Waves Seminar Series

Department of Mathematical Sciences and Center for Applied Mathematics and Statistics

New Jersey Institute of Technology

Fall 2009

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

Provisional

J. Douglas Wright, Drexel University, TBA (abstract)

Roy Goodman

10/21

Maria Cameron, Courant Institute, NYU, Analysis of methods for the study of rare events and transition paths (abstract)

Yuan-nan Young
(joint w/ fluids seminar)

10/28

Jean-Marc Vanden-Broeck, University College London, The effects of electric fields on inviscid and viscous nonlinear free surface flows. (abstract)

Linda Cummings
(joint w/ fluids seminar)

12/2

Chee Wei Wong, Columbia University, Nonlinear and quantum optics in photonic crystal nanostructures (abstract)

Roy Goodman

September 4, J. Douglas Wright, Drexel University, TBA

Abstract to be included

October 21, Maria Cameron, Courant Institute, NYU, Analysis of methods for the study of rare events and transition paths

The overdamped Langevin equation is often used as a model in the molecular dynamics. At low temperatures, a system evolving according to such an equation spends most of the time near the potential minima and performs rare transitions between the neighborhoods of different minima. A number of methods have been developed to study the most likely transition paths. I will focus on two of them: the string method and the MaxFlux functional.

The string method is designed to find so called minimum energy paths, which correspond to the most likely transition paths at temperature zero. I will consider the string method as a dynamical system in the continuous-time, continuous-space setting. If the potential contains Morse index 2 or higher critical points, there are continuum families of minimum energy paths such that the transitions along each of them have the same likelihood. I will discuss the possible evolution of the path according to the string method equation in the case of such physical ambiguity.

The MaxFlux functional has been around for almost 30 years but not widely used because it is hard-to-minimize. Its minimizer provides a path of maximum likelihood at a given finite temperature. I will show two ways to derive it in the framework of the transition path theory and present an efficient way to minimize the maxflux functional numerically. I will demonstrate its the application to the problem of finding the most likely transition paths in the Lennard-Jones-38 cluster between the face-centered-cubic and the icosahedral structure.

October 28 , Jean-Marc Vanden-Broeck, University College London, The effects of electric fields on inviscid and viscous nonlinear free surface flows.

Abstract to be included

December 2 , Chee Wei Wong, Columbia University, Nonlinear and quantum optics in photonic crystal nanostructures

Abstract: The effects of electric fields on nonlinear free surface flows are investigated. Both inviscid and Stokes flows are considered. Fully nonlinear solutions are computed by boundary integral equation methods and weakly nonlinear solutions are obtained by using long wave asymptotics and lubrication theory. In addition applications to coating flows are presented.


Links to Old Seminar Schedules

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