A Nonstationary Space-Time Gaussian Process Model for Partially Converged Simulations

In the context of expensive numerical experiments, a promising solution for alleviating the computational costs consists of using partially converged simulations instead of exact solutions. The gain in computational time is at the price of precision in the response. This work addresses the issue of fitting a Gaussian process model to partially converged simulation data for further use in prediction. The main challenge consists of the adequate approximation of the error due to partial convergence, which is correlated in both design variables and time directions. Here, we propose fitting a Gaussian process in the joint space of design parameters and computational time. The model is constructed by building a nonstationary covariance kernel that reflects accurately the actual structure of the error. Practical solutions are proposed for solving parameter estimation issues associated with the proposed model. The method is applied to a computational fluid dynamics test case and shows significant improvement in prediction compared to a classical kriging model.

Petrogenesis of rift-related tephrites, phonolites and trachytes (Central European Volcanic Province, Rhon, FRG): Constraints from Sr, Nd, Pb and O isotopes

The volcanic rocks of the Rhön area (Central European Volcanic Province, Germany) belong to a moderately alkali basaltic suite that is associated with minor tephriphonolites, phonotephrites, tephrites, phonolites and trachytes. Based on isotope sytematics (87Sr/86Sr: 0.7033–0.7042; 143Nd/144Nd: 0.51279–0.51287; 206Pb/204Pb: 19.1–19.5), the inferred parental magmas formed by variable degrees of partial melting of a common asthenospheric mantle source (EAR: European Asthenospheric Reservoir of Cebriá and Wilson, 1995). Tephrites, tephriphonolites, phonotephrites, phonolites and trachytes show depletions and enrichments in some trace elements (Sr, Ba, Nb, Zr, Y) indicating that they were generated by broadly similar differentiation processes that were dominated by fractionation of olivine, clinopyroxene, amphibole, apatite and titaniferous magnetite ± plagioclase ± alkalifeldspar. The fractionated samples seem to have evolved by two distinct processes. One is characterized by pure fractional crystallization indicated by increasing Nb (and other incompatible trace element) concentrations at virtually constant 143Nd/144Nd ~ 0.51280 and 87Sr/86Sr ~ 0.7035. The other process involved an assimilation–fractional crystallization (AFC) process where moderate assimilation to crystallization rates produced evolved magmas characterized by higher Nb concentrations at slightly lower 143Nd/144Nd down to 0.51275. Literature data for some of the evolved rocks show more variable 87Sr/86Sr ranging from 0.7037 to 0.7089 at constant 143Nd/144Nd ~ 0.51280. These features may result from assimilation of upper crustal rocks by highly differentiated low-Sr (< 100 ppm Sr) lavas. However, based on the displacement of the differentiated rocks from this study towards lower 143Nd/144Nd ratios and modeled AFC processes in 143Nd/144Nd vs. 87Sr/86Sr and 207Pb/204Pb vs. 143Nd/144Nd space assimilation of lower crustal rocks seems more likely. The view that assimilation of lower crustal rocks played a role is confirmed by high-precision double-spike Pb isotope data that reveal higher 207Pb/204Pb ratios (15.62–15.63) in the differentiated rocks than in the primitive basanites (15.58–15.61). This is compatible with incorporation of radiogenic Pb from lower crustal xenoliths (207Pb/204Pb: 15.63–15.69) into the melt. However, 206Pb/204Pb ratios are similar for the differentiated rocks (19.13–19.35) and the primitive basanites (19.12–19.55) implying that assimilation involved an ancient crustal end member with a higher U/Pb ratio than the mantle source of the basanites. In addition, alteration-corrected δ18O values of the differentiated rocks range from c. 5 to 7‰ which is the same range as observed in the primitive alkaline rocks. This study confirms previous interpretations that highlighted the role of AFC processes in the evolution of alkaline volcanic rocks in the Rhön area of the Central European Volcanic Province.

Apoptosis of ligamentous cells of the cranial cruciate ligament from stable stifle joints of dogs with partial cranial cruciate ligament rupture

OBJECTIVE To describe the presence and amount of apoptotic ligamentous cells in different areas of partially ruptured canine cranial cruciate ligaments (prCCLs) and to compare these findings with apoptosis of ligamentous cells in totally ruptured cranial cruciate ligaments (trCCLs). ANIMALS 20 dogs with prCCLs and 14 dogs with trCCLs. PROCEDURES Dogs with prCCLs or trCCLs were admitted to the veterinary hospital for stifle joint treatment. Biopsy specimens of the intact area of prCCLs (group A) and the ruptured area of prCCLs (group B) as well as specimens from trCCLs (group C) were harvested during arthroscopy. Caspase-3 and poly (ADP-ribose) polymerase (PARP) detection were used to detect apoptotic ligamentous cells by immunohistochemistry. RESULTS No difference was found in the degree of synovitis or osteophytosis between prCCLs and trCCLs. No difference was found in degenerative changes in ligaments between groups A and B. A substantial amount of apoptotic cells could be found in > 90% of all stained slides. A correlation (r(s) = 0.71) was found between the number of caspase-3-and PARP-positive cells. No significant difference was found in the amount of apoptotic cells among the 3 groups. No significant correlation could be detected between the degree of synovitis and apoptotic cells or osteophyte production and apoptotic cells. CONCLUSIONS AND CLINICAL RELEVANCE The lack of difference between the 3 groups indicates that apoptosis could be a factor in the internal disease process leading to CCL rupture and is not primarily a consequence of the acute rupture of the ligament.

The Interplay between Melting, Refertilization and Carbonatite Metasomatism in Off-Cratonic Lithospheric Mantle under Zealandia: an Integrated Major, Trace and Platinum Group Element Study

It is widely accepted that stabilization of the continental crust requires the presence of sub-continental lithospheric mantle. However, the degree of melt depletion required to stabilize the lithosphere and whether widespread refertilization is a significant process remain unresolved. Here, major and trace element, including platinum group elements (PGE), characterization of 40 mantle xenoliths from 13 localities is used to constrain the melt depletion, refertilization and metasomatic history of lithospheric mantle underneath the micro-continent Zealandia. Our previously published Re–Os isotopic data for a subset of these xenoliths indicate Phanerozoic to Paleoproterozoic ages and, reinterpreted with the new major and trace element data presented here, demonstrate that a large volume (>2 million km3) of lithospheric mantle with an age of 1·99 ± 0·21 Ga is present below the much younger crust of Zealandia. A peritectic melting model using moderately incompatible trace elements (e.g. Yb) in bulk-rocks demonstrates that these peridotites experienced a significant range of degrees of partial melting, between 3 and 28%. During subsolidus equilibration clinopyroxene gains significant rare earth elements (REE), which then leads to the underestimation of the degree of partial melting by ≤12% in fertile xenoliths. A new approach taking into account the effects of subsolidus re-equilibration on clinopyroxene composition effectively removes discrepancies in the calculated degree of melting and provides consistent estimates of between 4 and 29%. The estimated amount of melting is independent of the Re–Os model ages of the samples. The PGE patterns record simple melt depletion histories and the retention of primary base metal sulfides in the majority of the xenoliths. A rapid decrease in Pt/IrN observed at c. 1·0 wt % Al2O3 is a direct result of the exhaustion of sulfide in the mantle residue at c. 20–25% partial melting and the inability of Pt to form a stable alloy phase. Major elements preserve evidence for refertilization by a basaltic component that resulted in the formation of secondary clinopyroxene and low-forsterite olivine. The majority of xenoliths show the effects of cryptic metasomatic overprinting, ranging from minor to strong light REE enrichments in bulk-rocks (La/YbN = 0·16–15·9). Metasomatism is heterogeneous, with samples varying from those with weak REE enrichment and notable positive Sr and U–Th anomalies and negative Nb–Ta anomalies in clinopyroxene to those that have extremely high concentrations of REE, Th–U and Nb. Chemical compositions are consistent with a carbonatitic component contributing to the metasomatism of the lithosphere under Zealandia. Notably, the intense metasomatism of the samples did not affect the PGE budget of the peridotites as this was controlled by residual sulfides.