Fall 2017
Time & Location: Typically talks will be on Fridays in Gibson Hall 414 at 3:30 PM.
Organizers: Glatt-Holtz, Nathan and Zhao, Kun
September 15
Linear Stability for 2D Boussinesq Equations
Lizheng Tao | University of California (Host Kun Zhao)
Abstract:
The 2D Boussinesq model is a partial differential equation system that models the incompressible fluid with a gravity driven components, such as temperature and density. Physically, it stands at the center of turbulence theories concerning turbulent thermal convection, like the Raleigh-Bernard convection. Mathematically, the model is also considered an insight into the 3D Navier-Stokes equations. In this talk, we will present some recent result regarding the linear stability of the solutions around the Couette flow. The perturbed solutions shows an exponential decay in the Hilbert norm stronger than the one caused by solo dissipation. This is largely due to the enhanced dissipation property of the Couette flow. The result is achieved by the hypo-coercivity theorem and a set of functionals which are equivalent to the H^s norm.
October 20
Self-organized dynamics: aggregation and flocking
Dr. Changhui TanRice University
Abstract:
Self-organized behaviors are commonly observed in nature and human societies, such as bird flocks, fish swarms and human crowds. In this talk, I will present some celebrated mathematical models, with simple small-scale interactions which lead to the emergence of global behaviors: aggregation and flocking. I will discuss the models in different scales: from microscopic agent-based dynamics, through kinetic mean-field descriptions, to macroscopic fluid systems. In particular, the macroscopic models can be viewed as compressible Euler equations with nonlocal interactions. I will show some recent results on the global wellposedness theory of the systems, large time behaviors, and interesting connections to some classical equations in fluid mechanics.
October 27
Persistence of ecological communities with evolutionary feedbacks
Swati PatelTulane University
Abstract:
A fundamental question in ecology and evolutionary biology is to understand the mechanisms that lead to the diversity that we observe in natural communities. In recent years, there has been empirical evidence that feedbacks between species densities and trait evolution, termed eco-evolutionary feedbacks, may play a role in maintaining diversity. In this talk, I will first discuss a mathematical framework for understanding diversity and the role of eco-evolutionary feedbacks. Then, I discuss results from applying this framework to understand the coexistence of two prey that share one predator.
November 3
Transition Probabilities for ASEP on the ring
Axel SaenUniversity of Virginia
Abstract:
For ASEP on the line, the system may never reach equilibrium dynamics depending on the initial conditions. Whereas for ASEP on the ring, one expects the system to reach equilibrium dynamics given enough time. In the special case of TASEP on the ring, there are recent result that give the specific crossover from KPZ dynamics and equilibrium dynamics. In collaboration with Z. Liu and D. Wang, we obtain the transition probability formulas for the periodic ASEP model. These formulas specialize to the formulas of ASEP on the line and TASEP on the ring, which are a first step to generalize the results of ASEP on the line and TASEP on the ring.
December 1
Regularity Problems of some Boussinesq Equations
Prof. Chongsheng CaoFlorida International University
Abstract:
Boussinesq systems are governing equations to the fluid flow of oceans and atmosphere. The systems are the Navier-Stokes equations and a heat transport equation. The global wellposedness of the 3D Boussinesq equations is still open. In this talk we will discuss some reduced 3D Boussinesq systems and also 2D Boussinesq systems. We will present results about the global regularity to these systems.
