An Avron rule for fragments of R-mingle

Axiomatic bases of admissible rules are obtained for fragments of the substructural logic R-mingle. In particular, it is shown that a ‘modus-ponens-like’ rule introduced by Arnon Avron forms a basis for the admissible rules of its implication and implication–fusion fragments, while a basis for the admissible rules of the full multiplicative fragment requires an additional countably infinite set of rules. Indeed, this latter case provides an example of a three-valued logic with a finitely axiomatizable consequence relation that has no finite basis for its admissible rules.

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.