Disjoint edges in topological graphs and the tangled-thrackle conjecture

It is shown that for a constant $t\in \mathbb{N}$, every simple topological graph on $n$ vertices has $O(n)$ edges if it has no two sets of $t$ edges such that every edge in one set is disjoint from all edges of the other set (i.e., the complement of the intersection graph of the edges is $K_{t,t}$-free). As an application, we settle the \emph{tangled-thrackle} conjecture formulated by Pach, Radoi\v{c}i\'c, and T\'oth: Every $n$-vertex graph drawn in the plane such that every pair of edges have precisely one point in common, where this point is either a common endpoint, a crossing, or a point of tangency, has at most $O(n)$ edges

Anisotropy and Strong-Coupling Effects on the Collective Mode Spectrum of Chiral Superconductors: Application to Sr2_2RuO4_4

Recent theories of Sr$_2$RuO$_4$ based on the interplay of strong interactions, spin-orbit coupling and multi-band anisotropy predict chiral or helical ground states with strong anisotropy of the pairing states, with deep minima in the excitation gap, as well as strong phase anisotropy for the chiral ground state. We develop time-dependent mean field theory to calculate the Bosonic spectrum for the class of 2D chiral superconductors spanning $^3$He-A to chiral superconductors with strong anisotropy. Chiral superconductors support a pair of massive Bosonic excitations of the time-reversed pairs labeled by their parity under charge conjugation. These modes are degenerate for 2D $^3$He-A. Crystal field anisotropy lifts the degeneracy. Strong anisotropy also leads to low-lying Fermions, and thus to channels for the decay of the Bosonic modes. Selection rules and phase space considerations lead to large asymmetries in the lifetimes and hybridization of the Bosonic modes with the continuum of un-bound Fermion pairs. We also highlight results for the excitation of the Bosonic modes by microwave radiation that provide clear signatures of the Bosonic modes of an anisotropic chiral ground state.Comment: 11 pages with 8 figures. Presented as an invited talk as SCES14, Grenoble, France, July 201

LAND-USE CHANGE AND CARBON SEQUESTRATION IN THE FORESTS OF OHIO, INDIANA, AND ILLINOIS: SENSITIVITY TO POPULATION AND MODEL CHOICE

This study develops a model of land use change in the Midwestern States of Ohio, Indiana, and Illinois. Given the emergence of spatial econometrics, three models are compared to assess the sensitivity of the estimates to alternative assumptions about the distribution of their errors. Projections of future land use change are then developed, and the results are compared across different assumptions about population growth and models. We then estimate carbon sequestration potential in the region and compare the costs of different programs across the population assumptions and the alternative models. Different assumptions about population growth and error terms do not appear to affect the carbon sequestration cost estimates.Environmental Economics and Policy, Land Economics/Use,

Metallic nanorings for broadband, enhanced extraction of light from solid-state emitters

We report on the increased extraction of light emitted by solid-state sources embedded within high refractive index materials. This is achieved by making use of a local lensing effect by sub-micron metallic rings deposited on the sample surface and centered around single emitters. We show enhancements in the intensity of the light emitted by InAs/GaAs single quantum dot lines into free space as high as a factor 20. Such a device is intrinsically broadband and therefore compatible with any kind of solid-state light source. We foresee the fabrication of metallic rings via scalable techniques, like nano-imprint, and their implementation to improve the emission of classical and quantum light from solid-state sources. Furthermore, while increasing the brightness of the devices, the metallic rings can also act as top contacts for the local application of electric fields for carrier injection or wavelength tuning.Comment: 10 pages, 3 figure

High temperature fatigue behavior of tungsten copper composites

The high temperature fatigue behavior of a 9 vol percent, tungsten fiber reinforced copper matrix composite was investigated. Load-controlled isothermal fatigue experiments at 260 and 560 C and thermomechanical fatigue (TMF) experiments, both in phase and out of phase between 260 and 560 C, were performed. The stress-strain response displayed considerable inelasticity under all conditions. Also, strain ratcheting was observed during all the fatigue experiments. For the isothermal fatigue and in-phase TMF tests, the ratcheting was always in a tensile direction, continuing until failure. The ratcheting during the out-of-phase TMF test shifted from a tensile direction to a compressive direction. This behavior was thought to be associated with the observed bulging and the extensive cracking of the out-of-phase specimen. For all cases, the fatigue lives were found to be controlled by damage to the copper matrix. Grain boundary cavitation was the dominant damage mechanism of the matrix. On a stress basis, TMF loading reduced lives substantially, relative to isothermal cycling. In-phase cycling resulted in the shortest lives, and isothermal fatigue at 260 C, the longest

A creep cavity growth model for creep-fatigue life prediction of a unidirectional W/Cu composite

A microstructural model was developed to predict creep-fatigue life in a (0)(sub 4), 9 volume percent tungsten fiber-reinforced copper matrix composite at the temperature of 833 K. The mechanism of failure of the composite is assumed to be governed by the growth of quasi-equilibrium cavities in the copper matrix of the composite, based on the microscopically observed failure mechanisms. The methodology uses a cavity growth model developed for prediction of creep fracture. Instantaneous values of strain rate and stress in the copper matrix during fatigue cycles were calculated and incorporated in the model to predict cyclic life. The stress in the copper matrix was determined by use of a simple two-bar model for the fiber and matrix during cyclic loading. The model successfully predicted the composite creep-fatigue life under tension-tension cyclic loading through the use of this instantaneous matrix stress level. Inclusion of additional mechanisms such as cavity nucleation, grain boundary sliding, and the effect of fibers on matrix-stress level would result in more generalized predictions of creep-fatigue life

Characterization of failure processes in tungsten copper composites under fatigue loading conditions

A fractographic and metallographic investigation was performed on specimens of a tungsten fiber reinforced copper matrix composite (9 vol percent), which had experienced fatigue failures at elevated temperatures. Major failure modes and possible failure mechanisms, with an emphasis placed on characterizing fatigue damage accumulation, were determined. Metallography of specimens fatigued under isothermal cyclic loading suggested that fatigue damage initiates in the matrix. Cracks nucleated within the copper matrix at grain boundaries, and they propagated through cavity coalescence. The growing cracks subsequently interacted with the reinforcing tungsten fibers, producing a localized ductile fiber failure. Examinations of interrupted tests before final failure confirmed the suggested fatigue damage processes

Heat-evoked activation of TRPV4 channels in an HEK-293 cell expression system and in native mouse aorta endothelial cells

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