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A nonlinear dynamical systems modelling approach unveils chaotic dynamics in simulations of large strain behaviour of a granular material under biaxial compression

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AIP conference Proceedings 2013年第1期1542卷 173-176页

作者： Michael Small David Walker Antoinette Tordesillas School of Mathematics and Statistics The University of Western Australia Crawley WA 6009 Australia School of Mathematics and Statistics Melbourne University Parkville Victoria 3010 Australia

We consider bulk measurements of shear stress in a discrete element simulation of biaxial compression of a densely packed granular assembly in the failure regime in the presence of a single persistent shear band. The strain evolution of the stress ratio is treated as a time series and data based methods from nonlinear dynamical systems theory are applied to characterise the underlying dynamics — assuming a low-dimensional deterministic description. Standard nonlinear time series methods are used to characterise the psuedo-time series as consistent with chaos. nonlinear modelling combined with novel complex network based descriptors of model simulations (which allow for a precise characterisation of the underlying dynamics) indicate that the original system can be described as a bistable transient chaotic dynamical system. There exist two different chaotic basins of attraction — one corresponding to slow and large amplitude dynamics and one to fast and small amplitude. The as yet unknown high-dimensional dynamics of multiscale grain rearrangments modelled here as the presence of dynamical noise forces the system to switch between the two regimes.

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Introduction of Topological Horseshoe Theory in Chaotic Research

Introduction of Topological Horseshoe Theory in Chaotic Rese...

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2013 2nd International conference on Mechanical Properties of Materials and Information Technology(ICMPMIT 2013)

作者： Youjie Ma Shuang Song Xuesong Zhou Tianjin University of Technology Tianjin Key Laboratory for Control Theory & Applications in Complicated Systems Nankai District

Over the past 10 years, nonlinear dynamics and chaotic theory attracted scholars and people got a deeper understanding of chaos. There are many methods for chaos research, and the method of using topological horseshoe is an important branch of those methods. So far, this is one of the core methods with mathematical rigor for chaos research. Based on simple thinking of geometric space, topological horseshoe build a bridge for numerical and theoretical studies of complex behavior of nonlinear systems so that people can carry out a series of studies for chaotic behavior. This paper introduces the basic content of topological horseshoe theory and the application to a simple power system.

关键词： Chaotic theory nonlinear dynamics Topological horseshoe Geometric theory Poincare sections Topological entropy

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Compressed exponential relaxation as superposition of dual structure in pattern dynamics of nematic liquid crystals

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AIP conference Proceedings 2013年第1期1518卷 403-410页

作者： T. Narumi F. Nugroho J. Yoshitani Y. Hidaka M. Suzuki S. Kai Department of Applied Quantum Physics and Nuclear Engineering Kyushu Univ. Fukuoka 819-0395 Japan Physics Department Gadjah Mada Univ. Yogyakarta 55281 Indonesia

Soft-mode turbulence (SMT) is the spatiotemporal chaos observed in homeotropically aligned nematic liquid crystals, where non-thermal fluctuations are induced by nonlinear coupling between the Nambu-Goldstone and convective modes. The net and modal relaxations of the disorder pattern dynamics in SMT have been studied to construct the statistical physics of nonlinear nonequilibrium systems. The net relaxation dynamics is well-described by a compressed exponential function and the modal one satisfies a dual structure, dynamic crossover accompanied by a breaking of time-reversal invariance. Because the net relaxation is described by a weighted mean of the modal ones with respect to the wave number, the compressed-exponential behavior emerges as a superposition of the dual structure. Here, we present experimental results of the power spectra to discuss the compressed-exponential behavior and the dual structure from a viewpoint of the harmonic analysis. We also derive a relationship of the power spectra from the evolution equation of the modal autocorrelation function. The formula will be helpful to study non-thermal fluctuations in experiments such as the scattering methods.

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Stability Analysis of Digital State Feedback Controlled Boost Converters

Stability Analysis of Digital State Feedback Controlled Boos...

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Annual conference of the IEEE Industrial Electronics Society

作者： Damian Giaouris Christos Yfoulis Spyridon Voutetakis Simira Papadopoulou Honeywell FM & T/NM Sandia National Laboratories

ISBN: (纸本)9781479902255

In this paper we investigate the nonlinear dynamics of DC-DC boost converters under state feedback controllers. We demonstrate that it is possible to have multiple equilibria, which can further bifurcate and result in a torus or even chaos. More specifically, by changing the feedback gains we show that it is possible to have a saddle node and then a period 2 bifurcation. These are then followed by a slow scale bifurcation that results in a 2T torus. Also, the nominal or desired equilibrium hits a border in the state space that forces the steady state duty cycle to become 0. Obviously the occurrence of saturation in the duty cycle or the existence of instabilities can greatly decrease the converter's performance. In this paper we study this behavior: we use semi-analytical methods to locate the stable and unstable period 1 and period 2 orbits, the unstable manifold of the period 1 orbit;and by using the theory of the monodromy matrix enhanced with the saltation matrix we determine the stability of the converter. The latter can be used for design purposes in order to guarantee a stable and satisfactory performance.

关键词： State feedback Boost converters Bifurcation nonlinear dynamics boost converters State feedback nonlinear dynamics BIFURCATION DUTY CYCLE Stability analysis state space toruses state feedback controller

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Analyses of dynamics Nature about nonlinear and Chaotic Economic Time Series

Analyses of Dynamics Nature about Nonlinear and Chaotic Econ...

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2013 International conference on Economic,Business Management and Education Innovation(EBMEI 2013)

作者： Fenglan Wang Chang Fa Wang School of Mechanical Engineering Shenyang University

The dynamics characters of the chaotic time series are studied by using time series analyzing methods. The complicated dynamical nature of stock market ——the chaotic nature and fractal feature in stock market are introduced in this paper. Focused on the judgment on stock market chaos, the calculation of the correlation dimension of the chaotic attractor and the method for determining the economic system chaotic critical spot, hence we lay a foundation for the short forecast about the price fluctuation in stock market. In this paper, some useful results are obtained by taking daily closing quotation composite index of Shanghai Stock Exchange from 2001.5 to 2002.11 as an example of calculation and analysis.

关键词： Caotic Factal Te correlation dimension Caotic attractor Caotic critical spot

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Weak Signal Detection Based on the nonlinear Dynamic Model

Weak Signal Detection Based on the Nonlinear Dynamic Model

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International conference on Mechatronics and Applied Mechanics (ICMAM 2011)

作者： Liu, Xuan Chao Li, Pei Pei Xian Shiyou Univ Elect Engn Coll Xian Shaanxi Provinc Peoples R China

ISBN: (纸本)9783037853801

In order to obtain new ways of weak signal detection, we analyzed the motion states of nonlinear dynamic model Duffing oscillator in the case of different amplitude of input signals by solving the Duffing equation and expounded the basic principles of weak signal detection based on Duffing oscillator phase-change characteristics, further illustrated the relationship between signal detection accuracy and detection time by the experimental, researched the impact on signal detection coming from Gaussian white noise and also pointed out how to use intermittent chaos state to implement weak signal detection. The results showed that Duffing oscillator can be effectively detect the slight changes of input signal in the strong noises background, so as to achieve the purpose of weak signal detection. Compared with existing methods, it could greatly improve the detection results.

关键词： weak signal detection nonlinear dynamics chaos Duffing oscillator white noise

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Nostradamus: Modern methods of Prediction, Modeling and Analysis of nonlinear Systems 2013

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丛书名： Advances in Intelligent Systems and Computing

2012年

作者： Ivan Zelinka Otto E. Rössler Václav Snásel Ajith Abraham Emilio S. Corchado

ISBN: (纸本)3642332269;9783642332265

This proceeding book of Nostradamus conference (http://***) contains accepted papers presented at this event in 2012. Nostradamus conference was held in the one of the biggest and historic city of Ostrava (the Czech Republic, http://***/en), in September 2012. conference topics are focused on classical as well as modern methods for prediction of dynamical systems with applications in science, engineering and economy. Topics are (but not limited to): prediction by classical and novel methods, predictive control, deterministic chaos and its control, complex systems, modelling and prediction of its dynamics and much more.

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Dynamic response analysis of turbocharger rotor of UAV during hovering movements

Dynamic response analysis of turbocharger rotor of UAV durin...

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16th International conference on Mechatronics Technology, ICMT 2012

作者： Yang, Jiao Cao, Shu-Qian School of Mechanical Engineering Tianjin University Tianjin China Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control Tianjin China State Key Laboratory of Engines Tianjin University Tianjin China

ISBN: (纸本)9787900769428

A model of turbocharger rotor of Unmanned Aerial Vehicle (UAV) under hovering movement is presented, while Runge-Kutta numerical method is applied to solve the equation, and the dynamic response analysis under different rotating speeds in a hovering state is developed. The result shows, disk center trajectory of the turbocharger rotor is changed significantly because of UAV horizontal hovering movement, and rotor vibration amplitude varies at different rotating speeds.

关键词： Numerical methods

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A spectral projection approach for fuzzy uncertainty propagation in structural dynamics

A spectral projection approach for fuzzy uncertainty propaga...

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International conference on Noise and Vibration Engineering (ISMA) / International conference on Uncertainty in Structural dynamics (USD)

作者： Adhikari, S. Swansea Univ Sch Engn Chair Aerosp Engn Swansea SA2 8PP W Glam Wales

ISBN: (纸本)9789073802896

Propagation of uncertainties in complex engineering dynamical systems is receiving increasing attention. When uncertainties are modelled by fuzzy variables, the equations of motion of discretised dynamical systems can be expressed by coupled ordinary differential equations with fuzzy coefficients. This paper proposes a Polynomial chaos type of spectral approach based on orthogonal function expansion. A fuzzy variable is represented as a set of interval variables via the membership function. The intervals variables are further transformed into the standard interval [-1,1]. Smooth nonlinear functions of standard interval variables are projected in the basis of Legendre polynomials by exploiting its orthogonal properties over the interval [-1,1]. The coefficients associated with the basis functions are obtained by a Galerkin type of error minimisation. The method is first illustrated using scalar functions of multiple fuzzy variables. Later the method is proposed for linear dynamic problems where the technique is extended to vector valued functions with multiple fuzzy variables. The response of such systems can be expressed in the complete basis of multivariate Legendre polynomials. The coefficients, obtained by Galerkin type of error minimisation, can be calculated from the solution of an extended set of linear algebraic equations. A numerical example of axial vibration of a rod with fuzzy axial stiffness is considered to illustrate the proposed methods. The results are compared with direct numerical simulation results to investigate the accuracy of the proposed method.

关键词： Orthogonal functions

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Performance Improvement of Heuristic Algorithms for Large Scale Combinatorial Optimization Problems using Lebesgue Spectrum Filter

Performance Improvement of Heuristic Algorithms for Large Sc...

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International Joint conference on Neural Networks (IJCNN)

作者： Kato, Tomohiro Hasegawa, Mikio Aihara, Kazuyuki Tokyo Univ Sci Dept Elect Engn Chiyoda Ku 1-14-6 Kudankita Tokyo 162 Japan Univ Tokyo Inst Ind Sci Meguro Ku Tokyo 1538505 Japan

ISBN: (纸本)9781467314909

In this paper, we analyze effectiveness of a new metaheuristic approach, which utilizes ideal spatio-temporal chaotic dynamics generated by Lebesgue Spectrum Filter (LSF). In the previous researches on the additive chaotic noise to the heuristic searches for combinatorial optimization problems, it has been shown that the chaotic sequences with negative autocorrelation improve the performance of asynchronously updated algorithms, such as mutually connected neural networks, asynchronous heuristic searches and so on. The effectiveness of chaos can be understood by the conventional theory of the chaotic CDMA, which showed that the cross-correlation between the sequences with negative autocorrelation becomes lowest. The spatio-temporal chaotic searching dynamics with such lowest cross-correlation has been shown effective to improve asynchronously updated combinatorial optimization algorithms. In this paper, as such asynchronously updated combinatorial optimization algorithms, we introduce the 2-exchange method, the k-opt method, the Lin-Kernighan method, and the Or-opt method, and improve the performance of them by applying the LSF. Our numerical simulation results show that the performances of all above heuristic methods could be improved by using negative autocorrelation.

关键词： component Combinatorial Optimization Problems k-opt Lin-Kernighan Or-opt nonlinear dynamics Lebesgue Spectrum Filter

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