Phase-space structure of two-dimensional excitable localized structures

In this work we characterize in detail the bifurcation leading to an excitable regime mediated by localized structures in a dissipative nonlinear Kerr cavity with a homogeneous pump. Here we show how the route can be understood through a planar dynamical system in which a limit cycle becomes the homoclinic orbit of a saddle point (saddle-loop bifurcation). The whole picture is unveiled, and the mechanism by which this reduction occurs from the full infinite-dimensional dynamical system is studied. Finally, it is shown that the bifurcation leads to an excitability regime, under the application of suitable perturbations. Excitability is an emergent property for this system, as it emerges from the spatial dependence since the system does not exhibit any excitable behavior locally.Comment: 10 pages, 9 figure

Effects of a localized beam on the dynamics of excitable cavity solitons

We study the dynamical behavior of dissipative solitons in an optical cavity filled with a Kerr medium when a localized beam is applied on top of the homogeneous pumping. In particular, we report on the excitability regime that cavity solitons exhibits which is emergent property since the system is not locally excitable. The resulting scenario differs in an important way from the case of a purely homogeneous pump and now two different excitable regimes, both Class I, are shown. The whole scenario is presented and discussed, showing that it is organized by three codimension-2 points. Moreover, the localized beam can be used to control important features, such as the excitable threshold, improving the possibilities for the experimental observation of this phenomenon.Comment: 9 Pages, 12 figure

Large optical gain from four-wave mixing instabilities in semiconductor quantum wells

Based on a microscopic many-particle theory, we predict large optical gain in the probe and background-free four-wave mixing directions caused by excitonic instabilities in semiconductor quantum wells. For a single quantum well with radiative-decay limited dephasing in a typical pump-probe setup we discuss the microscopic driving mechanisms and polarization and frequency dependence of these instabilities

The Rising Light Curves of Type Ia Supernovae

We present an analysis of the early, rising light curves of 18 Type Ia supernovae (SNe Ia) discovered by the Palomar Transient Factory (PTF) and the La Silla-QUEST variability survey (LSQ). We fit these early data flux using a simple power-law $(f(t) = {\alpha\times t^n})$ to determine the time of first light $({t_0})$, and hence the rise-time $({t_{rise}})$ from first light to peak luminosity, and the exponent of the power-law rise ($n$). We find a mean uncorrected rise time of $18.98 {\pm} 0.54$ days, with individual SN rise-times ranging from $15.98$ to $24.7$ days. The exponent n shows significant departures from the simple 'fireball model' of $n = 2$ (or ${f(t) \propto t^2}$) usually assumed in the literature. With a mean value of $n = 2.44 {\pm} 0.13$, our data also show significant diversity from event to event. This deviation has implications for the distribution of 56Ni throughout the SN ejecta, with a higher index suggesting a lesser degree of 56Ni mixing. The range of n found also confirms that the 56Ni distribution is not standard throughout the population of SNe Ia, in agreement with earlier work measuring such abundances through spectral modelling. We also show that the duration of the very early light curve, before the luminosity has reached half of its maximal value, does not correlate with the light curve shape or stretch used to standardise SNe Ia in cosmological applications. This has implications for the cosmological fitting of SN Ia light curves.Comment: 19 pages, 19 figures, accepted for publication in MNRA

Spatial correlations in hexagons generated via a Kerr nonlinearity

We consider the hexagonal pattern forming in the cross-section of an optical beam produced by a Kerr cavity, and we study the quantum correlations characterizing this structure. By using arguments related to the symmetry broken by the pattern formation, we identify a complete scenario of six-mode entanglement. Five independent phase quadratures combinations, connecting the hexagonal modes, are shown to exhibit sub-shot-noise fluctuations. By means of a non-linear quantum calculation technique, quantum correlations among the mode photon numbers are demonstrated and calculated.Comment: ReVTeX file, 20 pages, 7 eps figure

Fluctuations and correlations in hexagonal optical patterns

We analyze the influence of noise in transverse hexagonal patterns in nonlinear Kerr cavities. The near field fluctuations are determined by the neutrally stable Goldstone modes associated to translational invariance and by the weakly damped soft modes. However these modes do not contribute to the far field intensity fluctuations which are dominated by damped perturbations with the same wave vectors than the pattern. We find strong correlations between the intensity fluctuations of any arbitrary pair of wave vectors of the pattern. Correlation between pairs forming 120 degrees is larger than between pairs forming 180 degrees, contrary to what a naive interpretation of emission in terms of twin photons would suggest.Comment: 10 pages, 13 figure

Steps towards a map of the nearby universe

We present a new analysis of the Sloan Digital Sky Survey data aimed at producing a detailed map of the nearby (z < 0.5) universe. Using neural networks trained on the available spectroscopic base of knowledge we derived distance estimates for about 30 million galaxies distributed over ca. 8,000 sq. deg. We also used unsupervised clustering tools developed in the framework of the VO-Tech project, to investigate the possibility to understand the nature of each object present in the field and, in particular, to produce a list of candidate AGNs and QSOs.Comment: 3 pages, 1 figure. To appear in Nucl Phys. B, in the proceedings of the NOW-2006 (Neutrino Oscillation Workshop - 2006), R. Fogli et al. ed

Food and mood:how do diet and nutrition affect mental wellbeing?

Poor nutrition may be a causal factor in the experience of low mood, and improving diet may help to protect not only the physical health but also the mental health of the population. Depression and anxiety are the most common mental health conditions worldwide, making them a leading cause of disability.1 Even beyond diagnosed conditions, subclinical symptoms of depression and anxiety affect the wellbeing and functioning of a large proportion of the population.2 Therefore, new approaches to managing both clinically diagnosed and subclinical depression and anxiety are needed