Brown Bag Seminar

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

Spring 2008

February

02/01
Rosalyn Rael
Graduate Student, Program in Applied Mathematics
University of Arizona

Who eats whom? Ecological structure and the effects of extinction on food webs

Energy flows through a complex interacting network of living organisms, from primary producers such as algae and plants, to top predators such as sharks and parasites. Food webs are graphs representing these energy flows. These graphs can be viewed as couplings in a complex dynamical system that describes changes in population sizes over time. Because of the interconnected nature of living organisms, extinction of one species may have secondary effects that ripple throughout the ecosystem to varying degrees. In this talk, I will give a basic introduction to food webs, and discuss the basic network structures associated with them, as well as the methods used to generate model food webs. I will also discuss food web dynamics, and the effects of removing various types of organisms from an ecosystem network.

02/29
Bob Jenkins
Graduate Student, Program in Applied Mathematics
University of Arizona

Adventures in the Complex Plane

In this talk I will introduce the idea of a Riemann-Hilbert problem. In a nutshell, this problem ask you to recover a complex function from its non-analytic behavior. We will derive a solution for a family of simple RH problems, and use some contour integral chicanery to solve a few examples. If time permits, I will describe how such problems are related to the inverse scattering transform used to solve nonlinear integrable PDEs.

March

03/07
Daniel Reich

The Most Likely Path

In this talk, we present a stochastic shortest path problem that we refer to as the Most Likely Path Problem. On a fairly general class of networks, i.e., series-parallel networks, we will show that lower and upper bounds for the probability of the Most Likely Path (MLP) can be computed efficiently. We will then present a dynamic programming algorithm for identifying the MLP on series-parallel networks.

03/14
Zhiying Sun

Phyllotactic pattern propagation

Plyllotaxis, namely the arrangement of phylla (leaves, florets, etc) has intrigued natural scientists for over four hundred years. Current theories and models of the formation of phyllotactic patterns at the plant apical meristem focus on either transport of the growth hormone auxin or the mechanical buckling of the plant tunica. Each of the mechanisms alone can give rise to an instability that leads to patterned states. However, it is known that the two mechanisms interact with each other instead of acting independently. We (Alan C Newell, Patrick Shipman and I) develop a model that incorporates the coupling of biochemistry and mechanics. I will discuss the parameter choices under which the two mechanisms may cooperate in determining the pattern, or under which one or the other mechanism may dominate. Analysis of these equations shows that the coupling of the two mechanisms acts like a positive-feed-back system and relaxes the condition for primordium initiation.

Also, on real plants, the pattern doesn't form all at once. Rather, the primordia are formed sequentially over time and gradually add to the existing pattern. Therefore, between the stable patterned state and the unstable non-patterned state, there exists a front that propagates with some finite velocity into the non-patterned state. I will discuss how this idea of front propagation coincides with a well-accepted conceptual model for phyllotaxis proposed over a hundred years ago by Hofmeister and Snow&Snow.

03/28
Rebecca Vandiver

Tissue Tension and Axial Growth in Cylindrical Elastic Structures

In many cylindrical structures in biology, residual stress fields are created through differential growth. In particular, if the outer and inner layers of a cylinder grow at different rates, parts of the cylinder will be in a state of axial compression and other parts will be in tension. These tissue tensions play a fundamental role in the overall rigidity and stability of the cylinder. Here, we present an analysis based on nonlinear elasticity to study the effect of tissue tension on the mechanical properties of growing cylinders and we reveal a subtle interplay between geometry, growth, and nonlinear elastic responses that help us understand some of the remarkable properties of stems and other biological tissues.

April

04/04
Carlos Chiquete

Receptivity of Plane Idealized One-reaction Detonation to Three-dimensional Perturbations

Detonation is a combustion-driven supersonic shock wave that can reach speeds of several kilometers per second. Applications range widely, from jet propulsion to the theory of supernova explosions. In our work we investigate the linear stability and receptivity of the Zel'dovich-von Neumann-Doering (ZND) detonation wave model. The solution of the initial-value problem for small three-dimensional perturbations in a ZND detonation is presented as an expansion into modes of discrete and continuous spectra. The result provides a tool to predict initial amplitudes of the unstable modes depending on the initial perturbation. The results for different types of introduced perturbations are discussed.

04/11
Robert G. Erdmann
Department of Materials Science & Engineering and Program in Applied Mathematics
University of Arizona

Python for Scientific Computing

In developing software for scientific computation, one has typically been forced to choose between the fast development but slow program execution associated with high-level programming languages and the fast execution but slow development associated with low-level languages like FORTRAN. Another alternative has been the use of commercial software such as MATLAB (R) or Mathematica (R), but these applications are expensive and closed-source, thereby inhibiting sharing and collaboration with those portions of the scientific community who can't afford these applications. Such commercial codes are also highly specialized, making it difficult to extend them to wider problem domains.

The recent arrival of the SciPy package of high-level scientific computation modules for the Python programming language allows for the development of scientific computations suffering from none of these drawbacks. Python is a very high-level language, allowing for extremely rapid development of robust and sophisticated software. The speed-critical components of SciPy (linear algebra, FFTs, numerical quadrature, etc.) are called from within Python but are implemented in FORTRAN or C, enabling rapid execution speed. Furthermore, all of Python and SciPy are completely free and open-source, enabling scientific codes developed in Python to be distributed freely. And by using Python to develop scientific computations, one has access to a huge library of other general functionality, enabling for example easy development of software that has sophisticated graphical user interfaces (GUIs) and interfaces with databases, or that uses the internet to send e-mail or retrieve data.

The talk will provide a brief high-level overview of the Python programming language, followed by several examples of the ease with which powerful scientific computations can be performed using SciPy. Examples will include image processing, signal processing, solution of PDEs using sparse matrix solvers, advanced scientific visualization, and interactive distributed and parallel supercomputing.

04/18
Suzanne Robertson

Spatial Patterns in Stage-structured Populations with Density-Dependent Dispersal

Spatial patterns are commonly observed among dispersing populations in nature. When stored in a homogenous flour medium, the larval and adult stages of the flour beetle Tribolium brevicornis will spatially segregate. In this talk we explore stage-structured integro-difference equation models with density-dependent dispersal kernels through mathematical analysis. We will also use computer simulations to investigate the mathematical mechanisms that lead to spatial patterns such as those observed in T. brevicornis.

May

05/02
John Gemmer

How to Control a Front-Wheel-Drive Bike

In this talk, we will present some of the basic notions of controllability and optimality of affine control systems subject to a payoff functional. We will illustrate these ideas by studying control systems that model physical devices such as rocket-powered cars, springs, etc. In particular, we will present our recent results in how to parallel park a bike in the least amount of time, subject to the constraint that the bike's wheels rotate at a fixed speed.