Seminars and Colloquia by Series

A global analysis of a multistrain viral model with mutations

Series
CDSNS Colloquium
Time
Monday, January 26, 2009 - 16:30 for 2 hours
Location
Skiles 255
Speaker
Sergei Pilyugin – University of Florida
I will present a generalization of a classical within-host model of a viral infection that includes multiple strains of the virus. The strains are allowed to mutate into each other. In the absence of mutations, the fittest strain drives all other strains to extinction. Treating mutations as a small perturbation, I will present a global stability result of the perturbed equilibrium. Whether a particular strain survives is determined by the connectivity of the graph describing all possible mutations.

The dynamics of two classes of singular traveling wave systems

Series
CDSNS Colloquium
Time
Monday, November 17, 2008 - 16:30 for 2 hours
Location
Skiles 255
Speaker
Jibin Li – Kunming Univeristy of Science and Technology and Zhejiang Normal University
Nonlinear wave phenomena are of great importance in the physical world and have been for a long time a challenging topic of research for both pure and applied mathematicians. There are numerous nonlinear evolution equations for which we need to analyze the properties of the solutions for time evolution of the system. As the first step, we should understand the dynamics of their traveling wave solutions. There exists an enormous literature on the study of nonlinear wave equations, in which exact explicit solitary wave, kink wave, periodic wave solutions and their dynamical stabilities are discussed. To find exact traveling wave solutions for a given nonlinear wave system, a lot of methods have been developed. What is the dynamical behavior of these exact traveling wave solutions? How do the travelling wave solutions depend on the parameters of the system? What is the reason of the smoothness change of traveling wave solutions? How to understand the dynamics of the so-called compacton and peakon solutions? These are very interesting and important problems. The aim of this talk is to give a more systematic account for the bifurcation theory method of dynamical systems to find traveling wave solutions and understand their dynamics for two classes of singular nonlinear traveling systems.

Hausdorff dimension of oscillatory motions for the three-body problem

Series
CDSNS Colloquium
Time
Monday, September 8, 2008 - 16:30 for 2 hours
Location
Skiles 269
Speaker
Vadim Yu Kaloshin – Mathematics Department, Penn State
Consider the classical Newtonian three-body problem. Call motions oscillatory if as times tends to infinity limsup of maximal distance among the bodies is infinite, while liminf it finite. In the '50s Sitnitkov gave the first rigorous example of oscillatory motions for the so-called restricted three-body problem.  Later in the '60s Alexeev extended this example to the three-body. A long-standing conjecture, probably going back to Kolmogorov, is that oscillatory motions have measure zero. We show that for the Sitnitkov example and for the so-called restricted planar circular three-body problem these motions have maximal Hausdorff dimension. This is a joint work with Anton Gorodetski.

Zonal jets as transport barriers in planetary atmospheres - An application of KAM theory for Hamiltonians with degeneracy

Series
CDSNS Colloquium
Time
Monday, August 25, 2008 - 16:30 for 2 hours
Location
Skiles 269
Speaker
Francisco J. Beron-Vera – Marine & Atmospheric Science, University of Miami
The connection between transport barriers and potential vorticity (PV) barriers in PV-conserving flows is investigated with a focus on zonal jets in planetary atmospheres. A perturbed PV-staircase model is used to illustrate important concepts. This flow consists of a sequence of narrow eastward and broad westward zonal jets with a staircase PV structure; the PV-steps are at the latitudes of the cores of the eastward jets. Numerically simulated solutions to the quasigeostrophic PV conservation equation in a perturbed PV-staircase flow are presented. These simulations reveal that both eastward and westward zonal jets serve as robust meridional transport barriers. The surprise is that westward jets, across which the background PV gradient vanishes, serve as robust transport barriers. A theoretical explanation of the underlying barrier mechanism is provided, which relies on recent results relating to the stability of degenerate Hamiltonians under perturbation. It is argued that transport barriers near the cores of westward zonal jets, across which the background PV gradient is small, are found in Jupiter's midlatitude weather layer and in the Earth's summer hemisphere subtropical stratosphere.

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