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      Spiraling Solitons: a Continuum Model for Dynamical Phyllotaxis and Beyond

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          Abstract

          A novel, 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-Gornon-like systems, our solitons can exist between non-degenerate structure, imply a power flow through the system, dynamics of 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.

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          Two-dimensional melting

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            Toroidal triblock copolymer assemblies.

            A stable phase of toroidal, or ringlike, supramolecular assemblies was formed by combining dilute solution characteristics critical for both bundling of like-charged biopolymers and block copolymer micelle formation. The key to toroid versus classic cylinder micelle formation is the interaction of the negatively charged hydrophilic block of an amphiphilic triblock copolymer with a positively charged divalent organic counterion. This produces a self-attraction of cylindrical micelles that leads to toroid formation, a mechanism akin to the toroidal bundling of semiflexible charged biopolymers such as DNA. The toroids can be kinetically trapped or chemically cross-linked. Insight into the mechanism of toroid formation can be gained by observation of intermediate structures kinetically trapped during film casting.
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              Author and article information

              Journal
              14 July 2009
              Article
              10.1103/PhysRevE.80.026110
              0907.2576

              http://arxiv.org/licenses/nonexclusive-distrib/1.0/

              Custom metadata
              Physical Review E 80 (2), 026110 (2009)
              8 Pages, 6 Figures, Phys Rev E in press
              cond-mat.soft cond-mat.mes-hall

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