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Related Experiment Video

Updated: Jun 29, 2026

Experimental Investigation of the Flow Structure over a Delta Wing Via Flow Visualization Methods

Experimental Investigation of the Flow Structure over a Delta Wing Via Flow Visualization Methods

Published on: April 23, 2018

Modulation analysis of large-scale discrete vortices.

Luis A Cisneros¹, Antonmaria A Minzoni, Panayotis Panayotaros

¹Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131-0001, USA. cisneros@math.unm.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 15, 2008

Summary

Large-scale vortices in discrete nonlinear Schrödinger equation systems are stabilized by self-generated potentials. This study explores vortex behavior and finds evidence for long-lived, localized, quasiperiodic structures.

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Preparation of Free-Surface Hyperbolic Water Vortices

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Last Updated: Jun 29, 2026

Experimental Investigation of the Flow Structure over a Delta Wing Via Flow Visualization Methods

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Published on: April 23, 2018

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

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Published on: July 19, 2016

Preparation of Free-Surface Hyperbolic Water Vortices

Preparation of Free-Surface Hyperbolic Water Vortices

Published on: July 28, 2023

Area of Science:

Nonlinear dynamics
Condensed matter physics
Mathematical physics

Background:

The discrete nonlinear Schrödinger equation models various physical phenomena, including light propagation in photonic lattices and Bose-Einstein condensates.
Vortices, or localized wave structures, are crucial in these systems, but their stability and behavior in discrete lattices are complex.
Previous studies primarily focused on the anticontinuum limit, leaving behavior away from this limit less explored.

Purpose of the Study:

To investigate the behavior and stabilization mechanisms of large-scale vortices in discrete nonlinear systems.
To analyze circular, polygonal, and straight vortices beyond the anticontinuum limit.
To identify conditions leading to the formation of long-lived, localized structures.

Main Methods:

Application of a discrete version of modulation theory to analyze vortex dynamics.
Numerical simulations of large-scale circular, polygonal, and straight vortices.
Investigation of vortex stabilization by self-consistent potentials and standing waves.

Main Results:

Vortices are trapped and stabilized by the Peierls-Nabarro potential they generate within the lattice.
Large-scale circular and polygonal vortices exhibit stable behavior away from the anticontinuum limit.
Straight structures are stabilized by nonconstant mean levels created by standing waves at their ends.
Numerical evidence for the existence of long-lived, localized, quasiperiodic structures.

Conclusions:

Self-consistent Peierls-Nabarro potentials play a key role in vortex stabilization in discrete nonlinear systems.
The study extends the understanding of vortex behavior in discrete systems beyond the anticontinuum limit.
The findings suggest the possibility of creating and maintaining complex localized structures in discrete nonlinear media.