The helix is a ubiquitous motif for biopolymers. We propose a heuristic, entropically based model that predicts helix formation in a system of hard spheres and semiflexible tubes. We find that the entropy of the spheres is maximized when short stretches of the tube form a helix with a geometry close to that found in natural helices. Our model could be directly tested with wormlike micelles as the tubes, and the effect could be used to self-assemble supramolecular helices.

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Entropically Driven Helix Formation

In this paper we investigate the relations between a general helix and a slant helix. Moreover, we obtain some differential equations which they are characterizations for a space curve to be a slant helix. Also, we obtain the slant helix equations and its Frenet aparatus.

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Characterizations of slant helices in Euclidean 3-space

A new version of Bishop frame and an application to spherical images

We consider a curve = (s) in Minkowski 3-space E 3 and denote by f T;N;Bg the Frenet frame of . We say that is a slant helix if there exists a xed direction U of E 3 such that the function ⟨N(s);U ⟩ is constant. In this work we give characterizations of slant helices in terms of the curvature and torsion of . Finally, we discuss the tangent and binormal indicatrices of slant curves, proving that they are helices in E 3.

http://www.ndsl.kr/soc_img/society/kms/DBSHBB/2011/v48n1/DBSHBB_2011_v48n1_159.pdf

Slant helices in minkowski space e 3

Associated curves of a Frenet curve and their applications

On slant helix and its spherical indicatrix

/pdf/split-quaternions-and-rotations-in-semi-euclidean-space-e-4-7u59blkpon.pdf

Split quaternions and rotations in semi euclidean space e 4 2

In n-dimensional Euclidean space E n , harmonic curvatures of a non-degenerate curve defined by Ozdamar and Hacisalihoglu [Ozdamar E, Hacisalihoglu HH. A characterization of Inclined curves in Euclidean n-space. Comm Fac Sci Univ Ankara, Ser A1 1975;24:15–23]. In this paper, we give some characterizations for a non-degenerate curve α to be a generalized helix by using its harmonic curvatures. Also we define the generalized Darboux vector D of a non-degenerate curve α in n-dimensional Euclidean space E n and we show that the generalized Darboux vector D lies in the kernel of Frenet matrix M(s) if and only if the curve α is a generalized helix in the sense of Hayden.

Harmonic curvatures and generalized helices in En

In this paper, two new Hamilton operators are defined and the algebra of dual split quaternions isdeveloped using these operators. It is shown that finite screw motions in Minkowski 3-space can be expressedby dual-number ( 3×3 ) matrices in dual Lorentzian space. Moreover, by means of Hamilton operators, screwmotion is obtained in 3-dimensional Minkowski space 3R1

http://ijsts.shirazu.ac.ir/article_2758_1cbee7993f19305b6988ff68bebce4a5.pdf

Levent Kula

Papers

On slant helix and its spherical indicatrix

Characterizations of slant helices in Euclidean 3-space

Split quaternions and rotations in semi euclidean space e 4 2

Harmonic curvatures and generalized helices in En

Dual split quaternions and screw motion in minkowski 3-space