Random input problem for the nonlinear Schrödinger equation

We consider the random input problem for a nonlinear system modeled by the integrable one-dimensional self-focusing nonlinear Schrödinger equation (NLSE). We concentrate on the properties obtained from the direct scattering problem associated with the NLSE. We discuss some general issues regarding soliton creation from random input. We also study the averaged spectral density of random quasilinear waves generated in the NLSE channel for two models of the disordered input field profile. The first model is symmetric complex Gaussian white noise and the second one is a real dichotomous (telegraph) process. For the former model, the closed-form expression for the averaged spectral density is obtained, while for the dichotomous real input we present the small noise perturbative expansion for the same quantity. In the case of the dichotomous input, we also obtain the distribution of minimal pulse width required for a soliton generation. The obtained results can be applied to a multitude of problems including random nonlinear Fraunhoffer diffraction, transmission properties of randomly apodized long period Fiber Bragg gratings, and the propagation of incoherent pulses in optical fibers.

Ultra-long raman laser with a feedback based on the Rayleigh scattering

This paper reports the Rayleigh scattering effects in ultra-long Raman fibre laser. It has been found that in a long fibre cavity (-100 km) the distributed feedback due to Rayleigh back scattering at propagation of light between fibre Bragg grating reflectors may be comparable with the lumped feedback provided by the FBG itself. As a result, Raman lasing in the fibre span limited by lumped (FBG) reflector at one side only appears possible due to significant reflection from the RS-based "random" distributed mirror at the other side. Thus, it concludes that a distributed Rayleigh scattering "random" mirror can form a cavity together with a single FBG spliced to the opposite cavity end.

Nonlinear multicore waveguiding structures with balanced gain and loss

We study existence, stability, and dynamics of linear and nonlinear stationary modes propagating in radially symmetric multicore waveguides with balanced gain and loss. We demonstrate that, in general, the system can be reduced to an effective PT-symmetric dimer with asymmetric coupling. In the linear case, we find that there exist two modes with real propagation constants before an onset of the PT-symmetry breaking while other modes have always the propagation constants with nonzero imaginary parts. This leads to a stable (unstable) propagation of the modes when gain is localized in the core (ring) of the waveguiding structure. In the case of nonlinear response, we show that an interplay between nonlinearity, gain, and loss induces a high degree of instability, with only small windows in the parameter space where quasistable propagation is observed. We propose a novel stabilization mechanism based on a periodic modulation of both gain and loss along the propagation direction that allows bounded light propagation in the multicore waveguiding structures.

Super-Gaussian conical refraction beam

We demonstrate the transformation of Gaussian input beams into super-Gaussian beams with a quasi flat-top transverse profile by means of the conical refraction phenomenon by adjusting the ratio between the ring radius and the waist radius of the input beam to 0.445. We discuss the beam propagation of the super-Gaussian beam and show that it has a confocal parameter three times larger than the one that would be obtained from a Gaussian beam. The experiments performed with a KGd(WO4)2 biaxial crystal are in good agreement with the theoretical predictions. © 2014 Optical Society of America.

Nonlinear Waves: An Introduction

This book deals with equations of mathematical physics as the different modifications of the KdV equation, the Camassa-Holm type equations, several modifications of Burger's equation, the Hunter-Saxton equation, conservation laws equations and others. The equations originate from physics but are proposed here for their investigation via purely mathematical methods in the frames of university courses. More precisely, we propose classification theorems for the traveling wave solutions for a sufficiently large class of third order nonlinear PDE when the corresponding profiles develop different kind of singularities (cusps, peaks), existence and uniqueness results, etc. The orbital stability of the periodic solutions of traveling type for mKdV equations are also studied. Of great interest too is the interaction of peakon type solutions of the Camassa-Holm equation and the solvability of the classical and generalized Cauchy problem for the Hunter-Saxton equation. The Riemann problem for special systems of conservation laws and the corresponding -shocks are also considered. As it concerns numerical methods we apply the CNN approach. The book is addressed to a broader audience including graduate students, Ph.D. students, mathematicians, physicist, engineers and specialists in the domain of PDE.

Reflectionless potentials for slow whispering gallery modes in surface nanoscale axial photonic fiber resonators

We consider an optical fiber with a nanoscale variation of the effective fiber radius that supports whispering gallery modes slowly propagating along the fiber, and reveal that the radius variation can be designed to support the reflectionless propagation of these modes. We show that reflectionless modulations can realize control of the transmission amplitude and temporal delay, while enabling close packing due to the absence of cross talk, in contrast to the conventional potentials.

Magnetoencephalography in epilepsy

Magnetoencephalographic (MEG) signals, like electroencephalographic (EEG) measures, are the direct extracranial manifestations of neuronal activation. The two techniques can detect time-varying changes in electromagnetic activity with a sub-millisecond time resolution. Extra-cranial electromagnetic measures are the cornerstone of the non-invasive diagnostic armamentarium in patients with epilepsy. Their extremely high temporal resolution – comparable to intracranial recordings – is the basis for a precise definition of onset and propagation of ictal and interictal abnormalities. Given the cost of the infrastructure and equipment, MEG has yet to develop into a routinely applicable diagnostic tool in clinical settings. However, in recent years, an increasing number of patients with epilepsy have been investigated – usually in the context of presurgical evaluation of refractory epilepsies – and initial encouraging results have been reported. We will briefly review the principles and the technology behind MEG and its contribution in the diagnostic work-up of patients with epilepsy.

Stokes waves revisited:exact solutions in the asymptotic limit

The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic “secular variation” in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.

Stable optical vortices in nonlinear multicore fibers

The multicore fiber (MCF) is a physical system of high practical importance. In addition to standard exploitation, MCFs may support discrete vortices that carry orbital angular momentum suitable for spatial-division multiplexing in high-capacity fiber-optic communication systems. These discrete vortices may also be attractive for high-power laser applications. We present the conditions of existence, stability, and coherent propagation of such optical vortices for two practical MCF designs. Through optimization, we found stable discrete vortices that were capable of transferring high coherent power through the MCF.

Um algoritmo paralelo eficiente de migração reversa no tempo (rtm) 3d com granularidade fina

The reverse time migration algorithm (RTM) has been widely used in the seismic industry to generate images of the underground and thus reduce the risk of oil and gas exploration. Its widespread use is due to its high quality in underground imaging. The RTM is also known for its high computational cost. Therefore, parallel computing techniques have been used in their implementations. In general, parallel approaches for RTM use a coarse granularity by distributing the processing of a subset of seismic shots among nodes of distributed systems. Parallel approaches with coarse granularity for RTM have been shown to be very efficient since the processing of each seismic shot can be performed independently. For this reason, RTM algorithm performance can be considerably improved by using a parallel approach with finer granularity for the processing assigned to each node. This work presents an efficient parallel algorithm for 3D reverse time migration with fine granularity using OpenMP. The propagation algorithm of 3D acoustic wave makes up much of the RTM. Different load balancing were analyzed in order to minimize possible losses parallel performance at this stage. The results served as a basis for the implementation of other phases RTM: backpropagation and imaging condition. The proposed algorithm was tested with synthetic data representing some of the possible underground structures. Metrics such as speedup and efficiency were used to analyze its parallel performance. The migrated sections show that the algorithm obtained satisfactory performance in identifying subsurface structures. As for the parallel performance, the analysis clearly demonstrate the scalability of the algorithm achieving a speedup of 22.46 for the propagation of the wave and 16.95 for the RTM, both with 24 threads.

Aprender e ensinar na escola inclusiva: desafios na construção da identidade de pedagogos

The democratization of Brazilian education and discussion about the educational rights of persons with disabilities in refer to reflection on the conceptions of teaching and learning and the folding of these concepts in practice and in the formation of professional identity of the teacher educator. Thus, the proposed research in this dissertation aimed to describe educational processes developed by educators in classrooms in which they are enrolled students with disabilities a view to considering how these processes affect the construction of their professional identity of the pedagogue. As the methodology used to research is classified as Case Study. This methodological approach enables the analysis of singularities of educational contexts. In this work, the case investigated consisted of the analytical study of the pedagogical practices developed in classrooms where there are students with disabilities and their relation to the establishment of the professional identity of the teacher in a school linked to a non-governmental organization supporting people with disabilities in the city of Natal / RN. The Data were collected through the use of the following instruments: exploratory questionnaires, observation and respective registration in the field diary of research and interviews with educators in different professional cycles proposed by Huberman. The data reveal didactic and pedagogical aspects common in educational processes in the observed classes and differences concerning the specifics of pedagogues in the teaching profession in different moments of their professional careers. The analysis of the conceptions tell us the nuances of meanings constructed on teaching and learning and its interface with the reflection on teaching practice. As to the meaning assigned to be pedagogue research highlights the professional identification related to the meanings of teaching and learning in school. The experiences in the teaching profession according to the survey data point to changes in teachers conceptions about teaching and learning disabled people in the perspective of inclusion. Therefore, the study concludes that the pedagogical practices with students with disabilities the different experiences add up and can transform conceptions of teachers about teaching and learning interfering with constant reflection on practices and the construction of professional identities of pedagogues.

Estudos de distúrbios ionosféricos propagantes de larga escala (LSTID’S) na região equatorial durante grandes tempestades magnéticas: estudo de casos

The Ionospheric Disturbances – TIDs – are irregularities on the ionospheric plasma propagating in speeds in the order of tens to a few hundreds of meters per second. This present study detected and characterized the TIDs of LSTIDs (Large Scale Travelling Ionospheric Disturbance) type at low latitudes during intense geomagnetic storms and its propagation over the Brazilian sector. This work also shows as being the first to report systematically propagation of gravity waves over Natal. For this purpose, we used ionospheric records obtained from type of digisonde CADI (Canadiam Advanced Digital Ionosonde) located in Natal and the type DSP (Digisonde Portable Souder) located in Cachoeira Paulista, Fortaleza and São Luis, whereupon we used a dataset of 12 years collected by INPE (National Institute of Space Research). In this study, both calm days, that preceded the storms, and the geomagnetically disturbed days were related during the years 2000 and 1012, which cover a period of maximum and minimum solar activity. And it is presented the variations that happened in the electron density from region F of the ionosphere over the Brazilian sector, especially near the Equator (Natal, Fortaleza and São Luis), caused by ionospheric disturbances in the equatorial region during intense geomagnetic storms, because, as we know of the literature in this area, this phenomenon contributes positively to the emergence of LSTIDs in the auroral region, which may move to the equatorial region where a few cases have been documented and studied systematically. From the observation of signatures if TIDs in ionogram records, a study of the morphology of these events was performed and compared with the main characteristics of the wave of this phenomenon during great magnetic storms, i.e., DST <(-200 nT) and KP > 6. Thus, we obtained the main characteristics of TIDs over our region, i.e., period, vertical wavelength, phase and propagation speed, as well as the delay of these disturbances compared to the beginning of the magnetic storms to the Brazilian Sector.

Entre a cruz e a espada, a foice e o martelo: a representação do anticomunismo no Rio Grande do Norte

The objective of this dissertation is to investigate the propagation of an anticommunism movement in Rio Grande do Norte Estate, Brazil, in a process that started on the first decades of the twentieth century and shows reflections until today. Firstly, we introduce the operation promoted by the catholic oriented newspaper A Ordem. Through the analysis of publications from 1935 to 1945, we observe its role in an image campaign of the “Communist Conspiracy” event, in an attempt to legitimate the power of Right wing groups, specially the Catholic Church and the Military Police. The newspapers discourse is analyzed in serial, quantitative and qualitative perspectives. Secondly, we search to understand the space dynamic of the anticommunism discourse thought the creation of evocation and representation spaces that ended up becoming memory places. Our considerations are based on the concept of representation by Roger Chartier, observing the way communism is represented by A Ordem, as well as the spatial category used to reactivate the anticommunist memory and represent it. We analyze the interests that are served by the construction of the monuments, the Oral History, as well as the relation between the local communities with them. Thirdly, we establish a parallel with many authors, in an approach that gathers Cultural and Social elements and Political History, in order to find explanations for the articulation of these discourses.

Organic matter deposition/resuspension in a one-dimensional physical-biogeochemical model. A modelling study

The shallow water configuration of the gulf of Trieste allows the propagation of the stress due to wind and waves along the whole water column down to the bottom. When the stress overcomes a particular threshold it produces resuspension processes of the benthic detritus. The benthic sediments in the North Adriatic are rich of organic matter, transported here by many rivers. This biological active particulate, when remaining in the water, can be transported in all the Adriatic basin by the basin-wide circulation. In this work is presented a first implementation of a resuspension/deposition submodel in the oceanographic coupled physical-biogeochemical 1-dimensional numerical model POM-BFM. At first has been considered the only climatological wind stress forcing, next has been introduced, on the surface, an annual cycle of wave motion and finally have been imposed some exceptional wave event in different periods of the year. The results show a strong relationship between the efficiency of the resuspension process and the stratification of the water column. During summer the strong stratification can contained a great quantity of suspended matter near to the bottom, while during winter even a low concentration of particulate can reach the surface and remains into the water for several months without settling and influencing the biogeochemical system. Looking at the biologic effects, the organic particulate, injected in the water column, allow a sudden growth of the pelagic bacteria which competes with the phytoplankton for nutrients strongly inhibiting its growth. This happen especially during summer when the suspended benthic detritus concentration is greater.

Temperature variabilty in the southeastern Black-Sea during 64-20ka BP

The Eurasian inland propagation of temperature anomalies during glacial millennial-scale climate variability is poorly understood but this knowledge is crucial to understanding hemisphere-wide atmospheric teleconnection patterns and climate mechanisms. Based on biomarkers and geochemical paleothermometers, a pronounced continental temperature variability between 64,000 and 20,000 years ago, coinciding with the Greenland Dansgaard-Oeschger cycles, was determined in a well-dated sediment record from the formerly enclosed Black Sea. Cooling during Heinrich events was not stronger than during other stadials in the Black Sea. This is corroborated by modeling results showing that regular Dansgaard-Oeschger cycles penetrated deeper into the Eurasian continent than Heinrich events. The pattern of coastal ice-rafted detritus suggests a strong dependence on the climate background state, with significantly milder winters during periods of reduced Eurasian ice sheets and an intensified meridional atmospheric circulation.