The disruption of the L chondrite parent body (LCPB) at ~470 Ma is currently the best‐documented catastrophic celestial impact event, based on the large number of L chondritic materials associated with this event. Uranium‐lead (U‐Pb) dating of apatite and its high‐pressure decomposition product, tuite, in the Sixiangkou L6 chondrite provides a temporal link to this event. The U‐Pb system of phosphates adjacent to shock melt veins was altered to varying degrees and the discordance of the U‐Pb system correlates closely with the extent of apatite decomposition. This suggests that the U‐Pb system of apatite could be substantially disturbed by high‐temperature pulse during shock compression from natural impacts, at least on the scale of mineral grains. Although many L chondrites can be temporally related to the catastrophic LCPB impact event, the shock conditions experienced by each individual meteorite vary. This could be due to the different geologic settings of these meteorites on their parent body. The shock pressure and duration derived from most meteorites may only reflect local shock features rather than the impact conditions, although they could provide lower limits to the impact conditions. The Sixiangkou shock duration (~4 s), estimated from high‐pressure transformation kinetics, provides a lower limit to the high‐pressure pulse of the LCPB disruption impact. Combined with available literature data of L chondrites associated with this impact event, our results suggest that the LCPB suffered a catastrophic collision with a large projectile (with a diameter of at least 18–22 km) at a low impact velocity (5–6 km s−1). This is consistent with astronomical estimates based on the dynamical evolution of L chondritic asteroids.
This paper focuses on planar typical Bézier curves with a single curvature extremum, which is a supplement of typical curves with monotonic curvature by Y. Mineur et al. We have proven that the typical curve has at most one curvature extremum and given a fast calculation formula of the parameter at the curvature extremum. This will allow designers to execute a subdivision at the curvature extremum to obtain two pieces of typical curves with monotonic curvature. In addition, we put forward a sufficient condition for typical curve solutions under arbitrary degrees for the G1 interpolation problem. Some numerical experiments are provided to demonstrate the effectiveness and efficiency of our approach.
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