Berlin 2015 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
DY: Fachverband Dynamik und Statistische Physik
DY 44: Pattern Formation
DY 44.9: Vortrag
Donnerstag, 19. März 2015, 11:45–12:00, BH-N 333
Homoclinic snaking near the surface instability of a polarizable fluid — David J.B. Lloyd1, Christian Gollwitzer2, Ingo Rehberg2, and •Reinhard Richter2 — 1Department of Mathematics, Univ. of Surrey, Guildford, GU2 7XH, UK — 2Experimentalphysik V, Universität Bayreuth, D-95440 Bayreuth, Germany
We report on localized patches of cellular hexagons observed on the surface of a magnetic fluid in a vertical magnetic field. These patches are spontaneously generated by jumping into the neighborhood of the unstable branch of the domain covering hexagons of the Rosensweig instability. They are found to co-exist in intervals around this branch. We derive a general energy functional for the system and a corresponding Hamiltonian that provides a pattern selection principle allowing us to compute Maxwell points for general magnetic permeabilities. Using numerical continuation techniques we investigate the existence of localized hexagons in the Young-Laplace equation coupled to the Maxwell equations. We find cellular hexagons possess a Maxwell point where the energy of a single hexagon is equal to the energy of the flat state providing an energetic explanation for the multitude of measured hexagon patches. Furthermore, it is found that planar hexagon fronts and hexagon patches undergo homoclinic snaking corroborating the experimentally detected intervals.