Applied
and Computational Mathematics Seminar
Spring 2009
Time & location: All talks are in Gibson 325 at 3:00-3:50 P.M. unless otherwise noted.
Organizer: Ricardo Cortez
Friday, January 23, 2009
| Speaker | Damir Khismatullin , Biomedical Engineering, Tulane |
| Description | "Application of the viscoelastic Volume-of-Fluid algorithm to biological systems" Biological systems are characterized by a significant level of heterogeneity and, on the macro-scale, behave as viscoelastic materials. To study the mechanical behavior of biological systems, we have developed a novel parallel algorithm for fully three-dimensional numerical simulation of multiphase viscoelastic flow. The algorithm consists of the second order Volume-of-Fluid method for tracking fluid-fluid interfaces, the projection method for solving the Navier-Stokes equations, and the semi-implicit factorized scheme for the constitutive equation for the stress tensor (Giesekus, Oldroyd-B, or Upper-Convected Maxwell fluid). In this presentation, we will talk about the application of the algorithm to the problems in microvascular hemodynamics, such as leukocyte-endothelial cell adhesion and blood flow in channels with complex geometry. Proposals for extending the algorithm to other biological problems will also be discussed. |
| Location | Gibson Hall 325 |
| Time | 3:00pm |
Friday, January 30, 2009
| Speaker | TBA , Institution |
| Description | "TBA" |
| Location | Gibson Hall 325 |
| Time | 3:00pm |
Friday, February 6, 2009
| Speaker | TBA , Institution |
| Description | "TBA" |
| Location | Gibson Hall 325 |
| Time | 3:00pm |
Friday, February 13, 2009
| Speaker | TBA , Institution |
| Description | "TBA" |
| Location | Gibson Hall 325 |
| Time | 3:00pm |
Friday, February 20, 2009
| Speaker | Michael Nicholas , Tulane |
| Description | "A Very Accurate Algorithm for 3D Doubly Periodic Electromagnetic Scattering" Periodic electromagnetic scattering involves some issues that are not present in free space scattering problems. I will outline the periodic electromagnetic scattering problem, will discuss some of the numerical issues involved, and will show a new method that is in process of development. The method separates singularities via a partition of unity. The resulting smooth integrals can easily be approximated to high order. The singular integrals are treated through a polar coordinate transformation that also yields highly accurate integration. The result is a method in which the electromagnetic integral equations can be evaluated with very high accuracy. |
| Location | Gibson Hall 325 |
| Time | 3:00pm |
Friday, February 27, 2009
| Speaker | David Elad , Biomedical Engineering, Tel Aviv University, Israel |
| Description | "Transport Models in the Female Genital Tract" Human conception is the outcome of a set of correlated transport phenomena. The detached ovum is transported to the fallopian tube. Spermatozoa are transported in the uterine fluid towards the ampulla where fertilization occurs. The resultant embryo (zygote) is driven to the uterine cavity within four days of ovulation, and the embryo is then conveyed during another four days to an optimal implantation site in the fundal area at the upper part of the uterus. Fulfillment of these essential events within the time limits, first for fertilization and then for implantation, depends on concomitant intrauterine fluid motion induced by uterine wall motility, which is the result of spontaneous myometrial contractions towards the fundus. The myometrium is made of smooth muscle cells, which are the fundamental contractile elements that also pass the electrical signals required to coordinate the contractions of the uterine wall. When a single myometrial cell, or a group of cells contract, the deformation results in a local geometric change according to viscoelastic properties of the tissue. As a result, the neighboring regions are also forced to undergo some deformation. Summation of all the deformations from all the cells provides the instantaneous geometry of the intra-uterine fluid-tissue interface. The dynamics of the intra-uterine fluid-tissue interface induces the forces that control intra-uterine pressures as well as intra-uterine fluid motions in the non-pregnant uterus. This combined action moves the embryo towards the fundus. The presentation will describe our biofluid studies on the role of uterine peristalsis in embryo transport to its implantation site; the transport characteristics of embryos during their return to the uterus after laboratory fertilization (computational and in vitro analyses); and the electro-mechano-physiology of the uterine wall dynamics. |
| Location | Stanley Thomas Hall 101 |
| Time | 3:00pm |
Friday, March 6, 2009
| Speaker | Ramgopal Mettu, University of Massachusetts Amherst |
| Description | "Computational Methods for Protein Structure Determination" The molecular structure and activity of proteins essentially define the machinery of life in an organism. Determination of the three-dimensional structure of proteins, however is one of the primary bottlenecks in understanding their behavior and activity. While experimental methods such as Nuclear Magnetic Resonance (NMR) spectroscopy and X-ray crystallography can provide geometric information about protein structure, the resulting data is often sparse and/or noisy. Furthermore, existing computational methods to predict structure are not able to utilize other sources of data and are often lacking in useful guarantees on solution quality and/or efficiency.In this talk, I will present two computational methods for determining protein structure that provide strong guarantees on both solution quality and running time. The first method solves protein backbone structure using geometric restraints from Nuclear Magnetic Resonance data. We use techniques from algebraic geometry to demonstrate that a combination of distance and angular restraints is sufficient to reconstruct a best-fit backbone molecular structure in polynomial time. We show that an implementation of our algorithm can quickly and accurately reconstruct backbone structure from experimental NMR data. Given a backbone, the second method focuses on finding a minimum-energy set of sidechain conformations. We cast this problem as a statistical one, using a natural relationship between probability and energy defined by the Boltzmann distribution. We develop an interesting adaptive algorithm that makes use of a novel data structure for representing a sparse statistical network. Our algorithm is able to quickly incorporate updates to a given model and compute marginal distributions in logarithmic time. We make use of our approach to rapidly update a minimum-energy protein structure when any part of the structure is modified. I will present some initial experimental results showing the promise of our approach for computational mutagenesis and protein-ligand binding studies. |
| Location | Gibson Hall 325 |
| Time | 3:00pm |
Friday, March 13, 2009
| Speaker | Yekaterina Epshteyn, Carnegie Mellon University |
| Description | "The Method of Difference Potentials and Application to the Domain Decomposition Problem" In this talk, we will first give a brief introduction to the Method of Difference Potentials (MDP) for the numerical approximation of the interior and exterior boundary value problems for partial differential equations.Next we will propose the scheme based on MDP for the solution of the boundary value problems in the composite domains. The proposed scheme requires neither difference approximations of the boundary conditions nor matching conditions on the boundary between the subdomains and is well suited for parallel computations. Some numerical example to illustrate the performance of the developed method will be presented. This is joint work with Victor Ryaben'kii and Victor Turchaninov. |
| Location | Gibson Hall 325 |
| Time | 3:00pm |
Friday, March 20, 2009
| Speaker | Colleen Mitchell , University of Iowa |
| Description | "A Stochastic Model for the Vocabulary Explosion" Children at about age 18 months experience acceleration in word learning. This vocabulary explosion is a robust phenomenon, though the exact shape and timing vary from child to child. One class of explanations, which we term collectively as leveraged learning, posits that knowledge of some words helps with the learning of others. In this framework, the child initially knows no words and so learning is slow. As more words are acquired, new words become easier and thus it is the acquisition of early words that fuels the explosion in learning. In this talk, we will examine the role of leveraged learning in the vocabulary spurt by proposing a simple model of leveraged learning. Our results show that leverage can change both the shape and timing of the acceleration but that it can not create acceleration if it did not exist in the corresponding model without leveraging. This model is then applied to the Zipfian distribution of word frequencies, which confirm that leveraging does not create acceleration, but that the relationship between frequency and the difficulty of learning a word may be complex. |
| Location | Gibson Hall 325 |
| Time | 3:00pm |
Friday, March 27, 2009
| SPRING BREAK |
Friday, April 3, 2009
| Speaker | TBA , Institution |
| Description | "TBA" |
| Location | Gibson Hall 325 |
| Time | 3:00pm |
Friday, April 10, 2009
| EASTER BREAK |
Friday, April 17, 2009
| Speaker | Stephen Shipman , LSU |
| Description | "Resonant scattering by open periodic waveguides" When classical electromagnetic or acoustic modes of a waveguide interact with plane waves that impinge upon the guide, resonant scattering occurs. The resonance is similar to the "Fano resonance" in quantum mechanics. We will present the model of Fano and then show a rigorous derivation for classical electromagnetics that generalizes the Fano resonance for very general periodic structures. Joint work with N. Ptitsyna and S. Venakides. |
| Location | Gibson Hall 325 |
| Time | 3:00pm |
Friday, April 24, 2009
| Speaker | James Greenberg,Carnegie Mellon University |
| Description | "Discrete Lagrangian Traffic Models" In this talk I will discuss some of the more popular Discrete Lagrangian Traffic Models. I will focus my attention on two of such models, namely the various variants Optimal Velocity Model and the Intelligent Driver Model. Both of these describe cars traveling on a unidirectional, one-lane highway.New Material will include A-Priori estimates which are independent of the number of cars on the road. These estimates guarantee that the models are well posed; specifically they imply no car collisions and no velocity reversals. I will also investigate Large Amplitude Stop and Go Waves which are Traveling Wave solutions of the underlying system. Typically, such solutions exits and are stable when the "Equilibrium Solutions" where cars are uniformly spaced have a large, linearly unstable region. As with Wilson's studies on this subject the small wave number dispersion relation will be a critically important tool. I will also discuss how to obtain PDE models with the same basic properties. The work on the Intelligent Driver Model is joint with Michel Rascle. |
| Location | Gibson Hall 325 |
| Time | 3:00pm |
| Mathematics
Department Tulane University 6823 St. Charles Ave New Orleans, LA 70118 phone: (504) 865-5727 fax: (504) 865-5063 |
Last Updated:
October 29, 2009
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