A three-dimensional phase space dynamical model of the Earth’s radiation belt

1996 ◽  
Author(s):  
D. M. Boscher ◽  
T. Beutier ◽  
S. Bourdarie
Keyword(s):  
Phase Space ◽  
Radiation Belt ◽  
Three Dimensional ◽  
Dynamical Model ◽  
Dimensional Phase Space ◽  
Earth’S Radiation Belt

Superconductivity and the existence of Nambu's three-dimensional phase space mechanics

1984 ◽  
Vol 104 (2) ◽  
pp. 106-108 ◽  
Author(s):  
Reinaldo Angulo ◽  
Simón Codriansky ◽  
Carlos A. Gonzalez-Bernardo ◽  
Andrés J. Kalnay ◽  
Freddy Perez-M ◽  
...  
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Dimensional Phase Space ◽  
Space Mechanics

scholarly journals Constraining cluster masses from the stacked phase space distribution at large radii

2019 ◽  
Vol 489 (1) ◽  
pp. 1344-1356
Author(s):  
Akinari Hamabata ◽  
Masamune Oguri ◽  
Takahiro Nishimichi
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Space Distribution ◽  
Line Of Sight ◽  
Mass Dependence ◽  
Mass Measurements ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
Transverse Distance ◽  
Hubble Flow

Abstract Velocity dispersions have been employed as a method to measure masses of clusters. To complement this conventional method, we explore the possibility of constraining cluster masses from the stacked phase space distribution of galaxies at larger radii, where infall velocities are expected to have a sensitivity to cluster masses. First, we construct a two-component model of the three-dimensional phase space distribution of haloes surrounding clusters up to 50 $\, h^{-1}$ Mpc from cluster centres based on N-body simulations. We confirm that the three-dimensional phase space distribution shows a clear cluster mass dependence up to the largest scale examined. We then calculate the probability distribution function of pairwise line-of-sight velocities between clusters and haloes by projecting the three-dimensional phase space distribution along the line of sight with the effect of the Hubble flow. We find that this projected phase space distribution, which can directly be compared with observations, shows a complex mass dependence due to the interplay between infall velocities and the Hubble flow. Using this model, we estimate the accuracy of dynamical mass measurements from the projected phase space distribution at the transverse distance from cluster centres larger than $2\, h^{-1}$ Mpc. We estimate that, by using 1.5 × 105 spectroscopic galaxies, we can constrain the mean cluster masses with an accuracy of 14.5 per cent if we fully take account of the systematic error coming from the inaccuracy of our model. This can be improved down to 5.7 per cent by improving the accuracy of the model.

scholarly journals Time evolution of companies towards a stable scaling curve obtained from flow diagrams in three-dimensional phase space

2019 ◽  
Vol 21 (4) ◽  
pp. 043038
Author(s):  
Yuh Kobayashi ◽  
Hideki Takayasu ◽  
Shlomo Havlin ◽  
Misako Takayasu
Keyword(s):  
Phase Space ◽  
Time Evolution ◽  
Three Dimensional ◽  
Dimensional Phase Space ◽  
Flow Diagrams

scholarly journals CANONICAL TRANSFORMATIONS IN THREE-DIMENSIONAL PHASE-SPACE

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4769-4788 ◽  
Author(s):  
TEKİN DERELİ ◽  
ADNAN TEĞMEN ◽  
TUĞRUL HAKİOĞLU
Keyword(s):  
Phase Space ◽  
Canonical Transformation ◽  
Generating Functions ◽  
General Framework ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Canonical Transformations ◽  
Dimensional Phase Space ◽  
Nambu Bracket ◽  
Definition Of

Canonical transformation in a three-dimensional phase-space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed based on canonoid transformations. It is shown that generating functions, transformed Hamilton functions and the transformation itself for given generating functions can be determined by solving Pfaffian differential equations corresponding to that quantities. Types of the generating functions are introduced and all of them are listed. Infinitesimal canonical transformations are also discussed. Finally, we show that the decomposition of canonical transformations is also possible in three-dimensional phase space as in the usual two-dimensional one.

scholarly journals Features of pulsed synchronization of an autooscillatory system with a three-dimensional phase space

2006 ◽  
Vol 32 (4) ◽  
pp. 343-346 ◽  
Author(s):  
A. P. Kuznetsov ◽  
N. V. Stankevich ◽  
L. V. Tyuryukina
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Dimensional Phase Space

scholarly journals Complexity of a Microblogging Social Network in the Framework of Modern Nonlinear Science

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Andrey Dmitriev ◽  
Vasily Kornilov ◽  
Svetlana Maltseva
Keyword(s):  
Dynamical System ◽  
Social Network ◽  
Phase Space ◽  
Adiabatic Approximation ◽  
Three Dimensional ◽  
Evolutionary Model ◽  
Random Dynamical System ◽  
New Paradigm ◽  
Dimensional Phase Space ◽  
Nonlinear Science

Recent developments in nonlinear science have caused the formation of a new paradigm called the paradigm of complexity. The self-organized criticality theory constitutes the foundation of this paradigm. To estimate the complexity of a microblogging social network, we used one of the conceptual schemes of the paradigm, namely, the system of key signs of complexity of the external manifestations of the system irrespective of its internal structure. Our research revealed all the key signs of complexity of the time series of a number of microposts. We offer a new model of a microblogging social network as a nonlinear random dynamical system with additive noise in three-dimensional phase space. Implementations of this model in the adiabatic approximation possess all the key signs of complexity, making the model a reasonable evolutionary model for a microblogging social network. The use of adiabatic approximation allows us to model a microblogging social network as a nonlinear random dynamical system with multiplicative noise with the power-law in one-dimensional phase space.

Phase Space Interpretation and Stability Analysis of a Self Excited, Friction Damped Turbine Airfoil

1997 ◽  
Author(s):  
E. Pesheck ◽  
C. Pierre
Keyword(s):  
Stability Analysis ◽  
Phase Space ◽  
Asymptotic Methods ◽  
Three Dimensional ◽  
Space Representation ◽  
Free Response ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Dimensional Phase Space ◽  
Phase Space Representation

Abstract The free response motion of a self excited, friction damped, single-degree of freedom, turbine airfoil model is determined utilizing both exact and asymptotic methods. A three-dimensional phase space representation is used to examine the system’s global stability, and to further intuitive understanding of the system dynamics. Conclusions are reached regarding the validity and application of stability predictions through comparison of approximate and exact solutions.

BREAKDOWN OF LIBRATIONAL INVARIANT SURFACES

1999 ◽  
Vol 09 (05) ◽  
pp. 975-982
Author(s):  
MIQUEL ANGEL ANDREU ◽  
ALESSANDRA CELLETTI ◽  
CORRADO FALCOLINI
Keyword(s):  
Phase Space ◽  
Numerical Investigation ◽  
Invariant Tori ◽  
Three Dimensional ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
The Moon ◽  
Dimensional Phase Space ◽  
Invariant Surfaces ◽  
The Stability

A numerical investigation of the stability of invariant librational tori is presented. The method has been developed for a model describing the spin-orbit coupling in Celestial Mechanics. Periodic orbits approaching the librational torus are computed by means of Newton's method. According to Greene's criterion, their stability is strictly related to the survival of invariant tori. We consider librational tori around the main spin-orbit resonances (1:1, 3:2). Their existence provides the stability of the resonances, due to the confinement properties in the three-dimensional phase space associated to our model. The results are consistent with the actual observations of the eccentricity and of the oblateness parameter. A different behavior of the Moon and Mercury around the main resonances is evidenced, providing interesting suggestions about the different probabilities of capture in a resonance.

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