dynamics of periodic solutions to nonlinear partial differential equations (PDEs) arising from applications. We will develop some of the intuition for these techniques using ordinary differential equations (ODEs) and integral transforms. This intuition will then allow us to investigate the stability and dynamics of several PDEs when subjected to various types of perturbations.