Search

The main objective of the present work was to accurately predict the dynamic response of a gear transmission system. First, a nonlinear mathematical model is introduced. In this model, the housing of the gearbox is modeled by using finite elements, while the essential effects of the gear-pair, the bearings and the shafts are taken into account via a lumped nonlinear mathematical model. This model possesses strongly nonlinear characteristics, accounting for gear backlash, meshing stiffness, transmission error properties and bearing stiffness nonlinearities. Then, a Bayesian uncertainty quantification and propagation (UQ&P) framework is adopted in order to estimate the optimal values of the gearbox, gear-pair and bearing model parameters. In order to identify the values of the parameters, accelerations time histories are used, obtained during various operating conditions of the gearbox. These measurements are recorded from a special experimental device, which was designed and set up for this purpose. The effect of correlation in the prediction error models postulated in the Bayesian model selection and parameter estimation technique is investigated. Finally the experimental results was compared to those from the numerical model for verification of the numerical procedure and improvement of the numerical modeling of the gear transmission components. [ABSTRACT FROM AUTHOR]

Nonlinearities have long been avoided in the design of structural systems. This was done to make problems tractable, to fit within current design paradigms, and often with the assumption that the resulting design would be conservative. Computational methods have made the investigation of nonlinear systems possible, which may yield more accurate and optimal designs. However, in venturing into the nonlinear regime, a designer must be aware of potential pitfalls, one of which is the possibility of unsafe responses ˵hiding in the weeds″ of parameter or initial condition space. In this paper, an experimental study on a damped, post-buckled beam in the presence of noise is used to show that co-existing stationary solutions may be present in real-world scenarios. Stochastic resonance, a surprising phenomenon in which a small harmonic load interacts with, and magnifies the response to, an otherwise pure random load, is also studied and observed to occur in the beam. [ABSTRACT FROM AUTHOR]

A key feature of many nonlinear dynamical systems is the presence of co-existing solutions, i.e, nonlinear systems are often sensitive to initial conditions. While there have been many studies to explore this behavior from a numerical perspective, in which case it is trivial to prescribe initial conditions (for example using a regular grid), this is more challenging from an experimental perspective. This paper will discuss the basins of attraction in a simple mechanical experiment. By applying both small and large stochastic perturbations to steady-state behavior, it is possible to interrogate the initial condition space and map-out basins of attraction as system parameters are changed. This tends to provide a more complete picture of possible behavior than conventional bifurcation diagrams with their focus on local steady-state behavior. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model to investigate the nonlinear dynamic behavior of a high speed rotor-bearing system due to surface waviness with varying number of waves. In the formulation, the contact between rolling elements and inner/outer races are considered as nonlinear springs with nonlinear damping incorporated, which is developed by correlating the contact damping force with the equivalent contact stiffness and contact deformation rate. The equations of motion are formulated using Lagrange΄s equation, considering the vibration characteristics of the individual components such as inner race, outer race, rolling elements and rotor. For high speed rolling element bearing supported by a rigid balanced rotor with defective bearings, nonlinear dynamic responses are found to be associated with wave passage frequency and also with the interactive effect of wave passage and inner race frequencies (ωinner). Results presented in the form of fast Fourier transformation are in agreement with authors΄ various experimental results. [ABSTRACT FROM AUTHOR]

It is well established that noise, despite its mostly detrimental effects, can play a constructive role for information transfer. The best known example is stochastic resonance (SR) phenomena. SR means that there is an optimal level of noise for the detection of weak signals. In this study, a Hodgkin-Huxley type model neuron with subthreshold oscillations has been used to demonstrate that the noise effects essentially depend on the neuron's activity state. These data shall emphasize more general aspects of stochastic encoding (SE) which, beyond tuning of noise, can be achieved with appropriate adjustment of physiological control parameters. [ABSTRACT FROM AUTHOR]

A mathematical model describing the interactions between viral infection and acquired immunity is proposed. The model is formulated in terms of a system of partial integro-differential bilinear equations. Results of numerical experiments are presented. [ABSTRACT FROM AUTHOR]

Nonlinear dynamics of a kicked particle in a square billiard with the central symmetric kick source is studied. Time-dependence of the average energy is explored and compared with that for a kicked free particle. Dependence of the acceleration on different localizations of the kick source is considered. [ABSTRACT FROM AUTHOR]

The theory of adiabatic invariants has a long history, and very important implications and applications in many different branches of physics, classically and quantally, but is rarely founded on rigorous results. Here we treat the general time-dependent one-dimensional linear (harmonic) oscillator, whose Newton equation ]> cannot be solved in general. We follow the time-evolution of an initial ensemble of phase points with sharply defined energy E0 at time t = 0 (microcanonical ensemble) and calculate rigorously the distribution of energy E1 after time t = T, which is fully (all moments, including the variance μ2) determined by the first moment E¯1. For example, ]> , and all higher even moments are powers of μ2, whilst the odd ones vanish identically. This distribution function does not depend on any further details of the function É(t) and is in this sense universal, it is a normalized distribution function given by ]> , where ]> and μ2 can be calculated exactly in some cases. In ideal adiabaticity ]> , and the variance μ2 is zero, whilst for finite T we calculate ]> , and μ2 for the general case using exact WKB-theory to all orders. We prove that if ω(t) is of class Cm (all derivatives up to and including the order m are continuous) μ2∞T−2(m+1), whilst for class C∞ it is known to be exponential μ2 exp(-α T). Due to the positivity of μ2 we also see that the adiabatic invariant ]> at the average energy ]> never decreases. [ABSTRACT FROM AUTHOR]

We review recent progress in the field of optomechanics, where one studies the effects of radiation on mechanical motion. The paradigmatic example is an optical cavity with a movable mirror, where the radiation pressure can induce cooling, amplification and nonlinear dynamics of the mirror. [ABSTRACT FROM AUTHOR]

We briefly describe the state-of-the-art concerning Fermi acceleration in twodimensional driven billiards by reviewing the corresponding literature with a focus on our recent work on the time-dependent ellipse and some new results on the breathing mode of a certain oval billiard. In a way, these two systems represent the ˵missing links″ in the studies of two-dimensional driven billiards and help to clarify the conditions under which Fermi acceleration will arise. [ABSTRACT FROM AUTHOR]

The Grassberger-Procaccia algorithm for computation of the correlation dimension is widely used nonlinear dynamical analysis techniques for EEG time series analysis. Even though the correlation dimension D2 is the easiest dimension to compute, major drawback of the Grassberger-Procaccia algorithm is its extensive computational requirements. To overcome this, we introduce a modified computational algorithm referred to as the partial correlation integral. The partial correlation integral algorithm provides an approximation of the correlation dimension referred to as the dimensional exponent. Similar to the correlation dimension, the dimensional exponent can serve as a relative index of the complexity of a nonlinear dynamical system. In this study, the partial correlation integral algorithm is applied to analyze neonatal EEG sleep data. From the computational results, conclusions consistent with those made in previous studies using the correlation dimension are obtained. [ABSTRACT FROM AUTHOR]

Simulation results of bistable perception due to ambiguous visual stimuli are presented which are obtained with a nonlinear dynamics model using delayed perception–attention–memory coupling. Percept reversals are induced by attention fatigue with an attention bias which balances the relative percept duration. Periodic stimulus simulations as a function of stimulus off-time yields the reversal rate variation in surprisingly good quantitative agreement with classical experimental results reported in the literature [1] when selecting a fatigue time constant of 1 – 2 s. Coupling of the bias to the perception state introduces memory effects which are quantified through the Hurst parameter H, exhibiting significant long range correlations (H > 0.5) in agreement with recent experimental results [2]. Percept transition times of 150 – 200 ms and mean percept dwell times of 3 – 5 s as reported in the literature, are correctly predicted if a feedback delay of 40 ms is assumed as mentioned in the literature (e.g. [21]). [ABSTRACT FROM AUTHOR]

In this paper, we report the dynamics of VSF-Network. VSF-Network is a neural network for the incremental learning and it is a hybrid neural network combining the chaos neural network with a hierarchical network. VSF-Network can find the unknown elements from input with clusters generated by the chaos neuron. We introduce new incremental learning model to explain the dynamics of VSF-Network in this paper. We show the result of analysis of the dynamics of VSF-Network. In the analysis, we focused on the connection weights between layers and neuron cluster generated by the chaotic behavior. [ABSTRACT FROM AUTHOR]

A FitzHugh–Nagumo type spiking neuron model equipped with an asymmetric activation function is investigated. An analogue nonlinear electrical circuit imitating the dynamics of the model is proposed. It is demonstrated that a simple first order linear filter coupled to the system can inhibit spiking and stabilize the system on an unstable steady state, the position of which is not required to be known, since the filter operates as an adaptive controller. Analytical, numerical and experimental results are presented. [ABSTRACT FROM AUTHOR]

We present a mathematical model of cellular immune response to viral infection. The model is a bilinear system of integro-differential equations of Boltzmann type. Results of numerical experiments are presented. [ABSTRACT FROM AUTHOR]

Shifts in the nonlinear rotational frequency of magnetic beads (microspheres) offer a new and dynamic approach for the detection of single cells. We present the first demonstration of this capability by measuring the changes in the nonlinear rotational frequency of magnetic beads driven by an external magnetic field. The presence of an Escherichia coli bacterium on the surface of a 2.0 μm magnetic bead affects the drag of the system, thus changing the nonlinear rotation rate. Measurement of this rotational frequency is straight-forward utilizing standard microscopy techniques. [ABSTRACT FROM AUTHOR]

Evolution of cardiac activity is investigated by means of nonlinear dynamics, namely the method of temporal localization on the attractor reconstructed from a digitized electrocardiogram signal. Convergence for the function of topological instability at changing dimensionality is proven both theoretically and numerically, independently from personal features of subjects in a latter case. This provides an opportunity to estimate the complexity (expressed through the number of freedom degrees) of cardiac dynamics. On the other hand, this instability function normalized by its average displays a different kind of behavior that somewhat differs for various persons and reflects their individual features. The essential reduction of computation time and necessary statistics are also attained by means of the developed algorithm. [ABSTRACT FROM AUTHOR]

Complex computing systems begin to overwhelm the capacities of software developers and administrators. Self-organization has been a successful strategy of evolution to handle the increasing complexity of organisms with the emergence of novel structures and behavior. Thus, self-organization and emergence are fundamental concepts of organic computing. But these concepts are often used in a more or less intuitive manner. In the theory of complex systems and nonlinear dynamics, self-organization and emergence can be mathematically defined. Actually, these concepts are independent of biological applications, but universal features of dynamical systems. We get an interdisciplinary framework to understand self-organizing complex systems and to ask for applications in organic computing. In technology, the emergence of order and structures displays desired and undesired synergetic effects. Thus, controlled emergence is a challenge of computational systems simulating self-organizing organic systems of evolution. The question arises how far can we go in simulating high dimensional complex systems and avoiding uncontrolled risks. [ABSTRACT FROM AUTHOR]

A numerical model for the simulation of dynamic compression of a nonlinear multilayer structure subjected to transient compressive excitation is described and tested. It is shown that impacts induce a chaotic collapse of crumple layers. The simulations predict shock pulses and intralaminar forces. Simulated shock pulses that a free-falling mass is subjected to, and the corresponding animated deformation histories of the layers, are compared with the high-speed videography. Cushioning performance maps and shock response spectrums maps obtained from the simulations are presented. [ABSTRACT FROM AUTHOR]

A recently proposed measure, namely Transfer Entropy (TE), is used to estimate the direction of information flow between coupled linear and nonlinear systems. In this study, we suggest improvements in the selection of parameters for the estimation of TE that significantly enhance its accuracy and robustness in identifying the direction of information flow and quantifying the level of interaction between observed data series from coupled systems. We demonstrate the potential usefulness of the improved method through simulation examples with coupled nonlinear chaotic systems. The statistical significance of the results is shown through the use of surrogate data. The improved TE method is then used for the study of information flow in the epileptic human brain. We illustrate the application of TE to electroencephalographic (EEG) signals for the study of localization of the epileptogenic focus and the dynamics of its interaction with other brain sites in two patients with Temporal Lobe Epilepsy (TLE). [ABSTRACT FROM AUTHOR]

We have previously reported preictal spatiotemporal transitions in human mesial temporal lobe epilepsy (MTLE) using short term Lyapunov exponent (STLmax) and average angular frequency ( ]> ). These results have prompted us to apply the quantitative nonlinear methods to a limbic epilepsy rat (CLE), as this model has several important features of human MTLE. The present study tests the hypothesis that preictal dynamical changes similar to those seen in human MTLE exist in the CLE model. Forty-two, 2-hr epoch data sets from 4 CLE rats (mean seizure duration 74±20 sec) are analyzed, each containing a focal onset seizure and intracranial data beginning 1 hr before the seizure onset. Three nonlinear measures, correlation integral, short-term largest Lyapunov exponent and average angular frequency are used in the current study. Data analyses show multiple transient drops in STLmax values during the preictal period followed by a significant drop during the ictal period. Average angular frequency values demonstrate transient peaks during the preictal period followed by a significant peak during the ictal period. Convergence among electrode sites is also observed in both STLmax and ]> values before seizure onset. Results suggest that dynamical changes precede and accompany seizures in rat CLE. Thus, it may be possible to use the rat CLE model as a tool to refine and test real-time seizure prediction, and closed-loop intervention techniques. [ABSTRACT FROM AUTHOR]