Numerical approximation of statistical solutions of scalar conservation laws

We propose efficient numerical algorithms for approximating statistical solutions of scalar conservation laws. The proposed algorithms combine finite volume spatio-temporal approximations with Monte Carlo and multi-level Monte Carlo discretizations of the probability space. Both sets of methods are proved to converge to the entropy statistical solution. We also prove that there is a considerable gain in efficiency resulting from the multi-level Monte Carlo method over the standard Monte Carlo method. Numerical experiments illustrating the ability of both methods to accurately compute multi-point statistical quantities of interest are also presented

The Colorado Plateau Coring Project (CPCP): 100 Million Years of Earth System History

Lasting over 100 million years, the early Mesozoic (252 to 145 Ma) is punctuated by two of the five major mass extinctions of the Phanerozoic (Permo-Triassic and Triassic-Jurassic) plus several smaller extinction events. It witnessed the evolutionary appearance of the modem terrestrial biota including frogs, salamanders, turtles, lizards, crocodilians, dinosaurs, birds, and mammals, and spans a time of dramatic climate changes on the continents. What is arguably the richest record of these events lies in the vast (- 2.5 million km2) complex of epicontinental basins in the western part of Pangea, now largely preserved on the Colorado Plateau (Fig.l). Since the mid-19th century, classic studies of these basins, their strata, and their fossils have made this succession instrumental in framing our context of the early Mesozoic Earth system as reflected in the international literature. Despite this long and distinguished history of study of the Colorado Plateau region, striking ambiguities in temporal resolution, major uncertainties in global correlations, and significant doubts about paleolatitudinal position hamper incorporation of the huge amount of information from the region into-tests of major competing climatic, biotic, and tectonic hypotheses and a fundamental understanding of Earth system processes

Earliest Palaeocene purgatoriids and the initial radiation of stem primates

Plesiadapiform mammals, as stem primates, are key to understanding the evolutionary and ecological origins of Pan-Primates and Euarchonta. The Purgatoriidae, as the geologically oldest and most primitive known plesiadapiforms and one of the oldest known placental groups, are also central to the evolutionary radiation of placentals and the Cretaceous-Palaeogene biotic recovery on land. Here, we report new dental fossils of Purgatorius from early Palaeocene (early Puercan) age deposits in northeastern Montana that represent the earliest dated occurrences of plesiadapiforms. We constrain the age of these earliest purgatoriids to magnetochron C29R and most likely to within 105–139 thousand years post- K/Pg boundary. Given the occurrence of at least two species, Purgatorius janisae and a new species, at the locality, we provide the strongest support to date that purgatoriids and, by extension, Pan-Primates, Euarchonta and Placentalia probably originated by the Late Cretaceous. Within 1 million years of their arrival in northeastern Montana, plesiadapiforms outstripped archaic ungulates in numerical abundance and dominated the arboreal omnivore–frugivore niche in mammalian local faunas

40Ar/39Ar ages of the sill complex of the Karoo large igneous province: implications for the Pliensbachian-Toarcian climate change.

Reliable geochronological results gathered so far (n = 76) have considerably constrained the timing of the emplacement of the Karoo large igneous province (LIP). Yet strikingly missing from this dating effortis the huge southern sill complex cropping out in the >0.6 x 10(6) km2 Main Karoo sedimentary basin. We present 16 new 40Ar/39Ar analyses carried out on fresh plagioclase and biotite separates from 15 sill samples collected along a N-S trend in the eastern part of the basin. The results show a large range of plateau and miniplateau ages (176.2 +- 1.3 to 183.8 +- 2.4 Ma), with most dates suggesting a -3 Ma (181-184 Ma) duration for the main sill events. The available age database allows correlation of the Karoo LIP emplacement with the Pliensbachian-Toarcian second-order biotic extinction, the global warming, and the Toarcian anoxic event (provided that adequate calibration between the 40K and 238U decay constant ismade). The mass extinction and the isotopic excursions recorded at the base of the Toarcian appear to be synchronous with both the increase of magma emission of the Karoo LIP and the emplacement of the sills.The CO2 and SO2 derived from both volcanic emissions as well as carbon-rich sedimentary layers intrudedby sills might be the main culprits of the Pliensbachian-Toarcian climate perturbations. We propose that the relatively low eruption rate of the Karoo LIP is one of the main reasons explaining why its impact on thebiosphere is relatively low contrary to, e.g., the CAMP (Triassic-Jurassic) and Siberia (Permo-Triassic) LIPs

Colorado Plateau Coring Project, Phase I (CPCP-I): a continuously cored, globally exportable chronology of Triassic continental environmental change from western North America

Phase 1 of the Colorado Plateau Coring Project (CPCP-I) recovered a total of over 850&thinsp;m of stratigraphically overlapping core from three coreholes at two sites in the Early to Middle and Late Triassic age largely fluvial Moenkopi and Chinle formations in Petrified Forest National Park (PFNP), northeastern Arizona, USA. Coring took place during November and December of 2013 and the project is now in its post-drilling science phase. The CPCP cores have abundant detrital zircon-producing layers (with survey LA-ICP-MS dates selectively resampled for CA-ID-TIMS U-Pb ages ranging in age from at least 210 to 241&thinsp;Ma), which together with their magnetic polarity stratigraphy demonstrate that a globally exportable timescale can be produced from these continental sequences and in the process show that a prominent gap in the calibrated Phanerozoic record can be filled. The portion of core CPCP-PFNP13-1A for which the polarity stratigraphy has been completed thus far spans  ∼ 215 to 209&thinsp;Ma of the Late Triassic age, and strongly validates the longer Newark-Hartford Astrochronostratigraphic-calibrated magnetic Polarity Time-Scale (APTS) based on cores recovered in the 1990s during the Newark Basin Coring Project (NBCP).Core recovery was  ∼ 100&thinsp;% in all holes (Table 1). The coreholes were inclined  ∼ 60–75° approximately to the south to ensure azimuthal orientation in the nearly flat-lying bedding, critical to the interpretation of paleomagentic polarity stratigraphy. The two longest of the cores (CPCP-PFNP13-1A and 2B) were CT-scanned in their entirety at the University of Texas High Resolution X-ray CT Facility in Austin, TX, and subsequently along with 2A, all cores were split and processed at the CSDCO/LacCore Facility, in Minneapolis, MN, where they were scanned for physical property logs and imaging. While remaining the property of the Federal Government, the archive half of each core is curated at the NSF-sponsored LacCore Core Repository and the working half is stored at the Rutgers University Core Repository in Piscataway, NJ, where the initial sampling party was held in 2015 with several additional sampling events following. Additional planned study will recover the rest of the polarity stratigraphy of the cores as additional zircon ages, sedimentary structure and paleosol facies analysis, stable isotope geochemistry, and calibrated XRF core scanning are accomplished. Together with strategic outcrop studies in Petrified Forest National Park and environs, these cores will allow the vast amount of surface paleontological and paleoenvironmental information recorded in the continental Triassic of western North America to be confidently placed in a secure context along with important events such as the giant Manicouagan impact at  ∼ 215.5&thinsp;Ma (Ramezani et al., 2005) and long wavelength astronomical cycles pacing global environmental change and trends in atmospheric gas composition during the dawn of the dinosaurs.</p

Global Taxonomic Diversity of Anomodonts (Tetrapoda, Therapsida) and the Terrestrial Rock Record Across the Permian-Triassic Boundary

The end-Permian biotic crisis (∼252.5 Ma) represents the most severe extinction event in Earth's history. This paper investigates diversity patterns in Anomodontia, an extinct group of therapsid synapsids (‘mammal-like reptiles’), through time and in particular across this event. As herbivores and the dominant terrestrial tetrapods of their time, anomodonts play a central role in assessing the impact of the end-Permian extinction on terrestrial ecosystems. Taxonomic diversity analysis reveals that anomodonts experienced three distinct phases of diversification interrupted by the same number of extinctions, i.e. an end-Guadalupian, an end-Permian, and a mid-Triassic extinction. A positive correlation between the number of taxa and the number of formations per time interval shows that anomodont diversity is biased by the Permian-Triassic terrestrial rock record. Normalized diversity curves indicate that anomodont richness continuously declines from the Middle Permian to the Late Triassic, but also reveals all three extinction events. Taxonomic rates (origination and extinction) indicate that the end-Guadalupian and end-Permian extinctions were driven by increased rates of extinction as well as low origination rates. However, this pattern is not evident at the final decline of anomodont diversity during the Middle Triassic. Therefore, it remains unclear whether the Middle Triassic extinction represents a gradual or abrupt event that is unique to anomodonts or more common among terrestrial tetrapods. The end-Permian extinction represents the most distinct event in terms of decline in anomodont richness and turnover rates

The Sail-Backed Reptile Ctenosauriscus from the Latest Early Triassic of Germany and the Timing and Biogeography of the Early Archosaur Radiation

Background Archosaurs (birds, crocodilians and their extinct relatives including dinosaurs) dominated Mesozoic continental ecosystems from the Late Triassic onwards, and still form a major component of modern ecosystems (>10,000 species). The earliest diverse archosaur faunal assemblages are known from the Middle Triassic (c. 244 Ma), implying that the archosaur radiation began in the Early Triassic (252.3–247.2 Ma). Understanding of this radiation is currently limited by the poor early fossil record of the group in terms of skeletal remains. Methodology/Principal Findings We redescribe the anatomy and stratigraphic position of the type specimen of Ctenosauriscus koeneni (Huene), a sail-backed reptile from the Early Triassic (late Olenekian) Solling Formation of northern Germany that potentially represents the oldest known archosaur. We critically discuss previous biomechanical work on the ‘sail’ of Ctenosauriscus, which is formed by a series of elongated neural spines. In addition, we describe Ctenosauriscus-like postcranial material from the earliest Middle Triassic (early Anisian) Röt Formation of Waldhaus, southwestern Germany. Finally, we review the spatial and temporal distribution of the earliest archosaur fossils and their implications for understanding the dynamics of the archosaur radiation. Conclusions/Significance Comprehensive numerical phylogenetic analyses demonstrate that both Ctenosauriscus and the Waldhaus taxon are members of a monophyletic grouping of poposauroid archosaurs, Ctenosauriscidae, characterised by greatly elongated neural spines in the posterior cervical to anterior caudal vertebrae. The earliest archosaurs, including Ctenosauriscus, appear in the body fossil record just prior to the Olenekian/Anisian boundary (c. 248 Ma), less than 5 million years after the Permian–Triassic mass extinction. These earliest archosaur assemblages are dominated by ctenosauriscids, which were broadly distributed across northern Pangea and which appear to have been the first global radiation of archosaurs