AWM at SIAM 2012 Abstracts

AWM Workshop: Research Talks by Recent Ph.D.s

Parametric and Other Exact Solutions to Einsteins Equations in Terms of Special Functions

Jennie DAmbroise, Bard College jdambroi@bard.edu

In certain cosmological models the Einstein equations of general relativity reduce to a differential equation whose solutions can be found in terms of Jacobi or Weierstrass elliptic functions. In recent joint work with Floyd L. Williams we find more widespread applications of special functions for other cosmological models. I will give an overview of techniques we employed in finding such special solutions that may be of use to a more general audience.

A Method for Earthquake Cycle Simulations

Brittany Erickson, Stanford University baericks@stanford.edu

We are developing a method to understand and simulate full earthquake cycles with multiple events on geometrically complex faults, with rate-and-state friction and off- fault plasticity. The method advances the model over long interseismic periods using the quasi- static equations, and through dynamic rupture using the elastodynamic formulation. To obtain an efficient and provably strictly stable
method, we use high-order summation-by- parts finite difference schemes and weak enforcement of boundary conditions through the simultaneous approximation term.

A Gamma-Convergence Analysis of the Quasicontinuum Method

Malena Ines Espanol, California Institute of Technology mespanol@caltech.edu

Continuum mechanics models of solids have certain limitations as the length scale of interest approaches the atomistic scale. A possible solution in such situations is to use a pure atomistic model. However, this approach could be computational prohibited as we are dealing with billion of atoms. The quasicontinuum method is a computational technique that reduces the atomic degrees of free- dom. In this talk, we review the quasicontinuum method and present a Gamma-convergence analysis of it.

Video Stabilization of Atmospheric Turbulence Distortion

Yifei Lou, School of Electrical and Computer Engineering Georgia Institute of Technology louyifei@gmail.com

The image or the video sequence captured in a long-range system, such as surveillance and astronomy, is often corrupted by the atmospheric turbulence degradation. We propose to stabilize the video sequence using Sobolev gra- dient sharpening with the temporal smoothing. One latent image is found further utilizing the lucky-region method. With these method without any prior knowledge, the video sequence is stabilized while keeping sharp details and the latent image shows more consistent straight edges.

AWM Workshop: Mathematical Biology Research Talks by Recent Ph.D.s

The Post-Fragmentation Density Function for Bacterial Aggregates

Erin Byrne, Harvey Mudd College byrne@math.hmc.edu

The post-fragmentation probability density of daughter flocs is one of the least understood aspects of modeling flocculation. A wide variety of functional forms have been
used over the years to characterize fragmentation, and few have had experimental data to aid in its construction. In this talk, we discuss the use of 3D positional data of K. pneumoniae bacterial flocs in suspension to construct a probability density of floc volumes after a fragmentation event. Computational results are provided which predict that the primary fragmentation mechanism for medium to large flocs is erosion, as opposed to the binary fragmentation mechanism (i.e. a fragmentation that results in two similarly-sized daughter flocs) traditionally assumed.

Modeling Cell Polarity: Theory to Experiments

Alexandra Jilkine University of Arizona jilkine@gmail.com

In order to migrate, cells recruit various proteins to the plasma membrance and spatially segregate them to form a front and back. I present two possible mechanisms for this symmetry breaking process, and explain how cells can regulate the transition from a homogeneous, ”resting cell”, state to a spatially heterogeneous state corresponding to a polarized cell. I then focus on experimentally distinguish- ing between various proposed polarity models in crawling cells through perturbations of cell geometry.

Epidemic Spread of Influenza Viruses: The Impact of Transient Populations on Disease Dynamics

Karen Rios-Soto, University of Puerto Rico at Mayaguez karen.rios3@upr.edu

Recent H1N1 pandemic and recent H5N1 outbreaks have brought increased attention to the study of the role of animal populations as reservoirs for pathogens that could invade human populations. Here we study the interactions between transient and resident bird populations and their role on dispersal and persistence. A meta-population framework based on a system of nonlinear ordinary differ- ential equations is used to study the transmission dynamics and control of avian diseases. Epidemiological time scales and singular perturbation methods are used to reduce the dimensionality of the model. Our results show that mix- ing of bird populations (involving residents and migratory birds) play an important role on the patterns of disease spread.

Modeling the Cofilin Pathway and Actin Dynamics in Cell Motility Activity of Mammary Carcinomas

Nessy Tania, Smith College, Mathematics and Statistics Department ntania@smith.edu

Polymerization of actin cytoskeleton leads to cell migra- tion, a vital part of normal physiology from embryonic development to wound healing. However, it also occurs in the pathological setting of cancer metastasis. Here I present mathematical models of actin regulation by cofilin which has been identified as a critical determinant of metastasis. I will discuss results obtained from simulations and steady state analysis and their biological implications, as well as modeling challenges that arise.