We use linear entropy of an exact quantum state to study the entanglement between internal electronic states and external motional states for a two-level atom held in an amplitude-modulated and tilted optical lattice....We use linear entropy of an exact quantum state to study the entanglement between internal electronic states and external motional states for a two-level atom held in an amplitude-modulated and tilted optical lattice. Starting from an unentangled initial state associated with the regular 'island' of classical phase space, it is demonstrated that the quantum resonance leads to entanglement generation, the chaotic parameter region results in the increase of the generation speed, and the symmetries of the initial probability distribution determine the final degree of entanglement. The entangled initial states are associated with the classical 'chaotic sea', which do not affect the final entanglement degree for the same initial symmetry. The results may be useful in engineering quantum dynamics for quantum information processing.展开更多
Linear transfer function approximations of the fractional integrators 1Is~ with m ^- 0.80-0.99 with steps of 0.01 are calculated systemically from the fractional order calculus and frequency-domain approximation metho...Linear transfer function approximations of the fractional integrators 1Is~ with m ^- 0.80-0.99 with steps of 0.01 are calculated systemically from the fractional order calculus and frequency-domain approximation method. To illustrate the effectiveness for fractional functions, the magnitude Bode diagrams of the actual and approximate transfer functions 1Ism with a slope of -20m dB//decade are depicted. By using the transfer function approxima- tions of the fractional integrators, a new fractional-order nonlinear system is investigated through the bifurcation diagram and Lyapunov exponent. The corresponding circuit of the fractional-order system is designed and the experimental results match perfectly with the numerical simulations.展开更多
Several nonlinear three-dimensional systems of ordinary differential equations are studied analytically and numerically in this paper in accordance with universal bifurcation theory of Feigenbaum-Sharkovskii-Magnitsky...Several nonlinear three-dimensional systems of ordinary differential equations are studied analytically and numerically in this paper in accordance with universal bifurcation theory of Feigenbaum-Sharkovskii-Magnitsky [1] [2]. All systems are autonomous and dissipative and display chaotic behaviour. The analysis confirms that transition to chaos in such systems is performed through cascades of bifurcations of regular attractors.展开更多
This paper studies the chaos dynamic mechanism of the migration, enrichment and mineralization of elements in the crust. The research shows that the interaction of the nonlinear process in the geological environment i...This paper studies the chaos dynamic mechanism of the migration, enrichment and mineralization of elements in the crust. The research shows that the interaction of the nonlinear process in the geological environment is an essential factor for the uneven distribution of elements and the mineralization in the crust, determining the element contents and the fractal structure of the distribution of the large and small sized mineral deposits. The logistic map is a better mathematical model describing the behavior of the chaos dynamic. The parameter μ , i.e., the mineralizing potential, is employed to divide the region into non mineralization region or mineralization region. The value of the parameter μ in model (3) with true data (in Xinjiang Au tomatio region, China) is obtained with the statistical method. The forecasting results are generally in accordance with those obtained with other methods, for example, with the characteristic analysis.展开更多
Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they a...Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they allow determining the conditions of stability and instability, as well as the possibility of chaotic behavior of systems in case of a stability loss. The methods are illustrated for nonlinear Lorenz and Rossler model problems.展开更多
The classic polynomial chaos method(PCM), characterized as an intrusive methodology,has been applied to uncertainty propagation(UP) in many dynamic systems. However, the intrusive polynomial chaos method(IPCM) r...The classic polynomial chaos method(PCM), characterized as an intrusive methodology,has been applied to uncertainty propagation(UP) in many dynamic systems. However, the intrusive polynomial chaos method(IPCM) requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method(NIPCM) that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11175064 and 11475060the Construct Program of the National Key Discipline of Chinathe Hunan Provincial Innovation Foundation for Postgraduates under Grant No CX2014B195
文摘We use linear entropy of an exact quantum state to study the entanglement between internal electronic states and external motional states for a two-level atom held in an amplitude-modulated and tilted optical lattice. Starting from an unentangled initial state associated with the regular 'island' of classical phase space, it is demonstrated that the quantum resonance leads to entanglement generation, the chaotic parameter region results in the increase of the generation speed, and the symmetries of the initial probability distribution determine the final degree of entanglement. The entangled initial states are associated with the classical 'chaotic sea', which do not affect the final entanglement degree for the same initial symmetry. The results may be useful in engineering quantum dynamics for quantum information processing.
基金Supported by the National Natural Science Foundation of China under Grant No 51475246the Natural Science Foundation of Jiangsu Province under Grant No Bk20131402the Ministry-of-Education Overseas Returnees Start-up Research Fund under Grant No[2012]1707
文摘Linear transfer function approximations of the fractional integrators 1Is~ with m ^- 0.80-0.99 with steps of 0.01 are calculated systemically from the fractional order calculus and frequency-domain approximation method. To illustrate the effectiveness for fractional functions, the magnitude Bode diagrams of the actual and approximate transfer functions 1Ism with a slope of -20m dB//decade are depicted. By using the transfer function approxima- tions of the fractional integrators, a new fractional-order nonlinear system is investigated through the bifurcation diagram and Lyapunov exponent. The corresponding circuit of the fractional-order system is designed and the experimental results match perfectly with the numerical simulations.
文摘Several nonlinear three-dimensional systems of ordinary differential equations are studied analytically and numerically in this paper in accordance with universal bifurcation theory of Feigenbaum-Sharkovskii-Magnitsky [1] [2]. All systems are autonomous and dissipative and display chaotic behaviour. The analysis confirms that transition to chaos in such systems is performed through cascades of bifurcations of regular attractors.
基金This paperis supported by the National Natural Science Foundationof China!(No.49873 0 2 7)the Open L aboratory of Ore Depo
文摘This paper studies the chaos dynamic mechanism of the migration, enrichment and mineralization of elements in the crust. The research shows that the interaction of the nonlinear process in the geological environment is an essential factor for the uneven distribution of elements and the mineralization in the crust, determining the element contents and the fractal structure of the distribution of the large and small sized mineral deposits. The logistic map is a better mathematical model describing the behavior of the chaos dynamic. The parameter μ , i.e., the mineralizing potential, is employed to divide the region into non mineralization region or mineralization region. The value of the parameter μ in model (3) with true data (in Xinjiang Au tomatio region, China) is obtained with the statistical method. The forecasting results are generally in accordance with those obtained with other methods, for example, with the characteristic analysis.
文摘Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they allow determining the conditions of stability and instability, as well as the possibility of chaotic behavior of systems in case of a stability loss. The methods are illustrated for nonlinear Lorenz and Rossler model problems.
基金supported by the National Natural Science Foundation of China (No. 51105034)the Doctoral Thesis Build Project of Beijing 2012 (China)
文摘The classic polynomial chaos method(PCM), characterized as an intrusive methodology,has been applied to uncertainty propagation(UP) in many dynamic systems. However, the intrusive polynomial chaos method(IPCM) requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method(NIPCM) that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.