Computational and Applied Mathematics (CAM) Seminar
CAM seminar talks are held on Wednesday from 2:00-3:00 PM in Snow Hall 306, unless otherwise noted.
Please contact Erik Van Vleck for arrangements.
|September 4||Organization meeting|
Hamid Mofidi (University of Kansas), Reversal potential of ionic channels via cPNP models
Abstract: Recent years have seen the proliferation of smart network-connected devices that exist on the ”edge” of large control systems that are capable of distributed calculations. In particular, the power grid has become progressively more complex, especially with the incorporation of distributed energy resources (DER’s). This increase of ”smart” devices results in a new attack surface reinforcing the need to avoid single points of failure that are common in centralized systems. Additionally, these devices also communicate unreliably with the network, meaning that changes in communication should not halt the entire distributed calculation. In order to remove these kinds of vulnerabilities, we need resilient algorithms to implement on decentralized infrastructure networks. This motivates the study of algorithms which can make use of collaborative autonomy. In this talk, we present a parallel asynchronous Jacobi iteration where each process is responsible for updating and distributing several components of the solution vector.
Abstract: We consider the linear dynamics of spectrally stable periodic stationary solutions of the Lugiato-Lefever equation (LLE). The LLE takes the form of an NLS equation with damping and external forcing, and has been widely studied in nonlinear fiber optics. Our main result establishes the linear asymptotic stability of spectrally stable periodic solutions of the LLE to perturbations which are localized , i.e. integrable on the line. We further show the long-time modulational dynamics are governed by an associated averaged system (known as the Whitham system). Specifically, this work justifies the predictions of Whitham’s theory of modulations for the LLE at the level of linear dynamics. This is joint work with Mariana Haragus (Univ. Bourgogne Franche-Comete) and Wesley Perkins (KU).
Mark Hoefer (University of Colorado Boulder), Five Conservative Regularizations of the Hopf Equation
Abstract: The Hopf equation, also known as the inviscid Burgers equation, is the simplest nonlinear wave equation and an introductory example for students studying hyperbolic, quasi-linear partial differential equations. The initial value problem exhibits finite time singularity formation (gradient catastrophe), which can be regularized in many ways. One common approach that is inspired by physical problems, e.g., gas dynamics, is to add higher order, dissipative smoothing terms and study the zero dissipation limit. Under quite general conditions, this vanishing-viscosity technique offers both mathematical and physical justifications for weak (entropy) solutions and the Rankine-Hugoniot conditions for shock waves. A completely different approach is to add higher order, conservative (dispersive) terms and study the small dispersion limit. This talk will present five distinct, physical, conservative regularizations that yield different small dispersion behavior for initial value problems. A rich variety of dispersive shock wave solutions for these models will be analyzed using nonlinear wave (Whitham) modulation theory, numerical simulation, and experiment. All conservative regularizations considered result in solutions that significantly deviate from the vanishing-viscosity approach.
Bing Pu (University of Kansas, Department of Geography and Atmospheric Science), TBA
HOST: Van Vleck
2:00 PM Andrew Steyer (Sandia), TBA
HOST: Van Vleck
Zoe Zhu (Harvard), TBA
Bob Eisenberg (Rush Medical), TBA
|November 20||Cassidy Krause (University of Kansas), TBA|
|November 27||Thanksgiving Break|
|December 4||Hongguo Xu (University of Kansas), TBA|