Construction of weaving and polycatenane motifs from periodic tilings of the plane

Doubly periodic weaves and polycatenanes embedded in the thickened Euclidean plane are three-dimensional complex entangled structures whose topological properties can be encoded in any generating cell of its infinite planar representation. Such a periodic cell, called motif, is a specific type of link diagram embedded on a torus consisting of essential simple closed curves for weaves, or null-homotopic for polycatenanes. In this paper, we introduce a methodology to construct such motifs using the concept of polygonal link transformations. This approach generalizes to the Euclidean plane existing methods to construct polyhedral links in the three-dimensional space. Then, we will state our main result which allows one to predict the type of motif that can be built from a given planar periodic tiling and a chosen polygonal link method.Comment: 21 pages, 11 figure

Stable configurations of entangled graphs and weaves with repulsive interactions

Entangled objects such as entangled graphs and weaves are often seen in nature. In the present article, two identical graphs entangled, and weaves with two different color threads are studied. A method to identify stable configurations in the three dimensional space of a given topological entangled structure, a planar graph with crossing information, is proposed by analyzing the steepest descent flow of the energy functional with repulsive interactions. The existence and uniqueness of a solution in the entangled case. In the untangled case, a weave has a unique tangle decomposition with height order, whose components are moving away each other in the order $t^{1/3}$ as time $t$ goes to the infinity.Comment: 37 pages, 4 figure

A Large X-ray Flare from a Single Weak-lined T Tauri Star TWA-7 Detected with MAXI GSC

We present a large X-ray flare from a nearby weak-lined T Tauri star TWA-7 detected with the Gas Slit Camera (GSC) on the Monitor of All-sky X-ray Image (MAXI). The GSC captured X-ray flaring from TWA-7 with a flux of $3\times10^{-9}$ ergs cm$^{-2}$ s$^{-1}$ in 2--20 keV band during the scan transit starting at UT 2010-09-07 18:24:30.The estimated X-ray luminosity at the scan in the energy band is 3$\times10^{32}$ ergs s$^{-1}$,indicating that the event is among the largest X-ray flares fromT Tauri stars.Since MAXI GSC monitors a target only during a scan transit of about a minute per 92 min orbital cycle, the luminosity at the flare peak might have been higher than that detected. At the scan transit, we observed a high X-ray-to-bolometric luminosity ratio, log $L_{\rm X}/L_{\rm bol}$ = $-0.1^{+0.2}_{-0.3}$; i.e., the X-ray luminosity is comparable to the bolometric luminosity. Since TWA-7 has neither an accreting disk nor a binary companion, the observed event implies that none of those are essential to generate such big flares in T Tauri stars.Comment: 4 pages, 2 figures, 1 table accepted for publication in PAS