Motion of vortices outside a cylinder

Abstract

The problem of motion of the vortices around an oscillating cylinder in the presence of a uniform flow is considered. The Hamiltonian for vortex motion for the case with no uniform flow and stationary cylinder is constructed, reduced, and constant Hamiltonian (energy) curves are plotted when the system is shown to be integrable according to Liouville. By adding uniform flow to the system and by allowing the cylinder to vibrate, we model the natural vibration of the cylinder in the flow field, which has applications in ocean engineering involving tethers or pipelines in a flow field. We conclude that in the chaotic case forces on the cylinder may be considerably larger than those on the integrable case depending on the initial positions of vortices and that complex phenomena such as chaotic capture and escape occur when the initial positions lie in a certain region.

Lyapunov-Exponent Spectrum From Noisy Time Series

“…The deterministic chaos of nonlinear dynamical systems has become a very interesting subject in many fields of science, including hydrodynamics [Wang, 2005;Tulu & Yilmaz, 2010;Schneider et al, 2007], economics [Chen, 2008;Medio et al, 2009;Wang et al, 2004], biomedicine [Brackley et al, 2010;Azarnoosh et al, 2011], and quantummechanics [Kowalski et al, 2003]. There are several important invariants to characterize deterministic chaos, which are Lyapunov exponents, Kolmogorov entropy, and fractal dimension.…”

µ-diff: A matlab toolbox for multiple scattering problems by disks

“…Even if disks can be considered as simple geometries, a reliable and highly accurate solution is required for wave propagation problems (acoustics, electromagnetics, optics, nanophotonics, elasticity) that involve many circular scatterers, modeling structured or disordered media, most particularly when k and M are large (see e.g. [9,15,19,20,21,22,24,33,34,35,36,39,40,42,45,49,50,52]). Let us note that all the developments in this paper directly apply to 2D TM/TE electromagnetic scattering waves [37] even if our presentation is more related to acoustics.…”