Mechanics of universal horizons

Modified gravity models such as Ho\v{r}ava-Lifshitz gravity or Einstein-{\ae}ther theory violate local Lorentz invariance and therefore destroy the notion of a universal light cone. Despite this, in the infrared limit both models above possess static, spherically symmetric solutions with "universal horizons" - hypersurfaces that are causal boundaries between an interior region and asymptotic spatial infinity. In other words, there still exist black hole solutions. We construct a Smarr formula (the relationship between the total energy of the spacetime and the area of the horizon) for such a horizon in Einstein-{\ae}ther theory. We further show that a slightly modified first law of black hole mechanics still holds with the relevant area now a cross-section of the universal horizon. We construct new analytic solutions for certain Einstein-{\ae}ther Lagrangians and illustrate how our results work in these exact cases. Our results suggest that holography may be extended to these theories despite the very different causal structure as long as the universal horizon remains the unique causal boundary when matter fields are added.Comment: Minor clarifications. References update

Development of an internal restraint system for an integrated restraint-pressure suit system Report, 7 Jun. 1965 - 28 Jun. 1966

Internal restraint system, composed of liquid filled garment and separate auxiliary system, for integrated restraint pressure suit for acceleration protection and thermal transpor

Sticky central limit theorems at isolated hyperbolic planar singularities

© 2015, University of Washington. Akll rights reserved.We derive the limiting distribution of the barycenter bn of an i.i.d. sample of n random points on a planar cone with angular spread larger than 2π. There are three mutually exclusive possibilities: (i) (fully sticky case) after a finite random time the barycenter is almost surely at the origin; (ii) (partly sticky case) the limiting distribution of √nb<inf>n</inf> comprises a point mass at the origin, an open sector of a Gaussian, and the projection of a Gaussian to the sector’s bounding rays; or (iii) (nonsticky case) the barycenter stays away from the origin and the renormalized fluctuations have a fully supported limit distribution—usually Gaussian but not always. We conclude with an alternative, topological definition of stickiness that generalizes readily to measures on general metric spaces

State of the Union: The Poverty and Inequality Report 2016

The Stanford Center on Poverty and Inequality (CPI), one of the country's three federally-funded poverty centers, is a nonpartisan organization dedicated to monitoring trends in poverty and inequality, examining what is driving those trends, and developing science-based policy on poverty and inequality. We present here our third annual report examining the "state of the union" on poverty, inequality, and labor market outcomes.The purpose of establishing this annual series of reports is to ensure that critical facts on poverty and inequality enjoy the same visibility as other indicators of the country's health. There are of course all manner of analyses that take on separately such issues as poverty, employment, income inequality, health inequality, economic mobility, or educational access. This report instead provides a unified analysis that brings together evidence across these and other domains and thus allows for a comprehensive assessment of where the country stands

Sensitivity of Hawking radiation to superluminal dispersion relations

We analyze the Hawking radiation process due to collapsing configurations in the presence of superluminal modifications of the dispersion relation. With such superluminal dispersion relations, the horizon effectively becomes a frequency-dependent concept. In particular, at every moment of the collapse, there is a critical frequency above which no horizon is experienced. We show that, as a consequence, the late-time radiation suffers strong modifications, both quantitative and qualitative, compared to the standard Hawking picture. Concretely, we show that the radiation spectrum becomes dependent on the measuring time, on the surface gravities associated with different frequencies, and on the critical frequency. Even if the critical frequency is well above the Planck scale, important modifications still show up.Comment: 14 pages, 7 figures. Extensive paragraph added in conclusions to clarify obtained result

Probabilistic Fréchet means for time varying persistence diagrams

© 2015, Institute of Mathematical Statistics. All rights reserved.In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In [23], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in (D<inf>p</inf>, W<inf>p</inf>), the space of persistence diagrams equipped with the p-th Wasserstein metric. In particular, they showed that the Fréchet mean of a finite set of diagrams always exists, but is not necessarily unique. The means of a continuously-varying set of diagrams do not themselves (necessarily) vary continuously, which presents obvious problems when trying to extend the Fréchet mean definition to the realm of time-varying persistence diagrams, better known as vineyards. We fix this problem by altering the original definition of Fréchet mean so that it now becomes a probability measure on the set of persistence diagrams; in a nutshell, the mean of a set of diagrams will be a weighted sum of atomic measures, where each atom is itself a persistence diagram determined using a perturbation of the input diagrams. This definition gives for each N a map (D<inf>p</inf>)^N→ℙ(D<inf>p</inf>). We show that this map is Hölder continuous on finite diagrams and thus can be used to build a useful statistic on vineyards

Past and future blurring at fundamental length scale

We obtain the $\kappa$-deformed versions of the retarded and advanced Green functions and show that their causality properties are blurred in a time interval of the order of a length parameter $q=1/(2\kappa)$. The functions also indicate a smearing of the light cone. These results favor the interpretation of $q$ as a fundamental length scale below which the concept of a point in spacetime should be substituted by the concept of a fuzzy region of radius $q$, as proposed long ago by Heisenberg.Comment: Essentially, this is the version published in the Phys. Rev. Lett. 105, 211601 (2010). It has 4 pages and contains 2 figure

Performance Cycle Analysis of a Two-Spool, Separate-Exhaust Turbofan With Interstage Turbine Burner

This paper presents the performance cycle analysis of a dual-spool, separate-exhaust turbofan engine, with an Interstage Turbine Burner serving as a secondary combustor. The ITB, which is located at the transition duct between the high- and the low-pressure turbines, is a relatively new concept for increasing specific thrust and lowering pollutant emissions in modern jet engine propulsion. A detailed performance analysis of this engine has been conducted for steady-state engine performance prediction. A code is written and is capable of predicting engine performances (i.e., thrust and thrust specific fuel consumption) at varying flight conditions and throttle settings. Two design-point engines were studied to reveal trends in performance at both full and partial throttle operations. A mission analysis is also presented to assure the advantage of saving fuel by adding ITB

Three Questions on Lorentz Violation

We review the basics of the two most widely used approaches to Lorentz violation - the Stardard Model Extension and Noncommutative Field Theory - and discuss in some detail the example of the modified spectrum of the synchrotron radiation. Motivated by touching upon such a fundamental issue as Lorentz symmetry, we ask three questions: What is behind the search for Lorentz violation? Is String Theory a physical theory? Is there an alternative to Supersymmetry?Comment: 16 pages; invited luecture at DICE2006 - Piombino, Italy - September 200