On the Penrose Inequality for general horizons

For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the ADM mass and the area of an outermost apparent horizon, if the data are restricted suitably. We prove this by generalizing Geroch's proof of monotonicity of the Hawking mass under a smooth inverse mean curvature flow, for data with non-negative Ricci scalar. Unlike Geroch we need not confine ourselves to minimal surfaces as horizons. Modulo smoothness issues we also show that our restrictions on the data can locally be fulfilled by a suitable choice of the initial surface in a given spacetime.Comment: 4 pages, revtex, no figures. Some comments added. No essential changes. To be published in Phys. Rev. Let

Putative spin liquid in the triangle-based iridate Ba3_3IrTi2_2O9_9

We report on thermodynamic, magnetization, and muon spin relaxation measurements of the strong spin-orbit coupled iridate Ba$_3$IrTi$_2$O$_9$, which constitutes a new frustration motif made up a mixture of edge- and corner-sharing triangles. In spite of strong antiferromagnetic exchange interaction of the order of 100~K, we find no hint for long-range magnetic order down to 23 mK. The magnetic specific heat data unveil the $T$-linear and -squared dependences at low temperatures below 1~K. At the respective temperatures, the zero-field muon spin relaxation features a persistent spin dynamics, indicative of unconventional low-energy excitations. A comparison to the $4d$ isostructural compound Ba$_3$RuTi$_2$O$_9$ suggests that a concerted interplay of compass-like magnetic interactions and frustrated geometry promotes a dynamically fluctuating state in a triangle-based iridate.Comment: Physical Review B accepte

Permutation sampling in Path Integral Monte Carlo

A simple algorithm is described to sample permutations of identical particles in Path Integral Monte Carlo (PIMC) simulations of continuum many-body systems. The sampling strategy illustrated here is fairly general, and can be easily incorporated in any PIMC implementation based on the staging algorithm. Although it is similar in spirit to an existing prescription, it differs from it in some key aspects. It allows one to sample permutations efficiently, even if long paths (e.g., hundreds, or thousands of slices) are needed. We illustrate its effectiveness by presenting results of a PIMC calculation of thermodynamic properties of superfluid Helium-four, in which a very simple approximation for the high-temperature density matrix was utilized

Model-Based Edge Detector for Spectral Imagery Using Sparse Spatiospectral Masks

Two model-based algorithms for edge detection in spectral imagery are developed that specifically target capturing intrinsic features such as isoluminant edges that are characterized by a jump in color but not in intensity. Given prior knowledge of the classes of reflectance or emittance spectra associated with candidate objects in a scene, a small set of spectral-band ratios, which most profoundly identify the edge between each pair of materials, are selected to define a edge signature. The bands that form the edge signature are fed into a spatial mask, producing a sparse joint spatiospectral nonlinear operator. The first algorithm achieves edge detection for every material pair by matching the response of the operator at every pixel with the edge signature for the pair of materials. The second algorithm is a classifier-enhanced extension of the first algorithm that adaptively accentuates distinctive features before applying the spatiospectral operator. Both algorithms are extensively verified using spectral imagery from the airborne hyperspectral imager and from a dots-in-a-well midinfrared imager. In both cases, the multicolor gradient (MCG) and the hyperspectral/spatial detection of edges (HySPADE) edge detectors are used as a benchmark for comparison. The results demonstrate that the proposed algorithms outperform the MCG and HySPADE edge detectors in accuracy, especially when isoluminant edges are present. By requiring only a few bands as input to the spatiospectral operator, the algorithms enable significant levels of data compression in band selection. In the presented examples, the required operations per pixel are reduced by a factor of 71 with respect to those required by the MCG edge detector

Magnetic Domain Patterns Depending on the Sweeping Rate of Magnetic Fields

The domain patterns in a thin ferromagnetic film are investigated in both experiments and numerical simulations. Magnetic domain patterns under a zero field are usually observed after an external magnetic field is removed. It is demonstrated that the characteristics of the domain patterns depend on the decreasing rate of the external field, although it can also depend on other factors. Our numerical simulations and experiments show the following properties of domain patterns: a sea-island structure appears when the field decreases rapidly from the saturating field to the zero field, while a labyrinth structure is observed for a slowly decreasing field. The mechanism of the dependence on the field sweeping rate is discussed in terms of the concepts of crystallization.Comment: 4 pages, 3 figure

Double polarization hysteresis loop induced by the domain pinning by defect dipoles in HoMnO3 epitaxial thin films

We report on antiferroelectriclike double polarization hysteresis loops in multiferroic HoMnO3 thin films below the ferroelectric Curie temperature. This intriguing phenomenon is attributed to the domain pinning by defect dipoles which were introduced unintentionally during film growth process. Electron paramagnetic resonance suggests the existence of Fe1+ defects in thin films and first principles calculations reveal that the defect dipoles would be composed of oxygen vacancy and Fe1+ defect. We discuss migration of charged point defects during film growth process and formation of defect dipoles along ferroelectric polarization direction, based on the site preference of point defects. Due to a high-temperature low-symmetry structure of HoMnO3, aging is not required to form the defect dipoles in contrast to other ferroelectrics (e.g., BaTiO3).Comment: 4 figure