Brown Bag Seminar

The Brown Bag Seminar is held on Fridays at 12:00 PM, in Mathematics 402.

Fall 2008

August

08/29
Bojan Durickovic
Program in Applied Mathematics
The University of Arizona

: Compact Waves on Planar Elastic Rods

Compact waves are finite-extent solitary waves. In the context of planar Kirchhoff rods with a linear constitutive relation, such solutions do not exist since the system is described by the pendulum equation. Stepping into the realm of nonlinear elasticity, however, the equation becomes singular, uniqueness of solutions no longer holds, and this proves to be a key ingredient for constructing a compact wave.

Additional food will be provided by SIAM. SIAM organizational meeting will follow the Brown Bag. Bring your ideas!

September

09/05
Scott Hottovy
Program in Applied Mathematics
The University of Arizona

Numerical Approximations on Null Controllability of Structurally Ramped Equations

The null controllability problem is considered for 2-D plates under hinged mechanical boundary conditions. The resulting partial differential equation (PDE) system referred to as a structurally damped equation is considered to obtain optimal rates of blowup for the associated minimal energy function E_2(T), as terminal time T->0. The optimal blowup rate is O(T3/2), which is abnormal, considering that null controllable PDEs generally have at least exponential blowup rates. It has been shown, in a paper by Roberto Trigianni, that finite dimensional spectral truncations of the PDE achieve the same rates. We set out to show that one achieves the same result by using the more complicated finite difference method to approximate the PDE.

09/12
Serina Diniega
Program in Applied Mathematics

Dunes and Dune Fields: What Sets their Sizes?

Dune modeling efforts are currently able to replicate isolated dune structures through consistent and reasonable parameter manipulation. However, these models often assume simple, steady environmental conditions. Additionally, they do not yield information about the apparent (ir)regularity and limitations that appear in actual dune fields. To understand how dunes evolve in the presence of other dunes and in complicated natural environments, we must consider models of dunes in complicated natural environments, and then relate that information into models of the higher-order structure: the dune field itself.

This past summer, I considered the larger-scale problem to isolate the influential elements in dune field evolution models. The aim was to address the open question about whether, in the presence of steady environmental conditions, dune fields exhibit self-organizing behavior or will continually coalesce. I was able to show that both how dunes are initialized at the start of the field and how dunes exchange sand through collisions are vitally important in predicting the long-term dynamics of a dune field. I am now back to considering the dune model, as I try to understand what processes and parameters are important in dune nucleation, and how dunes interact with variable topography and with other dunes.

This talk will present an overview of my work on both dune and dune field models. The mathematics I use is fairly basic, and should be accessible to all graduate students.

09/19
Robert Jenkins

Random Matrices and Orthogonal Polynomials

What do spacing probabilities of the Riemann zeta function, resonances of nuclear scattering, and the bus system in Cuernavaca, Mexico, have in common? Each of these has been modeled using random matrices. The goal of this talk is to sketch the crazy connection between random matrices and orthogonal polynomials. Using this connection we will then write down formulas for some of the important statistical quantities that arise in the problems mentioned above.

09/26
Suz Tolwinski
Program in Applied Mathematics

Bayesian Hierarchical Models for Reconstructions of Climate

Paleoclimatologists must rely on natural proxy records, such as tree rings, to make inferences about past climate. Classically, statistical relationships between the proxy signal and climate are calibrated during times when instrumental records of climate exist. These relationships are then extrapolated back into the past, when only the proxy records exist, to reconstruct climate.

In this talk, I will present Bayes's hierarchical models (BHMs) as a "new and improved" climate reconstruction method. I will argue that BHMs provide a framework in which information from multiple proxy signals can be combined more naturally, uncertainty can be quantified more rigorously and knowledge of the mechanistic relationships between proxy and climate can be exploited.

October

10/03
Jonathan Goodman
Courant Institute of Mathematical Sciences
New York University

An Introduction to the Theory of Dynamic Investment and the Effect of Transaction Costs

NOTE CHANGE OF VENUE FOR THIS DATE ONLY. This talk will consist of (1) two minutes on the subject of mathematicians in finance; (2) a survey of the basics of continuous-time financial modeling (geometric Brownian motion, continuous trading, backward equations for optimization); and (3) a very quick summary of my work with Dan Ostrov on the effect of transaction costs on all this.

10/10
John Kerl
Department of Mathematics
The University of Arizona

High-Performance Arithmetic

In an encore of a recruitment talk from my corporate days, I will discuss how one may build custom circuitry that can outperform an off-the-shelf processor. Along the way, I'll discuss the costs and benefits of doing so, how organizations can successfully accomplish such tasks, and -- most importantly -- give an idea of how computers actually compute things.