Helices

Chouaieb et al. 10.1073/pnas.0508370103.

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Fig. 5. Three helical configurations with identical helical centerlines but different registers. The dark lines on the tubes indicate the orientation of the directors d₁, d₂. (A) A uniform helical equilibrium, i.e., j' = 0; here the directors follow the normal and binormal vectors, and there is no excess twist. The absence of excess twist is the generic case for nonisotropic rods. (B) A nonuniform equilibrium for an isotropic rod. Here j = 4s, and the vector d₁ rotates in the normal plane with constant velocity as s increases. This situation is always possible for isotropic rods where an arbitrary linear register can be added to any helical configuration. (C) A nonuniform helical equilibrium obtained for a nonisotropic rod with quadratic energy (Eq. A20) and register (Eq. A21). Such examples are highly exceptional.