People

Faculty

• Richard Braun, Professor
Nonlinear BVPs, PDEs and free boundary problems in fluid mechanics, materials science and mathematical biology.
• L. Pamela Cook, Professor
Complex fluids, viscoelastic fluids: flows and modeling; transonic aerodynamics.
• Tobin Driscoll, Associate Professor
High-order and spectral methods for differential equations;  radial basis functions;  numerical conformal mapping.
• David Edwards, Associate Professor
Parabolic and reaction-diffusion PDEs using asymptotic and perturbation methods and sometimes numerical methods; applications in biochemical reactions and olfactory systems.
• John Pelesko, Associate Professor
Mathematical modeling of real world micro- and nanoscale devices. Problems arising in an industrial setting that involve continuum mechanics.
• Lou Rossi, Associate Professor
Neural networks, vortex methods, flow in porous media and fluid mechanics.
• Gilberto Schleiniger, Associate Professor
Fluid flow: viscoelastic and transonic flows; mathematical finance; mathematical biology.
• Anja Sturm, Assistant Professor
Probability; population genetics.

• Alfa Heryudono
  Computational mathematics for PDEs. Alfa is developing adaptive radial basis function methods for mathematical models of the human tear film and other problems.
• Kara Maki
  Computational mathematics for PDEs. Kara is working on overset grid methods for mathematical models of the human tear film.
• Xiaolin Yang
  Image processing for blinking. Xiaolin is a masters student working on image processing of lid motion in blinks to use as input for tear film models.

• Gloria Amakobe
• Drew Amis
  Gloria and Drew are working on the modeling of ant foraging trails in the MEC lab with Professor Rossi.
• Joe Hartnett
  Joe is an electrical engineeing major from Cornell who visited for the summer and worked with Professor Braun in epidemiology on networks.
• Linsey Norris
  Ms. Norris is developing a computational model of chemical reaction with transport inside a thin zone.

Projects and Activities

Howard Hughes Medical Institute: Quantitative Biology Major

Gilberto Schleiniger, UD schleini@math.udel.edu
John Pelesko, UD
Lou Rossi, UD
Tobin Driscoll, UD

The Mathematical Sciences and Biological Sciences Departments are designing a new joint undergraduate degree program in Quantitative Biology, to be started in fall 2007. This innovative program will build on existing core courses from mathematics, biology, chemistry, physics, and chemical engineering, as well as newly designed integrative seminars and a capstone experience created specifically for Quantitative Biology majors. The goal of the program is to help train the next generation of leaders in biological and medical research and practice, in accordance with the widespread recognition of the growing role of mathematics and computation in exploring biological frontiers. We anticipate that the development and initial implementation of the Quantitative Biology program will be generously supported by a science education grant from the Howard Hughes Medical Institute.

Population Genetics

Anja Sturm (PI) sturm@math.udel.edu

Recent improvements in genotyping technologies have led to unprecedented quantities of DNA sequence data. This genetic information has opened the door to new quantitative methods for understanding the genetic evolution, history and origin of humans and other species and for deciphering and ascertaining in detail the function of the (human) genome.

Realistic mathematical models of the inherently random processes that govern which genes are passed on from one generation to the next are prerequisite to the correct quantitative analysis and interpretation of the data. Recent models attempt to incorporate complicating factors like population substructure, interaction, competition, and selection.

Mathematical Modeling of Pattern Formation in Ant Foraging Trails and Swarms

Lou Rossi rossi@math.udel.edu

Drew Amis, UD

Gloria Amakobe, UD

Chien-Chung Shen, Computer and Information Sciences, UD

Iain Couzin, Princeton University

While most people know that ants are expert problem-solvers capable of finding food meters away from their nest, few people realize that there are over ten thousand distinct species of ants, or that constitute between 15 and 20% of the terrestrial biomass on Earth. In short, ants have won the battle for the planet Earth, and the best we can do is study their successful strategy. Clearly, their success is not a result of size, strength or speed. In fact, individual ants are rather inept. Most ant species are nearly blind, but their behavior is partially regulated by the secretion and detection of chemicals called pheromones. This chemical communication drives a complex social structure that gives ants a tremendous advantage. Undergraduate Katie Johnson and Professor Rossi reconciled observed traveling wave patterns in ant foraging trails with a new mathematical model presented in the Journal on Theoretical Biology 241 (2), pp 360-369 (July 2006). Undergraduates Drew Amis and Gloria Amakobe are extending this work in a number of directions. Also, Professors Rossi and Shen have been collaborating to apply some of these methods to routing problems in mobile ad-hoc networks.

Biochemical Reactions in Thin Reaction Zones

David Edwards , UD edwards@math.udel.edu

Linsey Norris, UD

Many biochemical reactions occur in thin reaction zones (along the surface of a cell, for instance). In order to better understand these systems, a detailed mathematical model is needed to include both the reaction processes and the transport near these layers. Dr. Edwards' work focuses on the study of the BIAcore, which is an experimental device used to measure rate constants of such reactions, but the work is immediately applicable to biological systems.

Ion Channel Distributions in Olfactory Cilia

Dorjsuren Badamdorj, UD badamdor@math.udel.edu

David Edwards , UD edwards@math.udel.edu

Don French, Cincinnati

When you smell something, odorant molecules react with receptors in the nose. These chemical signals are then transduced into electrical signals via ion channels in olfactory cilia membranes. The number and position of these channels are of intense interest, but the only measurable quantity of interest is the current of the electrical signal. Hence the system poses an ill-conditioned inverse problem which can be studied asymptotically and numerically.

Mathematical Modeling of the Human Tear Film: Adaptive Radial Basis Functions (RBFs)

Richard Braun, UD (PI) braun@math.udel.edu
L. Pamela Cook, UD
Tobin Driscoll, UD
Alfa Heryudono, UD
P. Ewen King-Smith, College of Optometry, Ohio State University

RBF methods are being developed for high order nonlinear PDEs that model the human tear film during a blink with challenging and realistic boundary conditions. The models are being compared to in vivo measurements of the tear film. We anticipate that this project will be supported by an NSF grant.

Mathematical Modeling of the Human Tear Film: Moving Overset Grid (MOG) methods

Richard Braun, UD (PI) braun@math.udel.edu

L. Pamela Cook, UD

Petri Fast, Lawrence Livermore National Laboratory

Kara Maki, UD

P. Ewen King-Smith, College of Optometry, Ohio State University

MOG methods are being developed and adapted from the Overture project at LLNL for high order nonlinear PDEs that model the human tear film during a blink with challenging and realistic boundary conditions. The models are being compared to in vivo measurements of the tear film. We anticipate that this project will be supported by an NSF grant.

Mathematical Modeling of Alcohol Problems on Social Networks

Richard Braun, UD braun@math.udel.edu

Bob Wilson, School of Urban Affairs and Public Policy, UD

John Pelesko, UD

James Gleeson, University College Cork, Ireland

Bob Buchanan, Millersville University

Joe Hartnett, Cornell University

In the 2004 MPI Workshop, Bob Wilson presented a problem seeking new ideas for modeling alcohol problems in society with an interest in developing a tool to help with policy decisions. In the workshop, an epidemiological model was developed and analyzed that used a model with cubic nonlinearities that was succeptible to cascades; computational and analytical results were obtained. The results (with some subsequent polishing) appeared in the Journal of Studies on Alcohol, 67(4): 591-599, (2006). Joe Hartnett extended this work in summer 2006 and a more mathematical follow-up paper is expected.

Mathematical modeling of spontaneous-contraction in a uterine smooth muscle cell

Dorjsuren Badamdorj, UD badamdor@math.udel.edu

A uterine smooth muscle cell contraction begins with change in a membrane potential which triggers calcium ion (Ca2+) influx into the cell through Ca2+ ion channels. A chain reactions initiated by the increase of the Ca2+ concentration within the cell, which lead to formation of cross bridges between actin and myosin filaments and contraction of the cell. By developing a mathematical model for the experiments spontaneous-contractions of the isolated uterine muscle tissue under different treatment and environment, we will discover detailed understanding of the biochemistry of uterine smooth muscle cell. Our model accounts a contraction stress of the whole tissue with modified a single cell contraction model which contains a calcium buffering and protein kinase C.