ALBERT

Description: Let $\|x\|$ denote the distance from $x$ to the nearest integer. We show that for any irrational $\alpha$ and for any $\tau 〈 \frac {8}{23},$ there are infinitely many $n$ which are the product of two primes for which \[\|n\alpha \|\leq n^{-\tau }.\] We also show that for all sufficiently large $b$ there exist $3$ -digit palindromes in base $b$ with precisely two prime factors.

Description: This study explores the petrogenesis of Shişr 161, an immature lunar regolith breccia meteorite with low abundances of incompatible elements, a feldspathic affinity, and a significant magnesian component. Our approach was to identify all clasts 〉0.5 mm in size in a thin section, characterize their mineral and melt components, and reconstruct their bulk major and minor element compositions. Trace element concentrations in representative clasts of different textural and compositional types indicate that the clast inventory of Shişr 161 is dominated by impact melts that include slowly cooled cumulate melt rocks with mafic magnesian mineral assemblages. Minor exotic components are incompatible-element-rich melt spherules and glass fragments, and a gas-associated spheroidal precipitate. Our hypothesis for the petrologic setting of Shişr 161 is that the crystallized melt clasts originate from the upper ~1 km of the melt sheet of a 300 to 500 km diameter lunar impact basin in the Moon’s feldspathic highlands. This hypothesis is based on size requirements for cumulate impact melts and the incorporation of magnesian components that we interpret to be mantle-derived. The glassy melts likely formed during the excavation of the melt sheet assemblage, by an impact that produced a 〉15 km diameter crater. The assembly of Shişr 161 occurred in a proximal ejecta deposit of this excavation event. A later impact into this ejecta deposit then launched Shişr 161 from the Moon. Our geochemical modeling of remote sensing data combined with the petrographic and chemical characterization of Shişr 161 reveals a preferred provenance on the Moon’s surface that is close to pre-Nectarian Riemann-Fabry basin.

Description: The lunar meteorite NWA 3163 (paired with NWA 4881, 4483) is a ferroan, feldspathic granulitic breccia characterized by pigeonite, augite, olivine, maskelynite and accessory Tichromite, ilmenite and troilite. Bulk rock geochemical signatures indicate the lack of a KREEP- derived component (Eu/Eu* = 3.47), consistent with previously studied lunar granulites and anorthosites. Bulk rock chondrite-normalized signatures are however distinct from the anorthosites and granulites sampled by Apollo missions and are relatively REE-depleted. In-situ analyses of maskelynite reveal little variation in anorthite content (average An% is 96.9 +/- 1.6, 2 sigma). Olivine is relatively ferroan and exhibits very little variation in forsterite content with mean Fo% of 57.7 +/- 2.0 (2 sigma). The majority of pyroxene is low-Ca pigeonite (En57Fs33Wo10). Augite (En46Fs21Wo33) is less common, comprising approximately 10% of analyzed pyroxene. Two pyroxene thermometry on co-existing orthopyroxene and augite yield an equilibrium temperature of 1070C which is in reasonable agreement with temperatures of 1096C estimated from pigeonite compositions. Rb-Sr isotopic systematics of separated fractions yield an average measured Sr-87/Sr-87 of 0.699282+/-0.000007 (2 sigma). Sr model ages are calculated using a modern day Sr-87/Sr-86 Basaltic Achondrite Best Initial (BABI) value of 0.70475, from an initial BABI value Sr-87/Sr-86 of 0.69891 and a corresponding Rb-87/Sr-97 of 0.08716. The Sr model Thermomechanical analysis (TMA) age, which represents the time of separation of a melt from a source reservoir having chondritic evolution, is 4.56+/-0.1 Ga. A Sr model T(sub RD) age, which is a Rb depletion age and assumes no contribution from Rb in the sample in the calculation, yields 4.34+/-0.1 Ga (i.e. a minimum age). The Ar-Ar dating of paired meteorite NWA 4881 reveals an age of c. 2 Ga, likely representing the last thermal event this meteorite experienced. An older Ar-40/Ar-39 age of c. 3.5 Ga may record the thermal event which produced the granulitic texture. Additional chronological constraints will be provided by Sm-Nd systematics. Ferroan Anorthosites like NWA 3163 have been interpreted to represent direct lunar magma ocean (LMO) crystallization products. If this is the case, trace element concentrations in NWA 3163 primary mineral phases should be in equilibrium with residual LMO liquids present during crystallization of those phases. Results from petrogenetic modeling suggest that the NWA 3163 protolith did not form from crystallization of an initially LREE depleted LMO but rather require an initially chondritic LMO with early garnet crystallization. Furthermore, a two-stage crystallization model where plagioclase crystalized prior to pyroxene (93% vs. 99.5% of LMO crystallization) is implied.

Description: Shergottites represent the majority of recovered Martian meteorites. As basic igneous rocks, they formed from magmas that were emplaced in the Martian crust [1]. Due to the low ambient pressure of the Martian atmosphere, subaerial lavas and shallow magma chambers are expected to outgas volatile metals (e.g., Cd, Te, Re, Bi) [2]. The planetary abundances of the volatile siderophile and chalcophile elements are important at establishing the depth of core formation for Mars, and must be known as a baseline for understanding volcanic outgassing on Mars, particularly the large enrichments of S and Cl observed in modern Martian soils [3]. There is little data on volatile siderophile and chalcophile elements from Martian meteorites, excluding a few well-analyzed samples [2]. Further, a large number of shergottites being recovered from North West Africa are in need of chemical analysis. All of the shergottites are in need of state-of-the art analysis for such ratios as Ge/Si and Ga/Al, which can now be accomplished by LA-ICP-MS [2].

Description: Northwest Africa (NWA) 5744 meteorite is a granulitic and troctolitic lunar breccia which may represent nearly pristine lunar crust (Fig. 1). NWA 5744 is unusually magnesian compared to other lunar breccias, with bulk [Mg/(Mg+Fe)] ~ 0.79 [1, 2]. Inspection shows impactor content is likely to be very minor, with low Ni content and a lack of metal grains. Some terrestrial contamination is present, evidenced by calcite within cracks. NWA 5744 has notably low concentrations of incompatible trace elements (ITEs) [2]. The goal of this study is to attempt to classify this lunar granulite through analyses of in situ phases.

Description: Recent remote sensing studies [e.g., 1-3] indicate that several un-sampled regions of the Moon have significantly higher concentrations of silicic material (also high in [K], [U], and [Th]) than sampled regions. Within these areas are morphological features that are best explained by the existence of chemically evolved volcanic rocks. Observations of silicic domes [e.g., 1-5] suggest that sizable networks of silicic melt were present during crust-formation. Because of these recent findings there is a renewed interest in the petrogenesis of lunar, felsic igneous rocks. Specific questions are: (1) when were these magmas generated?, and (2) what was the source material? The two main hypotheses for generating silicic melts on Earth are fractional crystallization or partial melting of preexisting crust. On the Moon silicic melts are thought to have been generated during extreme fractional crystallization involving end-stage silicate liquid immiscibility (SLI) [e.g. 6, 7]. However, SLI cannot account for the production of significant volumes of silicic melt and its wide distribution, as reported by the remote global surveys [1, 2, 3]. In addition, experimental and natural products of SLI show that U and Th, which are abundant in the lunar granites and seen in the remote sensing data of the domes, are preferentially partitioned into the depolymerized ferrobasaltic magma and not the silicic portion [8, 9]. If SLI is not the mechanism that generated silicic magmas on the Moon then alternative processes such as fractional crystallization (only crystal-liquid separation) or partial melting should be considered as viable possibilities to be tested.

Description: Recent remote sensing studies [e.g., 1-3] indicate that several un-sampled regions of the Moon have significantly higher concentrations of silicic material (also high in [K], [U], and [Th]) than sampled regions. Within these areas are morphological features that are best explained by the existence of chemically evolved volcanic rocks. Observations of silicic domes [e.g., 1-5] suggest that sizable networks of silicic melt were present during crust-formation. Because of these recent findings there is a renewed interest in the petrogenesis of lunar, felsic igneous rocks. Specific questions are: (1) when were these magmas generated?, and (2) what was the source material? The two main hypotheses for generating silicic melts on Earth are fractional crystallization or partial melting of preexisting crust. On the Moon silicic melts are thought to have been generated during extreme fractional crystallization involving end-stage silicate liquid immiscibility (SLI) [e.g. 6, 7]. However, SLI cannot account for the production of significant volumes of silicic melt and its wide distribution, as reported by the remote global surveys [1, 2, 3]. In addition, experimental and natural products of SLI show that U and Th, which are abundant in the lunar granites and seen in the remote sensing data of the domes, are preferentially partitioned into the depolymerized ferrobasaltic magma and not the silicic portion [8, 9]. If SLI is not the mechanism that generated silicic magmas on the Moon then alternative processes such as fractional crystallization (only crystal-liquid separation) or partial melting should be considered as viable possibilities to be tested.