Dynamically accelerated cover times

Among observables characterizing the random exploration of a graph or lattice, the cover time, namely, the time to visit every site, continues to attract widespread interest. Much insight about cover times is gained by mapping to the (spaceless) coupon collector problem, which amounts to ignoring spatiotemporal correlations, and an early conjecture that the limiting cover time distribution of regular random walks on large lattices converges to the Gumbel distribution in d ≥ 3 was recently proved rigorously. Furthermore, a number of mathematical and numerical studies point to the robustness of the Gumbel universality to modifications of the spatial features of the random search processes (e.g., introducing persistence and/or intermittence, or changing the graph topology). Here we investigate the robustness of the Gumbel universality to dynamical modification of the temporal features of the search, specifically by allowing the random walker to “accelerate” or “decelerate” upon visiting a previously unexplored site. We generalize the mapping mentioned above by relating the statistics of cover times to the roughness of 1 / f α Gaussian signals, leading to the conjecture that the Gumbel distribution is but one of a family of cover time distributions, ranging from Gaussian for highly accelerated cover, to exponential for highly decelerated cover. While our conjecture is confirmed by systematic Monte Carlo simulations in dimensions d > 3 , our results for acceleration in d = 3 challenge the current understanding of the role of correlations in the cover time problem

Analogue Gravity and ultrashort laser pulse filamentation

Ultrashort laser pulse filaments in dispersive nonlinear Kerr media induce a moving refractive index perturbation which modifies the space-time geometry as seen by co-propagating light rays. We study the analogue geometry induced by the filament and show that one of the most evident features of filamentation, namely conical emission, may be precisely reconstructed from the geodesics. We highlight the existence of favorable conditions for the study of analogue black hole kinematics and Hawking type radiation.Comment: 4 pages, revised versio

Origin of the approximate universality of distributions in equilibrium correlated systems

We propose an interpretation of previous experimental and numerical experiments, showing that for a large class of systems, distributions of global quantities are similar to a distribution originally obtained for the magnetization in the 2D-XY model . This approach, developed for the Ising model, is based on previous numerical observations. We obtain an effective action using a perturbative method, which successfully describes the order parameter fluctuations near the phase transition. This leads to a direct link between the D-dimensional Ising model and the XY model in the same dimension, which appears to be a generic feature of many equilibrium critical systems and which is at the heart of the above observations.Comment: To appear in Europhysics Letter

Ginzburg-Landau equation bound to the metal-dielectric interface and transverse nonlinear optics with amplified plasmon polaritons

Using a multiple-scale asymptotic approach, we have derived the complex cubic Ginzburg-Landau equation for amplified and nonlinearly saturated surface plasmon polaritons propagating and diffracting along a metal-dielectric interface. An important feature of our method is that it explicitly accounts for nonlinear terms in the boundary conditions, which are critical for a correct description of nonlinear surface waves. Using our model we have analyzed filamentation and discussed bright and dark spatially localized structures of plasmons.Comment: http://link.aps.org/doi/10.1103/PhysRevA.81.03385

Renormalization group theory for finite-size scaling in extreme statistics

We present a renormalization group (RG) approach to explain universal features of extreme statistics, applied here to independent, identically distributed variables. The outlines of the theory have been described in a previous Letter, the main result being that finite-size shape corrections to the limit distribution can be obtained from a linearization of the RG transformation near a fixed point, leading to the computation of stable perturbations as eigenfunctions. Here we show details of the RG theory which exhibit remarkable similarities to the RG known in statistical physics. Besides the fixed points explaining universality, and the least stable eigendirections accounting for convergence rates and shape corrections, the similarities include marginally stable perturbations which turn out to be generic for the Fisher-Tippett-Gumbel class. Distribution functions containing unstable perturbations are also considered. We find that, after a transitory divergence, they return to the universal fixed line at the same or at a different point depending on the type of perturbation.Comment: 15 pages, 8 figures, to appear in Phys. Rev.

Dynamic Nonlinear X-waves for Femtosecond Pulse Propagation in Water

Recent experiments on femtosecond pulses in water displayed long distance propagation analogous to that reported in air. We verify this phenomena numerically and show that the propagation is dynamic as opposed to self-guided. Furthermore, we demonstrate that the propagation can be interpreted as due to dynamic nonlinear X-waves whose robustness and role in long distance propagation is shown to follow from the interplay between nonlinearity and chromatic dispersion.Comment: 4 page

Effects of Supplementary Concentrate Level and Separate or Mixed Feeding of Grass Silage and Concentrates on Carcass Tissue Colour Traits in Steers

The level of supplementary concentrates fed with grass silage and the method of feeding (separate or mixed) may affect carcass tissue colour in steers. The objectives were to determine the effects of (1) supplementary concentrate level with grass silage, and (2) separate or mixed feeding of silage and concentrates, on muscle and fat colour