Each month, a joint PDE seminar between the Departments of Mathematics at Boston University and Brown University and the Division of Applied Mathematics at Brown University will be held. The schedule and location for these events can be found below. To view abstracts, move your mouse over a title. Please visit the BU/Brown PDE Seminar archive page for past events in this seminar series.
Fall 2009
- Wednesday, 23 September 2009, 3:30-5:30pm in Room 110 (182 George Street) at Brown University:
- Wednesday, 21 October 2009, 3:30-5:30pm in Room MCS 137 (111 Cummington Street) at Boston University:
| Speakers | Titles |
|---|
| James Nolen (Duke University) | Stability and fluctuations for traveling waves in an
inhomogeneous mediumI will talk about generalized traveling waves for scalar
reaction diffusion equations in an inhomogeneous environment. As the
name suggests, these solutions generalize the traditional notion of a
traveling wave, although the wave profile is not fixed and the wave
speed may not be well-defined. These solutions are stable attractors.
If the environment has a certain statistical structure, then the
asymptotic wave speed is well-defined, and the interface moves like a
Brownian motion with positive drift. |
| Thierry Gallay (University of Grenoble) | Three-dimensional stability of Burgers vorticesBurgers vortices are explicit solutions of the
three-dimensional Navier-Stokes equations which are often used to
model the vortex filaments observed in turbulent flows. Despite
obvious limitations, this model describes in a correct way the
fundamental mechanisms which are responsible for the persistence of
coherent structures in three-dimensional turbulence. In this
perspective, an important problem is to determine the stability of
Burgers vortices with respect to perturbations in the largest possible
class. This question has been open for almost three decades, and
rigorous answers have been obtained so far for small Reynolds
numbers only, or in the particular case of two-dimensional
perturbations. In this talk, I shall show how a detailed analysis of
the linearized operator allows to prove the stability of Burgers
vortices with respect to three-dimensional perturbations, for any
given value of the circulation number. This is a joint work with
Yasunori Maekawa (Kobe University). |
- Next: Wednesday, 18 November 2009, 3:30-5:30pm in Room 110 (182 George Street) at Brown University:
| Speakers | Titles |
|---|
| Jonathan Rubin (University of Pittsburgh) | The geometry of neuronal oscillator recruitmentOur ability to perceive and respond to transient external stimuli arises from the brain's ability to generate sustained, spatially localized activity in response to transient inputs.
Mathematical models designed to represent this process in networks of neurons must provide a mechanism for recruitment of neurons into an active group as well as a mechanism to limit the spread of activity and hence maintain its localization.
Analysis of such models often focuses on how different localization features, such as long-range inhibition, contribute to the existence and stability of sustained, localized activity patterns.
In this talk, I will discuss work on the recruitment of neuronal oscillators, in contexts where desynchronization of inputs or competition complicate outcomes.
I will consider discrete models, most of which are not specific to neurons, as well as a continuum limit.
This work involves a geometric perspective, and the talk assumes no background knowledge of neuroscience. |
| Vadim Zharnitsky (University of Illinois) | Near-linear dynamics in KdV with periodic boundary conditionsKdV equation is a standard model of weakly nonlinear long waves on the
surface of shallow water. It will be shown that in KdV with periodic
boundary conditions, high frequency solutions evolve almost as the
linear ones for large time. For KdV (or some other dispersive
equations) on the real line such behavior could be expected due to the
dispersive decay. While on the circle (i.e. periodic boundary
conditions) such dispersive decay is not possible, the dispersion
manifests itself in averaging out nonlinearity over high frequency
solutions. This result is obtained by the application of normal form
transformations in the appropriate spaces. The integrability
properties of KdV are not used, so similar results could be obtained
for other KdV like equations. The interaction of these high frequency
solutions with a cnoidal wave will be discussed, too. This work has
been motivated by an attempt to explain some phenomena in nonlinear
optics and fluid dynamics. This is a joint work with M.B. Erdogan and
N. Tzirakis (also University of Illinois). |
- Wednesday, 2 December 2009, 3:30-5:30pm in Room MCS 137 (111 Cummington Street) at Boston University:
| Speakers | Titles |
|---|
| Robert Ghrist (University of Pennsylvania) | TBA |
Spring 2010
- Wednesday, 3 February 2010, 3:30-5:30pm in
Room 110 (182 George Street) at Brown
| Speakers | Titles |
|---|
| Bob Rink (Vrije Universiteit Amsterdam) | TBA |
| Marta Lewicka (University of Minnesota) | TBA |
- Wednesday, 24 February 2010, 3:30-5:30pm in
Room MCS 137 (111 Cummington Street) at Boston University
- Wednesday, 17 March 2010, 3:30-5:30pm in
Room 110 (182 George Street) at Brown:
| Speakers | Titles |
|---|
| Arnd Scheel (University of Minnesota) | TBA |
- Wednesday, 28 April 2010, 3:30-5:30pm in
Room MCS 137 (111 Cummington Street) at Boston University
