Joint Dynamics and PDE Seminar

The Boston University Department of Mathematics and Statistics and Brown University's Department of Mathematics and Division of Applied Mathematics hold joint seminars on topics in dynamics and PDE. The schedule and locations for these events can be found below. For a list of all past events of the seminar please visit the BU/Brown PDE Seminar Archive.

The organizers for the Brown/BU Seminars are Jason Bramburger and Ryan Goh.  Please contact them at jason_bramburger@Brown.edu or rgoh@bu.edu.

Fall 2017

Thursday, November 30 2:00pm - 6:00pm at BU

Eric Chang

We identify three new structures that lie in the parameter plane of a family of quartic complex maps. There exists in the parameter plane a "Sierpindelbrot (SM) arc" of infinitely many alternating Mandelbrot sets and Sierpinski holes. In fact, there are two types of SM arcs, and there are infinitely many of each in the parameter plane.

Eric Cooper

Recent numerical studies have revealed certain families of functions play a crucial role in the long time behaviour of the 2D Navier-Stokes equation with periodic boundary conditions. These functions, called bar and dipole states, exist as quasi-stationary solutions and attract trajectories of all other initial conditions exponentially fast. If the domain is the symmetric torus, then the dipole states dominate, while on the asymmetric torus the bar states dominate.

Panayotis Kevrekidis

The aim of this talk is to give an overview of stability criteria as they apply to a variety of coherent structures on infinite dimensional dynamical systems. We will start with solitary waves of the discrete nonlinear Schrodinger equation (DNLS), discussing both stability classification from the anti-continuum (uncoupled site) lattice limit and the famous Vakhitov-Kolokolov (VK) criterion.

Melissa McGuirl

An agent based model has been developed by B. Sandstede and A. Volkening to better understand the pattern formation on zebrafish in early development. This model tracks the migration, birth, death, and form changes of 5 different pigment cells. These interactions are dependent on short- and long-range length scales and several other parameters, where different parameter regimes correspond to different types of cell mutations. While this model has provided new insight on the development of zebrafish stripes, the robustness of the model has yet to be explored.

Ross Parker

The fifth-order Korteweg-de Vries equation (KdV5) is a nonlinear partial differential equation used to model dispersive phenomena such as plasma waves and capillary-gravity water waves. For wave speeds exceeding a critical threshold, KdV5 admits a countable family of double-pulse traveling-wave solutions, where the two pulses are separated by a phase paramter multiplied by an integer N.

Feng Xie

In this talk I first recall some mathematical results in the study of classical Prandtl boundary layer theory. And then, I will focus on the related well-posedness and convergence theories for the characteristic MHD boundary layer. Under the assumption that the initial tangential magnetic field is not zero, we establish the local-in-time existence and uniqueness of solutions to the nonlinear MHD boundary layer equations.

Ying Zhang

Tethered enzymatic reactions are a key component in signaling transduction pathways. It is found that many surface receptors rely on the tethering of cytoplasic kinase to initiate and integrate signaling. A large number of compartment-based ODE and stochastic models have been developed to investigate properties of such pathways over the past decade.