Dynamical Systems Seminars

Fall 2017

The Dynamical Systems seminar is held on Monday afternoons at 4:00 PM in MCS 148. Tea beforehand is at 3:45 PM in MCS 144.

- September 11; José Antonio Carrillo
(Imperial College London)

Title: Swarming, Interaction Energies and PDEs

Abstract: I will present a survey of the main results about first and second order models of swarming where repulsion and attraction are modeled through pairwise potentials. We will mainly focus on the stability of the fascinating patterns that you get by random particle simulations, flocks and mills, and their qualitative behavior. Qualitative properties of local minimizers of the interaction energies are crucial in order to understand these complex behaviors. Compactly supported global minimizers determine the flock patterns whose existence is related to the classical H-stability in statistical mechanics and the classical obstacle problem for differential operators. - September 18; John Bush
(MIT)

Title: Pilot-wave hydrodynamics.

Abstract: A decade ago, Yves Couder and Emmanuel Fort discovered that droplets walking on a vibrating fluid bath exhibit several features previously thought to be exclusive to the microscopic, quantum realm. These walking droplets propel themselves by virtue of a resonant interaction with their own wavefield, and so represent the first macroscopic realization of a pilot-wave system of the form proposed for microscopic quantum dynamics by Louis de Broglie in the 1920s. New experimental and theoretical results in turn reveal and rationalize the emergence of quantization and quantum-like statistics from this hydrodynamic pilot-wave system in a number of settings. The potential and limitations of the walking droplet system as a hydrodynamic quantum analog are discussed. - September 25; Max Hess (University of Stuttgart)

Title: Validity of the Nonlinear Schrödinger approximation for quasilinear dispersive equations

We consider a nonlinear dispersive equation with a quasilinear quadratic term. We derive the Nonlinear Schrödinger (NLS) equation as a formal approximation equation describing the evolution of the envelopes of oscillating wave packet-like solutions to the quasilinear dispersive equation, and justify the NLS approximation with the help of error estimates between exact solutions to the quasilinear dispersive equation and their formal approximations obtained via the NLS equation. The proof relies on estimates of an appropriate energy whose construction is inspired by the method of normal-form transforms. Moreover, we have to overcome difficulties caused by the occurrence of resonances. The method of proof has been generalized to justify the validity of the NLS approximation for a larger class of quasilinear dispersive systems with resonances. Some ideas of this generalized method can be used to justify the NLS approximation for the arc length formulation of the two-dimensional water wave problem in case of finite depth of water and with and without surface tension. This is a joint work with Wolf-Patrick Düll. - October 2; Stephanie
Dodson (Brown University)

Title: TBA

- October 9; Holiday - No Seminar

- October 16; Casey Rodriguez (MIT)

Title: TBA

- October 23; Irving Epstein (Brandeis University)

Title: TBA

- October 30; Mickey Salins (BU)

Title: TBA

- November 6; Björn Sandstede (Brown)

Title: TBA

- November 13; Erin Compaan
(MIT)

Title: TBA

- November 20; TBA

Title: TBA

- November 27; TBA

Title: TBA

### Directions to BU Math Dept.

### Speakers from previous years