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

Nonlinear optics of fibre event horizons

The nonlinear interaction of light in an optical fibre can mimic the physics at an event horizon. This analogue arises when a weak probe wave is unable to pass through an intense soliton, despite propagating at a different velocity. To date, these dynamics have been described in the time domain in terms of a soliton-induced refractive index barrier that modifies the velocity of the probe. Here, we complete the physical description of fibre-optic event horizons by presenting a full frequency-domain description in terms of cascaded four-wave mixing between discrete single-frequency fields, and experimentally demonstrate signature frequency shifts using continuous wave lasers. Our description is confirmed by the remarkable agreement with experiments performed in the continuum limit, reached using ultrafast lasers. We anticipate that clarifying the description of fibre event horizons will significantly impact on the description of horizon dynamics and soliton interactions in photonics and other systems.Comment: 7 pages, 5 figure

On the stochastic mechanics of the free relativistic particle

Given a positive energy solution of the Klein-Gordon equation, the motion of the free, spinless, relativistic particle is described in a fixed Lorentz frame by a Markov diffusion process with non-constant diffusion coefficient. Proper time is an increasing stochastic process and we derive a probabilistic generalization of the equation $(d\tau)^2=-\frac{1}{c^2}dX_{\nu}dX_{\nu}$. A random time-change transformation provides the bridge between the $t$ and the $\tau$ domain. In the $\tau$ domain, we obtain an \M^4-valued Markov process with singular and constant diffusion coefficient. The square modulus of the Klein-Gordon solution is an invariant, non integrable density for this Markov process. It satisfies a relativistically covariant continuity equation

A simple and surprisingly accurate approach to the chemical bond obtained from dimensional scaling

We present a new dimensional scaling transformation of the Schrodinger equation for the two electron bond. This yields, for the first time, a good description of the two electron bond via D-scaling. There also emerges, in the large-D limit, an intuitively appealing semiclassical picture, akin to a molecular model proposed by Niels Bohr in 1913. In this limit, the electrons are confined to specific orbits in the scaled space, yet the uncertainty principle is maintained because the scaling leaves invariant the position-momentum commutator. A first-order perturbation correction, proportional to 1/D, substantially improves the agreement with the exact ground state potential energy curve. The present treatment is very simple mathematically, yet provides a strikingly accurate description of the potential energy curves for the lowest singlet, triplet and excited states of H_2. We find the modified D-scaling method also gives good results for other molecules. It can be combined advantageously with Hartree-Fock and other conventional methods.Comment: 4 pages, 5 figures, to appear in Phys. Rev. Letter

Non-Invasive Driver Drowsiness Detection System.

Drowsiness when in command of a vehicle leads to a decline in cognitive performance that affects driver behavior, potentially causing accidents. Drowsiness-related road accidents lead to severe trauma, economic consequences, impact on others, physical injury and/or even death. Real-time and accurate driver drowsiness detection and warnings systems are necessary schemes to reduce tiredness-related driving accident rates. The research presented here aims at the classification of drowsy and non-drowsy driver states based on respiration rate detection by non-invasive, non-touch, impulsive radio ultra-wideband (IR-UWB) radar. Chest movements of 40 subjects were acquired for 5 m using a lab-placed IR-UWB radar system, and respiration per minute was extracted from the resulting signals. A structured dataset was obtained comprising respiration per minute, age and label (drowsy/non-drowsy). Different machine learning models, namely, Support Vector Machine, Decision Tree, Logistic regression, Gradient Boosting Machine, Extra Tree Classifier and Multilayer Perceptron were trained on the dataset, amongst which the Support Vector Machine shows the best accuracy of 87%. This research provides a ground truth for verification and assessment of UWB to be used effectively for driver drowsiness detection based on respiration

Pheromone–mediated mating disruption in the millet stem borer, \u3ci\u3eConiesta ignefusalis\u3c/i\u3e (Lepidoptera: Pyralidae)

The millet stem borer, Coniesta ignefusalis Hampson (Lepidoptera: Pyralidae), is a major pest of pearl millet in the Sahelian region of Africa. The female sex pheromone has been identified and synthesized, and previous research had shown that the synthetic pheromone could cause high levels of reproductive communication disruption in small plots when released at rates of 640 mg/ha/day, using PVC resin formulation renewed every seven days to maintain efficiency. In the present research, in experiments in farmers’ fields in Niger, 86.8% (SE = 2.6%) communication disruption was achieved when polyethylene vials loaded with 0.5 mg pheromone at 400 dispensers/ha were used and replaced every 21 days. Polyethylene vials loaded with 80 mg pheromone gave uniform, zero–order release at approximately 0.05 mg/day at 27 °C. Experiments carried out on replicated 0.5 ha plots in farmers’ fields in Niger using a single application of these dispensers at 400 dispensers/ha resulted in at least 99% suppression of pheromone trap catches of male C. ignefusalis moths in treated plots relative to numbers in untreated plots for up to 3 months. However, sampling the central portions of these plots before and after harvest showed no significant differences in infestation, damage or yield loss between plots treated with pheromone and untreated plots. This may have been because of small plot size and the immigration of mated female moths into the treated plots which negated any reduction of mating of females within the treated plots. Comparisons of numbers of male C. ignefusalis moths in traps baited with the standard 0.5 mg monitoring lures and those baited with the 80 mg disruption dispensers showed catches in the latter were only 10–20% of those in the former; indicating high level communication disruptions in traps with high dose dispensers. Implications of using insect synthetic pheromones in the development of integrated management of C. ignefusalis in pearl millet cropping systems in the Sahel are discussed

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

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

Intermittent magnetic field excitation by a turbulent flow of liquid sodium

The magnetic field measured in the Madison Dynamo Experiment shows intermittent periods of growth when an axial magnetic field is applied. The geometry of the intermittent field is consistent with the fastest growing magnetic eigenmode predicted by kinematic dynamo theory using a laminar model of the mean flow. Though the eigenmodes of the mean flow are decaying, it is postulated that turbulent fluctuations of the velocity field change the flow geometry such that the eigenmode growth rate is temporarily positive. Therefore, it is expected that a characteristic of the onset of a turbulent dynamo is magnetic intermittency.Comment: 5 pages, 7 figure

Functional Status After Colon Cancer Surgery in Elderly Nursing Home Residents

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/91352/1/jgs3915.pd