"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 2009 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.

"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).

"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.

"TBA"

"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.

"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.

"TBA"

"TBA"