The effect of temperature evolution on the interior structure of H2{}_{2}O-rich planets

For most planets in the range of radii from 1 to 4 R$_{\oplus}$, water is a major component of the interior composition. At high pressure H${}_{2}$O can be solid, but for larger planets, like Neptune, the temperature can be too high for this. Mass and age play a role in determining the transition between solid and fluid (and mixed) water-rich super-Earth. We use the latest high-pressure and ultra-high-pressure phase diagrams of H${}_{2}$O, and by comparing them with the interior adiabats of various planet models, the temperature evolution of the planet interior is shown, especially for the state of H${}_{2}$O. It turns out that the bulk of H${}_{2}$O in a planet's interior may exist in various states such as plasma, superionic, ionic, Ice VII, Ice X, etc., depending on the size, age and cooling rate of the planet. Different regions of the mass-radius phase space are also identified to correspond to different planet structures. In general, super-Earth-size planets (isolated or without significant parent star irradiation effects) older than about 3 Gyr would be mostly solid.Comment: Accepted by ApJ, in print for March 2014 (14 pages, 3 colored figures, 1 table

Zero modes and charged Skyrmions in graphene bilayer

We show that the electric charge of the Skyrmion in the vector order parameters that characterize the quantum anomalous spin Hall state and the layer-antiferromagnet in a graphene bilayer is four and zero, respectively. The result is based on the demonstration that a vortex configuration in two broken symmetry states in bilayer graphene with the quadratic band crossing has the number of zero modes doubled relative to the single layer. The doubling can be understood as a result of Kramers' theorem implied by the "pseudo time reversal" symmetry of the vortex Hamiltonian. Disordering the quantum anomalous spin Hall state by Skyrmion condensation should produce a superconductor of an elementary charge 4e.Comment: 4+ pages, one table, one figure; (v2) improved pedagogy, new expression for the Pontryagin index derived, additional explanations; (v3) new and updated references, minor typos corrected, published versio

Single sided single pass submerged arc welding of austenitic stainless steel

The weld metal produced from a series of high productivity welds of 316LN austenitic stainless steel plate was examined to evaluate the effects of the use of a higher heat input process (> 2.5kJ/mm).This high heat input process was aimed at maximising single sided weld metal penetration in a single pass using simple square edge preparations and minimising time consuming handling operations. The evaluation was undertaken by correlating the local microstructure with the local toughness and microhardness of the cap, middle and root of the weld. It was established that the intermetallic phases / carbides present did not appear to have a significantly adverse effect on either corrosion or toughness. The phases observed and confirmed by the use of SAED were predominantly chi (χ) with some sigma( σ). No identifications were made of M23C6 which was observed in other studies of 316LN welds. A series of impact tests with variations in the notch positions showed that the thickness of the delta ferrite had an effect on the weld metal toughness. As a result of this work it was established that similar volume fractions of delta ferrite did not necessarily produce similar levels of weld metal toughness, but ferrite thickness did appear to have a contributory effect. Welding of 316LN stainless steel with a single sided single pass submerged arc welding process was satisfactorily undertaken up to 20mm plate thickness without preheat or post weld heat treatment. The ability to achieve this resulted in significant economic savings within the process for ship panel production combined with satisfactory weld metal properties

Traffic congestion in interconnected complex networks

Traffic congestion in isolated complex networks has been investigated extensively over the last decade. Coupled network models have recently been developed to facilitate further understanding of real complex systems. Analysis of traffic congestion in coupled complex networks, however, is still relatively unexplored. In this paper, we try to explore the effect of interconnections on traffic congestion in interconnected BA scale-free networks. We find that assortative coupling can alleviate traffic congestion more readily than disassortative and random coupling when the node processing capacity is allocated based on node usage probability. Furthermore, the optimal coupling probability can be found for assortative coupling. However, three types of coupling preferences achieve similar traffic performance if all nodes share the same processing capacity. We analyze interconnected Internet AS-level graphs of South Korea and Japan and obtain similar results. Some practical suggestions are presented to optimize such real-world interconnected networks accordingly.Comment: 8 page

Improved Compact Visibility Representation of Planar Graph via Schnyder's Realizer

Let $G$ be an $n$-node planar graph. In a visibility representation of $G$, each node of $G$ is represented by a horizontal line segment such that the line segments representing any two adjacent nodes of $G$ are vertically visible to each other. In the present paper we give the best known compact visibility representation of $G$. Given a canonical ordering of the triangulated $G$, our algorithm draws the graph incrementally in a greedy manner. We show that one of three canonical orderings obtained from Schnyder's realizer for the triangulated $G$ yields a visibility representation of $G$ no wider than $\frac{22n-40}{15}$. Our easy-to-implement O(n)-time algorithm bypasses the complicated subroutines for four-connected components and four-block trees required by the best previously known algorithm of Kant. Our result provides a negative answer to Kant's open question about whether $\frac{3n-6}{2}$ is a worst-case lower bound on the required width. Also, if $G$ has no degree-three (respectively, degree-five) internal node, then our visibility representation for $G$ is no wider than $\frac{4n-9}{3}$ (respectively, $\frac{4n-7}{3}$). Moreover, if $G$ is four-connected, then our visibility representation for $G$ is no wider than $n-1$, matching the best known result of Kant and He. As a by-product, we obtain a much simpler proof for a corollary of Wagner's Theorem on realizers, due to Bonichon, Sa\"{e}c, and Mosbah.Comment: 11 pages, 6 figures, the preliminary version of this paper is to appear in Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science (STACS), Berlin, Germany, 200

Network Lasso: Clustering and Optimization in Large Graphs

Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and scalable solvers are often specialized to only work on a narrow class of problems. Therefore, there is a need for simple, scalable algorithms that can solve many common optimization problems. In this paper, we introduce the \emph{network lasso}, a generalization of the group lasso to a network setting that allows for simultaneous clustering and optimization on graphs. We develop an algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve this problem in a distributed and scalable manner, which allows for guaranteed global convergence even on large graphs. We also examine a non-convex extension of this approach. We then demonstrate that many types of problems can be expressed in our framework. We focus on three in particular - binary classification, predicting housing prices, and event detection in time series data - comparing the network lasso to baseline approaches and showing that it is both a fast and accurate method of solving large optimization problems