ALBERT

Description: To evaluate compaction and interstitial melt expulsion during cumulate formation, a 20 m cumulate section including the UG2 and UG3 chromitites from a 264 m drill core through the Upper Critical Zone of the Bushveld Complex (South Africa) has been studied. The cumulates in the studied section are as follows: 3 m plagioclase pyroxenite to pyroxenite, pegmatoid footwall pyroxenite at the lower contact to UG2, 0·7 m UG2 chromitite, 6·8 m pyroxenite, 0·24 m UG3 chromitite, 2·0 m plagioclase-rich pyroxenite changing locally to norite, the two 5 cm leader stringers UG3a and UG3b, and 7 m total of olivine pyroxenites grading into plagioclase pyroxenites. All pyroxenites are dominated by orthopyroxene (opx) and the cumulate sequence is topped by mottled anorthosite grading into norite. Stratigraphic concentrations of major and trace elements of 52 bulk-rock samples were determined. Bulk-rock Mg-numbers are 0·79–0·81 throughout the silicate cumulate units, and 0·40–0·46 in the chromitite layers. The stratigraphic distribution of six incompatible trace elements (K, Rb, Ba, Cs, Zr and Th) has been used to determine the amount of trapped liquid ( F TL ) or paleo-porosity in the cumulate rocks. Final porosities (volume fractions), based on averages from the six trace elements, are 0·06–0·33 in the pyroxenites. In chromitite layers, trapped melt fractions of 0·12–0·36 are calculated from incompatible trace element concentrations, but bulk SiO 2 concentrations and X-ray tomography yield 0·04–0·17 higher porosities. Hence, the bulk silicate fraction in the chromitites may not necessarily correspond to the trapped liquid fraction, as poikilitic opx was crystallizing while the silicate melt still equilibrated. Using a previously derived experiment-based model for compaction time scales, gravitationally driven chemical compaction in the UG2–UG3–pyroxenite section is calculated to occur within 1–10 years. This time frame corresponds to the times necessary to cool a 20 m layer by 10–50°C, the temperature interval argued to encompass the liquidus and almost complete solidification. Compaction within a decade can in fact easily develop the paleo-porosities indirectly observed today and is probably stopped by crystallization of the interstitial liquid. Contrary to previous assertions, melt expulsion from the cumulate pile does not hinder compaction; calculated permeabilities would allow for the migration of an order of magnitude higher amount of melt than has to be expelled from the 20 m pile of cumulate. The pegmatoid zones in the chromitite footwalls enriched in incompatible trace elements are consistent with a collection of interstitial melts expelling from the underlying compacting pyroxenites. Their entrapment below the chromitite layers suggests that these act as permeability barriers. This is in part due to their finer grain size compared with the pyroxenites, but is mainly due to the crystallization of large poikilitic opx during compaction.

Description: Coinductive definitions, such as that of an infinite stream, may often be described by elegant logic programs, but ones for which SLD-refutation is of no value as SLD-derivations fall into infinite loops. Such definitions give rise to questions of lazy corecursive derivations and parallelism, as execution of such logic programs can have both recursive and corecursive features at once. Observational and coalgebraic semantics have been used to study them abstractly. The programming developments have often occurred separately and have usually been implementation-led. Here, we give a coherent semantics-led account of the issues, starting with abstract category theoretic semantics, developing coalgebra to characterize naturally arising trees and proceeding towards implementation of a new dialect, CoALP, of logic programming, characterised by guarded lazy corecursion and parallelism.