Related papers: The ancient art of laying rope
Closely packed conformations of helices formed on the ideal rope are considered. The pitch versus radius relations which define a closely packed helix are determined. The relations stem from the turn-to-turn distance and curvature limiting…
A classical two-stranded rope can be made by twisting two identical strands together under strain. Despite being conceptually simple, the contact-equations for helically twisted identical strands have only been solved within the last 20…
Helical structures, almost ubiquitous in biological systems, have inspired the design and manufacturing of helical devices with applications in nanoelecromechanical systems (NEMS), morphing structures, optoelectronics, micro-robotics and…
Helical ribbons arise in many biological and engineered systems, often driven by anisotropic surface stress, residual strain, and geometric or elastic mismatch between layers of a laminated composite. A full mathematical analysis is…
Using continuum elasticity theory, we describe the elastic behavior of helical coils with an asymmetric double-helix structure and identify conditions, under which they become very rigid. Theoretical insight gained for macro-structures…
Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, e.g. it can bend without…
Weaving typically involves forming a sufrace by interlacing fibers into a mechanically stable arrangement, effectively making a two-dimensional object out of one-dimensional objects. Moorish Fretwork involves interweaving solid helical…
For over a century, the structure of materials has been described by a combination of rotations, rotation-inversions and translational symmetries. By recognizing the reversal of static structural rotations between clockwise and…
Grasping mechanisms must both create and subsequently hold grasps that permit safe and effective object manipulation. Existing mechanisms address the different functional requirements of grasp creation and grasp holding using a single…
Helicity is a fundamental property of magnetic fields, conserved in ideal MHD. In flux rope topology, it consists of twist and writhe helicity. Despite the common occurrence of helical structures in the solar atmosphere, little is known…
We study simple, knotted and linked torus windings that are made of tubes of finite thickness. Knots which have the shortest rope length are often denoted ideal structures. Conventionally, the ideal structure are found by rope shortening…
Thin viscous fluid threads falling onto a moving belt behave in a way reminiscent of a sewing machine, generating a rich variety of periodic stitch-like patterns including meanders, W-patterns, alternating loops, and translated coiling.…
Soft elastic filaments that can be stretched, bent and twisted exhibit a range of topologically and geometrically complex morphologies that include plectonemes, solenoids, knot-like and braid-like structures. We combine numerical…
By enumerating all sequences of length 20, we study the designability of structures in a two-dimensional Hydrophobic-Polar (HP) lattice model in a wide range of inter-monomer interaction parameters. We find that although the histogram of…
Helical structures are ubiquitous in nature and engineering, ranging from DNA molecules to plant tendrils, from sea snail shells to nanoribbons. While the helical shapes in natural and engineered systems often exhibit nearly uniform radius…
This paper develops the foundations of Hom-heaps, Hom-trusses, and Hom-braces as natural Hom-type analogues of their classical counterparts. We establish the correspondence between Hom-heaps and Hom-groups, showing that the retract of a…
This article present the double-periodical lattice made of infinite elastic fibers that withstand bending and tension. The model describes the elastic properties of flat periodic structure. With this model the behavior of a two-dimensional…
An alternating torus knot or link may be constructed from a repeating double helix after connecting its two ends. A structure with additional helices may be closed to form a non-alternating torus knot or link. Previous work has optimized…
We solve several problems that involve imposing metrics on surfaces. The problem of a strip with a linear metric gradient is formulated in terms of a Lagrangean similar to those used for spin systems. We are able to show that the low energy…
Helical objects are often implemented in electronic or mechanical micro-systems, requiring a precise understanding of their mechanical properties. While helices formed by cylindrical filaments have been intensely investigated, little is…