Computational and Applied Mathematics (CAM) Seminar

Fall, 2009 – Spring, 2010

CAM seminar talks are held on Wednesday from 2:00-3:00PM in Snow Hall 306, unless otherwise noted.

Previous CAM talks: Fall, 2006; Spring, 2007; Fall, 2007; Spring, 2008; Fall, 2008; Spring, 2009

KU Numerical Analysis Group Webpage

Date	Speaker/Institution	Title and Abstract
Sept 2	Organizing meeting
Sept 9	Yaozhong Hu/KU	Title:  Some results on numerical solutions of stochastic differential equations. Abstract:  I will talk about some results that I have done some years ago about numerical solutions of stochastic (ordinary) differential equation. Particularly I will discuss how to make partition to increase the speed of convergence.  I will also mention some other work as well some recent relevant work.
Sept 16	Aaron Hoffman/Boston U	Title: "Nearly two-soliton" solutions in the Fermi-Pasta-Ulam-Tsingou model Abstract: We study the interaction of small amplitude, long-wavelength solitary waves in the Fermi-Pasta-Ulam Tsingou model with general nearest neighbor interaction potential.  These solutions are close to the linear superposition of two solitary waves for large positive and negative values of time; for intermediate values of time these solutions describe the interaction of two pulses.  These solutions are stable with respect to perturbations in $\ell^2$ and asymptotically stable with respect to perturbations which decay exponentially at spatial $\pm \infty$.
Sept 23	Hongguo Xu/KU	Title: Newton's Iteration for Polar Decomposition - Scaling and Backward Stability Abstract: We review Newton's iteration for computing the matrix polar decomposition and the scaling strategies for accelerating the convergence. We introduce a simple scaling strategy. With this scaling, Newton's method converges within 9 iterations on a computer with double precision for not extremely ill-conditioned matrices.  Moreover, it is proved that Newton's method with this scaling is backward stable.
Sept 30	Weizhang Huang/KU	Title: A Variational Mesh Adaptation Method Based on Mesh Equidistribution and Alignment
Oct 7	Hermen Jan Hupkes/Brown U	Title: Travelling Pulses for the Discrete FitzHugh-Nagumo System Abstract: The existence of fast travelling pulses of the discrete FitzHugh Nagumo equation is obtained in the weak-recovery regime. This result extends to the spatially discrete setting the well-known theorem that states that the FitzHugh-Nagumo PDE exhibits a branch of fast waves that bifurcates from a singular pulse solution. The key technical result that allows for the extension to the discrete case is the Exchange Lemma that we establish for functional differential equations of mixed type.
Oct 14	Erik Van Vleck/KU	Title: Approximation of Stability Spectra and Applications Abstract: We consider techniques for the approximation of stability spectra: Lyapunov exponents and Sacker-Sell spectrum. A perturbation theory is developed based upon matrix factorizations of fundamental matrix solutions. The result is a computable, quantitative perturbation theory that depends on {\it local} approximation errors, the normality, and spectral gaps, as characterized by integral or exponential separation, of fundamental matrix solutions. Applications of the theory are presented for some differential eigenvalue problems and determining exponential dichotomies. Extensions are obtained for differential-algebraic equations and certain classes of infinite dimensional problems.
Oct 21	Tim Dorn/KU	Title: Shear flow of nematic liquid crystals in a channel Abstract: A liquid-crystal is a phase of material between the solid and liquid phases, and is used often to model frictional phenomenon.  The shear flow in a channel is described by the Navier-Stokes equation, describing the velocity field, and an analogous equation describing a direction field, which are coupled through a viscosity term.  We present results on the existence of steady states as well as spectral analysis of the linearization about the steady state.
Oct 28	Xianping Li/KU	Title: Mesh adaptation for finite element solution of anisotropic diffusion problems
Nov 4	Mohamed Badawy/KU	Title: Error bounds for the QR-method in the computation of the Lyapunov exponents of a non-autonomous, linear, infinite dimensional system
Nov 11	Bjorn Sandstede/Brown U.	Title: Nonlinear stability of semidiscrete shocks Abstract: This talk is concerned with the nonlinear stability of Lax shocks in semidiscrete systems of conservation laws, where the spatial coordinate is discrete, while time is continuous. At the heart of the nonlinear stability result is the construction of a Green's function of the linearized problem, which turns out to be a functional differential equation of mixed type. The key difficulty in carrying out this construction for semidiscrete shocks is the lack of an Evan function which is not known to exist for functional differential equations. The goal of this talk is to give background information about semidiscrete systems and to illustrate the techniques that allow us to construct Green's functions.
Nov 18	Vahagn Manukian/KU	Title: Multi-hump pulses in systems with reflection and phase invariance
Dec 2	Atanas Stefanov/KU	Title: On the stability problem for the Navier-Stokes system Abstract: We study the stability problem for the Navier-Stokes problem, that is: if two solutions start close at time zero, do they stay close at later times? We show that in two spatial dimensions, in the scale of Sobolev spaces $H^s, 0\leq s<1$, one has in fact uniform in time Lipschitzness of the solution map, which implies stability (and no blow up). The question remains open for $H^s, s>=1$.
Dec 9	Aslihan Demirkaya/KU
Dec 16	José M. Arrieta/Universidad Complutense
Jan 27	Organizing meeting
Feb 3
Feb 10
Feb 17
Feb 24
Mar 3
Mar 10	Jean-Philippe Lessard/Princeton U
Mar 24
Mar 31
Apr 7
Apr 14
Apr 21
Apr 28
May 5