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For $\Omega\subseteq\mathbb{R}^{n}$ an open and bounded region we consider solutions $u\in W_{\text{loc}}^{1,p(x)}\big(\Omega;\mathbb{R}^{N}\big)$, with $N>1$, of the $p(x)$-Laplacian system \begin{equation} \nabla\cdot\left(a(x)|Du|^{p(x)-2}Du\right)=0\text{, a.e. }x\in\Omega,\notag \end{equation} where concerning the coefficient function $x\mapsto a(x)$ we assume only that \begin{equation} a\in W^{1,q}(\Omega)\cap L^{\infty}(\Omega),\notag \end{equation} where $q>1$ is essentially arbitrary. This implies that the coefficient in the PDE can be highly irregular, and yet in spite of this we still recover that \begin{equation} u\in\mathscr{C}_{\text{loc}}^{0,\alpha}\big(\Omega_0\big),\notag \end{equation} for each $0<\alpha<1$, where $\Omega_0\subseteq\Omega$ is a set of full measure. Due to the variational methodology that we employ, our results apply to the more general question of the regularity of the integral functional \begin{equation} \int_{\Omega}a(x)|Du|^{p(x)}\ dx.\notag \end{equation}, Comment: Journal of Differential Equations

Almahata Sitta (AhS) is classified as an anomalous, polymict ureilite and was observed prior to Earth impact as the F-type asteroid 2008 TC3 [e.g., 1-2]. As part of our characterization of this unusual meteorite [e.g., 3], we have been using microscopic infrared spectroscopy (µ-FTIR) to measure the mineralogy of fragments identified as carbonaceous chondrites (CC). In fragment 202 we have discovered unambiguous spectral evidence for a minimum of several vol% amphibole (specifically, tremolite), a mineral that is not known to occur in volumetrically significant abundances (defined here as >1%) in carbonaceous chondrites

Almahata Sitta (AhS) 202 from the UoK collection represents a clast from the polymict breccia asteroid 2008 TC3. AhS 202 was recognized as a unique carbonaceous chondrite (CC) with a high magnetite content. Here we report that it also contains a significant amount of amphibole, a mineral that is very rare in chondrites and has not previously been reported in significant abundance in a CC. We present new petrographic, oxygen isotope, and micro-FTIR data. We discuss petrogenesis and possible relationships to known CC.

There is an increasing number of Cr-O-Ti isotope studies that show that solar system materials are divided into two main populations, one carbonaceous chondrite (CC)-like and the other is non-carbonaceous (NCC)-like, with minimal mixing between them attributed to a gap opened in the propoplanetary disk due to Jupiter's formation. The Grand Tack model suggests that there should be a particular time in the disk history when this gap is breached and ensuring a subsequent large-scale mixing between S- and C-type asteroids (inner solar system and outer solar system materials), an idea supported by our recent work on chondrule (Delta)17O-(epsilon)54Cr isotope systematics.

Ureilites are differentiated meteorites (ultramafic rocks interpreted to be mantle residues) that contain as much carbon as the most carbon-rich carbonaceous chondrites (CCs). Reflectance spectra of ureilites are similar to those of some CCs. Hence, ureilitic asteroids may accidentally be categorized as primitive because their spectra could resemble those of C-complex asteroids, which are thought to be CC-like. We began spectral studies of progressively laser-weathered ureilites with the goals of predicting UV-VIS-IR spectra of ureilitic asteroids, and identifying features that could distinguish differentiated from primitive dark asteroids. Space weathering has not previously been studied for ureilites, and, based on space weathering studies of CCs and other C-rich materials, it could significantly alter their reflectance spectra.

The Almahata Sitta (AhS) polymict ureilite fell in 2008 when asteroid 2008 TC3 impacted over Sudan]. It is the first meteorite to originate from an asteroid that had been tracked and studied in space (with spectral classification) before impact, and provides a unique opportunity to correlate properties of meteorites with those of their parent asteroid. More than 700 monolithologic stones from the AhS fall were collected. Of those previously studied, approx. 70% were ureilites and approx. 30% were chondrites. It has been inferred that 2008 TC3 was loosely aggregated and porous and disintegrated in the atmosphere, with only its most coherent clasts falling as stones. However, understanding the structure of this asteroid is limited by incomplete study of the heterogeneous stones, and the loss of most of the mass of the asteroid. The University of Khartoum (UOK) AhS collection contains over >600 AhS stones with find coordinates. We are studying this collection to determine: 1) the proportion of ureilitic to various non-ureilitic stones; 2) the distribution of types of stones in the strewn field; and 3) the compositional and physical structure of 2008 TC3. We report on 61 new stones, including a unique sample that may represent the bulk of the material lost from 2008 TC3.

Polymict ureilites contain a variety of Less than or equal to mm to cm sized non-ureilitic clasts, many of which can be identifed as chondritic and achondritic meteorite types. Among them, dark clasts have been observed in polymict ureilites that are similar to CI chondrites in mineralogy, containing phyllosilicates, magnetite, sulfide and carbonates. Bulk oxygen isotope analyses of a dark clast in Nilpena plot along the CCAM line and above the terrestrial fractionation line, on the O-poor extension of the main group ureilite trend and clearly different from bulk CI chondrites. One possible origins of such dark clast is that they represent aqueously altered precursors of ureilite parent body (UPB) that were preserved on the cold surface of the UPB. Oxygen isotope analyses of dark clasts are key to better understanding their origins. Oxygen isotope ratios of magnetite are of special interest because they reflect the compositions of the fluids in asteroidal bodies. In primitive chondrites, Delta O (= Delta O - 0.52× Delta O) values of magnetites are always higher than those of the bulk meteorites and represent minimum Delta O values of the initial O-poor aqueous fluids in the parent body. Previous SIMS analyses on magnetite and fayalite in dark clasts from the DaG 319 polymict ureilite were analytically difficult due to small grain sizes, though data indicated positive Delta O values of 3-4 per mille, higher than that of the dark clast in Nilpena (1.49per mille).

The Almahata Sitta (AhS) polymict ureilite is the first meteorite to originate from a spectrally classified asteroid (2008 TC3) [1-3], and provides an unprecedented opportunity to correlate properties of meteorites with those of their parent asteroid. AhS is also unique because its fragments comprise a wide variety of meteorite types. Of approximately140 stones studied to-date, ~70% are ureilites (carbon-rich ultramafic achondrites) and 30% are various types of chondrites [4,5]. None of these show contacts between ureilitic and chondritic lithologies. It has been inferred that 2008 TC3 was loosely aggregated, so that it disintegrated in the atmosphere and only its most coherent clasts fell as individual stones [1,3,5]. Understanding the structure and composition of this asteroid is critical for missions to sample asteroid surfaces. We are studying [6] the University of Khartoum collection of AhS [3] to test hypotheses for the nature of 2008 TC3. We describe a sample that consists of both ureilitic and chondritic materials.

There is an increasing number of Cr-O-Ti isotope studies that show solar system materials are divided into two main populations, one carbonaceous chondrite (CC)-like and the other is non-carbonaceous (NC)-like, with minimal mixing attributed to a gap opened in the protoplanetary disk due to Jupiter's formation. The Grand Tack model suggests there should be large-scale mixing between S- and C-type asteroids, an idea supported by our recent work on chondrule (Delta)17O-ε54Cr isotope systematics. The Almahata Sitta (AhS) meteorite provides a unique opportunity to test the Grand Tack model. The meteorite fell to Earth in October 2008 and has been linked to the asteroid 2008 TC3 which was discovered just prior to the fall of the AhS stones. The AhS meteorite is composed of up to 700 individual pieces with approx.140 of those pieces having some geochemical and/or petrologic studies. Almahata Sitta is an anomalous polymict ureilite with other meteorite components, including enstatite, ordinary, and carbonaceous chondrites with an approximate abundance of 70% ureilites and 30% chondrites. This observation has lead to the suggestion that TC3 2008 was a loosely aggregated rubble pile-like asteroid with the non-ureilite sample clasts within the rubble-pile. Due to the loosely-aggregated nature of AhS, the object disintegrated during atmospheric entry resulting in the weakly held clasts falling predominantly as individual stones in the AhS collection area. However, recent work has identified one sample of AhS, sample 91A, which may represent two different lithologies coexisting within a single stone. The predominate lithology type in 91A appears to be that of a C2 chondrite based on mineralogy but also contains olivine, pyroxene, and albite that have ureilite-like compositions. Previous Cr isotope investigations into AhS stones are sparse and what data is available show nearly uniform isotopic composition similar to that of typical ureilites with negative ε54Cr values.

The recovery of meteorites from the impact of asteroid 2008 TC3 in the Nubian Desert of Sudan on October 7, 2008, marked the first time meteorites were collected from an asteroid observed in space by astronomical techniques before impacting. Search teams from the University of Khartoum traced the location of the strewn field and collected about 660 meteorites in four expeditions to the fall region, all of which have known fall coordinates. Upon further study, the Almahata Sitta meteorites proved to be a mixed bag of mostly ureilites (course grained, fine grained, and sulfide-metal assemblages), enstatite chondrites (EL3-6, EH3, EH5, breccias) and ordinary chondrites (H5-6, L4-5). One bencubbinite-like carbonaceous chondrite was identified, as well as one unique Rumuruti-like chondrite and an Enstatite achondrite. New analysis: The analysed meteorites so far suggest a high 30-40 percent fraction of non-ureilites among the recovered samples, but that high fraction does not appear to be in agreement with the meteorites in the University of Khartoum (UoK) collection. Ureilites dominate the meteorites that were recovered by the Sudanese teams. To better understand the fraction of recovered materials that fell to Earth, a program has been initiated to type the meteorites in the UoK collection in defined search areas. At this meeting, we will present some preliminary results from that investigation.

Introduction: Polymict ureilites are breccias interpreted to represent regolith formed on a ureilitic asteroid [1-3]. They consist of approximately 90-95% clasts of various ureilite types (olivine-pyroxene rocks with Fo 75-95), a few % indigenous feldspathic clasts, and a few % foreign clasts [4-20]. The foreign clasts are diverse, including fragments of H, L, LL and R chondrites, angrites, other achondrites, and dark clasts similar to CC [6,7,9-19]. We report a new type of foreign clast in polymict ureilite DaG 999. Methods: Clast 8 in Dar al Gani (DaG) 999/1 (Museum fur Naturkunde) was discovered during a survey of feldspathic clasts in polymict ureilites [19,20]. It was studied by BEI, EMPA, and X-ray mapping on the JEOL 8530F electron microprobe at ARES, JSC. Petrography and Mineral Compositions: Clast 8 is sub-rounded to irregular in shape, approximately 85 micrometers in diameter, and consists of approximately 68% pyroxene and 32% mesostasis (by area). Part of the pyroxene (top half of clast in Fig. 1a and 2) shows a coarse dendritic morphology; the rest appears massive. Mesostasis may be glassy and contains fine needles/grains of pyroxene. The pyroxene has very high CaO (23.5 wt.%) and Al2O3 (19.7 wt.%), with the formula: (Ca(0.91)Mg(0.63)Fe(0.01)Al(sup VI) (0.38)Cr(0.01)Ti(0.05)1.99 Si2O6. The bulk mesostasis also has very high Al2O3 (approximately 26 wt.%). A bulk composition for the clast was obtained by combining modal abundances with phase compositions (Table 1, Fig. 3). Discussion: The pyroxene in clast 8 has a Ca-Al-(Ti)- rich (fassaitic) composition that is clearly distinct from compositions of pyroxenes in main group ureilites [22] or indigenous feldspathic clasts in polymict ureilites [4-8]. It also has significantly higher Al than fassaite in angrites (up to approximately 12 wt.% [23]), which occur as xenoliths in polymict ureilites. Ca-Al-Ti rich pyroxenes are most commonly found in CAIs, Al-rich chondrules and other types of refractory inclusions in chondrites [21,24-31]. However, the clast 8 pyroxene matches only the most Al-Ca-rich of these, e.g., pyroxenes in type B CAIs in CV3 chondrites [25,30,31], a pyroxene-hibonite spherule and a pyroxene-anorthitespinel fragment from unique CC Acfer 094 [29], and one Al-rich chondrule from Chainpur (LL3.4) [21]. The mineralogy of clast 8 is not consistent with the mineral assemblages of any of these objects (since it lacks hibonite, spinel and/or anorthite), which suggests that it is unrepresentatively sectioned or is a fragment of a more mineralogically diverse object. Its bulk composition (Table 1; Fig. 3) is similar to bulk compositions of some Al-rich chondrules, as well as those of Type C CAIs (which plot in the sp+An+L field in Fig. 3), although it is enriched in silica relative to type C CAIs [e.g., 31]. This suggests a more likely affinity to Al-rich chondrules, although most Al-rich chondrules have less Al-Ca-rich pyroxene [21,26,27]. These bulk compositional comparisons may not be definitive, however, if the clast is unrepresentatively sampled. One of eleven Al-rich chondrules from UOCs described by [21] has textural and compositional characteristics that make it a possible progenitor type for clast 8. This chondrule (Chainpur 1251-14-2) is anorthiteporphyritic, with an interstitial dendritic intergrowth of pyroxene (similar in composition to that in clast 8) and plagioclase [21]. Clast 8 is conceivably a fragment from the interstitial area of such an object. The occurrence of glassy mesostasis (in clast 8) rather than plagioclase may not be a significant difference; it could result from a difference only in cooling rate. Al-rich chondrules with glassy mesostasis are rare, and known occurrences are Ca-poor [26], unlike clast 8. Polymict ureilites are known to contain xenoliths of various chondrites (including OC, R and CC) as well as individual ferromagnesian and silica-pyroxene chondrules probably derived from OC or RC [6,9,15,16,18]. This is the first report of an individual chondritic refractory inclusion as a xenolith in a polymict ureilite. An RC-like sample from anomalous polymict ureilite Almahata Sitta contains CAIs, but they are spinel-rich and not similar to clast 8 [13,14]. Further studies of this clast (which, unfortunately, may not be possible), or the discovery of additional (more representative?) materials of this type would be needed to determine the exact nature of this xenolith and the type of chondrite from which it is derived.

Almahata Sitta (AhS) is the first meteorite to originate from an asteroid (2008 TC3) that had been studied in space before it hit Earth [1,2]. It is also unique because the fallen fragments comprise a variety of types: approximately 69% ureilites (achondrites) and 31% chondrites [3]. Two models have been proposed for the origin 2008 TC3: 1) an accretionary model [3,4]; or 2) a regolith model [5,6]. Typical polymict ureilites are interpreted to represent regolith, and contain a few % foreign clasts [7,8]. The most common are dark (CC matrix-like) clasts similar to those in many meteoritic breccias [9]. A variety of other chondrites, as well as achondrites (angrites), have also been reported [7,9,10]. We have been working to determine the full diversity of these clasts [10-13] for comparison with AhS. We discuss implications for mixing of materials in the early solar system and the origin of 2008 TC3.

Almahata Sitta (AS) is a polymict breccia mainly composed of variable ureilite lithologies with small amounts of chondritic lithologies [1]. Fe metal is a common accessory phase in ureilites, but our earlier study on Fe metals in one of AS fragments (#44) revealed a unique mineralogy never seen in other ureilites [2,3]. In this abstract we report detailed transmission electron microscopy (TEM) on these metal grains to better understand the thermal history of ureilites. We prepared FIB sections of AS#44 by JEOL JIB-4000 from the PTS that was well characterized by SEM-EBSD in our earlier study [2]. The sections were then observed by STEM (JEOL JEM- 2100F). One of the FIB sections shows a submicron-sized symplectic intergrown texture composed of Fe metal (kamacite), Fe carbide (cohenite), Fe phosphide (schreibersite), and Fe sulfide (troilite). Each phase has an identical SAED pattern in spite of its complex texture, suggesting co-crystallization of all phases. This is probably caused by shock re-melting of pre-existing metal + graphite to form a eutectic-looking texture. The other FIB section is mostly composed of homogeneous Fe metal (93 wt% Fe, 5 wt% Ni, and 2 wt% Si), but BF-STEM images exhibited the presence of elongated lathy grains (approx. 2 microns long) embedded in the interstitial matrix. The SAED patterns from these lath grains could be indexed by alpha-Fe (bcc) while interstitial areas are gamma-Fe (fcc). The elongated alpha-Fe grains show tweed-like structures suggesting martensite transformation. Such a texture can be formed by rapid cooling from high temperature where gamma-Fe was stable. Subsequently alpha-Fe crystallized, but gamma-Fe remained in the interstitial matrix due to quenching from high temperature. This scenario is consistent with very rapid cooling history of ureilites suggested by silicate mineralogy.

Almahata Sitta (AS) is a polymict breccia mainly composed of various ureilite lithologies with lesser chondritic lithologies [1]. In the ureilite lithologies, Fe metal is a common accessory phase present either as large grain boundary grains or small particles formed by reduction of olivine and pyroxene. In our earlier studies on grain boundary metals in one of AS fragments (#44) we found unique features never seen in other ureilites [2,3]. In order to further characterize these metal grains, we performed a detailed TEM study on a FIB section prepared from one of AS #44 grain boundary metals and here discuss its thermal history.

The Almahata Sitta (hereafter "AHS") meteorite was derived from an impact of asteroid 2008TC3 on Earth and is classified as an anomalous polymict ureilite. More than 600 meteorite fragments have been recovered from the strewnfield. Previous reports indicate that these fragments consist mainly of ureilitic materials with textures and compositions, while some fragments are found to be chondrites of a wide range of chemical classes. Bulk oxygen three isotope analyses of ureilitic fragments from AHS fall close to the CCAM (Carbonaceous Chondrite Anhydrous Mineral) line similar to ureilites. In order to further compare AHS with known ureilites, we performed high precision SIMS (Secondary Ion Mass Spectrometer) oxygen isotope analyses of some AHS samples

Ureilites are ultramafic (harzburgitic) achondrites composed predominantly of olivine and pyroxenes, abundant carbon (graphites and shock-produced diamonds), some metal and sulfides. These rocks probably represent ultramafic mantles of differentiated parent asteroidal bodies. Age determinations of these rocks by Rb-Sr and Sm-Nd methods have been difficult because of their extremely low abundances of these parent-daughter elements. Nevertheless, Sm-Nd isochron ages were reported for Kenna, Goalpara, MET 78008 and PCA 82506 yielding ages of 3.74+/-0.02 Ga, approx.3.7 Ga, 4.09+/-0.08 Ga, 4.23+/-0.06 Ga, respectively [1-4]. These "young" Sm-Nd ages may represent secondary metasomatism events [1] related to impacts [5], as indicated by the similarly young Ar-39-Ar-40 degassing ages of 3.3-4.1 Ga for ureilites Kenna, Novo Urei and Havero [6]. Alternatively, it has been suggested that these rocks may have been contaminated with terrestrial crustal materials and the isochrons do not have any age significance [2,7]. Indications of old approx.4.56 Ga ages for ureilites were reported from the U-Pb and Sm-Nd model ages for MET 78008 [8]. More reliable evidences for old formation ages of ureilites were reported recently using the short-lived chronometers Hf-182-W-182, Al-26-Mg-26 and Mn-53-Cr-53. The deficits of 182W in ureilites suggest the metal-silicate segregation occurred very early, approx.1-2 Ma after CAI [9]. The Al-26-Mg-26 and Mn-53-Cr-53 studies for a feldspathic lithology [10] and the Mn-53-Cr-53 for olivine- and pyroxene-dominant lithologies [11] in ureilites revealed that they crystallized approx.5.4 Ma after CAI, i.e., at 4563.8+/-0.5 Ma relative to D.Orbigny. In this report, we present Sm-Nd isotopic data for a relatively fresh ureilite, Novo Urei, a rare ureilite fall (1886). We compare these data to Sm-Nd data for other ureilites, and discuss Novo Urei's petrogenesis