Seminár z kvalitatívnej teórie diferenciálnych rovníc - Roy Goodman (19.3.2026)

vo štvrtok 19.3.2026 o 14:00 hod. v miestnosti M 223

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Prednášajúci: Roy Goodman (New Jersey Institute of Technology)

Názov prednášky: Leapfrogging and scattering of point vortices

Termín: 19.3.2026 14:00 hod., M 223

Abstrakt: 
The interaction among vortices is a key process in fluid motion. The n-vortex problem, which models the movement of a finite number of vortices in a two-dimensional inviscid fluid, has been studied since the late 1800s and remains relevant due to its strong link to quantum fluid dynamics. A foundational document in this area is Walter Gröbli's 1877 doctoral dissertation. We apply modern tools from dynamical systems and Hamiltonian mechanics to several problems arising from this work. First, we study the linear stability and nonlinear dynamics of the so-called leapfrogging orbit of four vortices, utilizing Hamiltonian reductions and a numerical visualization method known as Lagrangian descriptors. Second, we analyze the scattering of vortex dipoles using tools from geometric mechanics.

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