相关论文: Helical close packings of ideal ropes

Helically close-packed states of filaments are common in natural and engineered material systems, ranging from nanoscopic biomolecules to macroscopic structural components. While the simplest models of helical close-packing, described by…

We describe several configurations of clasped ropes which are balanced and thus critical for the Gehring ropelength problem of arXiv:math.DG/0402212.

Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…

We theoretically study the conformations of a helical semi-flexible filament confined to a flat surface. This squeezed helix exhibits a variety of unexpected shapes resembling circles, waves or spirals depending on the material parameters.…

We characterize the tight closure of graded primary ideals in a homogeneous coordinate ring over an elliptic curve by numerical conditions and we show that it is in positive characteristic the same as the plus closure.

This note initiates an investigation of packing links into a region of Euclidean space to achieve a maximal density subject to geometric constraints. The upper bounds obtained apply only to the class of homotopically essential links and…

We explore the coupling between the helix-coil and coil-globule transitions of a helical polymer using Monte Carlo simulations. A very rich state diagram is found. Each state is characterized by a specific configuration of the chain which…

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…

The ropelength problem asks for the minimum-length configuration of a knotted diameter-one tube embedded in Euclidean three-space. The core curve of such a tube is called a tight knot, and its length is a knot invariant measuring…

Various packing problems and simulations of hard and soft interacting particles, such as microscopic models of nematic liquid crystals, reduce to calculations of intersections and pair interactions between ellipsoids. When constrained to a…

The problem of a suspended rope wrapped around a fixed cylinder is studied. If the suspension force is larger than a certain threshold (which is larger than the weight of the rope), the rope would remain tightly wrapped around the cylinder.…

A reformulation of the Hoop Conjecture based on the concept of trapped circle is presented. The problems of severe compactness in every spatial direction, and of how to superpose the hoops with the surface of the black hole, are resolved. A…

We explore the non-equilibrium dissipative dynamics of a system of identical charged particles trapped on a closed helix. The particles are subject to an external force accelerating them along the underlying structure. The effective…

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…

Helically coiled filaments are a frequent motif in nature. In situations commonly encountered in experiments coiled helices are squeezed flat onto two dimensional surfaces. Under such 2-D confinement helices form "squeelices" - peculiar…

We perform a compare-and-contrast investigation between the equilibrium shapes of physical and ideal trefoil knots, both in closed and open configurations. Ideal knots are purely geometric abstractions for the tightest configuration tied in…

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…

Loops are pervasive in robotics problems, appearing in mapping and localization, where one is interested in finding loop closure constraints to better approximate robot poses or other estimated quantities, as well as planning and…

Biological molecules can form hydrogen bonds between nearby residues, leading to helical secondary structures. The associated reduction of configurational entropy leads to a temperature dependence of this effect: the "helix-coil…

The parametric equations of the plane curves determining the equilibrium shapes that a uniform inextensible elastic ring or tube could take subject to a uniform hydrostatic pressure are presented in an explicit analytic form. The…