Waves Seminar Series

Department of Mathematical Sciences
and
Center for Applied Mathematics and Statistics

New Jersey Institute of Technology

Spring 2008

Talks in this series are held Wednesdays in Cullimore 611 at 2:45 pm unless noted otherwise. If you have any questions about a particular colloquium, please contact the person hosting the speaker. For general questions about the seminar schedule, please contact Roy Goodman.

Date
Speaker and title
Host
2/6 Jeremy Marzuola, Columbia University, Fast soliton scattering by delta impurities (abstract) Roy Goodman
3/12 Sanjeeva Balasuriya, Connecticut College, Wavespeed in perturbed combustion waves (abstract) Roy Goodman
3/26 Yassine Boubendire, NJIT, High-Frequency Multiple Scattering Problem: Acceleration of the Iterative Procedure (abstract)
4/2 (4 PM special time)Horacio Rotstein, NJIT, Evolution of fronts in reaction diffusion systems with global inhibitory feedback. (abstract)
4/9 Gideon Simpson, Columbia University, The Solid Earth: Coherent Structures & Constitutive Relations (abstract) Roy Goodman

For past talks, see the math department seminar archive.

February 6
Jeremy Marzuola, Columbia University Department of Applied Physics and Applied Mathematics
Title:   Fast soliton scattering by delta impurities
Abstract:  We study the Gross-Pitaevskii equation with a repulsive delta function potential.  We show that a high velocity incoming soliton is split into a transmitted component and a reflected component.  The transmitted mass (L2 norm squared) is shown to be in good agreement with the quantum transmission rate of the delta function potential.  We further show that the transmitted and reflected components resolve into solitons plus dispersive radiation, and quantify the mass and phase of these solitons.

March 12
Sanjeeva Balasuriya, Connecticut College,  Department of Mathematics
Title: Wavespeed in perturbed combustion waves
Abstract:
This talk focusses on determining wavespeed corrections to
perturbed combustion systems.  Two such asymptotic regimes are
high Lewis numbers (small fuel diffusivity in comparison to
that of temperature), and step-function kinetics as an approximation
to Arrhenius kinetics.  The latter situation is analyzed in a
variety of situations, including both unit and infinite Lewis
numbers, and second-order reactions.  The analysis is performed
using novel applications of techniques from dynamical systems:
geometric singular perturbation theory and Melnikov's
method (which is usually used to establish chaos in periodically
perturbed ODEs).

March 26
Yassine Boubendire, NJIT Department of Mathematical Sciences
Title: High-Frequency Multiple Scattering Problem: Acceleration of the Iterative Procedure
Abstract:
In this talk, we will discuss a high frequency method, involving
integral equation and asymptotic expression of the solution, in
the particular configuration of multiple scattering.
A new Krylov-subspace method that significantly accelerates the
convergence of the iterative procedures will be discussed. We will
also present a suitable preconditioning technique (based on Kirchhoff
approximation) to improve the whole algorithm.tba
abstract

April 2
Horatio Rotstein, NJIT Department of Mathematical Sciences
Title: Evolution of fronts in reaction diffusion systems with global inhibitory feedback.
Abstract:

April
Gideon Simpson,  Columbia University Department of Applied Physics and Applied Mathematics
Title: The Solid Earth: Coherent Structures & Constitutive Relations
Abstract:
This talk will introduce a nonlinear wave equation arising in magma dynamics. This dispersive equation may be seen as a surrogate for the full continuum mechanics models, and an indication of opportunities for the study of coherent structures in solid Earth problems.

One of the difficulties in treating this wave equation analytically has been the poorly constrained constitutive relations for the partially molten rock.  We will review a multi-scale approach to modeling partially molten rock, leading to an ensemble of boundary value problems for incompressible fluid flow.  Solving these problems efficiently relies on novel software for the automatic generation of finite element code along with a recently developed "optimal" preconditioner for incompressible flow.