Theory for correlation functions of processes driven by external colored noise

We study steady-state correlation functions of nonlinear stochastic processes driven by external colored noise. We present a methodology that provides explicit expressions of correlation functions approximating simultaneously short- and long-time regimes. The non-Markov nature is reduced to an effective Markovian formulation, and the nonlinearities are treated systematically by means of double expansions in high and low frequencies. We also derive some exact expressions for the coefficients of these expansions for arbitrary noise by means of a generalization of projection-operator techniques.

Intensity correlation functions of dye lasers: Comparison of colored-gain-noise and colored-loss-noise models

The intensity correlation functions C(t) for the colored-gain-noise model of dye lasers are analyzed and compared with those for the loss-noise model. For correlation times ¿ larger than the deterministic relaxation time td, we show with the use of the adiabatic approximation that C(t) values coincide for both models. For small correlation times we use a method that provides explicit expressions of non-Markovian correlation functions, approximating simultaneously short- and long-time behaviors. Comparison with numerical simulations shows excellent results simultaneously for short- and long-time regimes. It is found that, when the correlation time of the noise increases, differences between the gain- and loss-noise models tend to disappear. The decay of C(t) for both models can be described by a time scale that approaches the deterministic relaxation time. However, in contrast with the loss-noise model, a secondary time scale remains for large times for the gain-noise model, which could allow one to distinguish between both models.

Generation of spatiotemporal colored noise

We develop an algorithm to simulate a Gaussian stochastic process that is non-¿-correlated in both space and time coordinates. The colored noise obeys a linear reaction-diffusion Langevin equation with Gaussian white noise. This equation is exactly simulated in a discrete Fourier space.

Bistability driven by Gaussian colored noise: First-passage times

Herein we present a calculation of the mean first-passage time for a bistable one-dimensional system driven by Gaussian colored noise of strength D and correlation time ¿c. We obtain quantitative agreement with experimental analog-computer simulations of this system. We disagree with some of the conclusions reached by previous investigators. In particular, we demonstrate that all available approximations that lead to a state-dependent diffusion coefficient lead to the same result for small D¿c.

Fractal dimension for Gaussian colored processes

The exact analytical expression for the Hausdorff dimension of free processes driven by Gaussian noise in n-dimensional space is obtained. The fractal dimension solely depends on the time behavior of the arbitrary correlation function of the noise, ranging from DX=1 for Orstein-Uhlenbeck input noise to any real number greater than 1 for fractional Brownian motions.

Harmonic oscillators driven by colored noise: crossovers, resonances and spectra

We study second-order properties of linear oscillators driven by exponentially correlated noise. We focus our attention on dynamical exponents and crossovers and also on resonance phenomena that appear when the driving noise is dichotomous. We also obtain the power spectrum and show its different behaviors according to the color of the noise.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

Dynamics of sweeping through an instability: Passage-time statistics for colored noise

A calculation of passage-time statistics is reported for the laser switch-on problem, under the influence of colored noise, when the net gain is continuously swept from below to above threshold. Cases of fast and slow sweeping are considered. In the weak-noise limit, asymptotic results are given for small and large correlation times of the noise. The mean first passage time increases with the correlation time of the noise. This effect is more important for fast sweeping than for slow sweeping.

Instrumentum Domesticum romà del Museu Episcopal de Vic. La col·lecció de segells en àmfora, tegula i morter

Les 39 marques que presentem pertanyen al fons del Museu Episcopal de Vico Es tracta, basicament, de marques ben conservades en petits fragments de ceramica, majoritariament pertanyen a àmfora, pero també existeix un petit grup en tegula, i una sola marca en mortero.

Sobre el grupo episcopal de Corduba

En este trabajo se revisa de manera preliminar la documentación disponible sobre el grupo episcopal de Corduba, con la intención de exponer una serie de consideraciones relativas a su inserción topográfica en la ciudad. Asimismo, se estudian las estructuras excavadas, con la idea de retomar la interpretación de aquellas construcciones que mejor permiten avanzar en el conocimiento general del conjunto arquitectónico.

Un vaso apulo del estilo de figuras rojas en el Museo Episcopal de Vic (Barcelona)

Previo al inicio de nuestro estudio es obligado un recuerdo, y que éste sirva de pequeño homenaje al recientemente fallecido doctor Mons. Eduard Junyent Subid., Director de la Biblioteca-Archivo Episcopal y del Museo Astístico Arqueológico Episcopal de la ciudad de Vic, miembro de la Real Academia de las Buenas Letras de Barcelona, arqueólogo e ilustre historiador.

Meta-analysis of the influence of bonding parameters on the clinical outcome of tooth-colored cervical restorations

PURPOSE: To meta-analyze the literature on the clinical performance of Class V restorations to assess the factors that influence retention, marginal integrity, and marginal discoloration of cervical lesions restored with composite resins, glass-ionomer-cement-based materials [glass-ionomer cement (GIC) and resin-modified glass ionomers (RMGICs)], and polyacid-modified resin composites (PMRC). MATERIALS AND METHODS: The English literature was searched (MEDLINE and SCOPUS) for prospective clinical trials on cervical restorations with an observation period of at least 18 months. The studies had to report about retention, marginal discoloration, marginal integrity, and marginal caries and include a description of the operative technique (beveling of enamel, roughening of dentin, type of isolation). Eighty-one studies involving 185 experiments for 47 adhesives matched the inclusion criteria. The statistical analysis was carried out by using the following linear mixed model: log (-log (Y /100)) = β + α log(T ) + error with β = log(λ), where β is a summary measure of the non-linear deterioration occurring in each experiment, including a random study effect. RESULTS: On average, 12.3% of the cervical restorations were lost, 27.9% exhibited marginal discoloration, and 34.6% exhibited deterioration of marginal integrity after 5 years. The calculation of the clinical index was 17.4% of failures after 5 years and 32.3% after 8 years. A higher variability was found for retention loss and marginal discoloration. Hardly any secondary caries lesions were detected, even in the experiments with a follow-up time longer than 8 years. Restorations placed using rubber-dam in teeth whose dentin was roughened showed a statistically significantly higher retention rate than those placed in teeth with unprepared dentin or without rubber-dam (p < 0.05). However, enamel beveling had no influence on any of the examined variables. Significant differences were found between pairs of adhesive systems and also between pairs of classes of adhesive systems. One-step self-etching had a significantly worse clinically index than two-step self-etching and three-step etch-and-rinse (p = 0.026 and p = 0.002, respectively). CONCLUSION: The clinical performance is significantly influenced by the type of adhesive system and/or the adhesive class to which the system belongs. Whether the dentin/enamel is roughened or not and whether rubberdam isolation is used or not also significantly influenced the clinical performance. Composite resin restorations placed with two-step self-etching and three-step etch-and-rinse adhesive systems should be preferred over onestep self-etching adhesive systems, GIC-based materials, and PMRCs.