On the modulation instability development in optical fiber systems

Extensive numerical simulations were performed to investigate all stages of modulation instability development from the initial pulse of pico-second duration in photonic crystal fiber: quasi-solitons and dispersive waves formation, their interaction stage and the further propagation. Comparison between 4 different NLS-like systems was made: the classical NLS equation, NLS system plus higher dispersion terms, NLS plus higher dispersion and self-steepening and also fully generalized NLS equation with Raman scattering taken into account. For the latter case a mechanism of energy transfer from smaller quasi-solitons to the bigger ones is proposed to explain the dramatical increase of rogue waves appearance frequency in comparison to the systems when the Raman scattering is not taken into account.Comment: 9 pages, 54 figure

On the Hausdorff dimension of invariant measures of weakly contracting on average measurable IFS

We consider measures which are invariant under a measurable iterated function system with positive, place-dependent probabilities in a separable metric space. We provide an upper bound of the Hausdorff dimension of such a measure if it is ergodic. We also prove that it is ergodic iff the related skew product is.Comment: 16 pages; to appear in Journal of Stat. Phy

Curvature Diffusions in General Relativity

We define and study on Lorentz manifolds a family of covariant diffusions in which the quadratic variation is locally determined by the curvature. This allows the interpretation of the diffusion effect on a particle by its interaction with the ambient space-time. We will focus on the case of warped products, especially Robertson-Walker manifolds, and analyse their asymptotic behaviour in the case of Einstein-de Sitter-like manifolds.Comment: 34 page

Tradition and Prudence in Locke's Exceptions to Toleration

Why did Locke exclude Catholics and atheists from toleration? Not, I contend, because he was trapped by his context, but because his prudential approach and practica ljudgments led him to traditiona ltexts. I make this argumentfirst by outlining the connections among prudential exceptionality, practical judgments, and traditional texts. I then describe important continuities betweenc onventional English understandings of the relationship between state and religion and Locke's writings on toleration, discuss Locke's conception of rights, and illustrate his use of prudential exceptions and distinctions. I conclude by arguing that Locke's problems are relevant to assessingc ontemporary liberal discussions of tolerationa nd the separation of state and religion that lean heavily on practical justification

Hip Flexion Angles During Supine Range of Motion and Bodyweight Squats

International Journal of Exercise Science 14(1): 912-918, 2021. During the lowering phase of a squat, it has been observed that a posterior pelvic tilt (PPT) may occur when squatting to full depth. Research suggests that defaulting to compensatory movement strategies, such as PPT, during the squat may correlate with risk of lower extremity and trunk pathology. The purpose of this study was to examine hip flexion (HF) angles at the point when PPT occurs among three conditions: standard squats, heel raise squats, and supine passive HF; analyzing the differences in depth between standard and heel raise squats; and calculating differences in knee angles and ankle excursion between standard and heel raise squats. 28 participants performed bodyweight squats and underwent supine passive HF while outfitted with 32 retroreflective motion capture markers. Hip, knee, and ankle joint angles were extracted at the point of PPT. A one-way repeated measures ANOVA was used to determine differences in hip joint angles between conditions, and a paired sample t-test was used to compare knee angles, ankle excursion, and squat depth between standard and heel raise squats. HF angles at PPT remained unchanged across all conditions. However, significantly greater knee flexion, ankle excursion, and squat depth were observed in the heel raise squats compared to the standard squats. Results suggest that PPT is a compensatory movement that occurs as the femur compresses into the acetabulum once hip flexion has been exhausted

Unique Properties of Thermally Tailored Copper: Magnetically Active Regions and Anomalous X-ray Fluorescence Emissions

When high-purity copper (≥99.98%wt) is melted, held in its liquid state for a few hours with iterative thermal cycling, then allowed to resolidify, the ingot surface is found to have many small regions that are magnetically active. X-ray fluorescence analysis of these regions exhibit remarkably intense lines from “sensitized elements” (SE), including in part or fully the contiguous series V, Cr, Mn, Fe, and Co. The XRF emissions from SE are far more intense than expected from known impurity levels. Comparison with blanks and standards show that the thermal “tailoring” also introduces strongly enhanced SE emissions in samples taken from the interior of the copper ingots. For some magnetic regions, the location as well as the SE emissions, although persistent, vary irregularly with time. Also, for some regions extraordinarily intense “sensitized iron” (SFe) emissions occur, accompanied by drastic attenuation of Cu emissions

Statistical Consequences of Devroye Inequality for Processes. Applications to a Class of Non-Uniformly Hyperbolic Dynamical Systems

In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance function, the integrated periodogram, the correlation dimension, the kernel density estimator, the speed of convergence of empirical measure, the shadowing property and the almost-sure central limit theorem. We proved in \cite{CCS} that Devroye inequality holds for a class of non-uniformly hyperbolic dynamical systems introduced in \cite{young}. In the second appendix we prove that, if the decay of correlations holds with a common rate for all pairs of functions, then it holds uniformly in the function spaces. In the last appendix we prove that for the subclass of one-dimensional systems studied in \cite{young} the density of the absolutely continuous invariant measure belongs to a Besov space.Comment: 33 pages; companion of the paper math.DS/0412166; corrected version; to appear in Nonlinearit

Comparing plasma and faecal measures of steroid hormones in Adelie penguins Pygoscelis adeliae

Physiological measurements of both stress and sex hormones are often used to estimate the consequences of natural or human-induced change in ecological studies of various animals. Different methods of hormone measurement exist, potentially explaining variation in results across studies; methods should be cross-validated to ensure that they correlate. We directly compared faecal and plasma hormone measurements for the first time in a wild free-living species, the Adelie penguin (Pygoscelis adeliae). Blood and faecal samples were simultaneously collected from individual penguins for comparison and assayed for testosterone and corticosterone (or their metabolites). Sex differences and variability within each measure, and correlation of values across measures were compared. For both hormones, plasma samples showed greater variation than faecal samples. Males had higher mean corticosterone concentrations than females, but the difference was only statistically significant in faecal samples. Plasma testosterone, but not faecal testosterone, was significantly higher in males than females. Correlation between sample types was poor overall, and weaker in females than in males, perhaps because measures from plasma represent hormones that are both free and bound to globulins, whereas measures from faeces represent only the free portion. Faecal samples also represent a cumulative measure of hormones over time, as opposed to a plasma ‘snapshot’ concentration. Our data indicate that faecal sampling appears more suitable for assessing baseline hormone concentrations, whilst plasma sampling may best define immediate responses to environmental events. Consequently, future studies should ensure that they select the most appropriate matrix and method of hormone measurement to answer their research questions

Relativistic diffusion processes and random walk models

The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As well-known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equation, whose solutions avoid superluminal propagation speeds but suffer from singular (non-continuous) diffusion fronts on the light cone, which are unlikely to exist for massive particles. It is therefore advisable to explore other alternatives as well. In this paper, a generalized Wiener process is proposed that is continuous, avoids superluminal propagation, and reduces to the standard Wiener process in the non-relativistic limit. The corresponding relativistic diffusion propagator is obtained directly from the nonrelativistic Wiener propagator, by rewriting the latter in terms of an integral over actions. The resulting relativistic process is non-Markovian, in accordance with the known fact that nontrivial continuous, relativistic Markov processes in position space cannot exist. Hence, the proposed process defines a consistent relativistic diffusion model for massive particles and provides a viable alternative to the solutions of the telegraph equation.Comment: v3: final, shortened version to appear in Phys. Rev.