Synchronisation Induced by Repulsive Interactions in a System of van der Pol Oscillators

We consider a system of identical van der Pol oscillators, globally coupled through their velocities, and study how the presence of competitive interactions affects its synchronisation properties. We will address the question from two points of view. Firstly, we will investigate the role of competitive interactions on the synchronisation among identical oscillators. Then, we will show that the presence of an intermediate fraction of repulsive links results in the appearance of macroscopic oscillations at that signal's rhythm, in regions where the individual oscillator is unable to synchronise with a weak external signal

Divide and conquer: resonance induced by competitive interactions

We study an Ising model in a network with disorder induced by the presence of both attractive and repulsive links. This system is subjected to a subthreshold signal, and the goal is to see how the response is enhanced for a given fraction of repulsive links. This can model a network of spin-like neurons with excitatory and inhibitory couplings. By means of numerical simulations and analytical calculations we find that there is an optimal probability, such that the coherent response is maximal

Canonical Quantization of Spherically Symmetric Dust Collapse

Quantum gravity effects are likely to play a crucial role in determining the outcome of gravitational collapse during its final stages. In this contribution we will outline a canonical quantization of the LeMaitre-Tolman-Bondi models, which describe the collapse of spherical, inhomogeneous, non-rotating dust. Although there are many models of gravitational collapse, this particular class of models stands out for its simplicity and the fact that both black holes and naked singularity end states may be realized on the classical level, depending on the initial conditions. We will obtain the appropriate Wheeler-DeWitt equation and then solve it exactly, after regularization on a spatial lattice. The solutions describe Hawking radiation and provide an elegant microcanonical description of black hole entropy, but they raise other questions, most importantly concerning the nature of gravity's fundamental degrees of freedom.Comment: 19 pages no figures. Contribution to a festschrift in honor of Joshua N. Goldber

Quantum Gravitational Collapse and Hawking Radiation in 2+1 Dimensions

We develop the canonical theory of gravitational collapse in 2+1 dimensions with a negative cosmological constant and obtain exact solutions of the Wheeler--DeWitt equation regularized on a lattice. We employ these solutions to derive the Hawking radiation from black holes formed in all models of dust collapse. We obtain an (approximate) Planck spectrum near the horizon characterized by the Hawking temperature $T_{\mathrm H}=\hbar\sqrt{G\Lambda M}/2\pi$, where $M$ is the mass of a black hole that is presumed to form at the center of the collapsing matter cloud and $-\Lambda$ is the cosmological constant. Our solutions to the Wheeler-DeWitt equation are exact, so we are able to reliably compute the greybody factors that result from going beyond the near horizon region.Comment: 27 pages, no figure

The Quantum Stress-Tensor in Self-Similar Spherical Dust Collapse

We calculate the quantum stress tensor for a massless scalar field in the 2-d self-similar spherical dust collapse model which admits a naked singularity. We find that the outgoing radiation flux diverges on the Cauchy horizon. This may have two consequences. The resultant back reaction may prevent the naked singularity from forming, thus preserving cosmic censorship through quantum effects. The divergent flux may lead to an observable signature differentiating naked singularities from black holes in astrophysical observations.Comment: Latex File, 19 page

Quantum general relativity and Hawking radiation

In a previous paper we have set up the Wheeler-DeWitt equation which describes the quantum general relativistic collapse of a spherical dust cloud. In the present paper we specialize this equation to the case of matter perturbations around a black hole, and show that in the WKB approximation, the wave-functional describes an eternal black hole in equilibrium with a thermal bath at Hawking temperature.Comment: 13 pages, minor revisions in: (i) para 5 of Introduction, (ii) para following Eqn. (10). Revised version to appear in Phys. Rev.

Ulcerative colitis: let's talk about extent

Ulcerative colitis (UC) is a chronic inflammatory disease in which clinical course varies substantially between patients. The extent of the disease is usually pointed out as one of the factors responsible for this variation. With this study, we pretended to evaluate the differences in natural history and pharmacological therapy prescription between left-sided and extended UC