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Asymmetry Coefficients as Indicators of Chaos: Hyperchaotic Qi System

100%
Wąż P., Bielińska-Wąż D.
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EN
Statistical properties of the hyperchaotic Qi system are studied. The theory, recently formulated and applied for the damped driven pendulum, is used in this investigation. Asymmetry coefficients, related to the statistical moments of distributions composed from the time-series, are shown to behave in a different way for periodic, chaotic and hyperchaotic solutions and are proposed as indicators of chaos and hyperchaos.
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Asymmetry Coefficients as Indicators of Chaos

100%
Wąż P., Bielińska-Wąż D.
|
EN
The aim of this paper is to present a new simple indicator of chaos derived from the dynamics of the motion. For this purpose statistical methods are used. A function describing the motion of the analyzed system (in the example under consideration, the time dependence of the angle of a damped driven pendulum, ω(t)) is recorded in time intervals t∊〈 T_{s}, T_{f_{k}}〉, k = 1, 2,...K, with T_{f_{k}} > T_{f_{k-1}}. Each of the recorded functions is considered as a statistical distribution. The asymmetry coefficients of the set of distributions form a series and their behavior in periodic and chaotic regions is compared. It is shown that the behavior of this series in the chaotic and in the periodic regimes is entirely different. The changes of the asymmetry coefficients for the periodic cases are very regular and for the chaotic ones - random. In periodic cases, the coefficients converge to zero when the length of the distribution increases.
3
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Core Polarization Effects in the Relativistic Quantum-Defect-Orbital Theory

81%
Bielińska-Wąż D., Martin I., Karwowski J.
Acta Physica Polonica A
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1994
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vol. 85
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issue 5
805-812
EN
The quantum-defect-orbital method has been reformulated in order to include both relativistic effects and the electron correlation described by a core polarization potential. All quantities appearing in this formulation may be evaluated analytically. A comparison with experimental results demonstrates, on one hand, significance of the relativity-correlation corrections and, on the other, inadequacy of the relativistic quantum-defect-orbital approach when indirect relativistic effects are important, i.e. when atoms contain closed shells of d electrons.
4
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About Approximation of Convergence Superoperators in Quantum Perturbation Theory

81%
Bielińska-Wąż D., Paidarova I., Durand P.
Acta Physica Polonica A
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1997
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vol. 91
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issue 6
1061-1068
EN
Perturbation methods are generally used for solving wave operator equations associated with the determination of effective Hamiltonians. In many cases the standard Rayleigh-Schrodinger and Brillouin-Wigner series either converge slowly or diverge. Therefore it is necessary to modify or to renormalize the standard wave equations. For that purpose derivative and convergence superoperators within the Ralyeigh-Schrodinger and Brillouin-Wigner formalisms were introduced. A new efficient otential is obtained and further application to molecular dynamics is indicated.
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