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Conformally mapping water waves: top, bottom or sides.

Presented by: 
Andre Nachbin IMPA - Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro
Date: 
Monday 9th September 2019 - 15:00 to 15:30
Venue: 
INI Seminar Room 1
Abstract: 
I will present a brief overview of recent work showcasing conformal mapping's important role on surface water-wave dynamics. Conformal mapping can be used to flatten the free surface or a highly irregular bottom topography. It has also been used along the sides of forked channel regions, leading to a Boussinesq system with solitary waves on a graph. Mapping a highly variable bottom topography, among other features, allows the construction of a Dirichlet-to-Neumann operator over a polygonal bottom profile. One very recent example applies to a hydrodynamic pilot-wave model, capturing two bouncing droplets confined in cavities, where they can synchronize as nonlinearly coupled oscillators. Finally, on another topic, I will briefly present a very recent result displaying a spectrally accurate finite difference operator. This difference operator is constructed by unconventional means, having in mind complex analytic functions.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons