Applied/GPS/Fall2012

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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 Leland Jefferis 3D display technology using MATLAB and cardboard
Oct. 12 speaker title
Oct. 19 speaker title '
Oct. 26 Matthew D. Johnston Stochastic Chemical Reaction Networks
Nov. 2 Qin Li From the Boltzmann to the Euler: the study of the Knudsen layer
Nov. 9
Nov. 16
Nov. 30 Sarah Tumasz TBD
Dec. 7

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.

Friday, Oct 26: Matthew D. Johnston

Stochastic Chemical Reaction Networks

abstract

It is common to model systems of simultaneously occurring chemical reactions using ordinary differential equations. In this setting, we imagine reactions as continuous state space, deterministic processes over the chemical concentrations. This is only justified, however, if the effect of each individual reaction---an inherently discrete state, stochastic event---is small enough compared to the net effect of all the reactions occurring that we can average them together. This is clearly not the case for many practical systems. Many cellular processes, for instance, typically involve only tens or hundreds of individual reacting molecules. We cannot average these reactions together without losing valuable information about the dynamics of the system.

In this talk, I will present an introductory-level overview of the state of stochastic modeling in chemical reaction networks theory under the assumption of mass-action kinetics. In particular, I will present two common tools---Gillespie's algorithm and the Chemical Master Equation---and explain the strengths and drawbacks of both approaches.

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