Some Relations between Twisted K-theory and E8 Gauge Theory

Recently, Diaconescu, Moore and Witten provided a nontrivial link between K-theory and M-theory, by deriving the partition function of the Ramond-Ramond fields of Type IIA string theory from an E8 gauge theory in eleven dimensions. We give some relations between twisted K-theory and M-theory by adapting the method of Diaconescu-Moore-Witten and Moore-Saulina. In particular, we construct the twisted K-theory torus which defines the partition function, and also discuss the problem from the E8 loop group picture, in which the Dixmier-Douady class is the Neveu-Schwarz field. In the process of doing this, we encounter some mathematics that is new to the physics literature. In particular, the eta differential form, which is the generalization of the eta invariant, arises naturally in this context. We conclude with several open problems in mathematics and string theory.Comment: 23 pages, latex2e, corrected minor errors and typos in published versio

Area Invariance of Apparent Horizons under Arbitrary Boosts

It is a well known analytic result in general relativity that the 2-dimensional area of the apparent horizon of a black hole remains invariant regardless of the motion of the observer, and in fact is independent of the $t=constant$ slice, which can be quite arbitrary in general relativity. Nonetheless the explicit computation of horizon area is often substantially more difficult in some frames (complicated by the coordinate form of the metric), than in other frames. Here we give an explicit demonstration for very restricted metric forms of (Schwarzschild and Kerr) vacuum black holes. In the Kerr-Schild coordinate expression for these spacetimes they have an explicit Lorentz-invariant form. We consider {\it boosted} versions with the black hole moving through the coordinate system. Since these are stationary black hole spacetimes, the apparent horizons are two dimensional cross sections of their event horizons, so we compute the areas of apparent horizons in the boosted space with (boosted) $t = constant$, and obtain the same result as in the unboosted case. Note that while the invariance of area is generic, we deal only with black holes in the Kerr-Schild form, and consider only one particularly simple change of slicing which amounts to a boost. Even with these restrictions we find that the results illuminate the physics of the horizon as a null surface and provide a useful pedagogical tool. As far as we can determine, this is the first explicit calculation of this type demonstrating the area invariance of horizons. Further, these calculations are directly relevant to transformations that arise in computational representation of moving black holes. We present an application of this result to initial data for boosted black holes.Comment: 19 pages, 3 figures. Added a new section and 2 plots along with a coautho

Introduction to Isolated Horizons in Numerical Relativity

We present a coordinate-independent method for extracting mass (M) and angular momentum (J) of a black hole in numerical simulations. This method, based on the isolated horizon framework, is applicable both at late times when the black hole has reached equilibrium, and at early times when the black holes are widely separated. We show how J and M can be determined in numerical simulations in terms of only those quantities which are intrinsic to the apparent horizon. We also present a numerical method for finding the rotational symmetry vector field (required to calculate J) on the horizon.Comment: 14 pages, revtex4, 7 figures. Final PRD versio

Numerical analysis of thermofluids inside a porous enclosure with partially heated wall

In this study, heat transfer in a tall, rectangular permeable cavity with active thermal walls is investigated. Inside the enclosure, the two side walls' central portions are partially cooled at a fixed temperature. The central portion of the footwall is heated. Additionally, the top wall, the remaining portion of the footwall, and the side walls are insulated. The controlling equations are obtained from the Brinkman–Forchheimer-extended Darcy prototypical model using Boussinesq calculations. The leading equations are explained numerically by the finite element Galerkin method of weighted residuals. The computations are executed for some governing and physical parameters. The isotherms, streamlines and average heat transfer rate along with the partially active hot wall are shown for different groupings of governing parameters with respect to dimensionless time (τ). The outcomes indicated that the stream and thermal fields are strongly dependent on the considered parameters. It is also established that the average heat transfer rate is a function of these governing parameters

Toward gravitational wave detection

An overview of some tools and techniques being developed for data conditioning (regression of instrumental and environmental artifacts from the data channel), detector design evaluation (modeling the science "reach" of alternative detector designs and configurations), noise simulations for mock data challenges and analysis system validation, and analyses for the detection of gravitational radiation from gamma-ray burst sources

Trends in flood risk management in deltas around the world: Are we going ‘soft’?

Flood-risk management (FRM) is shaped by context: a society’s cultural background; physical possibilities and constraints; and the historical development of that society’s economy, politi- cal system, education, etc. These provide different drivers for change, in interaction with more global developments. We compare historical and current FRM in six delta areas and their con- texts: Rhine/Meuse/Scheldt (The Netherlands), Pearl River (China), Mekong (Vietnam), Ganges/ Brahmaputra/Meghna (Bangladesh) Zambezi/Limpopo (Mozambique), and Mississippi (USA). We show that in many countries the emphasis is shifting from ‘hard’ engineering, such as dikes, towards non-structural ‘soft’ measures, such as planning restrictions or early warning systems, while the ‘hard’ responses are softened in some by a ‘building with nature’ approach. However, this is by no means a universal development. One consistent feature of the application of ‘hard’ FRM technology to deltas is that it pushes them towards a technological ‘lock-in’ in which fewer and fewer ‘soft’ FRM alternatives are feasible due to increased ood risks. By contrast, ‘soft’ FRM is typically exible, allowing a range of future options, including future hard elements if needed and appropriate. These experiences should lead to serious re ection on whether ‘hard’ FRM should be recommended when ‘soft’ FRM options are still open