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Applied and Computational Mathematics Seminar
Spring 2010

Time & location: All talks are in Gibson 325 at 3:00 P.M. unless otherwise noted.

Organizer: Xuefeng Wang

Friday, September 18, 2010

Speaker Mac Hyman, Tulane University
Description

"Understanding the Novel H1N1 (Swine) Flu Pandemic: Where the virus came from and how it will impact the world"

We are in the mist of the 2010 World Influenza Pandemic. The novel H1N1 swine flu virus has quickly spread around the world to become the first major epidemic of the 21st century. This talk will begin with an overview for non-experts on what makes this virus different from the seasonal flu, how it originated, and the expected impact of the epidemic. I will discuss the current status of the world, national, and Louisiana epidemic, the status of vaccine development, how effective we expect the vaccines to be, and what individuals can do to protect themselves from infection. 

 

Science based simulations of virtual worlds are being used to understand where the virus came from, predict the course of the pandemic, and estimate how the epidemic could change daily lives. Applied mathematicians are fully engaged with the public health community to help control the current H1N1 swine epidemic. Mathematical models on the world's largest computers are helping us to understand and predict the spread of the disease. I will present insights these models have given us that can help guide the public health community in fighting this pandemic.

 

This overview lecture will make the underlying issues of the swine flu epidemic accessible to a general audience. It will then describe how these issues are being addressed through collaborative efforts of public health, medical, social, and mathematical scientists to slow the epidemic. The lecture will only lightly touch on the underlying mathematical theory.
Location Gibson Hall 325
Time  3:00pm

 

Friday, October 2, 2010

Speaker Alex Kurganov , Tulane University
Description

"Chemotaxis: modeling, analysis and numerics"

I will first briefly discuss some mathematical aspects of PDE-based models of chemotaxis (active orientation of cells and organisms along chemical gradients) and will present a classical Patlak-Keller-Segel (PKS) system. Solutions of the PKS system typically develop a spiky structure, which models the concentration phenomenon, and may blow up in finite time. Capturing such solutions numerically is a challenging task and I will show how to derive highly accurate and robust numerical methods for the PKS and related chemotaxis systems.

In the second part of the talk, I will discuss several regularizations of the PKS system: the goal is to obtain a chemotaxis system capable to accurately describe the concentration phenomenon without risking unphysical density blowup. I will present a new regularized model, for which we prove global existence of classical solutions and study (both analytically and numerically) its nontrivial (spiky) steady
states.

The talk is based on joint works with Alina Chertock (NC State University), Yekaterina Epshteyn (Carnegie Mellon University) and Xuefeng Wang (Tulane).

Location Gibson Hall 325
Time  3:00pm

 

Friday, October 9, 2010

Speaker Xiu Ye , University of Arkansas at Little Rock
Description

"A Posterior error estimate for finite element methods for the Stokes Equations"

We establish a posterior error analysis of finite element methods for the Stokes equations. This residual estimator can be applied to almost all the existing finite element methods for solving the Stokes equations including conforming, nonconforming and discontinuous finite elements.

Location Gibson Hall 325
Time  3:00pm

 

Friday, October 16, 2010

Fall Break

 

Friday, October 23, 2010

Speaker TBA, TBA
Description

"TBA"

Location Gibson Hall 325
Time  3:00pm

 

Friday, October 30, 2010

Speaker Bree Cummins, Tulane University
Description

"Determining the biomechanical response of a filiform hair array: A low Reynolds number fluid-structure model"

The cercal  system of the cricket has served as a model sensory  system over the last 30 years and has been the subject of many anatomical, developmental, functional, and theoretical studies during that time. This system is composed of two antenna-like appendages covered with hundreds of filiform mechanosensory hairs, and encodes information about the direction and dynamics of low-velocity air currents. Many previous studies have characterized the biomechanics of individual filiform hairs, but only a few have considered the fluid-mediated interaction of closely-packed hairs. These few studies suffer from one of two disadvantages: either the modeled  hair arrangements  are limited in extent or configuration, or the computational cost is prohibitive. I present a fast and scalable numerical model of filiform hair motion that can simulate the motion of arbitrary hair arrangements on the cricket cercus. Using this model, I perform numerical simulations that demonstrate the possibility for both damping and synergistic coupling within biologically realistic groupings of filiform hairs.

Location Gibson Hall 325
Time  3:00pm

 

Friday, November 6, 2010

Speaker Jian-Guo Liu, Duke University
Description

"Modeling and analysis of collective behavior of self-propelled agents"

Collective behaviors of self-propelled agents (representing birds, fishes, cars, etc) such as flocking, swarming, trail formulation, attract much of recent research activities in applied mathematics. In this talk, I will discuss some of the recent developments in modeling and analysis of these emergence behaviors. In particular, I will present some analysis of flocking estimates for Cucker-Smale modes and Vicsek modes for birds and fish. 

I will also discuss the connection and passage among particle models, kinetic models, and continuum models of these self-propelled agents.

Location Gibson Hall 325
Time  3:00pm

 

Friday, November 13, 2010

Speaker TBA, TBA
Description

"TBA"

Location Gibson Hall 325
Time  3:00pm

 

Friday, November 20, 2010

Speaker TBA, TBA
Description

"TBA"

Location Gibson Hall 325
Time  3:00pm

Friday, November 27, 2010

  Thanksgiving Holiday

 

Friday, December 4, 2010

Speaker Student Project Presentations
Description

 ----------- first half-hour talk ------- 

 

Modeling Chemotaxis by Discrete Random Walkers Reacting to a Diffusive Environment 

 

 

Vinodh Chellamuthu, Jeremy Dewar, Jason Miller, and Cody Pond 

Department of Mathematics 

Tulane University 

 

We present a method for modeling diffusion with random walks. The dynamics of physical phenomena are not always adequately captured using continuous models. For instance, modeling dynamics of a sparse population with PDEs yields solutions describing the average behavior of this particular population over a large number of trials. It is often more interesting to study only one possible outcome that is physically relevant. We extend existing discrete models of linear diffusion to diffusion with advection and nonlinear diffusion. We show agreement between our discrete models and continuous models. We apply our approach to chemotaxis (with predator/prey-like behavior) in which we use a hybrid approach to model the behavior of discrete members of a population whose motion is related to the gradient of a continuous attractant. 

 

----------- second half-hour  talk ------- 

 

Pattern formations in Predator-Prey systems with diffusion 

 

Yu Liu, Shanshan Shen and Qi Wang 

Department of Mathematics 

Tulane University 

 

Long-term changes in the population sizes of interacting predator and prey can be understood through a system of differential equations. We analyze the effect of diffusion on the spatial population dynamics of the Lotka-Volterra Predator-Prey systems. The biological dispersal is modeled as diffusion process. Diffusion is a smoothing process that can inhibit chaos and prevent spikes in the solutions. This is true for a single diffusion equation, but the situation can be quite different when it comes to systems of diffusion equations. For example, De Mottoni and Rothe proved, in 1974, that diffusion effect cannot destabilize the system of one-predator, one-prey, with "no flux" boundary condition. Not much information is known about the case in higher dimension. We investigate the higher-dimensional Predator-Prey diffusive system to see if the solutions can become chaotic. Furthermore, we study the formation of traveling wave, which modeled the connection between equilibrium points of the system, and give numerical approximation of the wave speed. Observing that it is not entirely reasonable to add diffusion to the population dynamics, since the species don't move around randomly, we will later study the system with cross-diffusion, which represents the dispersal pressure provided by the populations, and the effect of diffusion rate on the system pattern.
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: January 26, 2010
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