Math @ Duke

Anne Catlla, VIGRE Postdoc
Please note: Anne has left the Mathematics department at Duke University; some info here might not be up to date.  Contact Info:
Office Location:  220 Physics Bldg  Office Phone:  (919)6602850  Email Address:    Office Hours:
 Tuesday 12pm, Thursday 1011am, and by appointment
 Education:
Ph.D.  Northwestern University  2005 
M.S.  University of Kansas  2000 
BS  University of Kansas  1997 
 Specialties:

Applied Math
 Research Interests: Mathematical modeling in biology and pattern formation
Bifurcation analysis of a model of hepatitis B
Hepatitis B is a virus that attacks the liver. In most cases, the immune system is able to fight off the virus; however, in some cases the immune system is not able to do this and a chronic infection results. We are conducting a bifurcation analysis of a known model for the spread of the hepatitis B virus in the body. Based on the results of this analysis, we hope to better understand which aspects of the immune response are most important to preventing a chronic infection.
Pattern selection in reactiondiffusion equations near a TuringHopf bifurcation.
Alan Turing proposed in the 1950s that a chemical reaction with a rapidly diffusing activator and a slowly diffusing inhibitor could exhibit an instability to a patterned state with a predictable wavenumber. After decades, his intuition has been shown to be true. Reactiondiffusion systems are also known to exhibit a Hopf instability, an instability to a state which is spatially homogeneous but oscillates temporally with a predictable frequency. Recent experiments have looked at the effect of blinking light on a chemical reaction which is exhibiting a Turing pattern. They found that the blinking light could suppress the pattern and that the suppression was greatest at the Hopf frequency of the system. Using perturbation theory and symmetrybased nonlinear analysis, my collaborator and I are looking at the behavior of general reactiondiffusion equations near the codimension2 point where Turing and Hopf bifurcations occur simulaneously. The analysis will provide us with the tools to determine how external forcing (in the case of the aforementioned experiment, this would be the blinking light) could be used to contral the patterns seen in the reactiondiffusion system. Using a simulation we wrote of a the LengyelEpstein reactiondiffusion system, we can test these results numerically.
Mathematical modeling in neuroscience
Neurons and glial cells are two kinds of cells in the brain. Neurons communicate via rapid firing; glial cells communicate on a slower time scale via diffusion. Recently it has been shown that these two types of cells can also communicate with one another; however it is not clear what role neuroglia communcation plays in neural networks. A group of glial biologists have suggested that one effect is to enhance the activity of neurons near excited glial cells and to suppress the activity of neurons far from excited glial cells. Their suggestion was based on intuition about the chemical reactions which occur near excited glial cells. I am part of a collaboration that has developed a simple reactiondiffusion model to describe these reactions and are using it to explore the biologists' suggestion via simulation and analysis of parameter space.
 Areas of Interest:
Nonlinear dynamics Pattern formation Mathematical biology Neural networks Mathematical modeling
 Curriculum Vitae
 Recent Publications
 A. Catlla, D. Schaeffer, T. Witelski, E. Monson, A. Lin, On Spiking Models of Synaptic Activity and Impulsive Differential Equations,
SIAM Review
(Accepted, 2007)
 A. Catlla, J. Porter, M. Silber, Weakly nonlinear analysis of impulsivelyforced Faraday waves,
Physical Review E, vol. 72 no. 5
(November 17, 2005),
pp. 056212 [abs]
 Conferences Organized
 Canadian, American, Mexican Physics Graduate Student Conference 2005, Organizing Committee Member, August 19, 2005  August 21, 2005
 Canadian, American, Mexican Physics Graduate Student Conference 2003, Organizing Committee Member, October 24, 2003  October 26, 2003


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

