Title:
SOLITON AND RATCHET MOTIONS IN HELICES
Authors:
A.V.Zolotaryuk (Bogolyubov Institute for Theoretical Physics, 252143 Kyiv,
Ukraine; Department of Mathematical Modelling, Technical University of
Denmark, DK-2800 Lyngby, Denmark), P.L.Christiansen (Department of
Mathematical Modelling, Technical University of Denmark, DK-2800 Lyngby,
Denmark), B.Nord\'{e}n (Department of Physical Chemistry, Chalmers
University of Technology, S-412 96 Gothenburg, Sweden), A.V.Savin
(Department of Mathematical Modelling, Technical University of Denmark,
DK-2800 Lyngby, Denmark; State Institute for Problems of Physics and
Technology, 119034 Moscow, The Russian Federation)
The most simple and straightforward generalization of the standard one-dimensional molecular chain with nearest-neighbour interactions to three dimensions is shown to be a helix backbone with three types of intermolecular interactions, the chain with secondary structure (e.g., $\alpha$-helix in biology). The set of coupled nonlinear field equations with respect to the longitudinal and transverse displacements of the chain molecules is derived and stable non-topological three-component soliton solutions are found numerically. These solutions describe supersonic pulses of longitudinal compression accompanied by a localized transverse bulge and a localized torsional stretching of the helix backbone. Asymmetry caused by helicity of the backbone is shown to rectify zero-mean oscillating or fluctuating motions on a simple experimental mechanical model.
Comments: Figs. 3, Refs. 19, Tabs. 0.
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