Transition to complete synchronization in phase-coupled oscillators with nearest neighbor coupling

We investigate synchronization in a Kuramoto-like model with nearest neighbor coupling. Upon analyzing the behavior of individual oscillators at the onset of complete synchronization, we show that the time interval between bursts in the time dependence of the frequencies of the oscillators exhibits universal scaling and blows up at the critical coupling strength. We also bring out a key mechanism that leads to phase locking. Finally, we deduce forms for the phases and frequencies at the onset of complete synchronization.

Mobility and social network effects on extremist opinions

Understanding the emergence of extreme opinions and in what kind of environment they might become less extreme is a central theme in our modern globalized society. A model combining continuous opinions and observed discrete actions (CODA) capable of addressing the important issue of measuring how extreme opinions might be has been recently proposed. In this paper I show extreme opinions to arise in a ubiquitous manner in the CODA model for a multitude of social network structures. Depending on network details reducing extremism seems to be possible. However, a large number of agents with extreme opinions is always observed. A significant decrease in the number of extremists can be observed by allowing agents to change their positions in the network.

Ventilation behavior in trained and untrained men during incremental test: evidence of one metabolic transition point

This study aimed to describe and compare the ventilation behavior during an incremental test utilizing three mathematical models and to compare the feature of ventilation curve fitted by the best mathematical model between aerobically trained (TR) and untrained ( UT) men. Thirty five subjects underwent a treadmill test with 1 km.h(-1) increases every minute until exhaustion. Ventilation averages of 20 seconds were plotted against time and fitted by: bi-segmental regression model (2SRM); three-segmental regression model (3SRM); and growth exponential model (GEM). Residual sum of squares (RSS) and mean square error (MSE) were calculated for each model. The correlations between peak VO2 (VO2PEAK), peak speed (Speed(PEAK)), ventilatory threshold identified by the best model (VT2SRM) and the first derivative calculated for workloads below (moderate intensity) and above (heavy intensity) VT2SRM were calculated. The RSS and MSE for GEM were significantly higher (p < 0.01) than for 2SRM and 3SRM in pooled data and in UT, but no significant difference was observed among the mathematical models in TR. In the pooled data, the first derivative of moderate intensities showed significant negative correlations with VT2SRM (r = -0.58; p < 0.01) and Speed(PEAK) (r = -0.46; p < 0.05) while the first derivative of heavy intensities showed significant negative correlation with VT2SRM (r = -0.43; p < 0.05). In UT group the first derivative of moderate intensities showed significant negative correlations with VT2SRM (r = -0.65; p < 0.05) and Speed(PEAK) (r = -0.61; p < 0.05), while the first derivative of heavy intensities showed significant negative correlation with VT2SRM (r= -0.73; p < 0.01), Speed(PEAK) (r = -0.73; p < 0.01) and VO2PEAK (r = -0.61; p < 0.05) in TR group. The ventilation behavior during incremental treadmill test tends to show only one threshold. UT subjects showed a slower ventilation increase during moderate intensities while TR subjects showed a slower ventilation increase during heavy intensities.

Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells

This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark beta algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples. Copyright (C) 2009 H. B. Coda and R. R. Paccola.

Parametric model for the analysis of concrete expansion due to alkali-aggregate reaction

The alkali-aggregate reaction (AAR) is a chemical reaction that provokes a heterogeneous expansion of concrete and reduces important properties such as Young's modulus, leading to a reduction in the structure's useful life. In this study, a parametric model is employed to determine the spatial distribution of the concrete expansion, combining normalized factors that influence the reaction through an AAR expansion law. Optimization techniques were employed to adjust the numerical results and observations in a real structure. A three-dimensional version of the model has been implemented in a finite element commercial package (ANSYS(C)) and verified in the analysis of an accelerated mortar test. Comparisons were made between two AAR mathematical descriptions for the mechanical phenomenon, using the same methodology, and an expansion curve obtained from experiment. Some parametric studies are also presented. The numerical results compared very well with the experimental data validating the proposed method.

On the energy harvesting potential of piezoaeroelastic systems

This paper investigates the concept of piezoaeroelasticity for energy harvesting. The focus is placed on mathematical modeling and experimental validations of the problem of generating electricity at the flutter boundary of a piezoaeroelastic airfoil. An electrical power output of 10.7 mW is delivered to a 100 k load at the linear flutter speed of 9.30 m/s (which is 5.1% larger than the short-circuit flutter speed). The effect of piezoelectric power generation on the linear flutter speed is also discussed and a useful consequence of having nonlinearities in the system is addressed. (C) 2010 American Institute of Physics. [doi:10.1063/1.3427405]

Chaotic Patterns in Aeroelastic Signals

This work presents the analysis of nonlinear aeroelastic time series from wing vibrations due to airflow separation during wind tunnel experiments. Surrogate data method is used to justify the application of nonlinear time series analysis to the aeroelastic system, after rejecting the chance for nonstationarity. The singular value decomposition (SVD) approach is used to reconstruct the state space, reducing noise from the aeroelastic time series. Direct analysis of reconstructed trajectories in the state space and the determination of Poincare sections have been employed to investigate complex dynamics and chaotic patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincare mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents. Copyright (C) 2009 F. D. Marques and R. M. G. Vasconcellos.

Diffusive Synchronization of Hyperchaotic Lorenz Systems

The synchronizing properties of two diffusively coupled hyperchaotic Lorenz 4D systems are investigated by calculating the transverse Lyapunov exponents and by observing the phase space trajectories near the synchronization hyperplane. The effect of parameter mismatch is also observed. A simple electrical circuit described by the Lorenz 4D equations is proposed. Some results from laboratory experiments with two coupled circuits are presented. Copyright (C) 2009 Ruy Barboza.

Trajectory Sensitivity Method and Master-Slave Synchronization to Estimate Parameters of Nonlinear Systems

A combination of trajectory sensitivity method and master-slave synchronization was proposed to parameter estimation of nonlinear systems. It was shown that master-slave coupling increases the robustness of the trajectory sensitivity algorithm with respect to the initial guess of parameters. Since synchronization is not a guarantee that the estimation process converges to the correct parameters, a conditional test that guarantees that the new combined methodology estimates the true values of parameters was proposed. This conditional test was successfully applied to Lorenz's and Chua's systems, and the proposed parameter estimation algorithm has shown to be very robust with respect to parameter initial guesses and measurement noise for these examples. Copyright (C) 2009 Elmer P. T. Cari et al.

Effects of Variations in Nonlinear Damping Coefficients on the Parametric Vibration of a Cantilever Beam with a Lumped Mass

Uncertainties in damping estimates can significantly affect the dynamic response of a given flexible structure. A common practice in linear structural dynamics is to consider a linear viscous damping model as the major energy dissipation mechanism. However, it is well known that different forms of energy dissipation can affect the structure's dynamic response. The major goal of this paper is to address the effects of the turbulent frictional damping force, also known as drag force on the dynamic behavior of a typical flexible structure composed of a slender cantilever beam carrying a lumped-mass on the tip. First, the system's analytical equation is obtained and solved by employing a perturbation technique. The solution process considers variations of the drag force coefficient and its effects on the system's response. Then, experimental results are presented to demonstrate the effects of the nonlinear quadratic damping due to the turbulent frictional force on the system's dynamic response. In particular, the effects of the quadratic damping on the frequency-response and amplitude-response curves are investigated. Numerically simulated as well as experimental results indicate that variations on the drag force coefficient significantly alter the dynamics of the structure under investigation. Copyright (c) 2008 D. G. Silva and P. S. Varoto.

UNIQUENESS AND NONUNIQUENESS RESULTS FOR A CERTAIN CLASS OF ALMOST PERIODIC DISTRIBUTIONS

We consider distributions u is an element of S'(R) of the form u(t) = Sigma(n is an element of N) a(n)e(i lambda nt), where (a(n))(n is an element of N) subset of C and Lambda = (lambda n)(n is an element of N) subset of R have the following properties: (a(n))(n is an element of N) is an element of s', that is, there is a q is an element of N such that (n(-q) a(n))(n is an element of N) is an element of l(1); for the real sequence., there are n(0) is an element of N, C > 0, and alpha > 0 such that n >= n(0) double right arrow vertical bar lambda(n)vertical bar >= Cn(alpha). Let I(epsilon) subset of R be an interval of length epsilon. We prove that for given Lambda, (1) if Lambda = O(n(alpha)) with alpha < 1, then there exists epsilon > 0 such that u vertical bar I(epsilon) = 0 double right arrow u 0; (2) if Lambda = O(n) is uniformly discrete, then there exists epsilon > 0 such that u vertical bar I(epsilon) = 0 double right arrow u 0; (3) if alpha > 1 and. is uniformly discrete, then for all epsilon > 0, u vertical bar I(epsilon) = 0 double right arrow u = 0. Since distributions of the above mentioned form are very common in engineering, as in the case of the modeling of ocean waves, signal processing, and vibrations of beams, plates, and shells, those uniqueness and nonuniqueness results have important consequences for identification problems in the applied sciences. We show an identification method and close this article with a simple example to show that the recovery of geometrical imperfections in a cylindrical shell is possible from a measurement of its dynamics.

The Effect of Spatial Scale on Predicting Time Series: A Study on Epidemiological System Identification

A susceptible-infective-recovered (SIR) epidemiological model based on probabilistic cellular automaton (PCA) is employed for simulating the temporal evolution of the registered cases of chickenpox in Arizona, USA, between 1994 and 2004. At each time step, every individual is in one of the states S, I, or R. The parameters of this model are the probabilities of each individual (each cell forming the PCA lattice ) passing from a state to another state. Here, the values of these probabilities are identified by using a genetic algorithm. If nonrealistic values are allowed to the parameters, the predictions present better agreement with the historical series than if they are forced to present realistic values. A discussion about how the size of the PCA lattice affects the quality of the model predictions is presented. Copyright (C) 2009 L. H. A. Monteiro et al.

Dynamical models for computer viruses propagation

Nowadays, digital computer systems and networks are the main engineering tools, being used in planning, design, operation, and control of all sizes of building, transportation, machinery, business, and life maintaining devices. Consequently, computer viruses became one of the most important sources of uncertainty, contributing to decrease the reliability of vital activities. A lot of antivirus programs have been developed, but they are limited to detecting and removing infections, based on previous knowledge of the virus code. In spite of having good adaptation capability, these programs work just as vaccines against diseases and are not able to prevent new infections based on the network state. Here, a trial on modeling computer viruses propagation dynamics relates it to other notable events occurring in the network permitting to establish preventive policies in the network management. Data from three different viruses are collected in the Internet and two different identification techniques, autoregressive and Fourier analyses, are applied showing that it is possible to forecast the dynamics of a new virus propagation by using the data collected from other viruses that formerly infected the network. Copyright (c) 2008 J. R. C. Piqueira and F. B. Cesar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Border figure detection using a phase oscillator network with dynamical coupling

Oscillator networks have been developed in order to perform specific tasks related to image processing. Here we analytically investigate the existence of synchronism in a pair of phase oscillators that are short-range dynamically coupled. Then, we use these analytical results to design a network able of detecting border of black-and-white figures. Each unit composing this network is a pair of such phase oscillators and is assigned to a pixel in the image. The couplings among the units forming the network are also dynamical. Border detection emerges from the network activity.

Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.