scholarly journals Dynamical Temperature from the Phase Space Trajectory

2017 ◽  
Vol 45 (1) ◽  
pp. 1-3 ◽  
Author(s):  
András Baranyai
Keyword(s):  
System Theory ◽  
Phase Space ◽  
Dynamical Systems ◽  
Hamiltonian System ◽  
Statistical Mechanics ◽  
Chaotic System ◽  
Space Trajectories ◽  
Classical Statistical Mechanics ◽  
Phase Space Trajectory ◽  
Phase Space Trajectories

Abstract In classical statistical mechanics the trajectory in phase space represents the propagation of a classical Hamiltonian system. While trajectories play a key role in chaotic system theory, exploitation of a single trajectory has yet to be considered. This work shows that for ergodic dynamical systems the dynamical temperature can be derived using phase space trajectories.

scholarly journals Application of Recurrence Quantification Analysis for Non-Linear Dynamical Systems

2019 ◽  
Vol 9 (1S5) ◽  
pp. 92-94
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Dynamical Systems ◽  
Recurrence Plot ◽  
Recurrence Quantification Analysis ◽  
Recurrence Plots ◽  
Space Trajectories ◽  
Recurrence Quantification ◽  
Quantification Analysis ◽  
Phase Space Trajectories

The Recurrence plots (RPs) have been introduced in several different scientific and medical disciplines. The main purpose of recurrence plot is used to of identify the higher dimensional phase space trajectories. RPs are purely graphically representation which have been designed for the detection of hidden dynamical patterns and non-linearity present in the data, the evaluation of error which is caused by observational noise can be done by Recurrence Quantification Analysis (RQA). RQA method is initially used to minimize the error present in the given signals. RQA method is a basically a technique for the analysis of nonlinear data to quantify the number and duration of a dynamical systems. The recurrence plot is used for time series domain for multidimensional signal also. Recurrence is the property of non-stationary and dynamical system to characteristics the time series analysis in phase space trajectories. Recurrence Quantification Analysis is used to derive from recurrence plots, which are based upon distances matrices of time series.

scholarly journals Quantum revival patterns from classical phase-space trajectories

2019 ◽  
Vol 99 (4) ◽  
Author(s):  
Gabriel M. Lando ◽  
Raúl O. Vallejos ◽  
Gert-Ludwig Ingold ◽  
Alfredo M. Ozorio de Almeida
Keyword(s):  
Phase Space ◽  
Space Trajectories ◽  
Quantum Revival ◽  
Classical Phase Space ◽  
Phase Space Trajectories

scholarly journals Nonlinear multivariable analysis of SOI and local precipitation and temperature

2005 ◽  
Vol 12 (1) ◽  
pp. 67-74 ◽  
Author(s):  
Y.-H. Jin ◽  
A. Kawamura ◽  
K. Jinno ◽  
R. Berndtsson
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Southern Oscillation ◽  
Statistical Prediction ◽  
Meteorological Variables ◽  
Space Trajectories ◽  
Local Climate ◽  
Prediction Techniques ◽  
Precipitation And Temperature ◽  
Phase Space Trajectories

Abstract. Global climate variability affects important local hydro-meteorological variables like precipitation and temperature. The Southern Oscillation (SO) is an easily quantifiable major driving force that gives impact on regional and local climate. The relationships between SO and local climate variation are, however, characterized by strongly nonlinear processes. Due to this, teleconnections between global-scale hydro-meteorological variables and local climate are not well understood. In this paper, we suggest to study these processes in terms of nonlinear dynamics. Consequently, the nonlinear dynamic relationship between the Southern Oscillation Index (SOI), precipitation, and temperature in Fukuoka, Japan, is investigated using a nonlinear multivariable approach. This approach is based on the joint variation of these variables in the phase space. The joint phase-space variation of SOI, precipitation, and temperature is studied with the primary objective to obtain a better understanding of the dynamical evolution of local hydro-meteorological variables affected by global atmospheric-oceanic phenomena. The results from the analyses display rather clear low-order phase space trajectories when treating the time series individually. However, when plotting phase space trajectories for several time series jointly, complicated higher-order nonlinear relationships emerge between the variables. Consequently, simple data-driven prediction techniques utilizing phase-space characteristics of individual time series may prove successful. On the other hand, since either the time series are too short and/or the phase-space properties are too complex when analysing several variables jointly, it may be difficult to use multivariable statistical prediction techniques for the present investigated variables. In any case, it is essential to further pursue studies regarding links between the SOI and observed local climatic and other geophysical variables even if these links are not fully understood in physical terms.

Invariant Manifold Detection From Phase Space Trajectories

2008 ◽  
Author(s):  
Joseph Kuehl ◽  
David Chelidze
Keyword(s):  
Phase Space ◽  
Invariant Manifold ◽  
Invariant Manifolds ◽  
Basins Of Attraction ◽  
Detection Methods ◽  
Trajectory Data ◽  
Space Trajectories ◽  
Data Set ◽  
Phase Space Warping ◽  
Phase Space Trajectories

Invariant manifolds provide important information about the structure of flows. When basins of attraction are present, the stable invariant manifold serves as the boundary between these basins. Thus, in experimental applications such as vibrations problems, knowledge of these manifolds is essential to understanding the evolution of phase space trajectories. Most existing methods for identifying invariant manifolds of a flow rely on knowledge of the flow field. However, in experimental applications only knowledge of phase space trajectories is available. We provide modifications to several existing invariant manifold detection methods which enables them to deal with trajectory only data, as well as introduce a new method based on the concept of phase space warping. The method of Stochastic Interrogation applied to the damped, driven Duffing equation is used to generate our data set. The result is a set of trajectory data which randomly populates a phase space. Manifolds are detected from this data set using several different methods. First is a variation on manifold “growing,” and is based on distance of closest approach to a hyperbolic trajectory with “saddle like behavior.” Second, three stretching based schemes are considered. One considers the divergence of trajectory pairs, another quantifies the deformation of a nearest neighbor cloud, and the last uses flow fields calculated from the trajectory data. Finally, the new phase space warping method is introduced. This method takes advantage of the shifting (warping) experienced by a phase space as the parameters of the system are slightly varied. This results in a shift of the invariant manifolds. The region spanned by this shift, provides a means to identify the invariant manifolds. Results show that this method gives superior detection and is robust with respect to the amount of data.

Phase Space Reconstruction

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Dynamical Systems ◽  
Statistical Mechanics ◽  
State Space ◽  
Phase Plane ◽  
Material Point ◽  
The Other ◽  
Straight Line ◽  
Mathematical Construction

In this chapter we introduce an important concept concerning the study of both discrete and continuous dynamical systems, the concept of phase space or “state space”. It is an abstract mathematical construction with important applications in statistical mechanics, to represent the time evolution of a dynamical system in geometric shape. This space has as many dimensions as the number of variables needed to define the instantaneous state of the system. For instance, the state of a material point moving on a straight line is defined by its position and velocity at each instant, so that the phase space for this system is a plane in which one axis is the position and the other one the velocity. In this case, the phase space is also called “phase plane”. It is later applied in many chapters of the book.

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