Motivated by the recent successes of particle models in capturing the precession and interactions of vortex structures in quasi-two-dimensional Bose-Einstein condensates, we revisit the relevant systems of ordinary differential equations. We consider the number of vortices N as a parameter and explore the prototypical configurations ('ground states') that arise in the case of few or many vortic...

We propose a numerical scheme for obtaining the stationary vortex-ring solutions of the Gross–Pitaevskii (GP) equation for an axisymmetrically trapped Bose–Einstein condensate (BEC). The effective energy functional and the associated GP equation are derived by assuming a trial phase profile for the wavefunction that is subject to the condition of circulation quantization on the rz plane. The wa...

In this paper we apply dynamical systems analyses and computational tools to fluid transport in empirically measured vortex ring flows. Measurements of quasisteadily propagating vortex rings generated by a mechanical piston-cylinder apparatus reveal lobe dynamics during entrainment and detrainment that are consistent with previous theoretical and numerical studies. In addition, the vortex ring ...

We present three-dimensional direct numerical simulations of a vortex ring settling in sharply stratified miscible ambient fluids for near two-layer configurations, and comparisons of these simulations with the results from laboratory experiments. The core fluid of the vortex rings has density higher than both the top and the bottom layers of the ambient fluid, and is fully miscible in both lay...

We simulate wave propagation in the whole heart containing a local inhomogeneity whose properties mimic some properties of cardiac tissue during the acute phase of infarction. The dynamics of cardiac tissue is described by a FitzHugh–Nagumo (FHN) model. We show that two or several short-period stimulations of the heart lead to the development of a three-dimensional vortex ring, which is a tempo...

We simulate wave propagation in the whole heart containing a local inhomogeneity whose properties mimic some properties of cardiac tissue during the acute phase of infarction. The dynamics of cardiac tissue is described by a FitzHugh-Nagumo (FHN) model. We show that two or several short-period stimulations of the heart lead to the development of a three-dimensional vortex ring, which is a tempo...

The pulsed flow about a circular non-centred orifice inside a cylindrical duct is analysed to obtain insight into the basic three-dimensional vortex dynamics that may be expected behind natural cardiac valves. The problem is approached by a highresolution numerical simulation. Results show how a small finite eccentricity generates a fully three-dimensional vortex wake that evolves quite differe...

A vortex is a flow phenomenon that is very commonly observed in nature. More than a century, a vortex ring that forms during drop splashing has caught the attention of many scientists due to its importance in understanding fluid mixing and mass transport processes. However, the origin of the vortices and their dynamics remain unclear, mostly due to the lack of appropriate visualization methods....

This cumulative dissertation presents a complete model for simulating smoke using polygonal vortex filaments. Based on a Hamiltonian system for the dynamics of smooth vortex filaments, we develop an efficient and robust algorithm that allows simulations in real time. The discrete smoke ring flow allows to use coarse polygonal vortex filaments, while preserving the qualitative behavior of the sm...