Local Stereology of Tensors of Convex Bodies

In this paper, we present local stereological estimators of Minkowski tensors defined on convex bodies in ℝ d . Special cases cover a number of well-known local stereological estimators of volume and surface area in ℝ3, but the general set-up also provides new local stereological estimators of various types of centres of gravity and tensors of rank two. Rank two tensors can be represented as ellipsoids and contain information about shape and orientation. The performance of some of the estimators of centres of gravity and volume tensors of rank two is investigated by simulation.

Selective sampling during catastrophic disruption: Mapping the location of reaccumulated fragments in the original parent body

In this paper, we simulate numerically the catastrophic disruption of a large asteroid as a result of a collision with a smaller projectile and the subsequent reaccumulation of fragments as a result of their mutual gravitational attractions. We then investigate the original location within the parent body of the small pieces that eventually reaccumulate to form the largest offspring of the disruption as a function of the internal structure of the parent body. We consider four cases that may represent the internal structure of such a body (whose diameter is fixed at 250 km) in various early stages of the Solar System evolution: fully molten, half molten (i.e., a 26 km-deep outer layer of melt containing half of the mass), solid except a thin molten layer (8 km thick) centered at 10 km depth, and fully solid. The solid material has properties of basalt. We then focus on the three largest offspring that have enough reaccumulated pieces to consider. Our results indicate that the particles that eventually reaccumulate to form the largest reaccumulated bodies retain a memory of their original locations in the parent body. Most particles in each reaccumulated body are clustered from the same original region, even if their reaccumulations take place far away. The extent of the original region varies considerably depending on the internal structure of the parent. It seems to shrink with the solidity of the body. The fraction of particles coming from a given depth is computed for the four cases, which can give constraints on the internal structure of parent bodies of some meteorites. As one example, we consider the ureilites, which in some petrogenetic models are inferred to have formed at particular depths within their parent body. (C) 2014 Elsevier Ltd. All rights reserved.