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)
Seasonal Prediction Potential for Springtime Dustiness in the United States
Abstract: Severe dust storms reduce visibility and cause breathing problems
HOST: Van Vleck
2:00 PM Andrew Steyer (Sandia), Time-stepping in the E3SM nonhydrostatic atmosphere dynamic core
HOST: Van Vleck
Zoe Zhu (Harvard), Moiré of moiré: modeling mechanical relaxation and electronic states of incommensurate trilayer van der Waals heterostructures
Abstract: Incommensurate stacking provides an intriguing avenue for manipulating the physical properties of layered two-dimensional materials, but is a challenging problem from a theoretical perspective. Here, we present a multiscale model to obtain the mechanical relaxation pattern and electronic structure of twisted trilayer van der Waals heterostructures with two independent twist angles. This serves as a prototype system of a generally incommensurate system without a supercell description. To study mechanical properties, we adopt configuration space as a natural description of incommensurate layers, which describes the local environment of each atomic position. We minimize the total energy, parameterized using Density Functional Theory calculations, to obtain the relaxation pattern. For the electronic properties, we focus on twisted trilayer graphene. We adopt a k.p effective theory derived from a low-energy expansion around the Dirac point in monolayer graphene. Our results suggest that the twisted trilayer systems are interesting from theoretical and mathematical points of view, as well as a promising platform to study correlated physics.
Bob Eisenberg (Rush Medical), Cancelled
Hongguo Xu (University of Kansas), A core-chasing symplectic QR algorithm
Abstract: In this talk we will introduce the core-chasing version of the
QR algorithm for computing a Schur form. We will show then how to
adopt the idea to develop a core-chasing version of structure
preserving QR algorithm for a special type of symplectic matrices.
|November 27||Thanksgiving Break|
Bob Eisenberg (Rush Medical), The Lens of the Eye: Bidomain Model of an Osmotic Pump
Abstract: The lens of the eye has no blood vessels to interfere with vision. The lens is far too large for diffusion to provide food and clear wastes. Experimental, theoretical and computational work has shown that the lens supports its own microcirculation. It is an osmotic pump that implements what physiologists have long believed “Convection provides what diffusion cannot.” We introduce a general (non-electro-neutral) model that describes the steady-state relationships among ion fluxes, water flow and electric field inside cells, and in the narrow extracellular spaces within the lens. Using asymptotic analysis, we derive a simplified model exploiting the numerical values of physiological parameters. The model reduces to first generation ‘circuit’ models and shows the basis of computer simulations too large to easily understand. The full model resolves paradoxes that have perplexed molecular biologists: crucial physiological properties do not depend as expected on the molecular species involved in the coupling of lens fibers.