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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.

Organizers: Dave Kaspar and Kelly McQuighan

Spring 2017

Wednesday, April 12 2:00pm - 6:00pm at Brown

Jonasz Słomka (MIT)

Classical turbulence theory assumes that energy transport in a 3D turbulent flow proceeds through a Richardson cascade whereby larger vortices successively decay into smaller ones. By contrast, an additional inverse cascade characterized by vortex growth exists in 2D fluids and gases, with profound implications for meteorological flows and fluid mixing. The possibility of a helicity-driven inverse cascade in 3D fluids had been rejected in the 1970s based on equilibrium-thermodynamic arguments.

Vanja Dunjko (UMass Boston)

A key observable signature of integrability---of the existence of infinitely many "higher" conservation laws---in a system supporting solitons is the fact that a collision between solitons does not change their shape or size. But then, if solitons meet on top of a strong integrability-breaking barrier, one would expect the solitons to undergo some process consistent with energy conservation but not with higher conservation laws, such as the larger soliton cannibalizing the smaller one.

Bob Pego (Carnegie Mellon)

We study coagulation-fragmentation equations inspired by a simple model derived in fisheries science to explain data on the size distribution of schools of pelagic fish. Although the equations lack detailed balance and admit no H-theorem, we are able to develop a rather complete description of equilibrium profiles and large-time behavior, based on complex function theory for Bernstein and Pick functions. The generating function for discrete equilibrium profiles also generates the Fuss-Catalan numbers derived by Lambert in 1758) that count all ternary trees with n nodes.

Mareike Haberichter (UMass Amherst)

Topological solitons are stable, finite energy solutions to nonlinear field equations found in a variety of physical systems. Examples include vortices in superconductors, baby Skyrmions in condensed matter systems and the infamous Skyrmions of nuclear physics. In this talk, I will provide an introduction to topological solitons, with a particular focus on the solitons of Skyrme models. We will also discuss some of the nuclear physics applications of the Skyrme model.

Yujia Zhou (BU)

Theta (4-10 Hz) and gamma (30-90 Hz) rhythms in the brain are commonly associated with memory and learning. The precision of co-firing between neurons and incoming inputs is critical in these cognitive functions. We consider an inhibitory neuron model with M-current under forcing from gamma pulses and a sinusoidal current in theta frequency. The M-current has a long time constant (~100 ms) and it is shown to have resonance with theta frequencies. However, we have found that in our model, the presence of a slow M-current helps the cell phase-lock to a faster gamma input.