Holographic Holes and Differential Entropy

Recently, it has been shown by Balasubramanian et al. and Myers et al. that the Bekenstein-Hawking entropy formula evaluated on certain closed surfaces in the bulk of a holographic spacetime has an interpretation as the differential entropy of a particular family of intervals (or strips) in the boundary theory. We first extend this construction to bulk surfaces which vary in time. We then give a general proof of the equality between the gravitational entropy and the differential entropy. This proof applies to a broad class of holographic backgrounds possessing a generalized planar symmetry and to certain classes of higher-curvature theories of gravity. To apply this theorem, one can begin with a bulk surface and determine the appropriate family of boundary intervals by considering extremal surfaces tangent to the given surface in the bulk. Alternatively, one can begin with a family of boundary intervals; as we show, the differential entropy then equals the gravitational entropy of a bulk surface that emerges from the intersection of the neighboring entanglement wedges, in a continuum limit.Comment: 62 pages; v2: minor improvements to presentation, references adde

Basin-scale tidal measurements using acoustic tomography

Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 1990Travel-times of acoustic signals were measured between a bottom-mounted source near Oahu and four bottom-mounted receivers located near Washington, Oregon, and California in 1988 and 1989. This paper discusses the observed tidal signals. At three out of four receivers, observed travel times at M2 and S2 periods agree with predictions from barotropic tide models to within ±30° in phase and a factor of 1.6 in amplitude. The discrepancy at the fourth receiver can be removed by including predicted effects of phase-locked baroclinic tides generated by seamounts. Our estimates of barotropic M2 tidal dissipation by seamounts vary between 2 x 1016 and 1 X 1018 erg·s-1. The variation by two orders of magnitude is due to uncertainties in the numbers and sizes of seamounts. The larger dissipation (1 x 1018 erg·s-1) is the same order as previous estimates and amounts to 4% of the total dissipation at M2

Analysis of internal wave induced mode coupling effects on the 1995 SWARM experiment acoustic transmissions

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 1997As part of the Shallow Water Acoustics in a Random Medium (SWARM) experiment [1], a sixteen element WHOI vertical line array (WVLA) was moored in 70 meters of water off the New Jersey coast. This array was sampled at 1395 Hz or higher for the seven days it was deployed. Tomography sources with carrier frequencies of 224 and 400 Hz were moored about 32 km shoreward, such that the acoustic path was anti-parallel to the primary propagation direction for shelf generated internal wave solitons. Two models for the propagation of normal modes through a 2-D waveguide with solitary internal wave (soliton) scattering included are developed to help in understanding the very complicated mode arrivals seen at the WVLA. The simplest model uses the Preisig and Duda [2] sharp interface approximation for solitons, allowing for rapid analysis of the effects of various numbers of solitons on mode arrival statistics. The second model, using SWARM thermistor string data to simulate the actual SWARM waveguides, is more realistic, but much slower. The analysis of the actual WVLA data yields spread, bias, wander, and intensity fluctuation signals that are modulated at tidal frequencies. The signals are consistent with predicted relationships to the internal wave distributions in the waveguides.The funds for my education were provided by the Office of Naval Research through an ONR Fellowship (MIT award 002734-001); the funds for SWARM were also provided by the Office of Naval Research through ONR Grant N00014-95-0051

Strong subadditivity and the covariant holographic entanglement entropy formula

Headrick and Takayanagi showed that the Ryu-Takayanagi holographic entanglement entropy formula generally obeys the strong subadditivity (SSA) inequality, a fundamental property of entropy. However, the Ryu-Takayanagi formula only applies when the bulk spacetime is static. It is not known whether the covariant generalization proposed by Hubeny, Rangamani, and Takayanagi (HRT) also obeys SSA. We investigate this question in three-dimensional AdS-Vaidya spacetimes, finding that SSA is obeyed as long as the bulk spacetime satisfies the null energy condition. This provides strong support for the validity of the HRT formula.Comment: 38 page

Electrical, mechanical, and glass transition behavior of polycarbonate-based nanocomposites with different multi-walled carbon nanotubes

Five commercially available multi-walled carbon nanotubes (MWNTs), with different characteristics, were melt mixed with polycarbonate (PC) in a twin-screw micro compounder to obtain nanocomposites containing 0.25-3.0 wt.% MWNT. The electrical properties of the composites were assessed using bulk electrical conductivity measurements, the mechanical properties of the composites were evaluated using tensile tests and dynamic mechanical analysis (DMA), and the thermal properties of the composites were investigated using differential scanning calorimetry (DSC). Electrical percolation thresholds (pcs) were observed between 0.28 wt.% and 0.60 wt.%, which are comparable with other well-dispersed melt mixed materials. Based on measurements of diameter and length distributions of unprocessed tubes it was found that nanotubes with high aspect ratios exhibited lower pcs, although one sample did show higher pc than expected (based on aspect ratio) which was attributed to poorer dispersion achieved during mixing. The stress-strain behavior of the composites is only slightly altered with CNT addition; however, the strain at break is decreased even at low loadings. DMA tests suggest the formation of a combined polymer-CNT continuous network evidenced by measurable storage moduli at temperatures above the glass transition temperature (T g), consistent with a mild reinforcement effect. The composites showed lower glass transition temperatures than that of pure PC. Lowering of the height of the tanδ peak from DMA and reductions in the heat capacity change at the glass transition from DSC indicate that MWNTs reduced the amount of polymer material that participates in the glass transition of the composites, consistent with immobilization of polymer at the nanotube interface. © 2011 Elsevier Ltd. All rights reserved

Refractory for Black Liquor Gasifiers

The University of Missouri-Rolla will identify materials that will permit the safe, reliable and economical operation of combined cycle gasifiers by the pulp and paper industry. The primary emphasis of this project will be to resolve the materials problems encountered during the operation of low-pressure high-temperature (LFHT) and low-pressure low-temperature (LPLT) gasifiers while simultaneously understanding the materials barriers to the successful demonstration of high-pressure high-temperature (HPHT) black liquor gasifiers. This study will define the chemical, thermal and physical conditions in current and proposed gasifier designs and then modify existing materials and develop new materials to successfully meet the formidable material challenges. Resolving the material challenges of black liquor gasification combined cycle technology will provide energy, environmental, and economic benefits that include higher thermal efficiencies, up to three times greater electrical output per unit of fuel, and lower emissions. In the near term, adoption of this technology will allow the pulp and paper industry greater capital effectiveness and flexibility, as gasifiers are added to increase mill capacity. In the long term, combined-cycle gasification will lessen the industry's environmental impact while increasing its potential for energy production, allowing the production of all the mill's heat and power needs along with surplus electricity being returned to the grid. An added benefit will be the potential elimination of the possibility of smelt-water explosions, which constitute an important safety concern wherever conventional Tomlinson recovery boilers are operated. Developing cost-effective materials with improved performance in gasifier environments may be the best answer to the material challenges presented by black liquor gasification. Refractory materials may be selected/developed that either react with the gasifier environment to form protective surfaces in-situ; are functionally-graded to give the best combination of thermal, mechanical, and physical properties and chemical stability; or are relatively inexpensive, reliable repair materials. Material development will be divided into 2 tasks: Task 1, Development and property determinations of improved and existing refractory systems for black liquor containment. Refractory systems of interest include magnesia aluminate and baria aluminate spinels for binder materials, both dry and hydratable, and materials with high alumina contents, 85-95 wt%, aluminum oxide, 5.0-15.0 wt%, and BaO, SrO, CaO, ZrO and SiC. Task 2, Finite element analysis of heat flow and thermal stress/strain in the refractory lining and steel shell of existing and proposed vessel designs. Stress and strain due to thermal and chemical expansion has been observed to be detrimental to the lifespan of existing black liquor gasifiers. The thermal and chemical strain as well as corrosion rates must be accounted for in order to predict the lifetime of the gasifier containment materials

Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic

We develop an iterative method for finding solutions to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas recently developed by Donaldson. As illustrations, we construct numerically the hermitian Einstein metrics on the tangent bundle and a rank three vector bundle on P^2. In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic.Comment: 25 pages, 2 figure

Numerical Hermitian Yang-Mills Connections and Vector Bundle Stability in Heterotic Theories

A numerical algorithm is presented for explicitly computing the gauge connection on slope-stable holomorphic vector bundles on Calabi-Yau manifolds. To illustrate this algorithm, we calculate the connections on stable monad bundles defined on the K3 twofold and Quintic threefold. An error measure is introduced to determine how closely our algorithmic connection approximates a solution to the Hermitian Yang-Mills equations. We then extend our results by investigating the behavior of non slope-stable bundles. In a variety of examples, it is shown that the failure of these bundles to satisfy the Hermitian Yang-Mills equations, including field-strength singularities, can be accurately reproduced numerically. These results make it possible to numerically determine whether or not a vector bundle is slope-stable, thus providing an important new tool in the exploration of heterotic vacua.Comment: 52 pages, 15 figures. LaTex formatting of figures corrected in version 2

Entanglement Entropy for Singular Surfaces

We study entanglement entropy for regions with a singular boundary in higher dimensions using the AdS/CFT correspondence and find that various singularities make new universal contributions. When the boundary CFT has an even spacetime dimension, we find that the entanglement entropy of a conical surface contains a term quadratic in the logarithm of the UV cut-off. In four dimensions, the coefficient of this contribution is proportional to the central charge 'c'. A conical singularity in an odd number of spacetime dimensions contributes a term proportional to the logarithm of the UV cut-off. We also study the entanglement entropy for various boundary surfaces with extended singularities. In these cases, similar universal terms may appear depending on the dimension and curvature of the singular locus.Comment: 66 pages,4 figures. Some typos are removed and a reference is adde