Second harmonic generation in plasma in the presence of SBS

The mechanism of second harmonic generation in the presence of intense-radiation SBS in plasma is considered under the condition that the incident beam has no time for filamentation. The mechanism is based on the formation of low-frequency plasma-density perturbations that are optimal for this effect in the field of scattered waves. The theoretical calculations are compared with the experimental data.     

Exact neutrino solutions in the presence of torsion

A class of exact solutions to the Einstein-Cartan-Weyl theory is presented. Certain subclasses of solutions which were previously known as “ghost” neutrinos are discussed in this context.     

Delayed bifurcations in the presence of noise

We study how an additive or multiplicative gaussian white noise reduces the delay caused by a sweeping of the control parameter through a steady bifurcation point. In particular an analytic solution can be provided when the solution which becomes unstable is the trivial zero solution.     

A boundary element method for the calculation of noise barrier insertion loss in the presence of atmospheric turbulence

Atmospheric turbulence is an important factor that limits the amount of attenuation a barrier can provide in the outdoor environment. It is therefore important to develop a reliable method to predict its effect on barrier performance. The boundary element method (BEM) has been shown to be a very effective technique for predicting barrier insertion loss in the absence of turbulence. This paper develops a simple and efficient modification of the BEM formulation to predict the insertion loss of a barrier in the presence of atmospheric turbulence. The modification is based on two alternative methods: (1) random realisations of log-amplitude and phase fluctuations of boundary sources and (2) de-correlation of source coherence using the mutual coherence function (MCF). An investigation into the behaviours of these two methods is carried out and simplified forms of the methods developed. Some systematic differences between the predictions from the methods are found. When incorporated into the BEM formulation, the method of random realisations and the method of MCF de-correlation provide predictions that agree well with predictions by the parabolic equation method and by the scattering cross-section method on a variety of thin barrier configurations.     

Deterministic phase unwrapping in the presence of noise

We present a new Fourier-based exact solution for deterministic phase unwrapping from experimental maps of wrapped phase in the presence of noise and phase vortices. This single-step approach has superior performance for images with high phase gradients or insufficient digital sampling approaching 2pi/pixel and therefore performs as a fast and practical solution for the phase-unwrapping problem for experimental applications in applied optics, physics, and medicine.     

Thermal noise for SBS suppression in fiber optical parametric amplifiers

We demonstrate a new and simple solution to suppress stimulated Brillouin scattering in fiber optical parametric amplifiers. Cumbersome PRBS or sinusoidal generators used to broaden the pump spectrum are replaced by a filtered microwave noise source. Stimulated Brillouin scattering threshold can be increased up to large values still keeping an excellent quality of amplification of nonreturn to zero signals. The simplicity and the performances of this setup open the way for a wide variety of applications for FOPAs.     

Type-II intermittency characteristics in the presence of noise

We consider a type of intermittent behavior that occurs as the result of the interplay between dynamical mechanisms giving rise to type-II intermittency and random dynamics. We analytically deduce the law for the distribution of the laminar phases, which has never been obtained hitherto. The already known dependence of the mean length of the laminar phases on the criticality parameter [Phys. Rev. E 68, 036203 (2003)] follows as a corollary of the carried out research. We also prove that this dependence obtained earlier under the assumption of the fixed form of the reinjection probability does not depend on the relaminarization properties, and, correspondingly, the obtained expression of the mean length of the laminar phases on the criticality parameter remains correct for different types of the reinjection probability.     

Branch selection in the presence of coloured noise

We have experimentally studied the effects of exponentially correlated, gaussian, additive noise on an electronic bistable system whose instability is driven by a time dependent external control parameter. The results, which indicate that the noise correlation time has little influence on the statistics of branch selection, are in substantial agreement with the predictions of a simple, physically motivated theory outlined herein.     

Communication with chemical chaos in the presence of noise

We use control of chaos to encode information into the oscillations of the Belousov-Zhabotinsky reaction. An arbitrary binary message is encoded by forcing the chaotic oscillations to follow a specified trajectory. The information manipulating control requires only small perturbations to vary the binary message. In this paper we extend our recent theoretical work [Bollt and Dolnik, Phys. Rev. E 64, 1196 (1990)] by introducing a new and simplified encoding technique which can be utilized in the presence of experimental noise. We numerically and theoretically study several practical aspects of controlling symbol dynamics including: modeling noisy time-series, learning underlying symbol dynamics, and evaluation of derivatives for control by observing system responses to an intelligent and deliberate sequence of input parameter variations. All of the modeling techniques incorporated here are ultimately designed to learn and control symbol dynamics of experimental data known only as an observed time-series; the simulation assumes no global model. We find that noise affects reliability of encoding information and may cause coding errors. But, if the level of noise is confined to relatively small values, which are achievable in experiments, the control mechanism is robust to the noise. Thus we can still produce a desired symbolic code. However, scarce errors in encoding may occur due to rare but large fluctuations. These errors may be corrected during the decoding process by a variation of the filtering technique suggested by Rosa et al. [Phys. Rev. Lett. 78, 1247 (1997)]. (c) 1998 American Institute of Physics.     

Relaxation times in the presence of external dichotomous noise

A theory to evaluate relaxation times of non-markovian stochastic processes driven by external dichotomous noise is presented. Explicit results for the Verhulst model are discussed.     

Intensity correlations in the presence of additive background noise

The mean value of the intensity correlation function and intensity spectrum of a bar object are evaluated when a spatialy random intensity is added to the deterministic object. The mean value of both functions depends upon two terms in addition to the usual term involving the deterministic object, one involves the mean and the other involves the covariance of the random background intensity.     

Exact analytical theory of aberrations of centered optical systems

In the paper we present a new theory designed to overcome the deficiencies of the existing aberration theories. The main advantage is the theory’s capacity to perform analytical, direct, and accurate radius, and thickness calculations of aberration corrections for optical components and systems. Methodologically, we derive exact formulas for bilinear transformations from an object to an image space. Next, we introduce relative parameters in the matrix coefficients and by combining bilinear and matrix transformations we develop exact corrections on-axis aberrations and field aberrations such as distortion, astigmatism, and curvatures (including sagittal and tangential). The theory with an accuracy of 10^?8 mm (except for tangential and sagittal coma) allows precise radius and thickness calculation of components and systems for aberration corrections, sets exact coordinates of free-form surfaces, and enables the study of the surface and component capacities for aberration correction. The theory has supported the design of more than 10 different patented optical systems.     

Independent component analysis in the presence of noise in fMRI

A noisy version of independent component analysis (noisy ICA) is applied to simulated and real functional magnetic resonance imaging (fMRI) data. The noise covariance is explicitly modeled by an autoregressive (AR) model of order 1. The unmixing matrix of the data is determined using a variant of the FastICA algorithm based on Gaussian moments. The sources are estimated using the principle of maximum likelihood by modeling the source densities as asymmetric exponential functions. Effect of dimensionality reduction on the effective noise covariance used, accuracy of the obtained mixing matrix and degree of improvement in estimating fMRI sources are investigated. The primary conclusions after using this method of evaluation are as follows: (a) weighting matrix estimates are similar for noisy and conventional ICA in the realm of typical fMRI data, and (b) source estimates are improved by 5% (as measured by the correlation coefficient) in realistic simulated data by explicitly modeling the source densities and the noise, even when just a simple white noise model is used.     

Exact analytical solution of a nonlinear equation arising in heat transfer

This Letter shows that the nonlinear equation arising in heat transfer recently investigated in papers [D.D. Ganji, Phys. Lett. A 355 (2006) 337; S. Abbasbandy, Phys. Lett. A 360 (2006) 109; Hafez Tari, D.D. Ganji, H. Babazadeh, Phys. Lett. A 363 (2007) 213] and [M.S.H. Chowdhury, I. Hashim, Phys. Lett. A 372 (2008) 1240] is exactly solvable, analyses the equation fully and, furthermore, gives analytic exact solution in implicit form for each value of parameters of equation.