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1.
The accelerated Kepler problem (AKP) is obtained by adding a constant acceleration to the classical two-body Kepler problem.
This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses linear
momentum through the asymmetric jet-counterjet system it powers. The dynamics of the accelerated Kepler problem is analyzed
using physical as well as parabolic coordinates. The latter naturally separate the problem’s Hamiltonian into two unidimensional
Hamiltonians. In particular, we identify the origin of the secular resonance in the AKP and determine analytically the radius
of stability boundary of initially circular orbits that are of particular interest to the problem of radial migration in binary
systems as well as to the truncation of accretion disks through stellar jet acceleration. 相似文献
2.
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
3.
Giancarlo Benettin Massimiliano Guzzo Valerio Marini 《Celestial Mechanics and Dynamical Astronomy》2008,101(1-2):203-224
We provide evidences that the angular momentum of a symmetric rigid body in a spin–orbit resonance can perform large scale chaotic motions on time scales which increase polynomially with the inverse of the oblateness of the body. This kind of irregular precession appears as soon as the orbit of the center of mass is non-circular and the angular momentum of the body is far from the principal directions with minimum (maximum) moment of inertia. We also provide a quantitative explanation of these facts by using the theory of adiabatic invariants, and we provide numerical applications to the cases of the 1:1 and 1:2 spin–orbit resonances. 相似文献
4.
U. Heimhofer S. P. Hesselbo R. D. Pancost D. M. Martill P. A. Hochuli J. V. P. Guzzo 《地学学报》2008,20(5):347-354
Organic matter from two black shale units in the Santana Formation, Araripe Basin, NE Brazil, has been studied to investigate the palaeoenvironmental conditions prevailing during formation of this famous fossil lagerstätte. Optical and organic geochemical analyses indicate a predominantly autochthonous source with very limited terrestrial input. Molecular fossils of green sulphur bacteria show that the water column was stratified with euxinic conditions reaching up into the photic zone. Thus, mass‐mortality events of fish may be explained by intrusion of sulphide‐containing waters. The low quantity of material derived from land plants in this interior marine setting is interpreted to reflect a consequence of enhanced marine productivity, resulting in dilution of the continental signal. Different depositional scenarios are proposed to explain our findings including (1) coastal erosion and nutrient leaching during a transgressive event, (2) intrusion of euxinic waters during an early Albian OAE or (3) an estuarine circulation pattern associated with thermohaline stratification. 相似文献
5.
The charge compensation problem for Si−Al substitution in Brazilian natural quartz is investigated in relation to γ-irradiation
darkening response and impurity contents evaluated by atomic absorption spectrometry and infrared absorption spectroscopy.
Al+3 in as-grown natural quartz is compensated by Li+ and H+ to form Al−Li and Al−OH centers. The content ratios (Al−Li)/(Al−OH) and Li/(broad OH band) depend on the environmental conditions
of crystal growth and influence the formation of Al-hole centers due to γ-irradiation. Al−OH centers are the dominant Al-related
centers in quartz from hydrothermal origin while Al−Li centers are dominant for that of pegmatitic origin. The formation of
Al-hole centers is little in quartz with a high content of broad OH band which is from low temperature hydrothermal origin.
Received May 23, 1995 / Revised, accepted May 8, 1996 相似文献
6.
Elena Lega Massimiliano Guzzo Claude Froeschlé 《Celestial Mechanics and Dynamical Astronomy》2009,104(1-2):191-204
Using four-dimensional symplectic maps as a model problem, we numerically compute the unstable manifolds of the hyperbolic manifolds of the phase space related to the single resonances. We measure an exponential dependence of the size of the lobes of these manifolds through many orders of magnitude of the perturbing parameter. This is an indirect numerical verification of the exponential decay of the normal form, as predicted by the Nekhoroshev theorem. The variation of the size of the lobes turns out to be correlated to the diffusion coefficient. 相似文献
7.
Elena Lega Massimiliano Guzzo Claude Froeschlé 《Celestial Mechanics and Dynamical Astronomy》2010,107(1-2):115-127
Using numerical methods we study the hyperbolic manifolds in a model of a priori unstable dynamical system. We compare the numerically computed manifolds with their analytic expression obtained with the Melnikov approximation. We find that, at small values of the perturbing parameter, the topology of the numerically computed stable and unstable manifolds is the same as in their Melnikov approximation. Increasing the value of the perturbing parameter, we find that the stable and unstable manifolds have a peculiar topological transition. We find that this transition occurs near those values of the perturbing parameter for which the error terms of Melnikov approximations have a sharp increment. The transition value is also correlated with a change in the behaviour of dynamical quantities, such as the largest Lyapunov exponent and the diffusion coefficient. 相似文献
8.
Massimiliano Guzzo 《Celestial Mechanics and Dynamical Astronomy》2002,83(1-4):303-323
We describe a numerical application of the Nekhoroshev theorem to investigate the long-term stability of quasi-integrable systems. We extend the results of a previous paper to a class of degenerate systems, which are typical in celestial mechanics. 相似文献
9.
Elena Lega Massimiliano Guzzo Claude Froeschlé 《Celestial Mechanics and Dynamical Astronomy》2010,107(1-2):129-144
Using a three degrees of freedom quasi-integrable Hamiltonian as a model problem, we numerically compute the unstable manifolds of the hyperbolic manifolds of the phase space related to single resonances. We measure an exponential dependence of the splitting of these manifolds through many orders of magnitude of the perturbing parameter. This is an indirect numerical verification of the exponential decay of the normal form, as predicted by the Nekhoroshev theorem. We also detect different transitions in the topology of these manifolds related to the local rational approximations of the frequencies. The variation of the size of the homoclinic tangle as well as the topological transitions turn out to be correlated to the speed of Arnold diffusion. 相似文献
10.
Alessandro Morbidelli Massimiliano Guzzo 《Celestial Mechanics and Dynamical Astronomy》1996,65(1-2):107-136
The present paper reviews the Nekhoroshev theorem from the point of view of physicists and astronomers. We point out that Nekhoroshev result is strictly connected with the existence of a specific structure of the phase space, the existence of which can be checked with several numerical tools. This is true also for a degenerate system such as the one describing the motion of an asteroid in the so called main belt. The main difference is that in some parts of the belt, the Nekhoroshev result cannot apply a priori. Mean motion resonances of order smaller than the logarithm of the mass of Jupiter and first order secular resonances must be excluded. In the remaining parts, conversely, the Nekhoroshev theorem can be proved, provided someparameters, such as the masses, the eccentricities and the inclinations of the planets are small enough. At the light of this result, a massive campaign of numerical integrations of real and fictitious asteroids should allow to understand which is the real dynamical structure of the asteroid belt. 相似文献