相关论文: Braid forcing and star-shaped train tracks

We prove a number of results about countable Borel equivalence relations with forcing constructions and arguments. These results reveal hidden regularity properties of Borel complete sections on certain orbits. As consequences they imply…

The (forced) periodic orbit spectrum is calculated for a chaotic time series (BZ reaction).

We consider disordered solids in which the microscopic elements can deform plastically in response to stresses on them. We show that by driving the system periodically, this plasticity can be exploited to train in desired elastic…

Bars in galaxies are mainly supported by particles trapped around closed periodic orbits. These orbits respond to the bar's forcing frequency only and lack free oscillations. We show that a similar situation takes place in double bars:…

Juggling patterns can be described by a sequence of cards which keep track of the relative order of the balls at each step. This interpretation has many algebraic and combinatorial properties, with connections to Stirling numbers, Dyck…

Higher-order unification has been shown to be undecidable. Miller discovered the pattern fragment and subsequently showed that higher-order pattern unification is decidable and has most general unifiers. We extend the algorithm to…

The formation and dynamics of a wide variety of binary two-dimensional ordered structures and superlattices are investigated through a phase field crystal model with sublattice ordering. Various types of binary ordered phases, the phase…

We investigate a simple tight-binding Hamiltonian to understand the stability of spin-polarized transport of states with an arbitrary spin content in the presence of disorder. The general spin state is made to pass through a linear chain of…

We study the effect of external forcing on the saddle-node bifurcation pattern of interval maps. By replacing fixed points of unperturbed maps by invariant graphs, we obtain direct analogues to the classical result both for random forcing…

Derived braids have been used to classify categorical structures based on the braid underlying a braided monoidal category V. With four-strand braids underlying the composition morphisms of tensor products of categories enriched over V,…

The braided Hopf algebra structure of the generalized oscillator is investigated. Using the solutions two types of braided Fibonacci oscillators are introduced. This leads to two types of braided Biedenharn-Macfarlane oscillators.

A fundamental task in developmental biology is to identify the mechanisms which drive morphogenesis. In many cases, pattern formation is driven by the positional information determined by both the gradient of maternal factors and hard-wired…

The n-string braid group of a graph X is defined as the fundamental group of the n-point configuration space of the space X. This configuration space is a finite dimensional aspherical space. A. Abrams and R. Ghrist have conjectured that…

We study a general mass transport model on an arbitrary graph consisting of $L$ nodes each carrying a continuous mass. The graph also has a set of directed links between pairs of nodes through which a stochastic portion of mass, chosen from…

Many natural counting problems arise in connection with the normal form of braids--and seem to have never been considered so far. Here we solve some of them by analysing the normality condition in terms of the associated permutations, their…

In his seminal paper on complex reflection arrangements, Bessis introduces a Garside structure for the braid group of a well-generated irreducible complex reflection group. Using this Garside structure, he establishes a strong connection…

In this paper we study the reduction curves of a braid, and how they can be used to decompose the braid into simpler ones in a precise way, which does not correspond exactly to the decomposition given by Thurston theory. Then we study how a…

A special class of braids, called woven, is introduced and it is shown that every conjugation class of the braid group contains woven braids. In consequence, links can be presented as plats or closures of woven braids. Restricting on knots,…

In strongly correlated multi-orbital systems, various ordered phases appear. In particular, the orbital order in iron-based superconductors attracts much attention since it is considered to be the origin of the nematic state. In order to…

We examine the dynamics and stripe formation in a system with competing short and long range interactions in the presence of both an applied dc drive and quenched disorder. Without disorder, the system forms stripes organized in a labyrinth…