Seminars and Colloquia by Series

Navier-Stokes solver using Green's functions

Series
PDE Seminar
Time
Tuesday, April 12, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Prof. Divakar Viswanath – University of Michigan –
The incompressible Navier-Stokes equations provide an adequate physical model of a variety of physical phenomena. However, when the fluid speeds are not too low, the equations possess very complicated solutions making both mathematical theory and numerical work challenging. If time is discretized by treating the inertial term explicitly, each time step of the solver is a linear boundary value problem. We show how to solve this linear boundary value problem using Green's functions, assuming the channel and plane Couette geometries. The advantage of using Green's functions is that numerical derivatives are replaced by numerical integrals. However, the mere use of Green's functions does not result in a good solver. Numerical derivatives can come in through the nonlinear inertial term or the incompressibility constraint, even if the linear boundary value problem is tackled using Green's functions. In addition, the boundary value problem will be singularly perturbed at high Reynolds numbers. We show how to eliminate all numerical derivatives in the wall-normal direction and to cast the integrals into a form that is robust in the singularly perturbed limit. [This talk is based on joint work with Tobasco].

Club Math - From Flapping Birds to Space Telescopes - The Mathematics of Origami

Series
Other Talks
Time
Monday, April 11, 2011 - 17:00 for 1 hour (actually 50 minutes)
Location
Student Success Center, Clary Theater
Speaker
Robert Lang – Alamo, California

Please Note: Robert J. Lang is recognized as one of the foremost origami artists in the world as well as a pioneer in computational origami and the development of formal design algorithms for folding. With a Ph.D. in Applied Physics from Caltech, he has, during the course of work at NASA/Jet Propulsion Laboratory, Spectra Diode Laboratories, and JDS Uniphase, authored or co-authored over 80 papers and 45 patents in lasers and optoelectronics as well as authoring, co-authoring, or editing 9 books and a CD-ROM on origami. He is a full-time artist and consultant on origami and its applications to engineering problems but moonlights in physics: from 2007-2010 as the Editor-in-Chief of the IEEE Journal of Quantum Electronics.

The last decade of this past century has been witness to a revolution in the development and application of mathematical techniques to origami, the centuries-old Japanese art of paper-folding. The techniques used in mathematical origami design range from the abstruse to the highly approachable. In this talk, I will describe how geometric concepts led to the solution of a broad class of origami folding problems – specifically, the problem of efficiently folding a shape with an arbitrary number and arrangement of flaps, and along the way, enabled origami designs of mind-blowing complexity and realism, some of which you’ll see, too. As often happens in mathematics, theory originally developed for its own sake has led to some surprising practical applications. The algorithms and theorems of origami design have shed light on long-standing mathematical questions and have solved practical engineering problems. I will discuss examples of how origami has enabled safer airbags, Brobdingnagian space telescopes, and more. From 3:30pm-4:30pm, Informal Folding Session will take place in Skiles 236

Robert J. Lang - Origami Informal Folding Session

Series
Other Talks
Time
Monday, April 11, 2011 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 236
Speaker
Robert Lang – Alamo, California
Robert Lang is recognized as one of the foremost origami artists in the world as well as a pioneer in computational origami and the development of formal design algorithms for folding. Join him for an informal folding session before his presentation.

Towards Optimal Prediction of Chaotic Signals

Series
Math Physics Seminar
Time
Monday, April 11, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Howey W505
Speaker
Divarkar Viswanath – Department of Mathematics, University of Michigan

Please Note: Host: Predrag Cvitanovic, School of Physics

Suppose that x(t) is a signal generated by a chaotic system and that the signal has been recorded in the interval [0,T]. We ask: What is the largest value t_f such that the signal can be predicted in the interval (T,T+t_f] using the history of the signal and nothing more? We show that the answer to this question is contained in a major result of modern information theory proved by Wyner, Ziv, Ornstein, and Weiss. All current algorithms for predicting chaotic series assume that if a pattern of events in some interval in the past is similar to the pattern of events leading up to the present moment, the pattern from the past can be used to predict the chaotic signal. Unfortunately, this intuitively reasonable idea is fundamentally deficient and all current predictors fall well short of the Wyner-Ziv bound. We explain why the current methods are deficient and develop some ideas for deriving an optimal predictor. [This talk is based on joint work with X. Liang and K. Serkh]. To view and/or participate in the webinar from wherever you are, click on:EVO.caltech.edu/evoNext/koala.jnlp?meeting=MvM2Ml2M2tDvDn9n9nDe9v

Limiting distributions of Betti numbers

Series
Algebra Seminar
Time
Monday, April 11, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Fernando Rodriguez-Villegas – University of Texas Austin
We will discuss several instances of sequences of complex manifolds X_n whose Betti numbers b_i(X_n) converge, when properly scaled, to a limiting distribution. The varieties considered have Betti numbers which are described in a combinatorial way making their study possible. Interesting examples include varieties X for which b_i(X) is the i-th coefficient of the reliability polynomial of an associated graph.

Generalized Kashaev and Turaev-Viro 3-manifold invariants

Series
Geometry Topology Seminar
Time
Monday, April 11, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nathan Geer – Utah State University
I will consider two constructions which lead to information about the topology of a 3-manifold from one of its triangulation. The first construction is a modification of the Turaev-Viro invariant based on re-normalized 6j-symbols. These re-normalized 6j-symbols satisfy tetrahedral symmetries. The second construction is a generalization of Kashaev's invariant defined in his foundational paper where he first stated the volume conjecture. This generalization is based on symmetrizing 6j-symbols using *charges* developed by W. Neumann, S. Baseilhac, and R. Benedetti. In this talk, I will focus on the example of nilpotent representations of quantized sl(2) at a root of unity. In this example, the two constructions are equal and give rise to a kind of Homotopy Quantum Field Theory. This is joint work with R. Kashaev, B. Patureau and V. Turaev.

Modeling synthetic ciliated surfaces

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 11, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alex Alexeev – Georgia Tech Mechanical Engineering
Biomimetic synthetic cilia can be effectively utilized for regulating microscale transport processes at interfaces. Using computer simulations, we examine how polymeric cilia can be harnessed to control the motion of microscopic particles suspended in a viscous fluid. The cilia are modeled as deformable, elastic filaments and our simulations capture the complex fluid-structure interactions among these filaments, channel walls and surrounding solution. We show that non-motile cilia that are tilted with respect to the surface can hydrodynamically direct solid particles towards channel walls, thereby, inducing their rapid deposition. When synthetic cilia are actuated by a sinusoidal force that is applied at the free ends, the beating cilia can either drive particles downwards toward the substrate or expelled particles into the fluid above the actuated cilial layer. This dynamic behavior can be regulated by changing the driving frequency. The findings uncover new routes for controlling the deposition of microscopic particles in microfluidic devices.

Southeast Geometry Seminar

Series
Other Talks
Time
Sunday, April 10, 2011 - 09:00 for 8 hours (full day)
Location
Emory University
Speaker
Southeast Geometry Seminar – Emory University
The Southeast Geometry Seminar is a series of semiannual one-day events focusing on geometric analysis. These events are hosted in rotation by the following institutions: The University of Alabama at Birmingham;  The Georgia Institute of Technology;  Emory University;  The University of Tennessee Knoxville.  The following five speakers will give presentations on topics that include geometric analysis, and related fields, such as partial differential equations, general relativity, and geometric topology. Borin Rubin (Louisiana State Univ);  Joseph Fu (Univ of Georgia);  Paul Yang (Princeton U);  Robert Gulliver (Univ of Minnesota);  Ken Stephenson (U of Tennessee).   

Spaces of nonnegatively curved metrics II

Series
Geometry Topology Working Seminar
Time
Friday, April 8, 2011 - 14:05 for 2 hours
Location
Skiles 269
Speaker
Igor Belegradek – Georgia Tech
I will prove contractibility of the space of nonnegatively curved metrics on the 2-sphere via the uniformization, discuss difficulties of extending the result to metrics on the plane, and then discuss similar problems in higher dimensions.

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