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Susanna Carbonin Gabriella Salviulol Rosalba Munno Mirella Desiderio A. Dal Negro 《Mineralogy and Petrology》1989,41(1):1-10
Summary The crystal structures of 20 natural diopsides have been refined. For some samples, microprobe analyses show a Si deficiency in the tetrahedron with no A1 present; this suggests that some Ti4+ may enter the tetrahedral site. Geometrical variations in these samples with respect to the others are discussed in the light of this Si Ti4+ substitution. The volumes of their M1 sites are larger because of the absence of R3+ cations, the octahedron being very regular; in the same way, the volumes of M2 sites of these samples are greater not because of different site occupancies but because of significant charge modifications around the O3 and O1 oxygens, caused by the tetrahedral site. The low distortion of M1 site and the lengthening of (M2-O1) and M2-O3 bond lengths are a clue to the presence of small amounts of Ti at the tetrahedral site.
Kristallchemische untersuchung natürlicher diopside: Geometrische hinweise für tetraedrische Si-Ti substitution
Zusammenfassung Die Kristallstrukturen von zwanzig natürlichen Diopsiden sind verfeinert worden. In einigen Proben zeigen Mikrosondenanalysen zu geringe Si-Werte im Tetraeder ohne daß A1 anwesend wäre. Dies weist darauf hin, daß Ti4+ Tetraederplätze einnehmen könnte. Geometrische Variationen in diesen Proben werden im Lichte der genannten Substitution diskutiert. Die Volumen von M1-Plätzen sind größer wegen der Abwesenheit von R3+ Kationen, wobei das Oktaeder sehr gleichmäßig ist. Die Volumina von M2-Plätzen sind noch größer nicht wegen verschiedener Besetzungen dieser Plätze sondern wegen signifikanter Ladungsmodifikationen im Bereich von O3 und O1 Sauerstoffen, die durch die tetraedrische Position bewirkt wird. Die geringe Distortion der M1-Plätze und die Verlängerung der (M2-O1) und (M2-O3) Abstände weisen auf die Anwesenheit von geringen Titangehalten auf Tetraederplätzen hin.相似文献
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George Contopoulos Mirella Harsoula Georgios Lukes-Gerakopoulos 《Celestial Mechanics and Dynamical Astronomy》2012,113(3):255-278
We study the periodic orbits and the escapes in two different dynamical systems, namely (1) a classical system of two coupled oscillators, and (2) the Manko-Novikov metric which is a perturbation of the Kerr metric (a general relativistic system). We find their simple periodic orbits, their characteristics and their stability. Then we find their ordered and chaotic domains. As the energy goes beyond the escape energy, most chaotic orbits escape. In the first case we consider escapes to infinity, while in the second case we emphasize escapes to the central ??bumpy?? black hole. When the energy reaches its escape value, a particular family of periodic orbits reaches an infinite period and then the family disappears (the orbit escapes). As this family approaches termination it undergoes an infinity of equal period and double period bifurcations at transitions from stability to instability and vice versa. The bifurcating families continue to exist beyond the escape energy. We study the forms of the phase space for various energies, and the statistics of the chaotic and escaping orbits. The proportion of these orbits increases abruptly as the energy goes beyond the escape energy. 相似文献
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M. Harsoula C. Kalapotharakos 《Monthly notices of the Royal Astronomical Society》2009,394(3):1605-1619
We study the orbital structure in a series of self-consistent N -body configurations simulating rotating barred galaxies with spiral and ring structures. We perform frequency analysis in order to measure the angular and the radial frequencies of the orbits at two different time snapshots during the evolution of each N -body system. The analysis is done separately for the regular and the chaotic orbits. We thereby identify the various types of orbits, determine the shape and percentages of the orbits supporting the bar and the ring/spiral structures, and study how the latter quantities change during the secular evolution of each system. Although the frequency maps of the chaotic orbits are scattered, we can still identify concentrations around resonances. We give the distributions of frequencies of the most important populations of orbits. We explore the phase-space structure of each system using projections of the 4D surfaces of section. These are obtained via the numerical integration not only of the orbits of test particles, but also of the real N -body particles. We thus identify which domains of the phase space are preferred and which are avoided by the real particles. The chaotic orbits are found to play a major role in supporting the shape of the outer envelope of the bar as well as the rings and the spiral arms formed outside corotation. 相似文献
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The collapse of a spherical collisionless system of particles is studied. The initial conditions are consinstent with the scenario of galaxy formation from small initial density perturbations. An investigation of the effects of violent relaxation on wiping out the memory of initial conditions is presented. The final distribution of energies of individual particles depends on the radial profile of the initial density perturbation. When this profile becomes steeper, the spectrum of the times scales, in which collapsing of various shells occurs, broadens. The correlation found between the final and the initial distribution of energies is almost linear and the mean slope of this correlation depends on how wide the spectrum of the above time scales is. This slope can be a measure of the surviving memory of initial conditions in the system. The surviving memory is larger in the case when the collapse occurs gradually during a wider range of time scales. If the collapse is completed in a short time interval the relaxation occurs more violently, and the surviving memory is less. Moreover, an estimation of the collapse factors is made by calculating their dependence of the final radius of several fractions of the system's mass, reached at the relaxation. As a consequence, a better fitting of the final radial density profile is made, comparing with the one predicted by the similarity solution. 相似文献
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Stickiness is a temporary confinement of orbits in a particular region of the phase space before they diffuse to a larger region. In a system of 2-degrees of freedom there are two main types of stickiness (a) stickiness around an island of stability, which is surrounded by cantori with small holes, and (b) stickiness close to the unstable asymptotic curves of unstable periodic orbits, that extend to large distances in the chaotic sea. We consider various factors that affect the time scale of stickiness due to cantori. The overall stickiness (stickiness of the second type) is maximum near the unstable asymptotic curves. An important application of stickiness is in the outer spiral arms of strong-barred spiral galaxies. These spiral arms consist mainly of sticky chaotic orbits. Such orbits may escape to large distances, or to infinity, but because of stickiness they support the spiral arms for very long times. 相似文献
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We study the chaotic motions in the field of two fixed black holes M1, M2 by calculating (a) the asymptotic curves from the main unstable periodic orbits, (b) the asymptotic orbits, with particular emphasis οn the homoclinic and heteroclinic orbits, and (c) the basins of attraction of the two black holes. The orbits falling on M1and M2form fractal sets. The asymptotic curves consist of many arcs, separated by gaps. Every gap contains orbits falling on a black hole. The sizes of various arcs decrease as the mass ofM1 increases. The basins of attraction of the black holes M1, M2consist of large compact regions and of thin filaments. The relative area of the basin M2 tends to 100 as M1 → 0, and it decreases as M1 increases. The total area of the basins is found analytically, while the relative area of the basin M2 is given by an empirical formula. Further empirical formulae give the exponential decrease of the number of asymptotic orbits that have not yet reached a black hole after n iterations. 相似文献
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N. Voglis M. Harsoula CH. Efthymiopoulos 《Celestial Mechanics and Dynamical Astronomy》2000,78(1-4):265-278
As it is known, a good number of galaxies are observed to have counterrotating cores. A popular scenario to explain the formation of such galaxies is based on a secondary process of merging of galaxies with their satellites, or gas infall, or merger events between galaxies. An alternative mechanism, proposed by Voglis et al., 1991, and by Harsoula and Voglis 1998, could also be responsible for the formation of these galaxies directly from cosmological initial conditions (direct scenario). The novel mechanism was demonstrated by using quiet cosmological initial conditions in N-body simulations. In the present paper we extend our N-body simulations using clumpy initial conditions and show that this mechanism still works to create counterrotating galaxies. Counterrotation is a result of the considerable amount of memory of initial conditions surviving for times comparable to the Hubble time, despite the large degree of instability of individual orbits and the dramatic redistribution and mixing of the particles in phase space. We show, for example, that the particles remember, in a statistical sense, not only their distance from the center of mass (memory of energy), but also the initial orientation of their position relative to the direction of an external tidal field, which determines the sign and the amount of angular momentum that is transferred to the particles of the system. 相似文献