The "Nonlinear Waves and Coherent Structures Online Colloquium" is a monthly seminar that will have speakers from a diverse range of disciplines to speak on a broad range of topics connected to nonlinear waves and coherent structures. The organizers hope this series will help maintain a sense of community and provide a broad audience with access to research developments on the forefront of this field.
NWCS Colloquium
Andre Nachbin (Department of Mathematical Sciences, Worcester Polytechnic Institute)
Title: Bouncing droplets, Faraday waves and the spontaneous synchronization
of oscillators
Abstract: Couder and collaborators discovered that a droplet can bounce indefinitely and be self-
propelled, on the surface of a vibrating bath of silicon oil. At each bounce Faraday waves
are triggered leading to a wave-particle system, in a regime below the Faraday instability
threshold. This wave-particle system, not imagined to exist in classical mechanics, has
been shown to have many hydrodynamic quantum analogs.
In this presentation we will describe the weakly viscous potential theory formulation,
in a domain with highly irregular cavities which trap the droplets. Through
the Schwarz-Christoffel mapping a Dirichlet-to-Neumann operator is formulated, allowing
the 2D fluid-problem to be reduced to a 1D wave-particle system of equations. This
wave-droplet system is a novel dynamical system for an active particle on a potential of its own
making. When two droplets are bouncing at a distance, each droplet trapped in their
respective cavity, we observe a Kuramoto-like spontaneous synchronization of oscillations,
in regimes not considered by the celebrated Kuramoto model. We shall also exhibit a
case where two oscillators don't synchronize, but are correlated distance in a nontrivial
fashion.
How to join: An email containing the zoom link and password for the seminar will be sent out by 9:30am (Eastern Time) the day of the talk. To join the email list please register here
Speakers: To see the full list of upcoming speakers and recordings of prior talks, click here
Organizers:
Stathis Charalampidis, SDSU, San Diego
Sathyanarayanan Chandramouli, UMass Amherst
Panos Kevrekidis, UMass Amherst