Attractor comparisons based on density
Abstract
Recognizing a chaotic attractor can be seen as a problem in pattern recognition. Some feature vector must be extracted from the attractor and used to compare to other attractors. The field of machine learning has many methods for extracting feature vectors, including clustering methods, decision trees, support vector machines, and many others. In this work, feature vectors are created by representing the attractor as a density in phase space and creating polynomials based on this density. Density is useful in itself because it is a one dimensional function of phase space position, but representing an attractor as a density is also a way to reduce the size of a large data set before analyzing it with graph theory methods, which can be computationally intensive. The density computation in this paper is also fast to execute. In this paper, as a demonstration of the usefulness of density, the density is used directly to construct phase space polynomials for comparing attractors. Comparisons between attractors could be useful for tracking changes in an experiment when the underlying equations are too complicated for vector field modeling.
 Authors:
 US Naval Research Lab, Washington, DC 20375 (United States)
 Publication Date:
 OSTI Identifier:
 22402525
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 1; Other Information: (c) 2015 U.S. Government; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATTRACTORS; CHAOS THEORY; DECISION TREE ANALYSIS; DENSITY; GRAPH THEORY; LEARNING; ONEDIMENSIONAL CALCULATIONS; PATTERN RECOGNITION; PHASE SPACE; POLYNOMIALS; SIMULATION; VECTOR FIELDS; VECTORS
Citation Formats
Carroll, T. L., Email: Thomas.Carroll@nrl.navy.mil. Attractor comparisons based on density. United States: N. p., 2015.
Web. doi:10.1063/1.4906342.
Carroll, T. L., Email: Thomas.Carroll@nrl.navy.mil. Attractor comparisons based on density. United States. doi:10.1063/1.4906342.
Carroll, T. L., Email: Thomas.Carroll@nrl.navy.mil. 2015.
"Attractor comparisons based on density". United States.
doi:10.1063/1.4906342.
@article{osti_22402525,
title = {Attractor comparisons based on density},
author = {Carroll, T. L., Email: Thomas.Carroll@nrl.navy.mil},
abstractNote = {Recognizing a chaotic attractor can be seen as a problem in pattern recognition. Some feature vector must be extracted from the attractor and used to compare to other attractors. The field of machine learning has many methods for extracting feature vectors, including clustering methods, decision trees, support vector machines, and many others. In this work, feature vectors are created by representing the attractor as a density in phase space and creating polynomials based on this density. Density is useful in itself because it is a one dimensional function of phase space position, but representing an attractor as a density is also a way to reduce the size of a large data set before analyzing it with graph theory methods, which can be computationally intensive. The density computation in this paper is also fast to execute. In this paper, as a demonstration of the usefulness of density, the density is used directly to construct phase space polynomials for comparing attractors. Comparisons between attractors could be useful for tracking changes in an experiment when the underlying equations are too complicated for vector field modeling.},
doi = {10.1063/1.4906342},
journal = {Chaos (Woodbury, N. Y.)},
number = 1,
volume = 25,
place = {United States},
year = 2015,
month = 1
}

The structure of sodium electrosodalite (SES), Na{sub 8}(AlSiO{sub 4}){sub 6}, has been determined at 20 K using synchrotron powder diffraction. Subsequently the electron density was calculated through a periodic unrestricted HartreeFock approach and analyzed by topological methods. The F center is found to manifest itself as a maximum in the electron density at a nonnuclear position. Thus it possesses a separate identity and behaves quantum mechanically as an open system, bounded by a surface of local zero flux in the gradient vector field of the electron density. Different basis sets have been considered, and the introduction of a basis setmore »

DE/ISIS conjunction comparisons of highlatitude electron density features
Electron number density (N/sub e/) profiles determined remotely by ISIS 1 and 2 topside sounder measurements were compared with in situ ion and electron density measurements by the Dynamics Explorer 2 (DE 2) Langmuir probe during four highlatitude ISIS/DE magnetic fieldaligned conjunctions. In all cases, the universal time separations between the two data sets were small (less than 12 min). The horizontal separations away from conjunction were up to several thousand kilometers. The N/sub e/ comparisons near the conjunction times represents the first crosscalibration of in situ probe and remote topside sounding N/sub e/ measurements. The ISISderived N/sub e/ values,more » 
Modeling of SiO{sub 2} deposition in high density plasma reactors and comparisons of model predictions with experimental measurements
Highdensityplasma deposition of SiO{sub 2} is an important process in integrated circuit manufacturing. A list of gasphase and surface reactions has been compiled for modeling plasmaenhanced chemical vapor deposition of SiO{sub 2} from SiH{sub 4}, O{sub 2}, and Ar gas mixtures in highdensityplasma reactors. The gasphase reactions include electron impact, neutral{endash}neutral, ion{endash}ion, and ion{endash}neutral reactions. The surface reactions and deposition mechanism is based on insights gained from attenuated total reflection Fourier transform infrared spectroscopy experiments and includes radical adsorption onto the SiO{sub 2} surface, ionenhanced desorption from the surface layer, radical abstractions, as well as direct ionenergydependent sputtering of themore »