Related papers: Twisting Uneven Ropes
We obtain an exact formula for the probability that a uniformly random spanning tree of the $2$-by-$n$ square grid is ``balanced'' in the sense that it has an edge whose removal partitions its vertices into two sets of equal size. We…
Twisted ribbons subjected to a tension exhibit a remarkably rich morphology, from smooth and wrinkled helicoids, to cylindrical or faceted patterns. These shapes are intimately related to the instability of the natural, helicoidal symmetry…
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…
The geometrical coupling between strain and twist in double helices is investigated. Overwinding, where strain leads to further winding, is shown to be a universal property for helices, which are stretched along their longitudinal axis when…
The ropelength of a knot is the minimum contour length of a tube of unit radius that traces out the knot in three dimensional space without self-overlap, colloquially the minimum amount of rope needed to tie a given knot. Theoretical upper…
Marine cables under low tension and torsion on the sea floor can form highly contorted three-dimensional geometries that include loops (e.g. hockles) and tangles. These geometries arise from the conversion of torsional strain energy to…
A weave is the lift to the Euclidean thickened plane of a set of infinitely many planar crossed geodesics, that can be characterized by a number of sets of threads describing the organization of the non-intersecting curves, together with a…
Given a tree of weighted vertices, it is sometimes possible to break the tree into two equally-weighted subtrees within an allowable error. We give a fast algorithm that finds an edge which breaks the tree into equal-weight components or…
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…
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…
We study symmetries between untwisted and twisted strings on asymmetric orbifolds. We present a list of asymmetric orbifold models to possess intertwining currents which convert untwisted string states to twisted ones, and vice versa. We…
An account of the transversality conditions of variational problems gives rise to essential results in the analysis of different physical phenomena. This powerful and elegant approach has proven to be fruitful in a diversity of variational…
We analyze stability of a thin inextensible elastic rod which has non-vanishing spontaneous generalized torsions in its stress-free state. Two classical problems are studied, both involving spontaneously twisted rods: a rectilinear beam…
In the graph balancing problem the goal is to orient a weighted undirected graph to minimize the maximum weighted in-degree. This special case of makespan minimization is NP-hard to approximate to a factor better than 3/2 even when there…
It has long been known to mathematicians and physicists that while a full rotation in three-dimensional Euclidean space causes tangling, two rotations can be untangled. Formally, an untangling is a based nullhomotopy of the double-twist…
We investigate the elastic energy stored in a filament pair as a function of applied twist by measuring torque under prescribed end-to-end separation conditions. We show that the torque increases rapidly to a peak with applied twist when…
Based on the recent twisting-tensor approach [T. Opatrny, ArXiv:1408.3265 (2014)], a specific scenario for fast and deep spin squeezing is proposed. Initially the state is subjected to one-axis twisting under optimum orientation, enabling…
Twisted assemblies of filaments in ropes, cables and bundles are essential structural elements in wide use in macroscopic materials as well as within the cells and tissues of living organisms. We develop the unique, non-linear elastic…
The transmission of a vertex in a connected graph is the sum of distances from that vertex to all the other vertices. A connected graph is transmission irregular if any two distinct vertices have different transmissions. We present an…
A flip in a plane spanning tree $T$ is the operation of removing one edge from $T$ and adding another edge such that the resulting structure is again a plane spanning tree. For trees on a set of points in convex position we study two…