Helical close packings of ideal ropes

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 conditions. Plots of the relations are shown to cross each other. The physical sense of the crossing point is discussed.Comment: 14 pages, 10 figure

Ropelength of tight polygonal knots

A physical interpretation of the rope simulated by the SONO algorithm is presented. Properties of the tight polygonal knots delivered by the algorithm are analyzed. An algorithm for bounding the ropelength of a smooth inscribed knot is shown. Two ways of calculating the ropelength of tight polygonal knots are compared. An analytical calculation performed for a model knot shows that an appropriately weighted average should provide a good estimation of the minimum ropelength for relatively small numbers of edges.Comment: 27 pages, to appear in "Physical and Numerical Models in Knot Theory and their Application to the Life Sciences

The ideal trefoil knot

The most tight conformation of the trefoil knot found by the SONO algorithm is presented. Structure of the set of its self-contact points is analyzed.Comment: 11 pages, 8 figure

Two-dimensional melting far from equilibrium in a granular monolayer

We report an experimental investigation of the transition from a hexagonally ordered solid phase to a disordered liquid in a monolayer of vibrated spheres. The transition occurs as the intensity of the vibration amplitude is increased. Measurements of the density of dislocations and the positional and orientational correlation functions show evidence for a dislocation-mediated continuous transition from a solid phase with long-range order to a liquid with only short-range order. The results show a strong similarity to simulations of melting of hard disks in equilibrium, despite the fact that the granular monolayer is far from equilibrium due to the effects of interparticle dissipation and the vibrational forcing.Comment: 4 pages, 4 figure

The motion of the freely falling chain tip

The dynamics of the tip of the falling chain is analyzed. Results of laboratory experiments are presented and compared with results of numerical simulations. Time dependences of the velocity and the acceleration of the chain tip for a number of different initial conformations of the chain are determined. A simple analytical model of the system is also considered.Comment: 29 pages, 13 figure

Tropisms of the dowser texture

UID/CTM/50025/2019 M-ERA-NET2/0007/2016 Action EUTOPIA CA17139Due to its low symmetry C2υ, the dowser texture is characterised by a 2D unitary vector field or alternatively by a unitary complex field. For the same symmetry reasons, the dowser texture is sensitive, in first order, to perturbations such as thickness gradients, electric fields or flows. We will focus on corresponding properties called respectively: Cuneitropism, electrotropism and rheotropism. In particular we will show that topological defects, known as dowsons or monopoles, can be manipulated by means of these tropisms.publishersversionpublishe

On Generation, Motions, and Collisions of Dowsons

PTDC/CTM-BIO/6178/2014. M-ERA-NET2/0007/2016 (CellColor).Dowsons are ±2π point singularities of the unitary complex order parameter eiφ characterizing the so-called dowser texture in a thin nematic layer with homeotropic boundary conditions. Dowsons are therefore similar to disclinations in freely-standing smectic C films or to vortices in two-dimensional superfluids or superconductors. Using especially tailored setups called dowsons' colliders, pairs of dowsons of opposite signs are generated and set into motion on counter-rotating trajectories leading to collisions. In a first approximation, the velocity of dowsons is orthogonal and proportional to the local phase gradient (Formula presented.). The outcome of collisions, i.e., either annihilation or bypass, depends on the distance of trajectories Δφ in terms of the phase: for Δφ π the dowsons are passing by. This rule is valid only for quasi-static stationary wound up textures and can be easily broken by application of a Poiseuille flow in an appropriate direction.publishersversionpublishe