Dynamical phyllotaxis: transition modes and Sine-Gorden-like solitons

Repulsive particles constrained to a cylindrical surface generate a rich set of static spiral patterns known as phyllotaxis. The ground states and quasi-static transitions of phyllotaxis has been well understood based on the conventional hypothesis that particles always form a cylindrical lattice. We investigate inhomogeneous transition modes which break this helical symmetry to connect monojugate and multijugate patterns. Furthermore, traveling Sine-Gordon-like solitons in dynamical phyllotaxis are observed in numerical simulations and explained using a modified Frenkel-Kontorova model. We show that kinks propagate spirally along selected parastichies and carry an intrinsic dipole. Applications in different areas of physics are discussed.