PDE Seminars 2004-2005
Spring 2005
- Frithjof Lutscher, University of Alberta
- Title: "Persistence and spread in advective environments"
Wednesday, January 12, 4:00pm in SH203 - Gareth Roberts, College of the Holy Cross
- Wednesday, February 2, 4:00pm in SH203
Title: "Interesting symmetric orbits in the 3-body problem"
Abstract: Imagine three equal mass planets chasing each other around a symmetric figure-eight race track returning to their initial positions in time T. The bodies are spaced out equally with a phase shift of T/3. Remarkably, a rigorous proof using variational methods for the existence of such an orbit, called the "figure-eight," was proven by Chenciner and Montgomery in the year 2000. We will discuss their proof as well as some of the variational techniques currently being used to find hundreds of new wonderful orbits in the n-body problem. The linear stability of the figure-eight and other similar solutions will be explored analytically. - Joint presentation by Konstantin Lurie and Suzanne Weekes, WPI
- Wednesday, February 9, 4:00pm in SH203
Title: "Wave and Energy Transport through Checkerboard Material Assemblage in Space-Time" - Professor Frederic Dias, Ecole Normale Superieure de Cachan (visiting WPI)
- Wednesday, February 16, 4:00pm in SH203
Title: "On two problems related to water waves: I. Effect of dissipation on the Benjamin-Feir instability; II. Undular jumps."
Abstract: Part I is devoted to the Benjamin-Feir (BF) instability. It is a modulational instability in which a train of periodic Stokes travelling waves loses energy to a small perturbation of waves with slightly different wavelength. It is shown that there is an overlooked mechanism whereby the addition of dissipation may lead to an enhancement of the BF instability. This observation is new, and although it is counterintuitive, it is due to the fact that the BF instability involves the collision of modes with opposite energy sign (relative to the Stokes wave). Part II is devoted to undular jumps. They occur at the transition from a supercritical flow to a subcritical flow when the upstream Froude number is close to unity. The flow is characterized by free- surface undulations of decreasing amplitude, which extend for a considerable distance downstream of the transition. Undular jumps can be commonly observed and have been experimentally studied. Recently, we discovered a new type of 'steady' open-channel flow solution that we called 'generalized hydraulic jump.' It is shown that in fact the central part of the undular bore resembles a generalized hydraulic fall. - Marcus Sarkis, IMPA/WPI
- Wednesday, February 23, 4:00pm in SH203
Title: " Discretization via Homogenization Theory for Elliptic Equations with Rapidly Oscillating Periodic Coefficients" - Steven Levandosky, College of the Holy Cross
- Wednesday, March 2, 4:15pm in SH203
Title: "Solitary Waves of the Ostrovsky Equation"
Abstract: The Ostrovsky equation is a generalization of the KdV equation which takes into account the effect of the earth's rotation. We consider the behavior of solitary wave solutions, their stability and their limit as the rotation parameter vanishes. - Jan Medlock, Yale University
- Wednesday, March 16, 4:00pm in SH203
Title: "Integro-differential-equation models for infectious disease"
Abstract: Invasion of diseases into new territory is a worldwide problem. Examples include West Nile fever in the US, HIV in Africa and Asia, and dengue in Latin America. Traditionally, the spatial spread of disease has been modeled using a local process, diffusion, to model dispersal. However, if dispersal is non-local, diffusion can greatly underestimate speeds of invasion. In this talk, I will discuss integro-differential--equation models that incorporate knowledge about the dispersal of disease propagules and infected hosts to describe disease infection. These models are continuous-time analogues to the discrete-time integrodifference-equation models and share many of the same advantages. - Tim Reluga, Yale School of Medicine
- Wednesday, March 23, 4:00pm in SH203
Title: "Wave speeds in Epidemic models" - Natalia Sternberg, Clark University
- Wednesday, March 30, 4:00pm in SH203
Title: "Modeling Collisionless Magnetized Plasma - Wall Problem"
Abstract: A model for the collisionless plasma-wall problem under the action of an oblique magnetic field is developed and the behavior of the plasma characteristics are discussed. The plasma and the sheath are then modeled separately to obtain the position of the quasi-neutral plasma boundary and the sheath edge. Studying the behavior near the plasma boundary and the sheath edge, the plasma and the sheath solutions are patched together to approximate the solution of the plasma-wall problem. - Luis Roman, WPI
- Wednesday, April 6, 4:00pm in SH203
Title: "On Elliptic Stochastic PDEs"
Abstract: In mathematical studies of the transport of pollutants in groundwater and of oil recovery an elliptic equation with random coefficients arises. The randomness enters into the equation through the permeability tensor K(x,w), which models the properties of the rocks and these are not know with certainty. Some geostatistical models assume the permeability, K(x,w), to be a log-normal random field. The use of Monte Carlo methods to approximate the expected value of the solution u(x,w), higher moments, or other functionals of u(x,w), require solving similar system of equations as many times as trajectories are considered, thus it becomes expensive and impractical. In this talk, we present and explain several advantages of using the "White Noise" probability space as a natural framework for this problem. Applying properly and timely the Wiener-Ito Chaos decomposition, we obtain a symmetric positive definite linear system of equations whose solutions are the coefficients of a Galerkin-type approximation to the solution of the original equation. Moreover, this approach reduces the simulation of the approximation to u(x,w) for a fixed w, to the simulation of a finite number of independent normally distributed random variables. - Chris Larsen, WPI
- Wednesday, April 13, 4:00pm in SH203
Title: "Problems in the mathematical analysis and modeling of time-continuous fracture"
Abstract: I will describe some models for crack growth in materials, as well as some related problems describing debonding of thin films. These models are in some ways unsatisfactory, and I will discuss some ideas to improve and analyze them. - Alain Damlamian, Université Paris 12 Val de Marne
- Wednesday, April 20, 4:00pm in SH203
Title: "The periodic unfolding method: an introduction and examples"
Abstract: The talk will present the basic ingredients of the periodic unfolding method, its connection to two-scale convergence and its application to a model problem. - Shankar Subramaniam, PhD
- Wednesday, April 27, 4:00pm in SH203
Title: "Lagrangian grid-free vortex methods"
Abstract: Vortex methods originated on the basis of the fundamental importance of vorticity - and, on the promise of avoiding the problems related to pressure computations and complex meshes in Eulerian computations. While substantial progress has been made, fundamental problems persist. One such problem is computing the diffusion process in a grid-free manner. That was recently solved with the "Vorticity Redistribution" Method. The Redistribution Method is used to study the implusively started flow over a 2D circular cylinder. Some theoretical observations on unsteady separation process and its implications for a numerical computation will be discussed. The Redistribution Method has been successfully worked out for axisymmetric flows as well. More importantly, the central idea is layed out to extend the method to variable - viscosity parabolic PDE to handle large-eddy simulations.
Last modified: September 27, 2006 14:42:39