Conformally mapping water waves: top, bottom or sides.

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• Andre Nachbin (IMPA - Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro)
• Monday 09 September 2019, 15:00-15:30
• Seminar Room 1, Newton Institute.

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CATW01 - The complex analysis toolbox: new techniques and perspectives

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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