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Dynamical simulation of the motion of a wave-pocket centered in a roton frequency: note the envelope standing still while the phase moves rightward.

A system of repulsive particles constrained on a cylindrical surface has a surprisingly rich set of ground states. While its statics is described by the laws of Phyllotaxis (Levitov 1990), we have found that its dynamics provides new physics beyond what botany gives: rotons in the spectra of vibrations of stable structures, kinks and pulses that can travel as solitons. Applications include the study of alkali atoms adsorbed on carbon nanotubes, as well as Wigner crystals in cylindrical geometries. A macroscopic realization (Magnetic Cactus) of this model has been constructed out of bearings and magnets by N. Gabor, in J. Maynard group. It fulfills fairly well many of our predictions.

Spectra of phonons showing rotons
A dried cactus, beside N. Gabor's "magnetic cactus", which reproduced some of our findings with remarkable fidelity: its statics fulfill our predictions, it shows mobile kinks and pulses, and kinks have predicted shapes.
Experimental (dots) data from the magnetic cactus (N. Gabor) and calculated data (solid line) for a kink between two stable structures.
phyllotaxis movie

Dynamical simulation for the conversion of two solitons, emitted from free boundaries, into a different species after their collision. Top panel: Angular shift in radians between consecutive particles versus their magnetic index. A perfect helix corresponds to a constant angular shift between particles. Middle panel: A direct 3D rendering. Bottom panel: The lattice obtained by unwrapping the cylindrical geometry into a planar strip.

phyllotaxis movie 2

Initial conditions are such that a pair of counter-propagating solitary waves emerge from a domain boundary near an axial index of 40. Top panel: Angular shift in radians between consecutive particles versus their axial index. A perfect helix corresponds to a constant angular shift between particles. The data have been regularized by a symmetric moving average: Middle panel: A direct 3D rendering. Bottom panel: The lattice obtained by unwrapping the cylindrical geometry into a planar strip.

Publications

2009 · 2010 · All
C. Nisoli, N. Gabor, P. E. Lammert, J. D. Maynard and V. H. Crespi, "Annealing a magnetic cactus into phyllotaxis," Phys. Rev. E 81, 046107 (2010)
C. Nisoli, N. Gabor, P. E. Lammert, J. D. Maynard and V. H. Crespi, "Static and Dynamical Phyllotaxis in a Magnetic Cactus," Phys. Rev. Lett. 102, 186103 (2009) Abstract/Comments

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

V. H. Crespi : Dynamical Phyllotaxis