Global asymptotic stability for nonlinear systems of differential equations and applications to reactor dynamics

Archive for Rational Mechanics and Analysis -     

On the periodic solutions of differential inclusions and applications

The periodic problem of evolution inclusion is studied and its results are used toestablish existence theorems of periodic solutions of a class of semi-linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given forthis class of semi-linear differential inclusion. An application to some feedback control systems isdiscussed.     

Bifurcation analysis of a nonlinear pendulum using recurrence and statistical methods: applications to fault diagnostics

The problem of maintenance of expensive and heavy systems has increased the need for powerful tools to analyze their performance. The methods of recurrence plots (RPs) and statistical measurement have been used as data-driven tools for diagnostics with no possibility of classifying the nature of defect and poor ability to localize it. In order to enhance the efficiency of the forecast, innovative approaches consist of using physics-based features to train a data-based assessment methods. This requires proper analysis of the physical system using appropriate methods. For this purpose, this paper focusses on the bifurcation dynamics of nonlinear systems using the recurrence and statistical methods. Considering the nonlinear pendulum as a model, the qualitative behavior of the system is discussed through the bifurcation diagram of some recurrence quantification analysis (RQA) parameters, namely the recurrence rate, determinism, and laminarity. These parameters are used to measure the level of complexity and transition from regular to chaotic motion and vice versa. Statistical parameters such as crest factor, skewness, and kurtosis are used to identify various bifurcation and amplitudes in the system, and to measure the orientation and the level of asymmetry. Plots of recurrence diagrams and histograms are presented to support our observations. Examples of detection of dynamic changes using these two methods are provided. The interesting results obtained in this paper show that statistical methods complement results obtained from RPs. In addition, the paper demonstrates how the RPs can be employed in conjunction with the physics-based model.     

Guaranteed cost nonlinear sampled-data control: applications to a class of chaotic systems

Nonlinear Dynamics - This paper addresses the guaranteed cost sampled-data controller synthesis and analysis problems with application to nonlinear chaotic systems. A linear parameter-varying (LPV)...     

Compaction characteristics for the towed and driven conditions of a wheel operating in an agricultural soil

High axle loads, duration of strain as well as strain rate due to applied stresses, and field moisture condition have been found to contribute to compaction in the field. Numerous previous investigations on agricultural soil compaction were carried out with relatively dry soil. The aim of this study was to investigate the interrelationships between compaction, applied load, vehicle speed and a certain practical range of soil moisture content through a soil bin investigation of the compaction which results from the passage of a towed and a driven wheel. Soil pressure and the corresponding bulk density were analysed using a model proposed by Bailey et al. (J. agric Engng Res. 33, 257–262 (1986)) and ANOVA techniques. The results showed that compaction was higher at the higher moisture content level for both towed and driven conditions of the wheel, and that it was applied load that had the greatest contributory effect. Also, compaction was higher in the case of the driven wheel as compared to the towed wheel due to the phenomenon of slip sinkage. Bailey's model, it appears, can be utilized in the field for a practical estimation of compaction resulting from the passage of a towed wheel.     

Experimental study on wheel-soil interaction mechanics using in-wheel sensor and particle image velocimetry Part I: Analysis and modeling of normal stress of lightweight wheeled vehicles

This study aims to develop a wheel-soil interaction model for a lightweight wheeled vehicle by measuring the normal stress distribution beneath the wheel. The main contribution of this work is to clarify the wheel-soil interaction using a wheel testbed that equips multiple sensory systems. An in-wheel sensor accurately measures the normal stress distribution as well as the contact angles of the wheel. Particle image velocimetry with a standard off-the-shelf camera analyzes soil flow beneath the wheel. The proposed model for the normal stress distribution is formulated based on these experimental data and takes into account the following phenomena for the lightweight vehicles that have not been considered in the classical model: (1) the normal stress distribution takes the form of a Gaussian curve; (2) the normal stress distribution concentrates in the front region of the wheel contact patch; (3) the distribution is divided into two areas with the boundary determined by the maximum normal stress angle; and (4) the maximum normal stress exponentially decreases as the slip ratio increases. Then, the proposed model is experimentally validated. Furthermore, a simulation study for the wheel driving characteristics using the proposed model confirms the accuracy of the proposed model.     

高精度非线性格式WCNS的分析研究与其应用

首先将Fourier方法推广于高维方向研究了五阶精度WCNS的特性,并与其他高阶格式进行比较。分析结果表明WCNS的高精度特性普遍接近甚至好于迎风偏置五阶显式格式EUW-5与Pade′标准格式。然后开展了WCNS的应用研究,采用高效率的WCNS-E-5数值模拟了含强激波的高维复杂流场。算例包括二维高超声速边界层对自由流扰动波的吸收问题以及三维球头绕流问题。计算结果反映出WCNS-E-5对激波等间断的良好捕捉能力,图像清晰光滑,数据准确可靠。     

A new efficient procedure to solve the nonlinear dynamics of a cracked rotor

The dynamic analysis of a cracked rotor with a breathing crack leads to the formulation of a nonlinear time-dependent problem. For the simple Jeffcott rotor model, this problem has been addressed using numerical integration methods that are very time consuming. A first simplification can be done assuming that the stiffness is a time-dependent function obtained with the quasi-static displacements of the shaft. In this study, we propose a new procedure to analyze the nonlinear dynamic of such a kind of cracked rotors using an iterative technique that transforms the full nonlinear problem in a succession of time-dependent linear ones. We show with different examples that this technique virtually gives the same results as the classical integration methods, but being much more efficient and achieving a significant saving of computation time. The calculations using the proposed method are over a 100 times faster than the corresponding to integrate the full nonlinear problem, being very helpful in on-line crack identification procedures. Also, this analysis shows that, in cases for which the vertical whirl amplitude is greater than the shaft weight static deflection, the use of simplified methods based on the quasi-static stiffness matrix could not be adequate.     

Control of the nonlinear dynamics of a truck and trailer combination

Nonlinear Dynamics - The directional instability problem of a truck and trailer combination in a forward motion has been investigated by developing a dynamic model of the planar rigid-body dynamics...     

Implementation and study of the nonlinear dynamics of a memristor-based Duffing oscillator

An electronic model of Duffing oscillator with a characteristic memristive nonlinear element is proposed instead of the classical cubic nonlinearity. The memristive Duffing oscillator circuit system is mathematically modeled, and the stability analysis presents the evolution of the proposed system. The dynamical behavior of this circuit is investigated through numerical simulations, statistical analysis, and real-time hardware experiments, which have been carried out under the external periodic force. The chaotic dynamics of the circuit is studied by means of phase diagram. It is found that the proposed circuit system shows complex behaviors, like bifurcations and chaos, three tori, transient chaos, and intermittency for a certain range of circuit parameters. The observed phenomena and scenario are illustrated in detail through experimental and numerical studies of memristive Duffing oscillator circuit. The existence of regular and chaotic behaviors is also verified by using 0–1 test measurements. In addition, the robustness of the signal strength is confirmed through signal-to-noise ratio. The numerically observed results are confirmed from the laboratory experiment.     

On the dynamics of a string generator: Effect of delay in nonlinear feedback

We investigate the effect of delay in feedback on the oscillation characteristics (amplitude and frequency) of a string generator, which, as is well known, works in a self-induced oscillation mode and is a part of a string accelerometer (a device for measuring the acceleration of ballistic missiles, launch vehicles, and other moving objects). A mathematical model of the dynamics of a string generator is taken in the form of a quasilinear second-order hyperbolic equation with constant delay with respect to one of independent variables (time). For the analysis of the mathematical model, we use the one-frequency asymptotic Krylov-Bogolyubov-Mitropol'skii method (its first and second approximations) of nonlinear mechanics. We show that an increase in the delay in the nonlinear feedback amplifier results in a decrease in the frequency of self-induced oscillations, which transforms the string generator into a low-frequency device. __________ Translated from Neliniini Kolyvannya, Vol. 11, No. 2, pp. 168–190, April–June, 2008.     

Origins of group coordination: nonlinear dynamics and the role of verbalization

Coordination occurs when two or more people do the same or complimentary tasks simultaneously; its explanation game theory, nonlinear dynamics, and implicit learning theory. In the experiment, 12 four-person groups were allowed to discuss the coordination (card game) task while performing it; 12 other groups worked nonverbally. One to three group members were replaced during the game. Split-plot ANOVA showed that verbalizing groups performed better than nonverbalizing groups overall and showed more acute coordination learning curves, but verbalization did not compensate for the replacement of personnel. Groups that changed one or two players showed positive coordination transfer, but groups that changed three players did not. Nonlinear regression for temporal dynamics within verbalizing and nonverbalizing groups showed asymptotic stability for initial coordination learning and transfer to a difficult rule, a chaotic function when replacements were introduced, and asymptotic stability again when the team with replacements switched to the difficult rule.     

Methods of nonlinear statistical dynamics: The state of the art and prospects

Conclusion Our research permits us to draw the following conclusions. As our survey of methods for nonlinear statistical dynamics showed, at the present time, there is no universal approach (with the exception of efficient Monte Carlo methods) for obtaining reliable estimates of the probability of rare events in nonlinear monoparametric systems. From Proc. General Meeting of the National Committee of Ukraine on Theoretical and Applied Mechanics (Kiev, May 14, 1996). Translated from Prikladnaya Mekhanika, Vol. 33, No. 8, pp. 64–72, August, 1997.     

Study of a periodically forced magnetohydrodynamic system using Floquet analysis and nonlinear Galerkin modelling

Nonlinear Dynamics - We present a detailed study of Rayleigh–Bénard magnetoconvection with periodic gravity modulation and uniform vertical magnetic field. Linear stability analysis is...     

Vortex dynamics and scalar transport in the wake of a bluff body driven through a steady recirculating flow

The air ventilation system in wide-body aircraft cabins provides passengers with a healthy breathing environment. In recent years, the increase in global air traffic has amplified contamination risks by airborne flu-like diseases and terrorist threats involving the onboard release of noxious materials. In particular, passengers moving through a ventilated cabin may transport infectious pathogens in their wake. This paper presents an experimental investigation of the wake produced by a bluff body driven through a steady recirculating flow. Data were obtained in a water facility using particle image velocimetry and planar laser induced fluorescence. Ventilation attenuated the downward convection of counter-rotating vortices produced near the free-end corners of the body and decoupled the downwash mechanism from forward entrainment, creating stagnant contaminant regions.     

Chaos, creativity, and substance abuse: the nonlinear dynamics of choice

Artists create their work in conditions of disequilibrium, states of creative chaos that may appear turbulent but are capable of bringing forth new order. By absorbing information from the environment and discharging it negentropically as new work, artists can be modeled as dissipative systems. A characteristic of chaotic systems is a heightened sensitivity to stimuli, which can generate either positive experiences or negative ones that can lead some artists to substance abuse and misguided searches for a creative chaos. Alcohol and drug use along with inadequately addressed co-occurring emotional disorders interfere with artists' quest for the nonlinearity of creativity. Instead, metaphorically modeled by a limit cycle of addiction and then a spiral to disorder, the joys of a creative chaos become an elusive chimera for them rather than a fulfilling experience. Untreated mental illness and addiction to substances have shortened the lives of artists such as Vincent Van Gogh, Frida Kahlo, Henri de Toulouse-Lautrec, and Jackson Pollock, all of whom committed suicide. In contrast Edvard Munch and John Callahan, who chose to address their emotional problems and substance abuse, continued to live and remain creative. Choosing to access previously avoided moments of pain can activate the nonlinear power of self-transformation.