Numerical Analysis Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Andrea Bonito, Texas A&M University

Title: Finite Element Approximations of Bilayer Plates

Abstract: The bending of bilayer plates is a mechanism which allows for large deformations via small externally induced lattice mismatches of the underlying materials. We discuss its mathematical modeling, which consists of a nonlinear fourth order problem with a pointwise isometry constraint. We devise a finite element discretization based on Kirchhoff quadrilaterals and prove its Gamma-convergence. We propose a gradient flow based iterative method that decreases the energy and study its convergence to stationary configurations. We explore its performance, as well as reduced model capabilities, via several insightful numerical experiments involving large (geometrically nonlinear) deformations. We conclude with applications to drug delivery, which requires replacing the gradient flow relaxation by a physical flow.

Frontiers in Mathematics Lecture Series

Time: 4:00PM - 5:00PM

Location: Blocker 220

Speaker: Alicia Dickenstein, University of Buenos Aires

Title: Computational algebraic geometry and biochemical reaction networks (Colloquium)

Abstract: In recent years, techniques from computational algebraic geometry have been successfully used to address mathematical challenges in systems biology. (Bio)chemical reaction networks define systems of ordinary differential equations with (in general, unknown) parameters. Under mass-action kinetics, these equations depend polynomially on the concentrations of the chemical species. Biologically-relevant steady states correspond thus to the positive real solutions of a structured system of polynomial equations. I will give a gentle introduction to the subject, based on joint work with C. Conradi, E. Feliu, S. Mueller, M. Perez Millan, G. Regensburger, and A. Shiu.  One of the major questions is to preclude or to guarantee multiple positive steady states.  I will explain this motivation and I will present necessary and sufficient conditions in terms of sign vectors.  I will also describe the structural properties of MESSI biological systems, which include all the popular mechanisms which present modifications of type enzyme substrate or swap with intermediates. 

AMUSE

Time: 6:00PM - 6:15PM

Location: BLOC 113

Speaker: Amanda Schroeder, Texas A&M University, Department of Mathematics

Title: In the Mind of an Actuary Intern

Abstract: A brief overview of the daily tasks of an actuarial analyst intern at USAA. From social functions to functions that compute insurance premiums, an intern has many jobs. I will discuss the project I was given this summer as well as the general intern environment at USAA.

AMUSE

Time: 6:20PM - 6:35PM

Location: BLOC 113

Speaker: Madeline Hansalik, Texas A&M University, Department of Mathematics

Title: Magnetic Spectral Decimation on the Diamond Fractal

Abstract: The Laplacians for a large class of self-similar fractals and fractal graphs exhibit a property called spectral decimation, in which the spectra of different levels of approximation are related by a dynamical system involving a rational function. Expanding upon the work of Malozemov and Teplyaev, we extend some aspects of the spectral decimation method from the Laplacian operator to a magnetic Laplacian operator, and use this to numerically investigate properties of the magnetic spectrum of this operator on the diamond fractal. In particular, we identify the correct unitary transformations and projections to obtain the aforementioned rational functions.

AMUSE

Time: 6:40PM - 6:55PM

Location: BLOC 113

Speaker: James Cain, Texas A&M University, Department of Mathematics

Title: The Decline of Pension Plans in Corporate America

Abstract: In a modern world, preparing for the future is increasingly important. The three forms of retirement income, referred to as social security, personal savings, and pension plans, are continuously changing. As the pressure from governing bodies continues to demand fully funded retirement plans, companies are terminating their current pension plans. In this presentation, I will discuss some of the reasons companies are leaving their plans behind and the implications of the decline of pension plans.