Isolated, slowly evolving, and dynamical trapping horizons: geometry and mechanics from surface deformations

We study the geometry and dynamics of both isolated and dynamical trapping horizons by considering the allowed variations of their foliating two-surfaces. This provides a common framework that may be used to consider both their possible evolutions and their deformations as well as derive the well-known flux laws. Using this framework, we unify much of what is already known about these objects as well as derive some new results. In particular we characterize and study the "almost-isolated" trapping horizons known as slowly evolving horizons. It is for these horizons that a dynamical first law holds and this is analogous and closely related to the Hawking-Hartle formula for event horizons.Comment: 39 pages, 6 figures, version to appear in PRD : a few minor changes and many typos corrected in equation

The Weakly Coupled Pfaffian as a Type I Quantum Hall Liquid

The Pfaffian phase of electrons in the proximity of a half-filled Landau level is understood to be a p+ip superconductor of composite fermions. We consider the properties of this paired quantum Hall phase when the pairing scale is small, i.e. in the weak-coupling, BCS, limit, where the coherence length is much larger than the charge screening length. We find that, as in a Type I superconductor, the vortices attract so that, upon varying the magnetic field from its magic value at \nu=5/2, the system exhibits Coulomb frustrated phase separation. We propose that the weakly and strongly coupled Pfaffian states exemplify a general dichotomy between Type I and Type II quantum Hall fluids.Comment: 4 pages, 1 figur

Drag resistance of 2D electronic microemulsions

Motivated by recent experiments of Pillarisetty {\it et al}, \prl {\bf 90}, 226801 (2003), we present a theory of drag in electronic double layers at low electron concentration. We show that the drag effect in such systems is anomolously large, it has unusual temperature and magnetic field dependences accociated with the Pomeranchuk effect, and does not vanish at zero temperature

Propagation of coherent waves in elastically scattering media

A general method for calculating statistical properties of speckle patterns of coherent waves propagating in disordered media is developed. It allows one to calculate speckle pattern correlations in space, as well as their sensitivity to external parameters. This method, which is similar to the Boltzmann-Langevin approach for the calculation of classical fluctuations, applies for a wide range of systems: From cases where the ray propagation is diffusive to the regime where the rays experience only small angle scattering. The latter case comprises the regime of directed waves where rays propagate ballistically in space while their directions diffuse. We demonstrate the applicability of the method by calculating the correlation function of the wave intensity and its sensitivity to the wave frequency and the angle of incidence of the incoming wave.Comment: 19 pages, 5 figure

Scent of the familiar: An fMRI study of canine brain responses to familiar and unfamiliar human and dog odors

Understanding dogs’ perceptual experience of both conspecifics and humans is important to understand how dogs evolved and the nature of their relationships with humans and other dogs. Olfaction is believed to be dogs’ most powerful and perhaps important sense and an obvious place to begin for the study of social cognition of conspecifics and humans. We used fMRI in a cohort of dogs (N = 12) that had been trained to remain motionless while unsedated and unrestrained in the MRI. By presenting scents from humans and conspecifics, we aimed to identify the dimensions of dogs’ responses to salient biological odors – whether they are based on species (dog or human), familiarity, or a specific combination of factors. We focused our analysis on the dog\u27s caudate nucleus because of its well-known association with positive expectations and because of its clearly defined anatomical location. We hypothesized that if dogs’ primary association to reward, whether it is based on food or social bonds, is to humans, then the human scents would activate the caudate more than the conspecific scents. Conversely, if the smell of conspecifics activated the caudate more than the smell of humans, dogs’ association to reward would be stronger to their fellow canines. Five scents were presented (self, familiar human, strange human, familiar dog, strange dog). While the olfactory bulb/peduncle was activated to a similar degree by all the scents, the caudate was activated maximally to the familiar human. Importantly, the scent of the familiar human was not the handler, meaning that the caudate response differentiated the scent in the absence of the person being present. The caudate activation suggested that not only did the dogs discriminate that scent from the others, they had a positive association with it. This speaks to the power of the dog\u27s sense of smell, and it provides important clues about the importance of humans in dogs’ lives

Hamiltonian Frenet-Serret dynamics

The Hamiltonian formulation of the dynamics of a relativistic particle described by a higher-derivative action that depends both on the first and the second Frenet-Serret curvatures is considered from a geometrical perspective. We demonstrate how reparametrization covariant dynamical variables and their projections onto the Frenet-Serret frame can be exploited to provide not only a significant simplification of but also novel insights into the canonical analysis. The constraint algebra and the Hamiltonian equations of motion are written down and a geometrical interpretation is provided for the canonical variables.Comment: Latex file, 14 pages, no figures. Revised version to appear in Class. Quant. Gra

Band structures of P-, D-, and G-surfaces

We present a theoretical study on the band structures of the electron constrained to move along triply-periodic minimal surfaces. Three well known surfaces connected via Bonnet transformations, namely P-, D-, and G-surfaces, are considered. The six-dimensional algebra of the Bonnet transformations [C. Oguey and J.-F. Sadoc, J. Phys. I France 3, 839 (1993)] is used to prove that the eigenstates for these surfaces are interrelated at a set of special points in the Brillouin zones. The global connectivity of the band structures is, however, different due to the topological differences of the surfaces. A numerical investigation of the band structures as well as a detailed analysis on their symmetry properties is presented. It is shown that the presence of nodal lines are closely related to the symmetry properties. The present study will provide a basis for understanding further the connection between the topology and the band structures.Comment: 21 pages, 8 figures, 3 tables, submitted to Phys. Rev.

Covariant coarse-graining of inhomogeneous dust flow in General Relativity

A new definition of coarse-grained quantities describing the dust flow in General Relativity is proposed. It assigns the coarse--grained expansion, shear and vorticity to finite-size comoving domains of fluid in a covariant, coordinate-independent manner. The coarse--grained quantities are all quasi-local functionals, depending only on the geometry of the boundary of the considered domain. They can be thought of as relativistic generalizations of simple volume averages of local quantities in a flat space. The procedure is based on the isometric embedding theorem for S^2 surfaces and thus requires the boundary of the domain in question to have spherical topology and positive scalar curvature. We prove that in the limit of infinitesimally small volume the proposed quantities reproduce the local expansion, shear and vorticity. In case of irrotational flow we derive the time evolution for the coarse-grained quantities and show that its structure is very similar to the evolution equation for their local counterparts. Additional terms appearing in it may serve as a measure of the backreacton of small-scale inhomogeneities of the flow on the large-scale motion of the fluid inside the domain and therefore the result may be interesting in the context of the cosmological backreaction problem. We also consider the application of the proposed coarse-graining procedure to a number of known exact solutions of Einstein equations with dust and show that it yields reasonable results.Comment: 17 pages, 5 figures. Version accepted in Classical and Quantum Gravity