Common Features in Vector Nonlinear Time Series Models

This thesis consists of four manuscripts in the area of nonlinear time series econometrics on topics of testing, modeling and forecasting nonlinear common features. The aim of this thesis is to develop new econometric contributions for hypothesis testing and forecasting in these area. Both stationary and nonstationary time series are concerned. A definition of common features is proposed in an appropriate way to each class. Based on the definition, a vector nonlinear time series model with common features is set up for testing for common features. The proposed models are available for forecasting as well after being well specified. The first paper addresses a testing procedure on nonstationary time series. A class of nonlinear cointegration, smooth-transition (ST) cointegration, is examined. The ST cointegration nests the previously developed linear and threshold cointegration. An Ftypetest for examining the ST cointegration is derived when stationary transition variables are imposed rather than nonstationary variables. Later ones drive the test standard, while the former ones make the test nonstandard. This has important implications for empirical work. It is crucial to distinguish between the cases with stationary and nonstationary transition variables so that the correct test can be used. The second and the fourth papers develop testing approaches for stationary time series. In particular, the vector ST autoregressive (VSTAR) model is extended to allow for common nonlinear features (CNFs). These two papers propose a modeling procedure and derive tests for the presence of CNFs. Including model specification using the testing contributions above, the third paper considers forecasting with vector nonlinear time series models and extends the procedures available for univariate nonlinear models. The VSTAR model with CNFs and the ST cointegration model in the previous papers are exemplified in detail,and thereafter illustrated within two corresponding macroeconomic data sets.

A Comparison of the Effects of Nonlinear Damping on the Free Vibration of a Single-Degree-of-Freedom System

This article concerns the free vibration of a single-degree-of-freedom (SDOF) system with three types of nonlinear damping. One system considered is where the spring and the damper are connected to the mass so that they are orthogonal, and the vibration is in the direction of the spring. It is shown that, provided the displacement is small, this system behaves in a similar way to the conventional SDOF system with cubic damping, in which the spring and the damper are connected so they act in the same direction. For completeness, these systems are compared with a conventional SDOF system with quadratic damping. By transforming all the equations of motion of the systems so that the damping force is proportional to the product of a displacement dependent term and velocity, then all the systems can be directly compared. It is seen that the system with cubic damping is worse than that with quadratic damping for the attenuation of free vibration. [DOI: 10.1115/1.4005010]

Applied models to biodegradation kinetics of lubricant and vegetable oils in wastewater

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

Studying nonlinear effects on the early stage of phase ordering using a decomposition method

Nonlinear effects on the early stage of phase ordering are studied using Adomian's decomposition method for the Ginzburg-Landau equation for a nonconserved order parameter. While the long-time regime and the linear behavior at short times of the theory are well understood, the onset of nonlinearities at short times and the breaking of the linear theory at different length scales are less understood. In the Adomians decomposition method, the solution is systematically calculated in the form of a polynomial expansion for the order parameter, with a time dependence given as a series expansion. The method is very accurate for short times, which allows to incorporate the short-time dynamics of the nonlinear terms in a analytical and controllable way. (c) 2005 Elsevier B.V. All rights reserved.

On an Active Control for a Structurally Nonlinear Mechanical System, Taking Into Account an Energy Pumping

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

NONLINEAR SCALAR COUPLING MODELS AND PROTON-NUCLEUS SCATTERING OBSERVABLES

The effects of nonlinear scalar field couplings on elastic proton-nucleus scattering observables are investigated using a relativistic impulse approximation. Nonlinear couplings affect in a nontrivial way the effective nucleon mass and the nuclear scalar and vector densities. Modifications on the densities might have observable consequences on scattering observables. Our investigation indicates that the description of the observables for the reactions p-O-16 and p-Ca-40 at 200 MeV are not greatly modified with the use of nonlinear models in comparison with the description using linear models.

On nonlinear dynamics in a free fluid surface of a tank excited by a non-ideal power source

We investigate the nonlinear oscillations in a free surface of a fluid in a cylinder tank excited by non-ideal power source, an electric motor with limited power supply. We study the possibility of parametric resonance in this system, showing that the excitation mechanism can generate chaotic response. Additionally, the dynamics of parametrically excited surface waves in the tank can reveal new characteristics of the system. The fluid-dynamic system is modeled in such way as to obtain a nonlinear differential equation system. Numerical experiments are carried out to find the regions of chaotic solutions. Simulation results are presented as phase-portrait diagrams characterizing the resonant vibrations of free fluid surface and the existence of several types of regular and chaotic attractors. We also describe the energy transfer in the interaction process between the hydrodynamic system and the electric motor. Copyright © 2011 by ASME.

On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system

This paper discusses the dynamic behaviour of a nonlinear two degree-of-freedom system consisting of a harmonically excited linear oscillator weakly connected to a nonlinear attachment that behaves as a hardening Duffing oscillator. A system which behaves in this way could be a shaker (linear system) driving a nonlinear isolator. The mass of the nonlinear system is taken to be much less than that in the linear system and thus the nonlinear system has little effect on the dynamics of the linear system. Of particular interest is the situation when the linear natural frequency of the nonlinear system is less than the natural frequency of the linear system such that the frequency response curve of the nonlinear system bends to higher frequencies and thus interacts with the resonance frequency of the linear system. It is shown that for some values of the system parameters a complicated frequency response curve for the nonlinear system can occur; closed detached curves can appear as a part of the overall amplitude-frequency response. The reason why these detached curves appear is presented and approximate analytical expressions for the jump-up and jump-down frequencies of the system under investigation are given.

Structure and kinetics of formation of APTS/GPTS-derived organic/inorganic hybrids

The structure and the kinetics of formation of APTS/GPTS-derived organic/inorganic hybrids were studied in situ by small-angle-X-ray scattering. The data were interpreted in terms of a process of primary particles formation and growth of mass-fractal clusters. At the very early stage, the population of the nonfractal primary particles (D = 3) increases with time. As the mass-fractal clusters appear (D < 3) as a result of the aggregation process, the radius of gyration, Rg, of the clusters increases on average. At advanced stages of aggregation, the clusters grow in a mechanism in which the number of particles per clusters increases while the number of clusters diminishes with time, in such a way that the correlation volume of the clusters, Vc, fulfills the relationship Vc â̂ R g D, in agreement with a mass-fractal character of the clusters. These results supporting a cluster-cluster aggregation process, together with the typically very low value found for the mass-fractal dimension D, are in favor of a diffusion-controlled cluster aggregation mechanism. © 2013 American Chemical Society.

A Facile Measurement of Heterogeneous Electron Transfer Kinetics

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

Bifurcations Leading to Nonlinear Oscillations in a 3D Piecewise Linear Memristor Oscillator

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

Predicting soluble solid content in intact jaboticaba [Myrciaria jaboticaba (Vell.) O. Berg] fruit using near-infrared spectroscopy and chemometrics

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

On the Performance of a Two-Stage Vibration Isolation System Which has Geometrically Nonlinear Stiffness

Linear single-stage vibration isolation systems have a limitation on their performance, which can be overcome passively by using linear two-stage isolations systems. It has been demonstrated by several researchers that linear single-stage isolation systems can be improved upon by using nonlinear stiffness elements, especially for low-frequency vibrations. In this paper, an investigation is conducted into whether the same improvements can be made to a linear two-stage isolation system using the same methodology for both force and base excitation. The benefits of incorporating geometric stiffness nonlinearity in both upper and lower stages are studied. It is found that there are beneficial effects of using nonlinearity in the stiffness in both stages for both types of excitation. Further, it is found that this nonlinearity causes the transmissibility at the lower resonance frequency to bend to the right, but the transmissibility at the higher resonance frequency is not affected in the same way. Generally, it is found that a nonlinear two-stage system has superior isolation performance compared to that of a linear two-stage isolator.

Wave reflection at the end of a waveguide supported by a nonlinear spring

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

Polymerization kinetics and polymerization stress in resin composites after accelerated aging as a function of the expiration date

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)