Relaxation of collisionless plasmas

1994 ◽  
Vol 51 (2) ◽  
pp. 341-353 ◽  
Author(s):  
H. Wiechen ◽  
H. J. Ziegler
Keyword(s):  
Phase Space ◽  
Point Of View ◽  
Coarse Grained ◽  
Second Step ◽  
Final States ◽  
General Technique ◽  
One Dimensional ◽  
Collisionless Plasmas ◽  
Mixing Dynamics ◽  
Stable Equilibria

We present a new theory for the relaxation of two-dimensional collisionless quasi-neutral plasmas by mixing in phase space. In general, mixing in phase space does not lead to equilibrium states in the framework of exact, collisionless theory. However, filamentation on smaller and smaller scales can result in stationary states from a macroscopic (coarse-grained) point of view. In a first step we discuss a general technique to calculate suitably stable equilibria of collisionless plasmas. In a second step we develop a model relaxation that yields a simple transition to a description on macroscopic scales without following the details of the complicated mixing dynamics. Combination of both results allows calculation of final states of collisionless relaxation. We illustrate our approach with the help of a one-dimensional sheet configuration as a simple example.

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.

Introduction to molecular simulations in soft matter

2017 ◽  
Author(s):  
J.-L. Barrat ◽  
J. J. de Pablo
Keyword(s):  
Phase Space ◽  
Numerical Methods ◽  
Theoretical Basis ◽  
Soft Matter ◽  
Relevant Literature ◽  
Coarse Grained ◽  
Soft Interfaces ◽  
Molecular Scale ◽  
Soft Matter Physics ◽  
The Continuum

We describe the main features of the coarse-grained models that are typically useful in modelling soft interfaces, from force fields to the continuum descriptions involving density fields. We explain the theoretical basis of the main numerical methods that are used to explore the phase space associated with these models. Finally, three recent examples, illustrating the spirit in which relatively simple simulations can contribute to solving pending problems in soft matter physics, are briefly described. Clearly, a short series of lectures can offer, at best, a biased and restricted view of the available approaches. Our aim here will be to provide the reader with such an overview, with a focus on methods and descriptions that ‘bridge the scale’ between the molecular scale and the continuum or quasi-continuum one. The objective to present a guide to the relevant literature—which has now to a large extent appeared in the form of textbooks.

scholarly journals Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

2015 ◽  
Vol 22 (04) ◽  
pp. 1550021 ◽  
Author(s):  
Fabio Benatti ◽  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Classical Limit ◽  
Coherent States ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Wigner Functions ◽  
Quantum Mechanical Oscillators ◽  
Mechanical Oscillators ◽  
Space Noncommutativity

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

scholarly journals Landau damping in one dimensional periodic inhomogeneous collisionless plasmas

AIP Advances ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 025229
Author(s):  
Sanjeev Kumar Pandey ◽  
Rajaraman Ganesh
Keyword(s):  
Landau Damping ◽  
One Dimensional ◽  
Collisionless Plasmas

Rheology of hydrocarbon gels

1950 ◽  
Vol 200 (1061) ◽  
pp. 183-188 ◽  
Keyword(s):  
Mechanical Properties ◽  
Experimental Measurement ◽  
Theoretical Basis ◽  
Continuous Media ◽  
Point Of View ◽  
Coarse Grained ◽  
Testing Instrument ◽  
Fine Grained ◽  
Mineral Oils ◽  
Space And Time

Hydrocarbon gels contain a number of materials, such as rubber, greases, saponified mineral oils, etc., of great interest for various engineering purposes. Specific requirements in mechanical properties have been met by producing gels in appropriately chosen patterns of constituent components of visible, colloidal, molecular and atomic sizes, ranging from coarse-grained aggregates, represented by sponges, foams, emulsions, etc.; to fine-grained and apparently homogeneous ones, represented by optically clear compounds. The engineer who has to deal with the whole range of such materials will adopt a macroscopic point of view, based on an apparent continuity of all the material structures and of the distributions in space and time of the displacements and forces occurring under mechanical actions. It has been possible to determine these distributions in the framework of a comprehensive scheme in which the fundamental principles of the mechanics of continuous media provide the theoretical basis, and a testing instrument of new design, termed Rheogoniometer, the means of experimental measurement (Weissenberg 1931, 1934, 1946, 1947, 1948).

Poly[[μ2-1,3-bis(pyridin-4-yl)propane](μ3-1,4-phenylenediacetato)cadmium]

2012 ◽  
Vol 68 (2) ◽  
pp. m34-m36 ◽  
Author(s):  
Dong Liu
Keyword(s):  
Title Complex ◽  
Point Of View ◽  
Solvothermal Reaction ◽  
Dimensional Chain ◽  
Two Dimensional ◽  
One Dimensional ◽  
Connected Network ◽  
Dimensional Network

Solvothermal reaction between Cd(NO3)2, 1,4-phenylenediacetate (1,4-PDA) and 1,3-bis(pyridin-4-yl)propane (bpp) afforded the title complex, [Cd(C10H8O4)(C13H14N2)]n. Adjacent carboxylate-bridged CdIIions are related by an inversion centre. The 1,4-PDA ligands adopt acisconformation and connect the CdIIions to form a one-dimensional chain extending along thecaxis. These chains are in turn linked into a two-dimensional network through bpp bridges. The bpp ligands adopt ananti–gaucheconformation. From a topological point of view, each bpp ligand and each pair of 1,4-PDA ligands can be considered as linkers, while the dinuclear CdIIunit can be regarded as a 6-connecting node. Thus, the structure can be simplified to a two-dimensional 6-connected network.

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

A GALLERY OF CHUA ATTRACTORS PART VI

2007 ◽  
Vol 17 (06) ◽  
pp. 1801-1910 ◽  
Author(s):  
ELEONORA BILOTTA ◽  
GIANPIERO DI BLASI ◽  
FAUSTO STRANGES ◽  
PIETRO PANTANO
Keyword(s):  
Phase Space ◽  
Spatial Organization ◽  
Fractal Dimensions ◽  
Point Of View ◽  
Experimental Investigations ◽  
Technical Data ◽  
Future Studies ◽  
Small Set ◽  
Methodological Approaches

In this article, we conclude our series of papers on the analysis and visualization of Chua attractors and their generalizations. We present a gallery of 144 n-scroll, 15 hyperchaotic and 37 synchronized systems. Along with time series and FFT we provide 3D visualizations; for some attractors we also supply Lyapunov coefficients and fractal dimensions. The goal in constructing our Gallery has been to make the general public aware of the enormous variety of chaotic phenomena and to change the widespread impression that they are isolated rarities. The Gallery provides a valuable collection of images and technical data which can be used to analyze these phenomena and to reproduce them in future studies. From a scientific point of view, we have tried to identify new methodological approaches to the study of chaos, opening nontraditional perspectives on the complexity of this domain. In our papers, we have discussed a broad range of topics, ranging from techniques for visualizing Chua attractors to computational methods allowing us to make a statistical classification of attractors' positions in phase space and to describe the evolutionary processes through which their shapes change over time. We see these processes as analogous to population dynamics in artificial environments. Within these environments, we use experimental methods to identify the models which guide morphogenetic change and which organize genetic landscapes in parameter space. This paper is organized as follows. First, we provide formal descriptions of the attractors generated by n-scroll, hyperchaotic and synchronized systems. The next section describes a Gallery of Chua attractors, generated by gradually varying the parameters and analyzing the resulting bifurcation maps. We then describe software tools allowing us to perform statistical analyses on selected sets of attractors, to visualize them, to explore their organization in phase space, and to conduct experimental investigations of the morphogenetic processes through which a small set of base attractors can generate a broad range of different forms. In the last section, we describe the creation of a Virtual 3D Gallery displaying some of the attractors we have presented in our six papers. The attractors are organized by theme, as they might be in a museum. The environment allows users to explore the attractors, interact with shapes, listen to music and sounds generated by the attractors, change their spatial organization, and create new shapes. To complete the paper — and the series — we propose a number of general conclusions.

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.

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