Phase Space Structure, Attractor Dimension, Lyapunov Exponent and Nonlinear Prediction from Earth's Atmospheric Angular Momentum Time Series

1999 ◽  
Vol 156 (4) ◽  
pp. 719-736 ◽  
Author(s):  
R. K. Tiwari ◽  
K. N. N. Rao
Keyword(s):  
Time Series ◽  
Angular Momentum ◽  
Phase Space ◽  
Lyapunov Exponent ◽  
Space Structure ◽  
Atmospheric Angular Momentum ◽  
Nonlinear Prediction ◽  
Attractor Dimension ◽  
Phase Space Structure

scholarly journals Unfolding the Phase Space Structure of Noisy Time Series by means of Angular First-Return Maps

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Javier Villa Briongos ◽  
Jesús Gómez-Hernández ◽  
Daniel Serrano ◽  
Domingo Santana
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Joint Probability ◽  
Quantitative Information ◽  
Space Structure ◽  
Phase Space Structure ◽  
Clear Cut ◽  
Visitation Frequency ◽  
Noisy Time Series ◽  
Delay Coordinates

A new approach which uses the joint probability matrix computation of noisy time series is proposed to construct a phase space portrait which reflects the orbit visitation frequency of the different regions of the phase space. The resulting representation provides a clear cut of the dynamical reconstructed attractor giving both quantitative information and qualitative information about the attractor structure. The orbital distribution recovered in the map is studied by an angular first-return map where the orbital time used for the reconstruction is obtained from the magnitude information of the complex representation of the data belonging to the probability phase portrait. The resulting phase delay coordinates serve to identify phase intermittency. The Lorenz-like Shimizu-Morioka model and the Rossler model are used to present the methodology. Finally, some experimental pressure time series measured on gas-solid fluidized beds operated at different dynamical regimes are presented to analyze the reliability of the proposed method to deal with experimental noise time series.

Explicit symplectic-like integration with corrected map for inseparable Hamiltonian

2020 ◽  
Vol 501 (1) ◽  
pp. 1511-1519
Author(s):  
Junjie Luo ◽  
Weipeng Lin ◽  
Lili Yang
Keyword(s):  
Phase Space ◽  
Space Structure ◽  
Eighth Order ◽  
Time Step ◽  
Extended Phase ◽  
Energy Error ◽  
Phase Space Structure ◽  
Compact Binary ◽  
Three Body

ABSTRACT Symplectic algorithms are widely used for long-term integration of astrophysical problems. However, this technique can only be easily constructed for separable Hamiltonian, as preserving the phase-space structure. Recently, for inseparable Hamiltonian, the fourth-order extended phase-space explicit symplectic-like methods have been developed by using the Yoshida’s triple product with a mid-point map, where the algorithm is more effective, stable and also more accurate, compared with the sequent permutations of momenta and position coordinates, especially for some chaotic case. However, it has been found that, for the cases such as with chaotic orbits of spinning compact binary or circular restricted three-body system, it may cause secular drift in energy error and even more the computation break down. To solve this problem, we have made further improvement on the mid-point map with a momentum-scaling correction, which turns out to behave more stably in long-term evolution and have smaller energy error than previous methods. In particular, it could obtain a comparable phase-space distance as computing from the eighth-order Runge–Kutta method with the same time-step.

scholarly journals Discrete phase-space structure of n-qubit mutually unbiased bases

2009 ◽  
Vol 324 (1) ◽  
pp. 53-72 ◽  
Author(s):  
A.B. Klimov ◽  
J.L. Romero ◽  
G. Björk ◽  
L.L. Sánchez-Soto
Keyword(s):  
Phase Space ◽  
Space Structure ◽  
Mutually Unbiased Bases ◽  
Phase Space Structure ◽  
Discrete Phase

scholarly journals Phase space structure of generalized Gaussian cat states

2010 ◽  
Vol 374 (43) ◽  
pp. 4385-4392 ◽  
Author(s):  
Fernando Nicacio ◽  
Raphael N.P. Maia ◽  
Fabricio Toscano ◽  
Raúl O. Vallejos
Keyword(s):  
Phase Space ◽  
Space Structure ◽  
Phase Space Structure ◽  
Cat States

scholarly journals Characterisation of negative ion beam focusing based on phase space structure

2020 ◽  
Vol 22 (2) ◽  
pp. 023017 ◽  
Author(s):  
Yasuaki Haba ◽  
Kenichi Nagaoka ◽  
Katsuyoshi Tsumori ◽  
Masashi Kisaki ◽  
Haruhisa Nakano ◽  
...  
Keyword(s):  
Phase Space ◽  
Ion Beam ◽  
Space Structure ◽  
Negative Ion ◽  
Phase Space Structure ◽  
Beam Focusing
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