A map for heavy inertial particles in fluid flows

We introduce a map which reproduces qualitatively many fundamental properties of the dynamics of heavy particles in fluid flows. These include a uniform rate of decrease of volume in phase space, a slow-manifold effective dynamics when the single parameter $s$ (analogous of the Stokes number) approaches zero, the possibility of fold caustics in the "velocity field", and a minimum, as a function of $s$, of the Lyapunov (Kaplan-Yorke) dimension of the attractor where particles accumulate.Comment: 10 pages, 5 figure

Black Lawyers Matter: Enduring Racism in American Law Firms

Scholars and practitioners have extensively examined patterns of racial inequality in U.S. corporate law firms. In the corporate bar, pull factors that have long shaped legal professionals’ careers include promotions, outside job offers, and family priorities that may lead to leaving the labor force altogether. Push factors, such as discrimination, problems with management, and work-life conflict, also precipitate work transitions. Beyond corporate firms, however, an urgent question remains open to empirical scrutiny: How does race affect career moves in the contemporary American legal profession? In this Article, I address this question drawing upon data from the first nationally representative, longitudinal survey of U.S. lawyers. This study is one of few that uses event history analysis as a statistical technique to examine legal careers. It also draws on in-depth interviews to unravel how lawyers view their experiences at firms. These legal professionals detail how race influences assignment distribution and promotion within American law firms. Assessment of work histories of over 4,000 law school graduates, from the time they were admitted to practice in the year 2000, shows that, all else being equal, Black lawyers are pushed out of private law firms at much higher rates than white lawyers. As Black lawyers continue to strive for racial equality, these results indicate that race-conscious remedies remain critical not only for the future of law firms, but also for the broader legal profession

External Forces, Internal Dynamics: Foreign Legal Actors and Their Impact on Domestic Affairs (Book Review)

This Review examines the influence of foreign legal actors on jurisdictions that are not their own. Rachel Stern, a scholar of China, reflects on this point in her groundbreaking book published in 2013. In her penultimate chapter, Stern discusses how such foreign legal actors wield influence in China because of their presence on the ground. Building off of Stern\u27s research, this Review proceeds to ask whether foreign legal actors can influence a domestic environment when that environment prohibits them from permanently working there. The analysis below will suggest so, arguing that the forces of globalization can enable foreign legal actors to impact even a market that keeps its legal-services borders closed

Classical instability of Kerr-AdS black holes and the issue of final state

It is now established that small Kerr-Anti-de Sitter (Kerr-AdS) black holes are unstable against scalar perturbations, via superradiant amplification mechanism. We show that small Kerr-AdS black holes are also unstable against gravitational perturbations and we compute the features of this instability. We also describe with great detail the evolution of this instability. In particular, we identify its endpoint state. It corresponds to a Kerr-AdS black hole whose boundary is an Einstein universe rotating with the light velocity. This black hole is expected to be slightly oblate and to co-exist in equilibrium with a certain amount of outside radiation.Comment: 11 pages, RevTex4. v2: small typos corrected. Version to appear in Phys. Rev.

Small Kerr-anti-de Sitter black holes are unstable

Superradiance in black hole spacetimes can trigger instabilities. Here we show that, due to superradiance, small Kerr-anti-de Sitter black holes are unstable. Our demonstration uses a matching procedure, in a long wavelength approximation.Comment: 7 pages, 1 figure, RevTeX

Gravitational radiation in d>4 from effective field theory

Some years ago, a new powerful technique, known as the Classical Effective Field Theory, was proposed to describe classical phenomena in gravitational systems. Here we show how this approach can be useful to investigate theoretically important issues, such as gravitational radiation in any spacetime dimension. In particular, we derive for the first time the Einstein-Infeld-Hoffman Lagrangian and we compute Einstein's quadrupole formula for any number of flat spacetime dimensions.Comment: 32 pages, 10 figures. v2: Factor in eq. (3.11) fixed. References adde

Influence of discrete fibre reinforcement on the uniaxial compression response and seismic wave velocity of a cement-stabilised sandy-clay

A sandy clay from the northeast region of Portugal has been reinforced with polypropylene fibres and cement, and seismic wave velocity measurements and uniaxial compression strength tests were performed. Results showed that the fibre induce variations on the wave's velocity that cannot be related to real changes in the material stiffness. Therefore, care should be used when using this technique in fibre reinforced soils. The addition of fibres resulted in an increase of compression strength of the mixtures, for every cement content. Regarding the stiffness, the fibres proved to be increasingly effective with na increase in cementation, especially at the early stages of the stressestrain curve, when the secant deformability modulus increases with fibre content. However, no influence of the discrete reinforcement was detected on the peak and post-peak stages of the loading process. Fibre length showed also to be influential on strength and stiffness

Perturbations and absorption cross-section of infinite-radius black rings

We study scalar field perturbations on the background of non-supersymmetric black rings and of supersymmetric black rings. In the infinite-radius limit of these geometries, we are able to separate the wave equation, and to study wave phenomena in its vicinities. In this limit, we show that (i) both geometries are stable against scalar field perturbations, (ii) the absorption cross-section for scalar fields is equal to the area of the event horizon in the supersymmetric case, and proportional to it in the non-supersymmetric situation.Comment: ReVTeX4. 15 pages, 3 figures. References added. Published versio

Instability of non-supersymmetric smooth geometries

Recently certain non-supersymmetric solutions of type IIb supergravity were constructed [hep-th/0504181], which are everywhere smooth, have no horizons and are thought to describe certain non-BPS microstates of the D1-D5 system. We demonstrate that these solutions are all classically unstable. The instability is a generic feature of horizonless geometries with an ergoregion. We consider the endpoint of this instability and argue that the solutions decay to supersymmetric configurations. We also comment on the implications of the ergoregion instability for Mathur's `fuzzball' proposal.Comment: v2: typos corrected, reference adde

Nariai, Bertotti-Robinson and anti-Nariai solutions in higher dimensions

We find all the higher dimensional solutions of the Einstein-Maxwell theory that are the topological product of two manifolds of constant curvature. These solutions include the higher dimensional Nariai, Bertotti-Robinson and anti-Nariai solutions, and the anti-de Sitter Bertotti-Robinson solutions with toroidal and hyperbolic topology (Plebanski-Hacyan solutions). We give explicit results for any dimension D>3. These solutions are generated from the appropriate extremal limits of the higher dimensional near-extreme black holes in a de Sitter, and anti-de Sitter backgrounds. Thus, we also find the mass and the charge parameters of the higher dimensional extreme black holes as a function of the radius of the degenerate horizon.Comment: 10 pages, 11 figures, RevTeX4. References added. Published versio