Systematic weakly nonlinear analysis of radial viscous fingering

We present a weakly nonlinear analysis of the interface dynamics in a radial Hele-Shaw cell driven by both injection and rotation. We extend the systematic expansion introduced in [E. Alvarez-Lacalle et al., Phys. Rev. E 64, 016302 (2001)] to the radial geometry, and compute explicitly the first nonlinear contributions. We also find the necessary and sufficient condition for the uniform convergence of the nonlinear expansion. Within this region of convergence, the analytical predictions at low orders are compared satisfactorily to exact solutions and numerical integration of the problem. This is particularly remarkable in configurations (with no counterpart in the channel geometry) for which the interplay between injection and rotation allows that condition to be satisfied at all times. In the case of the purely centrifugal forcing we demonstrate that nonlinear couplings make the interface more unstable for lower viscosity contrast between the fluids.

Damage detection in nonlinear structures using discrete-time volterra series

Structural damage identification is basically a nonlinear phenomenon; however, nonlinear procedures are not used currently in practical applications due to the complexity and difficulty for implementation of such techniques. Therefore, the development of techniques that consider the nonlinear behavior of structures for damage detection is a research of major importance since nonlinear dynamical effects can be erroneously treated as damage in the structure by classical metrics. This paper proposes the discrete-time Volterra series for modeling the nonlinear convolution between the input and output signals in a benchmark nonlinear system. The prediction error of the model in an unknown structural condition is compared with the values of the reference structure in healthy condition for evaluating the method of damage detection. Since the Volterra series separate the response of the system in linear and nonlinear contributions, these indexes are used to show the importance of considering the nonlinear behavior of the structure. The paper concludes pointing out the main advantages and drawbacks of this damage detection methodology. © (2013) Trans Tech Publications.

Nonlinear features identified by Volterra series for damage detection in a buckled beam

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Characterization of the nonlinear behavior of a F-16 aircraft using discrete-time Volterra series

The linearity assumption in the structural dynamics analysis is a severe practical limitation. Further, in the investigation of mechanisms presented in fighter aircrafts, as for instance aeroelastic nonlinearity, friction or gaps in wing-load-payload mounting interfaces, is mandatory to use a nonlinear analysis technique. Among different approaches that can be used to this matter, the Volterra theory is an interesting strategy, since it is a generalization of the linear convolution. It represents the response of a nonlinear system as a sum of linear and nonlinear components. Thus, this paper aims to use the discrete-time version of Volterra series expanded with Kautz filters to characterize the nonlinear dynamics of a F-16 aircraft. To illustrate the approach, it is identified and characterized a non-parametric model using the data obtained during a ground vibration test performed in a F-16 wing-to-payload mounting interfaces. Several amplitude inputs applied in two shakers are used to show softening nonlinearities presented in the acceleration data. The results obtained in the analysis have shown the capability of the Volterra series to give some insight about the nonlinear dynamics of the F-16 mounting interfaces. The biggest advantage of this approach is to separate the linear and nonlinear contributions through the multiple convolutions through the Volterra kernels.

Measurement of the correlation between flow harmonics of different order in lead-lead collisions at root S-NN=2.76 TeV with the ATLAS detector

Correlations between the elliptic or triangular flow coefficients vm (m=2 or 3) and other flow harmonics vn (n=2 to 5) are measured using sNN−−−−√=2.76 TeV Pb+Pb collision data collected in 2010 by the ATLAS experiment at the LHC, corresponding to an integrated lumonisity of 7 μb−1. The vm-vn correlations are measured in midrapidity as a function of centrality, and, for events within the same centrality interval, as a function of event ellipticity or triangularity defined in a forward rapidity region. For events within the same centrality interval, v3 is found to be anticorrelated with v2 and this anticorrelation is consistent with similar anticorrelations between the corresponding eccentricities ϵ2 and ϵ3. On the other hand, it is observed that v4 increases strongly with v2, and v5 increases strongly with both v2 and v3. The trend and strength of the vm-vn correlations for n=4 and 5 are found to disagree with ϵm-ϵn correlations predicted by initial-geometry models. Instead, these correlations are found to be consistent with the combined effects of a linear contribution to vn and a nonlinear term that is a function of v22 or of v2v3, as predicted by hydrodynamic models. A simple two-component fit is used to separate these two contributions. The extracted linear and nonlinear contributions to v4 and v5 are found to be consistent with previously measured event-plane correlations.

Caracterização experimental de sistemas mecânicos com comportamento não-linear

Pós-graduação em Engenharia Mecânica - FEIS

Lateral boundary contributions to wave-activity invariants and nonlinear stability theorems for balanced dynamics

The slow advective-timescale dynamics of the atmosphere and oceans is referred to as balanced dynamics. An extensive body of theory for disturbances to basic flows exists for the quasi-geostrophic (QG) model of balanced dynamics, based on wave-activity invariants and nonlinear stability theorems associated with exact symmetry-based conservation laws. In attempting to extend this theory to the semi-geostrophic (SG) model of balanced dynamics, Kushner & Shepherd discovered lateral boundary contributions to the SG wave-activity invariants which are not present in the QG theory, and which affect the stability theorems. However, because of technical difficulties associated with the SG model, the analysis of Kushner & Shepherd was not fully nonlinear. This paper examines the issue of lateral boundary contributions to wave-activity invariants for balanced dynamics in the context of Salmon's nearly geostrophic model of rotating shallow-water flow. Salmon's model has certain similarities with the SG model, but also has important differences that allow the present analysis to be carried to finite amplitude. In the process, the way in which constraints produce boundary contributions to wave-activity invariants, and additional conditions in the associated stability theorems, is clarified. It is shown that Salmon's model possesses two kinds of stability theorems: an analogue of Ripa's small-amplitude stability theorem for shallow-water flow, and a finite-amplitude analogue of Kushner & Shepherd's SG stability theorem in which the ‘subsonic’ condition of Ripa's theorem is replaced by a condition that the flow be cyclonic along lateral boundaries. As with the SG theorem, this last condition has a simple physical interpretation involving the coastal Kelvin waves that exist in both models. Salmon's model has recently emerged as an important prototype for constrained Hamiltonian balanced models. The extent to which the present analysis applies to this general class of models is discussed.

Time-resolved study electronic and thermal contributions to the nonlinear refractive index of Nd3+: SBN laser crystals

The propagation of an optical beam through dielectric media induces changes in the refractive index, An, which causes self-focusing or self-defocusing. In the particular case of ion-doped solids, there are thermal and non-thermal lens effects, where the latter is due to the polarizability difference, Delta alpha, between the excited and ground states, the so-called population lens (PL) effect. PL is a pure electronic contribution to the nonlinearity, while the thermal lens (TL) effect is caused by the conversion of part of the absorbed energy into heat. In time-resolved measurements such as Z-scan and TL transient experiments, it is not easy to separate these two contributions to nonlinear refractive index because they usually have similar response times. In this work, we performed time-resolved measurements using both Z-scan and mode mismatched TL in order to discriminate thermal and electronic contributions to the laser-induced refractive index change of the Nd3+-doped Strontium Barium Niobate (SrxBa1-xNb2O6) laser crystal. Combining numerical simulations with experimental results we could successfully distinguish between the two contributions to An. (C) 2007 Elsevier B.V. All rights reserved.

Nonlinear refraction and absorption through phase transition in a Nd:SBN laser crystal

Time-resolved Z-scan measurements were performed in a Nd(3+)-doped Sr(0.61)Ba(0.39)Nb(2)O(6) laser crystal through ferroelectric phase transition. Both the differences in electronic polarizability (Delta alpha(p)) and cross section (Delta sigma) of the neodymium ions have been found to be strongly modified in the surroundings of the transition temperature. This observed unusual behavior is concluded to be caused by the remarkable influence that the structural changes associated to the ferro-to-paraelectric phase transition has on the 4f -> 5d transition probabilities. The maximum polarizability change value Delta alpha(p)=1.2x10(-25) cm(3) obtained at room temperature is the largest ever measured for a Nd(3+)-doped transparent material.

Fixed-point DSP implementation of nonlinear H(infinity) controller for large gap electromagnetic suspension system

Electromagnetic suspension systems are inherently nonlinear and often face hardware limitation when digitally controlled. The main contributions of this paper are: the design of a nonlinear H(infinity) controller. including dynamic weighting functions, applied to a large gap electromagnetic suspension system and the presentation of a procedure to implement this controller on a fixed-point DSP, through a methodology able to translate a floating-point algorithm into a fixed-point algorithm by using l(infinity) norm minimization due to conversion error. Experimental results are also presented, in which the performance of the nonlinear controller is evaluated specifically in the initial suspension phase. (C) 2009 Elsevier Ltd. All rights reserved.

Treatment of nonlinear optical properties due to large amplitude anharmonic vibrational motions: umbrella motion in NH3

A general reduced dimensionality finite field nuclear relaxation method for calculating vibrational nonlinear optical properties of molecules with large contributions due to anharmonic motions is introduced. In an initial application to the umbrella (inversion) motion of NH3 it is found that difficulties associated with a conventional single well treatment are overcome and that the particular definition of the inversion coordinate is not important. Future applications are described

Simple finite field method for calculation of static and dynamic vibrational hyperpolarizabilities: curvature contributions

In the static field limit, the vibrational hyperpolarizability consists of two contributions due to: (1) the shift in the equilibrium geometry (known as nuclear relaxation), and (2) the change in the shape of the potential energy surface (known as curvature). Simple finite field methods have previously been developed for evaluating these static field contributions and also for determining the effect of nuclear relaxation on dynamic vibrational hyperpolarizabilities in the infinite frequency approximation. In this paper the finite field approach is extended to include, within the infinite frequency approximation, the effect of curvature on the major dynamic nonlinear optical processes

Basis set and electron correlation effects on initial convergence for vibrational nonlinear optical properties of conjugated organic molecules

The level of ab initio theory which is necessary to compute reliable values for the static and dynamic (hyper)polarizabilities of three medium size π-conjugated organic nonlinear optical (NLO) molecules is investigated. With the employment of field-induced coordinates in combination with a finite field procedure, the calculations were made possible. It is stated that to obtain reasonable values for the various individual contributions to the (hyper)polarizability, it is necessary to include electron correlation. Based on the results, the convergence of the usual perturbation treatment for vibrational anharmonicity was examined

Initial convergence of the perturbation series expansion for vibrational nonlinear optical properties

Initial convergence of the perturbation series expansion for vibrational nonlinear optical (NLO) properties was analyzed. The zero-point vibrational average (ZPVA) was obtained through first-order in mechanical plus electrical anharmonicity. Results indicated that higher-order terms in electrical and mechanical anharmonicity can make substantial contributions to the pure vibrational polarizibility of typical NLO molecules

Efficient Optimization Algorithms for Nonlinear Data Analysis

Identification of low-dimensional structures and main sources of variation from multivariate data are fundamental tasks in data analysis. Many methods aimed at these tasks involve solution of an optimization problem. Thus, the objective of this thesis is to develop computationally efficient and theoretically justified methods for solving such problems. Most of the thesis is based on a statistical model, where ridges of the density estimated from the data are considered as relevant features. Finding ridges, that are generalized maxima, necessitates development of advanced optimization methods. An efficient and convergent trust region Newton method for projecting a point onto a ridge of the underlying density is developed for this purpose. The method is utilized in a differential equation-based approach for tracing ridges and computing projection coordinates along them. The density estimation is done nonparametrically by using Gaussian kernels. This allows application of ridge-based methods with only mild assumptions on the underlying structure of the data. The statistical model and the ridge finding methods are adapted to two different applications. The first one is extraction of curvilinear structures from noisy data mixed with background clutter. The second one is a novel nonlinear generalization of principal component analysis (PCA) and its extension to time series data. The methods have a wide range of potential applications, where most of the earlier approaches are inadequate. Examples include identification of faults from seismic data and identification of filaments from cosmological data. Applicability of the nonlinear PCA to climate analysis and reconstruction of periodic patterns from noisy time series data are also demonstrated. Other contributions of the thesis include development of an efficient semidefinite optimization method for embedding graphs into the Euclidean space. The method produces structure-preserving embeddings that maximize interpoint distances. It is primarily developed for dimensionality reduction, but has also potential applications in graph theory and various areas of physics, chemistry and engineering. Asymptotic behaviour of ridges and maxima of Gaussian kernel densities is also investigated when the kernel bandwidth approaches infinity. The results are applied to the nonlinear PCA and to finding significant maxima of such densities, which is a typical problem in visual object tracking.