Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

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.

Nonresonant third-order nonlinearity of antimony glasses at telecom wavelengths

We report measurements of the nonresonant nonlinear refractive index n(2) in antimony glasses at telecom wavelengths. The measurements were performed using the Z-scan technique with a 130 fs pulsed laser operating at five wavelengths in the range of 1400-1600 nm. Values of n(2)approximate to 10(-15) cm(2)/W were measured and a negligible two-photon absorption coefficient (< 0.003 cm/GW) was estimated for all glasses compositions. The samples present a good figure of merit for ultrafast all-optical switching. (c) 2006 American Institute of Physics.

Near-infrared Kerr nonlinearity of Pb(PO3)(2)-WO3 glasses

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Near-infrared third-order nonlinearity of PbO-GeO(2) films containing Cu and Cu(2)O nanoparticles

We report measurements of the nonlinear (NL) refractive index n(2) of lead-germanium films (LGFs) containing Cu and Cu(2)O nanoparticles (NPs). The thermally managed eclipse Z-scan technique with 150 fs pulses from a laser operating at 800 nm was used. The NL refractive index measured, n(2)=6.3x10(-12) cm(2)/W has electronic origin and the NL absorption coefficient alpha(2) is smaller than 660 cm/GW. The figure of merit n(2)/lambda alpha(2) is enhanced by more than two orders of magnitude in comparison with the result for the LGFs without the copper based NPs. (C) 2008 American Institute of Physics.

Soliton propagation in a medium with Kerr nonlinearity and resonant impurities: A variational approach

The soliton propagation in a medium with Kerr nonlinearity and resonant impurities was studied by a variational approach. The existence of a solitary wave was shown within the framework of a combined nonintegrable system composed of one nonlinear Schrödinger and a pair of Bloch equations. The analytical solution which was obtained, was tested through numerical simulations confirming its solitary wave nature.

Self-trapping of Fermi and Bose gases under spatially modulated repulsive nonlinearity and transverse confinement

We show that self-localized ground states can be created in the spin-balanced gas of fermions with repulsion between the spin components, whose strength grows from the center to periphery, in combination with the harmonic-oscillator (HO) trapping potential acting in one or two transverse directions. We also consider the ground state in the noninteracting Fermi gas under the action of the spatially growing tightness of the one- or two-dimensional (1D or 2D) HO confinement. These settings are considered in the framework of the Thomas-Fermi-von Weizsäcker (TF-vW) density functional. It is found that the vW correction to the simple TF approximation (the gradient term) is nearly negligible in all situations. The properties of the ground state under the action of the 2D and 1D HO confinement with the tightness growing in the transverse directions are investigated too for the Bose-Einstein condensate with the self-repulsive nonlinearity. © 2013 American Physical Society.

Near-infrared nonlinearity of a multicomponent tellurium oxide glass at 800 and 1,064 nm

We report on the nonlinear (NL) optical properties of glassy TeO2-GeO2-K2O-Bi2O3 at lambda = 800 nm and lambda = 1,064 nm. Using the Kerr gate technique with a laser delivering 150 fs pulses at 800 nm, we demonstrated the fast NL response of the samples. The modulus of the NL refractive index, n (2), at 800 nm was similar to 10(-15) cm(2)/W. The Z-scan technique was used to determine n (2) a parts per thousand +10(-15) cm(2)/W, at 1,064 nm with pulses of 17 ps. The two-photon absorption coefficient, alpha (2), was smaller than the minimum that we can measure (< 0.003 cm/GW). The figure of merit n (2)/alpha (2) lambda was calculated and indicates that this glass composition has large potential to be used for all-optical switching.

PT-symmetric coupler with chi((2)) nonlinearity

We introduce the notion of a PT-symmetric dimer with a chi((2)) nonlinearity. Similarly to the Kerr case, we argue that such a nonlinearity should be accessible in a pair of optical waveguides with quadratic nonlinearity and gain and loss, respectively. An interesting feature of the problem is that because of the two harmonics, there exist in general two distinct gain and loss parameters, different values of which are considered herein. We find a number of traits that appear to be absent in the more standard cubic case. For instance, bifurcations of nonlinear modes from the linear solutions occur in two different ways depending on whether the first-or the second-harmonic amplitude is vanishing in the underlying linear eigenvector. Moreover, a host of interesting bifurcation phenomena appear to occur, including saddle-center and pitchfork bifurcations which our parametric variations elucidate. The existence and stability analysis of the stationary solutions is corroborated by numerical time-evolution simulations exploring the evolution of the different configurations, when unstable.

Picosecond nonlinearity of GeO2-Bi2O3-PbO-TiO2 glasses at 532 and 1,064 nm

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nonlinearity as a resource for nonclassicality

Lo scopo di questo lavoro è cercare un'evidenza quantitativa a supporto dell'idea idea che la nonlinearità sia una risorsa per generare nonclassicità. Ci si concentrerà su sistemi unidimensionali bosonici, cercando soprattutto di connettere la nonlinearità di un oscillatore anarmonico, definito dalla forma del suo potenziale, alla nonclassicità del relativo ground state. Tra le numerose misure di nonclassicità esistenti, verranno impiegate il volume della parte negativa della funzione di Wigner e l'entanglement potential, ovvero la misura dell'entanglement prodotto dallo stato dopo il passaggio attraverso un beam splitter bilanciato avente come altro stato in ingresso il vuoto. La nonlinearità di un potenziale verrà invece caratterizzata studiando alcune proprietà del suo ground state, in particolare se ne misurerà la non-Gaussianità e la distanza di Bures rispetto al ground state di un oscillatore armonico di riferimento. Come principale misura di non-Gaussianità verrà utilizzata l'entropia relativa fra lo stato e il corrispettivo stato di riferimento Gaussiano, avente la medesima matrice di covarianza. Il primo caso che considereremo sarà quello di un potenziale armonico con due termini polinomiali aggiuntivi e il ground state ottenuto con la teoria perturbativa. Si analizzeranno poi alcuni potenziali il cui ground state è ottenibile analiticamente: l'oscillatore armonico modificato, il potenziale di Morse e il potenziale di Posch-Teller. Si andrà infine a studiare l'effetto della nonlinearità in un contesto dinamico, considerando l'evoluzione unitaria di uno stato in ingresso in un mezzo che presenta una nonlinearità di tipo Kerr. Nell'insieme, i risultati ottenuti con tutti i potenziali analizzati forniscono una forte evidenza quantitativa a supporto dell'idea iniziale. Anche i risultati del caso dinamico, dove la nonlinearità costituisce una risorsa utile per generare nonclassicità solo se lo stato iniziale è classico, confermano la pittura complessiva. Si sono inoltre studiate in dettaglio le differenze nel comportamento delle due misure di nonclassicità.

On nonlinearity in neural encoding models applied to the primary visual cortex

Within the regression framework, we show how different levels of nonlinearity influence the instantaneous firing rate prediction of single neurons. Nonlinearity can be achieved in several ways. In particular, we can enrich the predictor set with basis expansions of the input variables (enlarging the number of inputs) or train a simple but different model for each area of the data domain. Spline-based models are popular within the first category. Kernel smoothing methods fall into the second category. Whereas the first choice is useful for globally characterizing complex functions, the second is very handy for temporal data and is able to include inner-state subject variations. Also, interactions among stimuli are considered. We compare state-of-the-art firing rate prediction methods with some more sophisticated spline-based nonlinear methods: multivariate adaptive regression splines and sparse additive models. We also study the impact of kernel smoothing. Finally, we explore the combination of various local models in an incremental learning procedure. Our goal is to demonstrate that appropriate nonlinearity treatment can greatly improve the results. We test our hypothesis on both synthetic data and real neuronal recordings in cat primary visual cortex, giving a plausible explanation of the results from a biological perspective.

Aeroelastic characteristics of slender wing/bodies with freeplay non-linearities

This article presents a time domain approach to the flutter analysis of a missile-type wing/body configuration with concentrated structural non-linearities. The missile wing is considered fully movable and its rotation angle contains the structural freeplay-type non-linearity. Although a general formulation for flexible configurations is developed, only two rigid degrees of freedom are taken into account for the results: pitching of the whole wing/body configuration and wing rotation angle around its hinge. An unsteady aerodynamic model based on the slender-body approach is used to calculate aerodynamic generalized forces. Limit-cycle oscillations and chaotic motion below the flutter speed are observed in this study.

Residual delay maps unveil global patterns of atmospheric nonlinearity and produce improved local forecasts

We use residual-delay maps of observational field data for barometric pressure to demonstrate the structure of latitudinal gradients in nonlinearity in the atmosphere. Nonlinearity is weak and largely lacking in tropical and subtropical sites and increases rapidly into the temperate regions where the time series also appear to be much noisier. The degree of nonlinearity closely follows the meridional variation of midlatitude storm track frequency. We extract the specific functional form of this nonlinearity, a V shape in the lagged residuals that appears to be a basic feature of midlatitude synoptic weather systems associated with frontal passages. We present evidence that this form arises from the relative time scales of high-pressure versus low-pressure events. Finally, we show that this nonlinear feature is weaker in a well regarded numerical forecast model (European Centre for Medium-Range Forecasts) because small-scale temporal and spatial variation is smoothed out in the grided inputs. This is significant, in that it allows us to demonstrate how application of statistical corrections based on the residual-delay map may provide marked increases in local forecast accuracy, especially for severe weather systems.

The degree of nonlinearity and anisotropy of blood vessel elasticity

Blood vessel elasticity is important to physiology and clinical problems involving surgery, angioplasty, tissue remodeling, and tissue engineering. Nonlinearity in blood vessel elasticity in vivo is important to the formation of solitons in arterial pulse waves. It is well known that the stress–strain relationship of the blood vessel is nonlinear in general, but a controversy exists on how nonlinear it is in the physiological range. Another controversy is whether the vessel wall is biaxially isotropic. New data on canine aorta were obtained from a biaxial testing machine over a large range of finite strains referred to the zero-stress state. A new pseudo strain energy function is used to examine these questions critically. The stress–strain relationship derived from this function represents the sum of a linear stress–strain relationship and a definitely nonlinear relationship. This relationship fits the experimental data very well. With this strain energy function, we can define a parameter called the degree of nonlinearity, which represents the fraction of the nonlinear strain energy in the total strain energy per unit volume. We found that for the canine aorta, the degree of nonlinearity varies from 5% to 30%, depending on the magnitude of the strains in the physiological range. In the case of canine pulmonary artery in the arch region, Debes and Fung [Debes, J. C. & Fung, Y. C.(1995) Am. J. Physiol. 269, H433–H442] have shown that the linear regime of the stress–strain relationship extends from the zero-stress state to the homeostatic state and beyond. Both vessels, however, are anisotropic in both the linear and nonlinear regimes.