Nonlocal orientation-dependent dynamics of molecular strands

Details Nonlocal orientation-dependent dynamics of molecular strands Nonlocal orientation-dependent dynamics of molecular strands

2008-03-12

arxiv.org/abs/0803.1702v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

6 pages, 1 figure, 13 references. Submitted to Compte Rendus Acad Sci. Paris, Math

Scientific paper

Time-dependent Hamiltonian dynamics is derived for a curve (molecular strand) in $\mathbb{R}^3$ that experiences both nonlocal (for example, electrostatic) and elastic interactions. The dynamical equations in the symmetry-reduced variables are written on the dual of the semidirect-product Lie algebra $so(3) \circledS (\mathbb{R}^3\oplus\mathbb{R}^3\oplus\mathbb{R}^3\oplus\mathbb{R}^3)$ with three 2-cocycles. We also demonstrate that the nonlocal interaction produces an interesting new term deriving from the coadjoint action of the Lie group SO(3) on its Lie algebra $so(3)$. The new filament equations are written in conservative form by using the corresponding coadjoint actions.

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