Applied/GPS: Difference between revisions
No edit summary |
|||
| Line 81: | Line 81: | ||
=== | ===Friday, Sept 28: Zhennan Zhou=== | ||
'' | ''Computing Schrodinger equation in the semi-classical regime and physical observables'' | ||
abstract | abstract | ||
In this talk, we present a time splitting scheme for Schrodinger equation in the presence of electromagnetic field in the semi-classical regime, where wave function propagates O(\varepsilon) oscillation in both space and time. With operator splitting technique, the time evolution of the Schrodinger equation has been divided into three parts: the kinetic part, the convection part and the potential. With spectral approximation, the kinetic part and the potential part can be solved analytically. For the convection part, we proposed two numerical methods, a time explicit spectral method and a Lagrangian convection method. For the Lagrangian convection time splitting method, we prove the error estimate in L^{2} approximation of wave function, and by comparing with the semi-classical limit, we show this method can capture correct physical observable even if O(1) time step is taken. We implement this method in extensive numerical examples for both one dimensional and essentially two dimensional cases, and numerically verify that we achieve uniform time step error control in computing physical observables. | |||
== Archived semesters == | == Archived semesters == | ||
*[[Applied/GPS/Spring2012|Spring 2012]] | *[[Applied/GPS/Spring2012|Spring 2012]] | ||
*[[Applied/GPS/Fall2011|Fall 2011]] | *[[Applied/GPS/Fall2011|Fall 2011]] | ||
Revision as of 13:02, 26 September 2012
GPS Applied Mathematics Seminar
The GPS (Graduate Participation Seminar) is a weekly seminar by and for graduate students. If you're interested in presenting a topic or your own research, contact the organizers: Sarah Tumasz, Qin Li, Peter Mueller, and Bryan Crompton.
All seminars are on Fridays from 9:55-10:45 am in room 901 VV. Speakers should aim for their talk to last no longer than 45 minutes.
Fall 2012
| date | speaker | title | |
|---|---|---|---|
| Sept. 21, B219 | Saverio Spagnolie | Fluid-body interactions: from fish to flagella | |
| Sept. 28 | Zhennan Zhou | Computing Schrodinger equation in the semi-classical regime and physical observables. | |
| Oct. 5 | speaker | title | |
| Oct. 12 | Leland Jefferis | 3D display technology using MATLAB and cardboard | |
| Oct. 19 | speaker | "title" | ' |
| Oct. 26 | speaker | title | |
| Nov. 2 | Qin Li | From Boltzmann to Euler: the study of Knudsen layer | |
| Nov. 9 | Bryan Crompton | Mathematical Biology: Persistence in Chemical Reaction Network | |
| Nov. 16 | speaker | title | |
| Nov. 30 | Anakewit Boonkasame | TBA | |
| Dec. 7 | speaker | title |
Abstracts
Friday, Sept 21: Prof. Saverio Spagnolie
Fluid-body interactions: from fish to flagella
abstract: The length and velocity scales of swimming organisms on this planet vary by many orders of magnitude. Some swimming strategies work for small organisms but not for large ones, and vice versa, due to the scale-dependent nature of the fluid dynamics governing such systems. In this informal conversation, we will discuss some classical and recent efforts to understand fluid-body interactions at scales relevant to fish and birds, and separately to microorganisms. The methodology for their study will range from classical tools of applied mathematics to highly accurate numerical techniques. Questions to be addressed (briefly) include: what is the optimal waveform of an undulating flagellum?; what is the effect of boundaries on swimming microorganisms?; and what is the role of flexibility in flapping fins and wings?
Friday, Sept 28: Zhennan Zhou
Computing Schrodinger equation in the semi-classical regime and physical observables
abstract
In this talk, we present a time splitting scheme for Schrodinger equation in the presence of electromagnetic field in the semi-classical regime, where wave function propagates O(\varepsilon) oscillation in both space and time. With operator splitting technique, the time evolution of the Schrodinger equation has been divided into three parts: the kinetic part, the convection part and the potential. With spectral approximation, the kinetic part and the potential part can be solved analytically. For the convection part, we proposed two numerical methods, a time explicit spectral method and a Lagrangian convection method. For the Lagrangian convection time splitting method, we prove the error estimate in L^{2} approximation of wave function, and by comparing with the semi-classical limit, we show this method can capture correct physical observable even if O(1) time step is taken. We implement this method in extensive numerical examples for both one dimensional and essentially two dimensional cases, and numerically verify that we achieve uniform time step error control in computing physical observables.