Spiraling solitons: A continuum model for dynamical phyllotaxis of physical systems.
A protean topological soliton has recently been shown to emerge in systems of repulsive particles in cylindrical geometries, whose statics is described by the number-theoretical objects of phyllotaxis. Here, we present a minimal and local continuum model that can explain many of the features of the phyllotactic soliton, such as locked speed, screw shift, energy transport, and--for Wigner crystal on a nanotube--charge transport. The treatment is general and should apply to other spiraling systems. Unlike, e.g., sine-Gordon-like systems, our soliton can exist between nondegenerate structures and its dynamics extends to the domains it separates; we also predict pulses, both static and dynamic. Applications include charge transport in Wigner Crystals on nanotubes or A - to B -DNA transitions.
Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Cristiano
C
Nisoli