A phase-space boundary integration of the Vlasov equation for collisionless one-dimensional stellar systems

1971 ◽  
Vol 13 (2) ◽  
pp. 411-424 ◽  
Author(s):  
S. Cuperman ◽  
A. Harten ◽  
M. Lecar
Keyword(s):  
Phase Space ◽  
Vlasov Equation ◽  
Stellar Systems ◽  
One Dimensional ◽  
Boundary Integration ◽  
Space Boundary

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

One-dimensional coherent-state representation on a circle in phase space

1994 ◽  
Vol 50 (5) ◽  
pp. 4293-4297 ◽  
Author(s):  
P. Domokos ◽  
P. Adam ◽  
J. Janszky
Keyword(s):  
Phase Space ◽  
Coherent State ◽  
State Representation ◽  
One Dimensional

Local Geometric Projection-Based Noise Reduction for Vibration Signal Analysis in Rolling Bearings

2008 ◽  
Author(s):  
Ruqiang Yan ◽  
Robert X. Gao ◽  
Kang B. Lee ◽  
Steven E. Fick
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Noise Reduction ◽  
Signal Analysis ◽  
Signal To Noise Ratio ◽  
Multifractal Spectrum ◽  
Vibration Signal ◽  
Rolling Bearings ◽  
One Dimensional ◽  
Vibration Signal Analysis

This paper presents a noise reduction technique for vibration signal analysis in rolling bearings, based on local geometric projection (LGP). LGP is a non-linear filtering technique that reconstructs one dimensional time series in a high-dimensional phase space using time-delayed coordinates, based on the Takens embedding theorem. From the neighborhood of each point in the phase space, where a neighbor is defined as a local subspace of the whole phase space, the best subspace to which the point will be orthogonally projected is identified. Since the signal subspace is formed by the most significant eigen-directions of the neighborhood, while the less significant ones define the noise subspace, the noise can be reduced by converting the points onto the subspace spanned by those significant eigen-directions back to a new, one-dimensional time series. Improvement on signal-to-noise ratio enabled by LGP is first evaluated using a chaotic system and an analytically formulated synthetic signal. Then analysis of bearing vibration signals is carried out as a case study. The LGP-based technique is shown to be effective in reducing noise and enhancing extraction of weak, defect-related features, as manifested by the multifractal spectrum from the signal.

One-Dimensional Harmonic Oscillator in Quantum Phase Space

2011 ◽  
Vol 110-116 ◽  
pp. 3750-3754
Author(s):  
Jun Lu ◽  
Xue Mei Wang ◽  
Ping Wu
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Quantum Phase ◽  
Space Representation ◽  
Wave Mechanics ◽  
One Dimensional ◽  
Matrix Mechanics ◽  
The Matrix ◽  
Quantum Wave ◽  
The One

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.

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