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We present a novel way of constraining the thickness of the crystal mush in fractionated layered intrusions using detailed microstructural analysis. The results are combined with geochemical data to create a snapshot of the crystal mush on the floor of the Skaergaard magma chamber in the period immediately before and after the saturation of the bulk liquid in apatite (the UZa-b boundary). The step-change in the fractional latent heat (that part of the total enthalpy budget associated with crystallization) accompanying the arrival of a new liquidus phase is recorded by a step-change in the median clinopyroxene-plagioclase-plagioclase dihedral angle, Theta(cpp), in fully solidified cumulates. Dihedral angles are formed during the last stages of solidification and hence the change of Theta(cpp) associated with apatite-in marks a point close to the base of the mushy layer at the moment the bulk liquid became saturated in apatite, whereas the first appearance of abundant, homogeneously scattered, cumulus apatite crystals in the stratigraphy marks the top of the mushy layer at this moment. Comparison of the offset between these two markers in five widely spaced drill cores through the Skaergaard Layered Series suggests that the mushy layer was only a few metres thick at the UZa-b boundary in the centre and east of the floor, whereas it was similar to 100 m thick on the floor near the western margin. There is no correlation between the efficiency of liquid expulsion (as recorded by bulk-rock P2O5 concentrations and the stratigraphic distribution of reactive symplectites) and the recorded mush thickness at the moment of apatite saturation, suggesting that existing models of adcumulate formation that depend on mush thickness need to be reconsidered.

The Emmaville eucrite is a relatively poorly studied basaltic achondrite with an anomalous oxygen isotope signature. In this study, we report comprehensive mineralogical, petrographic, and geochemical data from Emmaville in order to understand its petrogenesis and relationship with the basaltic eucrites. Emmaville is an unusually fine-grained, hornfelsic-textured metabasalt with pervasive impact melt veins and mineral compositions similar to those of typical basaltic eucrites. The major and trace element bulk composition of Emmaville is also typical of a basaltic eucrite. Three separated individual lithologies were also analyzed for O isotopes; a dark gray fraction (E1), a shocked lithology (E2), and a lighter gray portion (E3). Fractions E1 and E2 shared similar O isotope compositions to the bulk sample (E-B), whereas the lighter gray portion (E3) is slightly elevated in Δ17O and significantly elevated in δ18O compared to bulk. No evidence for any exogenous material is observed in the thin sections, coupled with the striking compositional similarity to typical basaltic eucrites, appears to preclude a simple impact-mixing hypothesis. The O-isotopes of Emmaville are similar to those of Bunburra Rockhole, A-881394, and EET 92023, and thus distinct from the majority of the HEDs, despite having similarities in petrology, mineral, and bulk compositions. It would, therefore, seem plausible that all four of these samples are derived from a single HED-like parent body that is isotopically distinct from that of the HEDs (Vesta) but similar in composition.

Isotopic anomalies are departures from the laws of mass-dependent fractionation that cannot be explained by radioactive decay, cosmogenic effects, or exotic isotopic fractionation processes such as nuclear field shift or magnetic effects [1 and references therein]. These anomalies often have a nucleosynthetic origin and provide clues on the stellar origin and solar system processing of presolar dust. Anomalies are most often found in refractory elements of relatively low mass, so Sr is a prime target for study. The four stable isotopes of strontium are useful for discerning the various nucleosynthetic origins of early solar system building blocks and the timing of accretion processes. Strontium-84 is the least abundant (0.56%) of these isotopes, but is particularly significant in being a p-process only nuclide that is produced in core-collapse or type Ia supernovae [2,3]. The more abundant isotopes ^(86)Sr (9.86%), ^(87)Sr (7.00%) and ^(88)Sr (82.58%) are produced in s- and r-processes in asymptotic giant branch stars and other stellar types [4]. Additionally, ^(87)Sr is produced by ^(87)Rb decay in proportions that dominate over possible nucleosynthetic variations but provide timings of early solar system processes, most notably volatile element depletion [5-7]. Furthermore, variations in strontium isotopic ratios caused by high-temperature massdependent fractionation [8] are also important [9-12], as they provide insights into nebular and accretionary processes.

This paper proves a $\Gamma$-convergence result for the discrete energy (to the continuous one) of the matching problem for signals defined on surfaces. In particular, we highlight some geometric properties that must be guaranteed in the discretization process to ensure the convergence of minimizers. The proof is given in the framework of functional shapes introduced in \cite{ABN}. In particular, we consider a varifold-type attachment term, and a $BV$ penalty term is used instead of the original $L^2$ norm.

Our study is motivated by two aspects: i) the scientific motivation is to a) expand on previous studies of heavy noble gases in samples from terrestrial hot and cold deserts, thus to collect surface and subsurface (20 cm depth) samples from wind-blown desert soil and to b) study clay rich soil horizons for their microbiology and potential to serve as Mars analogue; and the ii) technological motivation is to field-test a prototype\ud sampling container for crew-based sample return missions to Mars, the Moon, or other celestial bodies.