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

Geochemistry in the modern soil survey program

Elemental analysis has played an important role in the characterization of soils since inception of the soil survey in the US. Recent efforts in analysis of trace and major elements (geochemistry) have provided necessary data to soil survey users in a variety of areas. The first part of this paper provides a brief overview of elemental sources, forms, mobility, and bioavailability; critical aspects important to users of soil survey geochemical data for appropriate use and interpretations. Examples are provided based on data gathered as part of the US soil survey program. The second part addresses the organization of sample collection in soil survey and how soil surveys are ideally suited as a sampling strategy for soil geochemical studies. Geochemistry is functional in characterization of soil types, determining soil processes, ecological evaluation, or issues related to soil quality and health, such as evaluating suitability of soils for urban or agricultural land use. Applications of geochemistry are on-going across the US and are documented herein. This analytical direction of soil survey complements historic efforts of the National Cooperative Soil Survey Program and addresses the increasing need of soil survey users for data that assists in understanding the influence of human activities on soil properties

Comparative bone histology of two thalattosaurians (Diapsida: Thalattosauria): Askeptosaurus italicus from the Alpine Triassic (Middle Triassic) and a Thalattosauroidea indet. from the Carnian of Oregon (Late Triassic)

Here, we present the first bone histological and microanatomical study of thalattosaurians, an enigmatic group among Triassic marine reptiles. Two taxa of thalattosaurians, the askeptosauroid Askeptosaurus italicus and one as yet undescribed thalattosauroid, are examined. Both taxa have a rather different microanatomy, tissue type, and growth pattern. Askeptosaurus italicus from the late Anisian middle Besano Formation of the southern Alpine Triassic shows very compact tissue in vertebrae, rib, a gastralium, and femora, and all bones are without medullary cavities. The tissue shows moderate to low vascularization, dominated by highly organized and very coarse parallel-fibred bone, resembling interwoven tissue. Vascularization is dominated by simple longitudinal vascular canals, except for the larger femur of Askeptosaurus, where simple vascular canals dominate in a radial arrangement. Growth marks stratify the cortex of femora. The vertebrae and humeri from the undescribed thalattosauroid from the late Carnian of Oregon have primary and secondary cancellous bone, resulting in an overall low bone compactness. Two dorsal vertebral centra show dominantly secondary trabeculae, whereas a caudal vertebral centrum shows much primary trabecular bone, globuli ossei, and cartilage, indicating an earlier ontogenetic stage of the specimens or paedomorphosis. The humeri of the thalattosauroid show large, simple vascular canals that are dominantly radially oriented in a scaffold of woven and loosely organized parallel-fibred tissue. Few of the simple vascular canals are thinly but only incompletely lined by parallel-fibered tissue. In the Oregon material, changes in growth rate are only indicated by changes in vascular organization but no distinct growth marks were identified. The compact bone of Askeptosaurus is best comparable to some pachypleurosaurs, whereas its combination of tissue and vascularity is similar to eosauropterygians in general, except for the coarse nature of its parallel-fibred tissue. The cancellous bone of the Oregon thalattosauroid resembles what is documented in ichthyosaurs and plesiosaurs. However, in contrast to these its tissue does not consist of fibro-lamellar bone type. Tissue types of both thalattosaurian taxa indicate rather different growth rates and growth patterns, associated with different life history strategies. The microanatomy reflects different life styles that fit to the different environments in which they had been found (intraplatform basin vs. open marine). Both thalattosaurian taxa differ from each other but in sum also from all other marine reptile taxa studied so far. Thalattosaurian bone histology documents once more that bone histology provides for certain groups (i.e., Triassic Diapsida) only a poor phylogenetic signal and is more influenced by exogenous factors. Differences in lifestyle, life history traits, and growth rate and pattern enabled all these Triassic marine reptiles to live contemporaneously in the same habitat managing to avoid substantial competition

Crocodylian diversity peak and extinction in the late Cenozoic of the northern Neotropics

Northern South America and South East Asia are today’s hotspots of crocodylian diversity with up to six (mainly alligatorid) and four (mainly crocodylid) living species respectively, of which usually no more than two or three occur sympatrically. In contrast, during the late Miocene, 14 species existed in South America. Here we show a diversity peak in sympatric occurrence of at least seven species, based on detailed stratigraphic sequence sampling and correlation, involving four geological formations from the middle Miocene to the Pliocene, and on the discovery of two new species and a new occurrence. This degree of crocodylian sympatry is unique in the world and shows that at least several members of Alligatoroidea and Gavialoidea coexisted. By the Pliocene, all these species became extinct, and their extinction was probably related to hydrographic changes linked to the Andean uplift. The extant fauna is first recorded with the oldest Crocodylus species from South America.Facultad de Ciencias Naturales y Muse

Structure and relaxations in liquid and amorphous Selenium

We report a molecular dynamics simulation of selenium, described by a three-body interaction. The temperatures T_g and T_c and the structural properties are in agreement with experiment. The mean nearest neighbor coordination number is 2.1. A small pre-peak at about 1 AA^-1 can be explained in terms of void correlations. In the intermediate self-scattering function, i.e. the density fluctuation correlation, classical behavior, alpha- and beta-regimes, is found. We also observe the plateau in the beta-regime below T_g. In a second step, we investigated the heterogeneous and/or homogeneous behavior of the relaxations. At both short and long times the relaxations are homogeneous (or weakly heterogeneous). In the intermediate time scale, lowering the temperature increases the heterogeneity. We connect these different domains to the vibrational (ballistic), beta- and alpha-regimes. We have also shown that the increase in heterogeneity can be understood in terms of relaxations

The extinct marine megafauna of the Phanerozoic

The modern marine megafauna is known to play important ecological roles and includes many charismatic species that have drawn the attention of both the scientific community and the public. However, the extinct marine megafauna has never been assessed as a whole, nor has it been defined in deep time. Here, we review the literature to define and list the species that constitute the extinct marine megafauna, and to explore biological and ecological patterns throughout the Phanerozoic. We propose a size cut-off of 1 m of length to define the extinct marine megafauna. Based on this definition, we list 706 taxa belonging to eight main groups. We found that the extinct marine megafauna was conspicuous over the Phanerozoic and ubiquitous across all geological eras and periods, with the Mesozoic, especially the Cretaceous, having the greatest number of taxa. Marine reptiles include the largest size recorded (21 m; Shonisaurus sikanniensis) and contain the highest number of extinct marine megafaunal taxa. This contrasts with today’s assemblage, where marine animals achieve sizes of >30 m. The extinct marine megafaunal taxa were found to be well-represented in the Paleobiology Database, but not better sampled than their smaller counterparts. Among the extinct marine megafauna, there appears to be an overall increase in body size through time. Most extinct megafaunal taxa were inferred to be macropredators preferentially living in coastal environments. Across the Phanerozoic, megafaunal species had similar extinction risks as smaller species, in stark contrast to modern oceans where the large species are most affected by human perturbations. Our work represents a first step towards a better understanding of the marine megafauna that lived in the geological past. However, more work is required to expand our list of taxa and their traits so that we can obtain a more complete picture of their ecology and evolution

First Evidence of Dinosaurian Secondary Cartilage in the Post-Hatching Skull of Hypacrosaurus stebingeri (Dinosauria, Ornithischia)

Bone and calcified cartilage can be fossilized and preserved for hundreds of millions of years. While primary cartilage is fairly well studied in extant and fossilized organisms, nothing is known about secondary cartilage in fossils. In extant birds, secondary cartilage arises after bone formation during embryonic life at articulations, sutures and muscular attachments in order to accommodate mechanical stress. Considering the phylogenetic inclusion of birds within the Dinosauria, we hypothesized a dinosaurian origin for this “avian” tissue. Therefore, histological thin sectioning was used to investigate secondary chondrogenesis in disarticulated craniofacial elements of several post-hatching specimens of the non-avian dinosaur Hypacrosaurus stebingeri (Ornithischia, Lambeosaurinae). Secondary cartilage was found on three membrane bones directly involved with masticatory function: (1) as nodules on the dorso-caudal face of a surangular; and (2) on the bucco-caudal face of a maxilla; and (3) between teeth as islets in the alveolar processes of a dentary. Secondary chondrogenesis at these sites is consistent with the locations of secondary cartilage in extant birds and with the induction of the cartilage by different mechanical factors - stress generated by the articulation of the quadrate, stress of a ligamentous or muscular insertion, and stress of tooth formation. Thus, our study reveals the first evidence of “avian” secondary cartilage in a non-avian dinosaur. It pushes the origin of this “avian” tissue deep into dinosaurian ancestry, suggesting the creation of the more appropriate term “dinosaurian” secondary cartilage

Modified Laminar Bone in Ampelosaurus atacis and Other Titanosaurs (Sauropoda): Implications for Life History and Physiology

BACKGROUND: Long bone histology of the most derived Sauropoda, the Titanosauria suggests that titanosaurian long bone histology differs from the uniform bone histology of basal Sauropoda. Here we describe the long bone histology of the titanosaur Ampelosaurus atacis and compare it to that of basal neosauropods and other titanosaurs to clarify if a special titanosaur bone histology exists. METHODOLOGY/PRINCIPAL FINDINGS: Ampelosaurus retains the laminar vascular organization of basal Sauropoda, but throughout most of cortical growth, the scaffolding of the fibrolamellar bone, which usually is laid down as matrix of woven bone, is laid down as parallel-fibered or lamellar bone matrix instead. The remodeling process by secondary osteons is very extensive and overruns the periosteal bone deposition before skeletal maturity is reached. Thus, no EFS is identifiable. Compared to the atypical bone histology of Ampelosaurus, the large titanosaur Alamosaurus shows typical laminar fibrolamellar bone. The titanosaurs Phuwiangosaurus, Lirainosaurus, and Magyarosaurus, although differing in certain features, all show this same low amount or absence of woven bone from the scaffolding of the fibrolamellar bone, indicating a clear reduction in growth rate resulting in a higher bone tissue organization. To describe the peculiar primary cortical bone tissue of Phuwiangosaurus, Ampelosaurus, Lirainosaurus, and Magyarosaurus, we here introduce a new term, "modified laminar bone" (MLB). CONCLUSIONS/SIGNIFICANCE: Importantly, MLB is as yet not known from extant animals. At least in Lirainosaurus and Magyarosaurus the reduction of growth rate indicated by MLB is coupled with a drastic body size reduction and maybe also a reduction in metabolic rate, interpreted as a result of dwarfing on the European islands during the Late Cretaceous. Phuwiangosaurus and Ampelosaurus both show a similar reduction in growth rate but not in body size, possibly indicating also a reduced metabolic rate. The large titanosaur Alamosaurus, on the other hand, retained the plesiomorphic bone histology of basal neosauropods