Phase space

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Phase space

A graph which shows all possible states of a system. In phase space we plot the value of a variable against possible values of the other variables at the same time. If a system had three descriptive variables, we plot the phase space in three dimensions, with each variable taking one dimension.
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1), the main parameters that should be determined in the phase-space reconstruction method are the delay and the embedding dimension parameters.
By establishing models with the actual historical data of a large wind power plant in China, this paper confirms their chaotic properties, based on which neural networks of Elman and BP are established with the approach of phase-space reconstruction for the short-term forecast of single units of wind farms.
The idea of PPD is based on a phase-space (the coordinates are composed of dx, dy ) partition over the image patch, see Fig.
Here, the discrimination criterion of each crack initiation mode is determined by considering the distribution conditions of the plots in the phase-space of the two-dimensional coordinate plane by both parameters.
e]) includes normalization constants, phase-space factors, and standard Coulomb corrections.
Recommendation: The single near-term issue that appears to be most critical for Heavy Ion Fusion is the physics limits to the maximum phase-space density of space-charge-dominated HI beams and the resulting implications for HEDP and fusion ignition.
Meyer says that one of these conditions (the "original phase-space volume") had to be precise to an accuracy of one part in ten billion multiplied by itself 123 times, an amount so great that it outnumbers the number of particles in the universe.
An interesting way to observe the energy evolution of an oscillating block is to examine its phase-space trajectory.
We describe a method that links Hilbert-space and phase-space operators.
In nonlinear systems, it is impossible to predict where each point will next be in the system's evolution; however, despite this seeming randomness in nonlinear system behavior, post hoc observation of phase-space studies reveals that the points are not randomly distributed.
Here is the moment when the phase-space analogy becomes applied.
Joseph Liouville, the unacknowledged legislator of narratological physics proposed a theorem according to which phase-space volume does not change with time-evolution.