2002-2003 Seminars
April 24th, 2003 (5:30-7:30pm) - VIGRE Presentations (Round Two)
Moorea Brega and Alejandro Cantarero
Image Segmentation using Active Contours
(Research under Dr. James Curry)
A common problem in image processing is to break an image into its constituent parts. This can be done based on various criteria including texture, color, and gradient information. In this presentation we will discuss and demonstrate a segmentation algorithm proposed by Chan and Vese based on the Mumford-Shah segmentation problem. The algorithm is formulated as a level set method. We will demonstrate how the benefits of the level set method, including automatic changes in topology, are applicable in the segmentation of several test images. We then will demonstrate the behaviour on two classes of real-world images, faces and images generated from an electron microscope.
Kristie Henderson and Hilary Snyder
Scott the Baker
(Research under Dr. Curry and Prof. Norris)
There are many different steps involved in the process of making bread at the Great Harvest Bread Company. One of the first steps is to mill the wheat, which produces flour. The grinding of the stones used in the mill adds heat to the flour. Before the flour can be used, it must be returned to room temperature. Therefore, Scott the Baker places the flour into large buckets with five copper tubes, which help speed up the cooling process. Mathematically, the cooling of flour over time can be described using partial differential equations. We will discuss how Fourier series and heat transfer ideas and methods can be used to model and analyze the temperature of the flour. We will also discuss the mathematical and physical significance of the copper tubes and what other steps could be taken to further speed up the cooling.
Ian and Patrick
Computational Aspects of PDE's
(Research under Luke Olson)
For this VIGRE research project, we study computational aspects of the numerical solution to partial differential equations. Numerical approximation of PDE's is an enormous area of active research with applications in many fields. In particular, we are interested in investigating time dependent PDE's of hyperbolic type. We have initiated a study of the stability of numerical methods for first order hyperbolic PDEs and the computational complexities involved in arriving at the time dependent solutions. We have also identified several projects of for future research.
April 10th, 2003 (5:30-7:30pm) - Modeling Presentations
Modeling presentations will be held Thursday April 10th, be sure to mark your calendar. Not only for the fine selection of cuisine, but because those hard-working undergraduate MCM teams will be giving talks about their solutions to the modelling contest problems. Among the speakers will be the SIAM Award Winning team (Outsanding Designation) of Darin Gillis, Aaron Windfield, & Dave Lindstone; (Meritorious Designation) Alejandro Cantarero, Corry Lee, & Moorea Brega; (Honorable Mention) Kimiko Kano, Ian Derrington, & Joseph Carrafa.
April 17th, 2003 (5:30-7:30pm) - VIGRE Presentations (Round One)
Jocelyn Renner
MATHEMATICAL MODEL OF DISPERSION USING LYAPUNOV EXPONENTS
(Research under Dr. Julien and Paul Mullowney)
Understanding the dynamics of systems involving dispersion of passive scalars is important in many fields of engineering and science. Dispersion can include the transport of particles such as contaminants or represent a property of the system such as heat. Ocean dynamics, weather patterns, engines, reactors, and rocket boosters all undergo mixing in different forms, and understanding the dynamics behind these systems is important for prediction of the behavior of the system. Mathematical models provide valuable insight into the complex transport processes that can occur in physical and engineering systems. Good models allow scientists and engineers to more accurately predict ocean currents and weather patterns as well as allowing them to build more efficient reactors and engines. With Dr. Keith Julien and Paul Mullowney, I am studying ways to numerically analyze dispersion in dynamical systems using Lyapunov exponents. I will present our findings of the application of this method to a new class of analytic three-dimensional rotating fluids.
Josh Nolting
Exploring and Implementing Finite Element Methods
(Research Under Dr. Mantueffel and Dr. McCormmick)
The presentation will encompass the process of learning and implementing finite element methods, beginning with brief descriptions of Galerkin and First Order Systems Least Squares (FOSLS) methods. The presentation will then detail a high level decomposition of the implementation procedures and describe complexities associated with these two methods. Finally, enhancements to an already implemented partial differential equation (PDE) solver will be discussed. The PDE solver (FOSPACK)* uses FOSLS method and is heavily used by the research group members. In order to make the solver extensible to a larger number of problems, the accuracy and generality needs to be improved. This means modifications to the program. A focus of the presentation is one of these modifications. It includes a module that formulates element node basis functions, derivatives to these basis functions and Gaussian quadrature node locations for varied element spaces and integration accuracy.
Michael Franklin
Image DeNoising using Nonlinear Total Variation & Anisotropic Heat Diffusion
Noise removal is essential in fields which rely on information transfer via images. Unfortunately most of these images are inherantly tainted by some amount of noise. The most common types of noise are salt & pepper, speckle, Gaussian, and Poisson noise. Many noise removing methods exist, each having their own individual characteristics. Some algorithms are specifically defined for certain types of noise while others are broader in scope. We will present the very powerful denoising methods of Nonlinear Total Variation and Anisotropic Heat Diffusion. Both algorithms are very powerful, and each algorithm has traits which make it preferable over the other depending on the denoising task. We will discuss the concepts, mathematical theory, implementation, and results from both denoising algorithms that we have examined.
Jan 30, 2003 - MVT & DU/CU Collaboration
Darin Gillis, amath homepage and Patrick Simek, cs homepage
Darin and Patrick have been working on the creation of educational software for the past two years in a joint effort between Sun Microsystems and the Applied Mathematics Department. There are two parts of the project. The first part, with Darin as the lead programmer/manager, is to extend the MVT, a Java based math graphing utility. While the second part, with Patrick as the lead programmer/manager, is to create online instructions for students that uses the MVT to give students a graphical representation of calculus applications. The technology being used for this project include: Java Applets, JSP, Servlets, XML, MySQL, and other internet technology.
Oct 17, 2002 - A Brief Tour of Computational Mathematics
Scott MacLachlan, amath homepage
In this talk, we discuss the current state and future prospects of computational mathematics, science, and engineering. The numerical simulation of physical, chemical, and biological systems is more and more prevalent in industrial development. Fast mathematical algorithms are used to analyse data in applications ranging from oil prospecting to ultrasound imaging. We examine these wide-ranging fields and how they repeatedly return to a few basic questions in applied math. Current research focuses on generalizing both these questions and their answers in the search for improved algorithms.
