Global Bifurcations of Periodic Solutions of the Restricted Three Body Problem

We describe global bifurcations from the libration points of non-stationary periodic solutions of the restricted three body problem. We show that the only admissible continua of non-stationary periodic solutions of the planar restricted three body problem, bifurcating from the libration points, can be the short-period families bifurcating from the Lagrange equilibria L ₄, L ₅. We classify admissible continua and show that there are possible exactly six admissible continua of non-stationary periodic solutions of the planar restricted three body problem. We also characterize admissible continua of non-stationary periodic solutions of the spatial restricted three body problem. Moreover, we combine our results with the Déprit and Henrard conjectures (see [8]), concerning families of periodic solutions of the planar restricted three body problem, and show that they can be formulated in a stronger way. As the main tool we use degree theory for SO(2)-equivariant gradient maps defined by the second author in [25].This revised version was published online in October 2005 with corrections to the Cover Date.     

Resurfacing history of Europa from pole-to-pole geological mapping

We produced geologic maps from two regional mosaics of Galileo images across the leading and trailing hemispheres of Europa in order to investigate the temporal distribution of units in the visible geologic record. Five principal terrain types were identified (plains, bands, ridges, chaos, and crater materials), which are interpreted to result from (1) tectonic fracturing and lineament building, (2) cryovolcanic reworking of surface units, with possible emplacement of sub-surface materials, and (3) impact cratering. The geologic histories of both mapped areas are essentially similar and reflect some common trends: Tectonic resurfacing dominates the early geologic record with the formation of background plains by intricate superposition of lineaments, the opening of wide bands with infilling of inter-plate gaps, and the buildup of ridges and ridge complexes along prominent fractures in the ice. It also appears that lineaments are narrower and more widely spaced with time. The lack of impact craters overprinted by lineaments indicate that the degree of tectonic resurfacing decreased rapidly after ridged plains formation. In contrast, the degree of cryovolcanic resurfacing appears to increase with time, as chaos formation dominates the later parts of the geologic record. These trends, and the transition from tectonic- to cryovolcanic-dominated resurfacing could be attributed to the gradual thickening of Europa's cryosphere during the visible geologic history, that comprises the last 2% or 30-80 Myr of Europa's history: An originally thin, brittle ice shell could be pervasively fractured or melted through by tidal and endogenic processes; the degree of fracturing and plate displacements decreased with time in a thickening shell, and lineaments became narrower and more widely spaced; formation of chaos regions could have occurred where the thickness threshold for solid-state convection was exceeded, and can be aided by preferential tidal heating of more ductile ice. In a long-term context it is not clear at this point whether this inferred thickening trend would reflect a drastic change in the thermal evolution of the satellite, or cyclic or irregular episodes of tectonic and cryovolcanic activity.     

Large impact features on middle-sized icy satellites

All of the large impact features of the middle-sized icy satellites of Saturn and Uranus that were clearly observed by the Voyager spacecraft are described. New image mosaics and stereo-and-photoclinometrically-derived digital elevation models are presented. Landforms related to large impact features, such as secondary craters and possible antipodal effects are examined and evaluated. Of the large impacts, Odysseus on Tethys appears to have had the most profound effect on its “target” satellite of any of the impact features we examined. Our modeling suggests that the Odysseus impact may have caused the prompt formation of Ithaca Chasma, a belt of tectonic troughs that roughly follow a great circle normal to the center of Odysseus, although other hypotheses remain viable. We identify probable secondary cratering from Tirawa on Rhea. We attribute a number of converging coalescing crater chains on Rhea to a putative, possibly relatively fresh, ∼350 km-diameter impact feature. We examine the antipodes of Odysseus, the putative ∼350 km-diameter Rhean impact feature, and Tirawa, and conclude that evidence from Voyager data for damage from seismic focusing is equivocal, although our modeling results indicate that such damage may have occurred. We propose a number of observations and tests for Cassini that offer the opportunity to differentiate among the various explanations and speculations reviewed and evaluated in this study.     

Characteristics of convection and overshooting in RGB and AGB stars

Based on the turbulent convection model (TCM) of Li & Yang, we have studied the characteristics of turbulent convection in the envelopes of 2 and 5M⊙ stars at the red giant branch and asymptotic giant branch phases. The TCM has been successfully applied over the entire convective envelopes, including the convective unstable zone and the overshooting regions. We find that the convective motions become progressively stronger when the stellar models are located farther up along the Hayashi line. In the convect...     

The flood of the Nenjiang river and the Songhua river in 1998 and the comprehensive management of the river basins

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Impact of water environmental characteristics in Dry-Hot valley of Jinsha river on soil desertification

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