Equipartition of energy in a one-dimensional model of diatomic molecules. II. Maximal Lyapunov exponent and phase-space trajectory separation

1991 ◽  
Vol 43 (4) ◽  
pp. 2031-2040 ◽  
Author(s):  
Alessandro Monge ◽  
E. G. D. Cohen ◽  
Jerome J. Erpenbeck
Keyword(s):  
Phase Space ◽  
Lyapunov Exponent ◽  
Diatomic Molecules ◽  
Maximal Lyapunov Exponent ◽  
Dimensional Model ◽  
One Dimensional ◽  
Equipartition Of Energy ◽  
Phase Space Trajectory

THE 2-D SEXTIC HAMILTONIAN OSCILLATOR

2013 ◽  
Vol 23 (06) ◽  
pp. 1330019
Author(s):  
F. J. MOLERO ◽  
J. C. VAN DER MEER ◽  
S. FERRER ◽  
F. J. CÉSPEDES
Keyword(s):  
Phase Space ◽  
Elliptic Functions ◽  
Singular Values ◽  
Nonlinear Oscillators ◽  
Momentum Mapping ◽  
Dimensional Model ◽  
Integrable Hamiltonian Systems ◽  
One Dimensional ◽  
Dimensional Phase Space ◽  
The One

The 2-D sextic oscillator is studied as a family of axial symmetric parametric integrable Hamiltonian systems, presenting a bifurcation analysis of the different flows. It includes the "elliptic core" model in 1-D nonlinear oscillators, recently proposed in the literature. We make use of the energy-momentum mapping, which will give us the fundamental fibration of the four-dimensional phase space. Special attention is given to the singular values of the energy-momentum mapping connected with rectilinear and circular orbits. They are related to the saddle-center and pitchfork scenarios with the associated homoclinic and heteroclinic trajectories. We also study how the geometry of the phase space evolves during the transition from the one-dimensional to the two-dimensional model. Within an elliptic function approach, the solutions are given using Legendre elliptic integrals of the first and third kind and the corresponding Jacobi elliptic functions.

The action of Vlasov waves on the velocity distribution in a plasma

1961 ◽  
Vol 10 (3) ◽  
pp. 473-479 ◽  
Author(s):  
J. W. Dungey
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Velocity Distribution ◽  
Thermal Equilibrium ◽  
Limited Range ◽  
Dimensional Model ◽  
One Dimensional ◽  
A Current

A one-dimensional model with no magnetic field is considered. It is supposed that the plasma starts in thermal equilibrium and then a current is forced to grow. Instability leads to the growth of waves, which are shown to stir the distribution in phase space, but only over a limited range of velocity. It is concluded that in order to restore stability the energy in the wave must become comparable to the energy of drift.

scholarly journals The two-spin model of a tracking chamber: a phase-space perspective

2021 ◽  
Author(s):  
Luigi Barletti
Keyword(s):  
Phase Space ◽  
Spin Model ◽  
Space Representation ◽  
Dimensional Model ◽  
Wigner Matrix ◽  
One Dimensional ◽  
Classical Localization ◽  
Relationship Of ◽  
The Relationship ◽  
Phase Space Representation

AbstractWe study the dynamics of classical localization in a simple, one-dimensional model of a tracking chamber. The emitted particle is represented by a superposition of Gaussian wave packets moving in opposite directions, and the detectors are two spins in fixed, opposite positions with respect to the central emitter. At variance with other similar studies, we give here a phase-space representation of the dynamics in terms of the Wigner matrix of the system. This allows a better visualization of the phenomenon and helps in its interpretation. In particular, we discuss the relationship of the localization process with the properties of entanglement possessed by the system.

DETECTING THE STATE OF THE DUFFING OSCILLATOR BY PHASE SPACE TRAJECTORY AUTOCORRELATION

2013 ◽  
Vol 23 (04) ◽  
pp. 1350065 ◽  
Author(s):  
VAHID RASHTCHI ◽  
MOHSEN NOURAZAR
Keyword(s):  
Phase Space ◽  
Lyapunov Exponent ◽  
Duffing Oscillator ◽  
Simple Calculation ◽  
The State ◽  
Detection Methods ◽  
Largest Lyapunov Exponent ◽  
Chaotic Oscillator ◽  
The Largest Lyapunov Exponent ◽  
Phase Space Trajectory

Detecting the state of the Duffing oscillator, a type of well-known chaotic oscillator, deeply affects the accuracy of its application. Considering this, the present paper introduced a novel method for detecting the state of the Duffing oscillator. Binary outputs, simple calculation, high precision and fast response time were the main advantages of the phase space trajectory autocorrelation. Also, this study explained the largest Lyapunov exponent as well as a number of other methods commonly employed in detecting the state of the Duffing oscillator. The precision and effectiveness of the method introduced was compared with other well-known state detection methods such as the 0-1 test and the largest Lyapunov exponent.

IONIZATION AND STABILIZATION OF A ONE-DIMENSIONAL MODEL ATOM: MAP APPROACH

1999 ◽  
Vol 13 (12) ◽  
pp. 1489-1502 ◽  
Author(s):  
TAIWANG CHENG ◽  
JIE LIU ◽  
SHIGANG CHEN
Keyword(s):  
Phase Space ◽  
Wigner Distribution ◽  
Ionization Rate ◽  
Intense Laser ◽  
Ionization Process ◽  
Space Region ◽  
Dimensional Model ◽  
One Dimensional ◽  
Quantum Version ◽  
Model Atom

In this paper, the interactions between a one-dimensional model atom and intense laser field is approximately described by a map. Both the classical version and quantum version of this map are studied. It is shown that besides classical stable islands which can bound some phase space region against ionization and then are responsible for the atomic stabilization, there is another structure in phase space, the unstable manifold, which can determine the ionization process of the system. Quantumly, the quantum quasienergy eigenstates (QE state) under absorptive boundaries, which directly related to the ionization process, are calculated. We define the QE state with smallest ionization rate as QE0 state, which represents the stabilization degree. The Wigner distribution of such QE0 state show clear fringe structures. Finally we show that the classical description and quantum description are in a correspondence manner.

scholarly journals Dynamical properties of a novel one dimensional chaotic map

2022 ◽  
Vol 19 (3) ◽  
pp. 2489-2505
Author(s):  
Amit Kumar ◽  
◽  
Jehad Alzabut ◽  
Sudesh Kumari ◽  
Mamta Rani ◽  
...  
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Behavior ◽  
Chaotic Map ◽  
Logistic Map ◽  
Maximal Lyapunov Exponent ◽  
Bifurcation Diagrams ◽  
One Dimensional ◽  
Dynamical Properties ◽  
Chaotic Logistic Map

<abstract><p>In this paper, a novel one dimensional chaotic map $ K(x) = \frac{\mu x(1\, -x)}{1+ x} $, $ x\in [0, 1], \mu &gt; 0 $ is proposed. Some dynamical properties including fixed points, attracting points, repelling points, stability and chaotic behavior of this map are analyzed. To prove the main result, various dynamical techniques like cobweb representation, bifurcation diagrams, maximal Lyapunov exponent, and time series analysis are adopted. Further, the entropy and probability distribution of this newly introduced map are computed which are compared with traditional one-dimensional chaotic logistic map. Moreover, with the help of bifurcation diagrams, we prove that the range of stability and chaos of this map is larger than that of existing one dimensional logistic map. Therefore, this map might be used to achieve better results in all the fields where logistic map has been used so far.</p></abstract>

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