Domain-wall free energy sigmaF, entropy sigmaS, and the correlation function C(temp) of sigmaF are measured independently in the four-dimensional +/-J Edwards-Anderson (EA) Ising spin glass. The stiffness exponent theta, the fractal dimension of domain walls d(s), and the chaos exponent zeta are extracted from the finite-size scaling analysis of sigmaF, sigmaS, and C(temp), respectively, well i...

This book is the most comprehensive and clear text for learning dynamics and many related topics of fractals and complexity that I have encountered. I t is appropriate for both classroom use, and for scientists working in a wide variety of fields. The emphasis is on concepts and applications rather than proofs and derivations. I t is ' hands-on' , with practical exercises and a programming proj...

This paper deals with the identification in high dimensions of a polynomial chaos expansion of random vectors from a set of realizations. Due to numerical and memory constraints, the usual polynomial chaos identification methods are based on a series of truncations that induce a numerical bias. This bias becomes very detrimental to the convergence analysis of polynomial chaos identification in ...

Chaos criterion for quantum field theory is proposed. Its accordance with classical chaos criterion is demonstrated in the semi-classical limit of quantum mechanics. Originally phenomenon of chaos was associated with problems of classical mechanics and statistical physics. Attempt of substantiation of statistical mechanics initiated intensive study of chaos and uncover its basic properties main...

Interrelations between dynamical and statistical laws in physics, on the one hand, and between the classical and quantum mechanics, on the other hand, are discussed with emphasis on the new phenomenon of dynamical chaos. The principal results of the studies into chaos in classical mechanics are presented in some detail, including the strong local instability and robustness of the motion, contin...

The paper proposes a mechanical model of SFD-sliding bearing flexible rotor system, employing RungeKutta method to tackle nonlinear differential equation, thus acquiring the dynamic response and the unbalanced response curve. Results obtained show the route of flexible rotor system from stable periodic motion to chaos state is: periodic motion—quasi-periodic motion—chaos —period doubling bifurc...

totoday’s market place is increasingly dynamic and volatile. in this area supply network issues recently have attracted a lot of attention from industrial practitioners and academics worldwide. chaos theory is the study of complex, nonlinear, dynamic systems. for chaotic systems, a tiny change in conditions may result in an enormous change in system output, whereas substantial changes in condit...

It is very important to localize the epileptogenic focus as accurately as possible for candidates undergoing epilepsy treatment through surgery. From earlier visual analysis to recent computer-assist quantitative calculation, the accuracy of the diagnosis improves with the innovation of the methods Gotman 1983; Mars 1977; Lieb et al. 1987]. In the past years, EEG signals recorded on the scalp h...

today we are facing with a turbulent world full of complexity and change. contemporary problems are too complicated for rational, logical solutions. they admit insights, not answers. chaos theory is a solution to reveal insights into the structure and the dynamics of complex systems. chaos theory is in formative stage, but we can use it in management practices. this article is about application...