共查询到20条相似文献，搜索用时 31 毫秒
1.
In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, \(S'\), estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, \(S'\) coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results. 相似文献
2.
In this study, we explore a particular type Hawking radiation which ends with zero temperature and entropy. The appropriate black holes for this purpose are the linear dilaton black holes. In addition to the black hole choice, a recent formalism in which the Parikh-Wilczek’s tunneling formalism amalgamated with quantum corrections to all orders in ? is considered. The adjustment of the coefficients of the quantum corrections plays a crucial role on this particular Hawking radiation. The obtained tunneling rate indicates that the radiation is not pure thermal anymore, and hence correlations of outgoing quanta are capable of carrying away information encoded within them. Finally, we show in detail that when the linear dilaton black hole completely evaporates through such a particular radiation, entropy of the radiation becomes identical with the entropy of the black hole, which corresponds to “no information loss”. 相似文献
3.
P. M. Cincotta C. M. Giordano J. G. Martí C. Beaugé 《Celestial Mechanics and Dynamical Astronomy》2018,130(1):7
We present numerical evidence that diffusion in the herein studied multidimensional near-integrable Hamiltonian systems departs from a normal process, at least for realistic timescales. Therefore, the derivation of a diffusion coefficient from a linear fit on the variance evolution of the unperturbed integrals fails. We review some topics on diffusion in the Arnold Hamiltonian and yield numerical and theoretical arguments to show that in the examples we considered, a standard coefficient would not provide a good estimation of the speed of diffusion. However, numerical experiments concerning diffusion would provide reliable information about the stability of the motion within chaotic regions of the phase space. In this direction, we present an extension of previous results concerning the dynamical structure of the Laplace resonance in Gliese-876 planetary system considering variations of the orbital parameters accordingly to the error introduced by the radial velocity determination. We found that a slight variation of the eccentricity of planet c would destabilize the inner region of the resonance that, though chaotic, shows stable when adopting the best fit values for the parameters. 相似文献
4.
In this paper we show that the Conditional Entropy of nearby orbits may be a useful tool to explore the phase space associated
to a given Hamiltonian. The arc length parameter along the orbits, instead of the time, is used as a random variable to compute
the entropy. In the first part of this work we summarise the main analytical results to support this tool while, in the second
part, we present numerical evidence that this technique is able to localise (stable) periodic and quasiperiodic orbits, 'aperiodic'
orbits (chaotic motion) and unstable periodic orbits (the 'source' of chaotic motion). Besides, we show that this technique
provides a measure of chaos which is similar to that given by the largest Lyapunov Characteristic Number. It is important
to remark that this method is very simple to compute and does not require long time integrations, just realistic physical
times.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
5.
Sylvie Jancart Anne Lemaitre Anne Istace 《Celestial Mechanics and Dynamical Astronomy》2002,84(2):197-221
We study the position and the stability of the equilibria for a generic Hamiltonian function developed up to the second harmonic and depending on two parameters; we describe the topology of the phase space for fixed values of these parameters. We show that for some values of the parameters asymmetric equilibria (unstable or stable) may appear. We deduce the conditions of capture into first order resonances for slowly drifting systems. We apply this model to the restricted three-body problem. 相似文献
6.
We address the occurrence of narrow planetary rings and some of their structural properties, in particular when the rings
are shepherded. We consider the problem as Hamiltonian scattering of a large number of non-interacting massless point particles in an effective potential. Using the existence of stable motion
in scattering regions in this set up, we describe a mechanism in phase space for the occurrence of narrow rings and some consequences
in their structure. We illustrate our approach with three examples. We find eccentric narrow rings displaying sharp edges,
variable width and the appearance of distinct ring components (strands) which are spatially organized and entangled (braids).
We discuss the relevance of our approach for narrow planetary rings. 相似文献
7.
Q. A. Wang 《Astrophysics and Space Science》2006,305(3):273-281
A path information is defined in connection with different possible paths of irregular dynamic systems moving in its phase space between two points. On the basis of the assumption that the paths are physically differentiated by their actions, we show that the maximum path information leads to a path probability distribution in exponentials of action. This means that the most probable paths are just the paths of least action. This distribution naturally leads to important laws of normal diffusion. A conclusion of this work is that, for probabilistic mechanics or irregular dynamics, the principle of maximization of path information is equivalent to the least action principle for regular dynamics.We also show that an average path information between the initial phase volume and the final phase volume can be related to the entropy change defined with natural invariant measure of dynamic system. Hence the principles of least action and maximum path information suggest the maximum entropy change. This result is used for some chaotic systems evolving in fractal phase space in order to derive their invariant measures. 相似文献
8.
The Fourier transform of cosmological density perturbations can be represented in terms of amplitudes and phases for each Fourier mode. We investigate the phase evolution of these modes using a mixture of analytical and numerical techniques. Using a toy model of one-dimensional perturbations evolving under the Zel'dovich approximation as an initial motivation, we develop a statistic that quantifies the information content of the distribution of phases. Using numerical simulations beginning with more realistic Gaussian random-phase initial conditions, we show that the information content of the phases grows from zero in the initial conditions, first slowly and then rapidly when structures become non-linear. This growth of phase information can be expressed in terms of an effective entropy. Gaussian initial conditions are a maximum entropy realization of the initial power spectrum; gravitational evolution decreases the phase entropy. We show that our definition of phase entropy results in a statistic that explicitly quantifies the information stored in the phases of density perturbations (rather than their amplitudes), and that this statistic displays interesting scaling behaviour for self-similar initial conditions. 相似文献
9.
The global validity of the symplectic integration method or mapping approach is discussed in this paper. The results show that in the regions of phase space where symplectic integration schemes and the Hamiltonian system possess the same topology, they are effective; but in the regions where the schemes possess some other fixed points than those of the Hamiltonian system, their topologies are different from that of the actual system, thus the symplectic integration method or mapping approach is not effective globally.Supported by the National Natural Science Foundation of China and a grant from the Ph.D. Foundation. 相似文献
10.
Sebastián Ferrer Juan Félix San-Juan Alberto Abad 《Celestial Mechanics and Dynamical Astronomy》2007,99(1):69-83
In the analytical approach to the main problem in satellite theory, the consideration of the physical parameters imposes a
lower bound for normalized Hamiltonian. We show that there is no elliptic frozen orbits, at critical inclination, when we
consider small values of H, the third component of the angular momentum. The argument used suggests that it might be applied also to more realistic
zonal and tesseral models. Moreover, for almost polar orbits, when H may be taken as another small parameter, a different approach that will simplify the ephemerides generators is proposed. 相似文献
11.
We investigate the Cassini's laws which describe the rotational motion in a 1:1 spin-orbit resonance. When this rotational motion follows the conventional Cassini's laws, the figure axis coincides with the angular momentum axis. In this case we underline the differences between the rotational Hamiltonian for a 'slow rotating' body like the Moon and for a 'fast rotating' body like Phobos. Then, we study a more realistic rotational Hamiltonian where the angle J between the figure axis and the angular momentum axis could be different from zero. This Hamiltonian has not been studied before. We have found a new particular solution for this Hamiltonian which could be seen as an extension of the Cassini's laws. In this new solution the angle J is constant, which is not zero, and the precession of the angular momentum plane is equal to the mean motion of the argument of pericenter of the rotating body. This type of rotational motion is only possible when the orbital eccentricity of the rotating body is not zero. This new law enables describing in particular, the Moon mean rotational motion for which the mean value of the angle J is found to be equal to 103.9±0.7 s of arc. 相似文献
12.
《New Astronomy Reviews》2002,46(1):13-39
The aim of this work is to review the fundamental ideas behind the stability problem, emphasizing the differences between two well-known mechanisms that could lead to chaos, namely overlap of resonances and Arnold diffusion. Here we restrict the discussion to multidimensional autonomous Hamiltonian systems which are of major relevance in Dynamical Astronomy. Arnold diffusion is reviewed in a standard mathematical language, by means of different tools such as heuristic reasoning, graphic and geometrical considerations and numerical experiments. In this direction the pioneer work due to Chirikov [PhR 52 (1979) 263] is followed, but including additional notes, further examples and useful discussions that may well illuminate the understanding of Arnold diffusion. We also summarize the main difficulties when coping with this instability, from both the analytical and numerical sides of the problem. The discussion whether Arnold diffusion could play any role in the dynamical evolution of, for instance elliptical galaxies, is also included. 相似文献
13.
F. Cachucho P. M. Cincotta S. Ferraz-Mello 《Celestial Mechanics and Dynamical Astronomy》2010,108(1):35-58
The theory of diffusion in many-dimensional Hamiltonian system is applied to asteroidal dynamics. The general formulation
developed by Chirikov is applied to the Nesvorny-Morbidelli analytic model of three-body (three-orbit) mean-motion resonances
(Jupiter-Saturn-asteroid). In particular, we investigate the diffusion along and across the separatrices of the (5, −2, −2) resonance of the (490) Veritas asteroidal family and their relationship to diffusion
in semi-major axis and eccentricity. The estimations of diffusion were obtained using the Melnikov integral, a Hadjidemetriou-type
sympletic map and numerical integrations for times up to 108 years. 相似文献
14.
We consider dynamics of a Sun–Jupiter–Asteroid system, and, under some simplifying assumptions, show the existence of instabilities in the motions of an asteroid. In particular, we show that an asteroid whose initial orbit is far from the orbit of Mars can be gradually perturbed into one that crosses Mars’ orbit. Properly formulated, the motion of the asteroid can be described as a Hamiltonian system with two degrees of freedom, with the dynamics restricted to a “large” open region of the phase space reduced to an exact area preserving map. Instabilities arise in regions where the map has no invariant curves. The method of MacKay and Percival is used to explicitly rule out the existence of these curves, and results of Mather abstractly guarantee the existence of diffusing orbits. We emphasize that finding such diffusing orbits numerically is quite difficult, and is outside the scope of this paper. 相似文献
15.
Claude Froeschlé Massimiliano Guzzo Elena Lega 《Celestial Mechanics and Dynamical Astronomy》2005,92(1-3):243-255
We detect and measure diffusion along resonances in a quasi-integrable symplectic map for different values of the perturbation parameter. As in a previously studied Hamiltonian case (Lega et al., 2003) results agree with the prediction of the Nekhoroshev theorem. Moreover, for values of the perturbation parameter slightly below the critical value of the transition between Nekhoroshev and Chirikov regime we have also found a diffusion of some orbits along macroscopic portions of the phase space. Such a diffusion follows in a spectacular way the peculiar structure of resonant lines. 相似文献
16.
In this paper the problem of two, and thus, after a generalization, of an arbitrary finite number, of rigid bodies is considered. We show that the Newton-Euler equations of motion are Hamiltonian with respect to a certain non-canonical structure. The system possesses natural symmetries. Using them we shown how to perform reduction of the number of degrees of freedom. We prove that on every stage of this process equations of motion are Hamiltonian and we give explicite form corresponding of non-canonical Poisson bracket. We also discuss practical consequences of the reduction. We prove the existence of 36 non-Lagrangean relative equilibria for two generic rigid bodies. Finally, we demonstrate that our approach allows to simplify the general form of the mutual potential of two rigid bodies. 相似文献
17.
G. Ciraolo C. Chandre R. Lima M. Vittot M. Pettini 《Celestial Mechanics and Dynamical Astronomy》2004,90(1-2):3-12
We present a technique to control chaos in Hamiltonian systems which are close to integrable. By adding a small and simple
control term to the perturbation, the system becomes more regular than the original one. We apply this technique to a forced pendulum
model and show numerically that the control is able to drastically reduce chaos. 相似文献
18.
HARRY DANKOWICZ 《Celestial Mechanics and Dynamical Astronomy》1997,67(1):63-85
We study the motion of grains in orbit around asteroids under the influence of radiation pressure originating in the flux
of solar photons. Of interest is the possibility of initially bound grains becoming unbound and leaving the vicinity of the
asteroid. The analysis extends the two-degree-of-freedom results of (Dankowicz, 1995) to three-degree-of-freedom motions.
In particular, we use a Melnikov-type approach for finding transversal points of intersection between high-dimensional perturbed
stable and unstable manifolds. As a consequence, the system is shown to be nonintegrable and the resulting homoclinic tangles
are suggested as a means for phase space transport along resonance layers, so-called Arnol'd diffusion. We discuss the implications
of the diffusion on the depletion of asteroid-bound particles and attempt to estimate the diffusion rate for physical comparison.
For particular values of physical parameters the time scale is shown to be on the order of hundreds of orbital revolutions
of the asteroid around the sun.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
19.
L.G. Althaus † A.M. Serenelli ‡ O.G. Benvenuto § 《Monthly notices of the Royal Astronomical Society》2001,324(3):617-622
The aim of this work is to investigate the effect of element diffusion on the evolution of helium white dwarfs. To this end, we couple the multicomponent flow equations that describe gravitational settling, chemical and thermal diffusion to an evolutionary code. We compute the evolution of a set of helium white dwarf models with masses ranging from 0.169 to 0.406 M⊙ . In particular, several low-mass white dwarfs have been found in binary systems as companion to millisecond pulsars. In these systems, pulsar emission is activated by mass transfer episodes so that, if we place the zero-age point at the end of such mass transfer, then the pulsar and the white dwarf ages should be equal. Interestingly enough, available models of helium white dwarfs neglect element diffusion. Using such models, good agreement has been found between the ages of the components of the PSR J1012+5307 system. However, recent observations of the PSR B1855+09 system cast doubts on the correctness of such models, which predict a white dwarf age twice as long as the spin-down age of the pulsar. In this work, we find that element diffusion induces thermonuclear hydrogen shell flashes for models in the mass interval 0.18≲ M /M⊙ ≲ 0.41 . We show, in particular, that the occurrence of these diffusion-induced flashes eventually leads to white dwarf models with hydrogen envelope masses too small to support any further nuclear burning, thus implying much shorter cooling ages than in the case when diffusion is neglected. In particular, excellent agreement is found between the ages of PSR B1855+09 system components, solving the age discrepancy from first principles. 相似文献
20.
A. Hennawi 《Celestial Mechanics and Dynamical Astronomy》1980,22(3):237-240
In a previous publication, Broucke [1] has studied the symplectic properties of the variational equations of a Lagrangian of a very particular form, withconstant coefficients. In this article, we generalize his results to the case of an arbitrary Lagrangian. We show that the characteristic exponents of a periodic solution can be computed in Lagrangian formulation as well as in the more usual Hamiltonian formulation. 相似文献