Movies of an Optical Vortex in a Liquid Crystal Hitting the Cell Wall and Becoming Unstable

Stable vortex

Unstable vortex

Movies of Beam Merging in a Nematic Liquid Crystal

Four nonlinear beams in a nematic liquid crystal interact.  They merge, resulting in an optical vortex.  The evolution of the beams is mathematically related to the interaction of four gravitating bodies in Newtonian gravitation.  The difference is that in Newtonian gravitation the masses do not merge!

Four beams

Movies of Nematicon (Solitary Wave) Bouncing Around in a Liquid Crystal Cell

Bouncing nematicon

Movies for Soliton Evolution for Two-Dimensional Sine-Gordon Equation

The Sine-Gordon equation is a nonlinear wave equation which has soliton solutions. It arises in laser optics and particle physics in the Skyrme model.

Evolution of 2D Lump for the Sine-Gordon Equation

Evolution of 2D Breather for the Sine-Gordon Equation



Movie of Soliton Evolution on the Surface of a Nano-Conductor

The high electron density on the surface of a nano-conductor can lead to the phenomenon of electromigration.  Electromigration is the bulk movement of conducting material due to the electrons and can lead to undesirable effects such as short circuits.  Mathematically electromigration can in certain circumstances be described by the Benjamin-Ono Zakharov-Kutznetsov equation, which has a soliton solution.  Under this approximation, the bulk conducting material moves as a soliton along the surface of the nano-conductor.

Evolution of a Defect on a Nano-Conductor