Impact of third-order dispersion on the evolution of parabolic pulses

We present a perturbation analysis that describes the effect of third-order dispersion on the similariton pulse solution of the nonlinear Schrödinger equation in a fibre gain medium. The theoretical model predicts with sufficient accuracy the pulse structural changes induced, which are observed through direct numerical simulations.

Soliton's eigenvalue based analysis on the generation mechanism of rogue wave phenomenon in optical fibers exhibiting weak third order dispersion

One of the extraordinary aspects of nonlinear wave evolution which has been observed as the spontaneous occurrence of astonishing and statistically extraordinary amplitude wave is called rogue wave. We show that the eigenvalues of the associated equation of nonlinear Schrödinger equation are almost constant in the vicinity of rogue wave and we validate that optical rogue waves are formed by the collision between quasi-solitons in anomalous dispersion fiber exhibiting weak third order dispersion.

Extended nonlinear analytical models of compliant parallelogram mechanisms: third-order models

This paper proposes extended nonlinear analytical models, third-order models, of compliant parallelogram mechanisms. These models are capable of capturing the accurate effects from the very large axial force within the transverse motion range of 10% of the beam length through incorporating the terms associated with the high-order (up to third-order) axial force. Firstly, the free-body diagram method is employed to derive the nonlinear analytical model for a basic compliant parallelogram mechanism based on load-displacement relations of a single beam, geometry compatibility conditions, and load-equilibrium conditions. The procedures for the forward solutions and inverse solutions are described. Nonlinear analytical models for guided compliant multi-beam parallelogram mechanisms are then obtained. A case study of the compound compliant parallelogram mechanism, composed of two basic compliant parallelogram mechanisms in symmetry, is further implemented. This work intends to estimate the internal axial force change, the transverse force change, and the transverse stiffness change with the transverse motion using the proposed third-order model in comparison with the first-order model proposed in the prior art. In addition, FEA (finite element analysis) results validate the accuracy of the third-order model for a typical example. It is shown that in the case study the slenderness ratio affects the result discrepancy between the third-order model and the first-order model significantly, and the third-order model can illustrate a non-monotonic transverse stiffness curve if the beam is thin enough.

Efficient split eld FDTD analysis of third-order nonlinear materials in two-dimensionally periodic media

In this work the split-field finite-difference time-domain method (SF-FDTD) has been extended for the analysis of two-dimensionally periodic structures with third-order nonlinear media. The accuracy of the method is verified by comparisons with the nonlinear Fourier Modal Method (FMM). Once the formalism has been validated, examples of one- and two-dimensional nonlinear gratings are analysed. Regarding the 2D case, the shifting in resonant waveguides is corroborated. Here, not only the scalar Kerr effect is considered, the tensorial nature of the third-order nonlinear susceptibility is also included. The consideration of nonlinear materials in this kind of devices permits to design tunable devices such as variable band filters. However, the third-order nonlinear susceptibility is usually small and high intensities are needed in order to trigger the nonlinear effect. Here, a one-dimensional CBG is analysed in both linear and nonlinear regime and the shifting of the resonance peaks in both TE and TM are achieved numerically. The application of a numerical method based on the finite- difference time-domain method permits to analyse this issue from the time domain, thus bistability curves are also computed by means of the numerical method. These curves show how the nonlinear effect modifies the properties of the structure as a function of variable input pump field. When taking the nonlinear behaviour into account, the estimation of the electric field components becomes more challenging. In this paper, we present a set of acceleration strategies based on parallel software and hardware solutions.

Ultrafast nonlinearity of antimony polyphosphate glasses

We report on the ultrafast nonlinearity of antimony polyphosphate glasses measured using the Kerr shutter technique. The nonlinear refractive index, n(2), was (1.1+/-0.2)x10(-14) cm(2)/W at 800 nm, and enhancement of n(2) by approximate to80% was observed by adding 10% of lead oxide in the glass composition. The full width at half-maximum of the third-order correlation signal was 150 fs, which implies a fast response of the samples (less than or equal to100 fs). Nonlinear absorption was negligible in the range of intensities used. (C) 2003 American Institute of Physics.

Antimony orthophosphate glasses with large nonlinear refractive indices, low two-photon absorption coefficients, and ultrafast response

Antimony glasses based on the composition Sb2O3-SbPO4 were prepared and characterized. The samples present high refractive index, good transmission from 380 to 2000 nm, and high thermal stability. The nonlinear refractive index, n(2), of the samples was studied using the optical Kerr shutter technique at 800 nm. The third-order correlation signals between pump and probe pulses indicate ultrafast response (<100 fs) for all compositions. Enhancement of n(2) was observed by adding lead oxide to the Sb2O3-SbPO4 composition. Large values of n(2)approximate to10(-14) cm(2)/W and negligible two-photon absorption coefficients (smaller than 0.01 cm/GW) were determined for all samples. The glass compositions studied present appropriate figure-of-merit for all-optical switching applications. (C) 2005 American Institute of Physics.

High-resolution sequence stratigraphic correlation in the Upper Jurassic (Kimmeridgian)–Upper Cretaceous (Cenomanian) peritidal carbonate deposits (Western Taurides, Turkey)

Upper Jurassic (Kimmeridgian)±Upper Cretaceous (Cenomanian) inner platform carbonates in the Western Taurides are composed of metre-scale upward-shallowing cyclic deposits (parasequences) and important karstic surfaces capping some of the cycles. Peritidal cycles (shallow subtidal facies capped by tidal-¯at laminites or fenestrate limestones) are regressive- and transgressive-prone (upward-deepening followed by upward-shallowing facies trends). Subtidal cycles are of two types and indicate incomplete shallowing. Submerged subtidal cycles are composed of deeper subtidal facies overlain by shallow subtidal facies. Exposed subtidal cycles consist of deeper subtidal facies overlain by shallow subtidal facies that are capped by features indicative of prolonged subaerial exposure. Subtidal facies occur characteristically in the Jurassic, while peritidal cycles are typical for the Lower Cretaceous of the region. Within the foraminiferal and dasyclad algal biostratigraphic framework, four karst breccia levels are recognized as the boundaries of major second-order cycles, introduced for the ®rst time in this study. These levels correspond to the Kimmeridgian±Portlandian boundary, mid-Early Valanginian, mid-Early Aptian and mid-Cenomanian and represent important sea level falls which affected the distribution of foraminiferal fauna and dasyclad ¯ora of the Taurus carbonate platform. Within the Kimmeridgian±Cenomanian interval 26 third-order sequences (types 1 and 2) are recognized. These sequences are the records of eustatic sea level ¯uctuations rather than the records of local tectonic events because the boundaries of the sequences representing 1±4 Ma intervals are correlative with global sea level falls. Third-order sequences and metre-scale cyclic deposits are the major units used for long-distance, high-resolution sequence stratigraphic correlation in the Western Taurides. Metre-scale cyclic deposits (parasequences) in the Cretaceous show genetical stacking patterns within third-order sequences and correspond to fourth-order sequences representing 100±200 ka. These cycles are possibly the E2 signal (126 ka) of the orbital eccentricity cycles of the Milankovitch band. The slight deviation of values, calculated for parasequences, from the mean value of eccentricity cycles can be explained by the currently imprecise geochronology established in the Cretaceous and missed sea level oscillations when the platform lay above fluctuating sea level.

Harmonic distortion of 2-MOS structures for MOSFET-C filters implemented with n-type unstrained and strained FINFETS

This work investigates the harmonic distortion (HD) in 2-MOS balanced structures composed of triple gate FinFETs. HD has been evaluated through the determination of the third-order harmonic distortion (HD3), since this represents the major non-linearity source in balanced structures. The 2-MOS structures with devices of different channel lengths (L) and fin widths (W(fin)) have been studied operating in the linear region as tunable resistors. The analysis was performed as a function of the gate voltage, aiming to verify the correlation between operation bias and HD3. The physical origins of the non-linearities have been investigated and are pointed out. Being a resistive circuit, the 2-MOS structure is generally projected for a targeted on-resistance, which has also been evaluated in terms of HD3. The impact of the application of biaxial strain has been studied for FinFETs of different dimensions. It has been noted that HD3 reduces with the increase of the gate bias for all the devices and this reduction is more pronounced both in narrower and in longer devices. Also, the presence of strain slightly diminishes the non-linearity at a similar bias. However, a drawback associated with the use of strain engineering consists in a significant reduction of the on-resistance with respect to unstrained devices. (C) 2011 Elsevier Ltd. All rights reserved.

Covariance functions for body weight from birth to maturity in Nellore cows

The objective of this study was to estimate (co)variance functions using random regression models on Legendre polynomials for the analysis of repeated measures of BW from birth to adult age. A total of 82,064 records from 8,145 females were analyzed. Different models were compared. The models included additive direct and maternal effects, and animal and maternal permanent environmental effects as random terms. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of animal age (cubic regression) were considered as random co-variables. Eight models with polynomials of third to sixth order were used to describe additive direct and maternal effects, and animal and maternal permanent environmental effects. Residual effects were modeled using 1 (i.e., assuming homogeneity of variances across all ages) or 5 age classes. The model with 5 classes was the best to describe the trajectory of residuals along the growth curve. The model including fourth- and sixth-order polynomials for additive direct and animal permanent environmental effects, respectively, and third-order polynomials for maternal genetic and maternal permanent environmental effects were the best. Estimates of (co) variance obtained with the multi-trait and random regression models were similar. Direct heritability estimates obtained with the random regression models followed a trend similar to that obtained with the multi-trait model. The largest estimates of maternal heritability were those of BW taken close to 240 d of age. In general, estimates of correlation between BW from birth to 8 yr of age decreased with increasing distance between ages.

Dynamic stability of laminated FGM plates based on higher-order shear deformation theory

This paper conducts a dynamic stability analysis of symmetrically laminated FGM rectangular plates with general out-of-plane supporting conditions, subjected to a uniaxial periodic in-plane load and undergoing uniform temperature change. Theoretical formulations are based on Reddy's third-order shear deformation plate theory, and account for the temperature dependence of material properties. A semi-analytical Galerkin-differential quadrature approach is employed to convert the governing equations into a linear system of Mathieu-Hill equations from which the boundary points on the unstable regions are determined by Bolotin's method. Free vibration and bifurcation buckling are also discussed as subset problems. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with FGM layers made of silicon nitride and stainless steel. The influences of various parameters such as material composition, layer thickness ratio, temperature change, static load level, boundary constraints on the dynamic stability, buckling and vibration frequencies are examined in detail through parametric studies.

Wigner higher-order spectra: definition, properties, computation and application to transient signal analysis

The Wigner higher order moment spectra (WHOS)are defined as extensions of the Wigner-Ville distribution (WD)to higher order moment spectra domains. A general class oftime-frequency higher order moment spectra is also defined interms of arbitrary higher order moments of the signal as generalizations of the Cohen’s general class of time-frequency representations. The properties of the general class of time-frequency higher order moment spectra can be related to theproperties of WHOS which are, in fact, extensions of the properties of the WD. Discrete time and frequency Wigner higherorder moment spectra (DTF-WHOS) distributions are introduced for signal processing applications and are shown to beimplemented with two FFT-based algorithms. One applicationis presented where the Wigner bispectrum (WB), which is aWHOS in the third-order moment domain, is utilized for thedetection of transient signals embedded in noise. The WB iscompared with the WD in terms of simulation examples andanalysis of real sonar data. It is shown that better detectionschemes can be derived, in low signal-to-noise ratio, when theWB is applied.

Computeralgebraische Herleitung und Auswertung atomarer Störungsreihen und deren Anwendung auf geschlossenschalige und einfache offenschalige Systeme

In der vorliegenden Arbeit wurde gezeigt, wie mit Hilfe der atomaren Vielteilchenstörungstheorie totale Energien und auch Anregungsenergien von Atomen und Ionen berechnet werden können. Dabei war es zunächst erforderlich, die Störungsreihen mit Hilfe computeralgebraischer Methoden herzuleiten. Mit Hilfe des hierbei entwickelten Maple-Programmpaketes APEX wurde dies für geschlossenschalige Systeme und Systeme mit einem aktiven Elektron bzw. Loch bis zur vierten Ordnung durchgeführt, wobei die entsprechenden Terme aufgrund ihrer großen Anzahl hier nicht wiedergegeben werden konnten. Als nächster Schritt erfolgte die analytische Winkelreduktion unter Anwendung des Maple-Programmpaketes RACAH, was zu diesem Zwecke entsprechend angepasst und weiterentwickelt wurde. Erst hier wurde von der Kugelsymmetrie des atomaren Referenzzustandes Gebrauch gemacht. Eine erhebliche Vereinfachung der Störungsterme war die Folge. Der zweite Teil dieser Arbeit befasst sich mit der numerischen Auswertung der bisher rein analytisch behandelten Störungsreihen. Dazu wurde, aufbauend auf dem Fortran-Programmpaket Ratip, ein Dirac-Fock-Programm für geschlossenschalige Systeme entwickelt, welches auf der in Kapitel 3 dargestellen Matrix-Dirac-Fock-Methode beruht. Innerhalb dieser Umgebung war es nun möglich, die Störungsterme numerisch auszuwerten. Dabei zeigte sich schnell, dass dies nur dann in einem angemessenen Zeitrahmen stattfinden kann, wenn die entsprechenden Radialintegrale im Hauptspeicher des Computers gehalten werden. Wegen der sehr hohen Anzahl dieser Integrale stellte dies auch hohe Ansprüche an die verwendete Hardware. Das war auch insbesondere der Grund dafür, dass die Korrekturen dritter Ordnung nur teilweise und die vierter Ordnung gar nicht berechnet werden konnten. Schließlich wurden die Korrelationsenergien He-artiger Systeme sowie von Neon, Argon und Quecksilber berechnet und mit Literaturwerten verglichen. Außerdem wurden noch Li-artige Systeme, Natrium, Kalium und Thallium untersucht, wobei hier die niedrigsten Zustände des Valenzelektrons betrachtet wurden. Die Ionisierungsenergien der superschweren Elemente 113 und 119 bilden den Abschluss dieser Arbeit.

A high-order arbitrarily unstructured finite-volume model of the global atmosphere: tests solving the shallow-water equations

Simulations of the global atmosphere for weather and climate forecasting require fast and accurate solutions and so operational models use high-order finite differences on regular structured grids. This precludes the use of local refinement; techniques allowing local refinement are either expensive (eg. high-order finite element techniques) or have reduced accuracy at changes in resolution (eg. unstructured finite-volume with linear differencing). We present solutions of the shallow-water equations for westerly flow over a mid-latitude mountain from a finite-volume model written using OpenFOAM. A second/third-order accurate differencing scheme is applied on arbitrarily unstructured meshes made up of various shapes and refinement patterns. The results are as accurate as equivalent resolution spectral methods. Using lower order differencing reduces accuracy at a refinement pattern which allows errors from refinement of the mountain to accumulate and reduces the global accuracy over a 15 day simulation. We have therefore introduced a scheme which fits a 2D cubic polynomial approximately on a stencil around each cell. Using this scheme means that refinement of the mountain improves the accuracy after a 15 day simulation. This is a more severe test of local mesh refinement for global simulations than has been presented but a realistic test if these techniques are to be used operationally. These efficient, high-order schemes may make it possible for local mesh refinement to be used by weather and climate forecast models.

Blind equalization of nonminimum phase channels: higher order cumulant based algorithm

Higher order cumulant analysis is applied to the blind equalization of linear time-invariant (LTI) nonminimum-phase channels. The channel model is moving-average based. To identify the moving average parameters of channels, a higher-order cumulant fitting approach is adopted in which a novel relay algorithm is proposed to obtain the global solution. In addition, the technique incorporates model order determination. The transmitted data are considered as independently identically distributed random variables over some discrete finite set (e.g., set {±1, ±3}). A transformation scheme is suggested so that third-order cumulant analysis can be applied to this type of data. Simulation examples verify the feasibility and potential of the algorithm. Performance is compared with that of the noncumulant-based Sato scheme in terms of the steady state MSE and convergence rate.

Pseudolikelihood equations for Potts MRF model parameter estimation on higher order neighborhood systems

This letter presents pseudolikelihood equations for the estimation of the Potts Markov random field model parameter on higher order neighborhood systems. The derived equation for second-order systems is a significantly reduced version of a recent result found in the literature (from 67 to 22 terms). Also, with the proposed method, a completely original equation for Potts model parameter estimation in third-order systems was obtained. These equations allow the modeling of less restrictive contextual systems for a large number of applications in a computationally feasible way. Experiments with both simulated and real remote sensing images provided good results.