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At least 1,369 records · Page 76

The Lithophile Element Budget of Earth’s Core

The relative composition of Earth’s core and mantle were set during core formation. By determining how elements partition between metal and silicate at high pressures and temperatures, measurements of the mantle composition and geophysical observations of the core can be used to understand the mechanisms by which Earth formed. Here we present the results of metal–silicate partitioning experiments for a range of nominally lithophile elements (Al, Ca, K, Mg, O, S, Si, Th, U) and S to 85 GPa and up to 5400 K. With our results and a compilation of literature data, we developed a parameterization for partitioning that accounts for compositional dependencies in both the metal and silicate phases. Using this parameterization in a range of planetary growth models, we find that, in general, lithophile element partitioning into the metallic phase is enhanced at high temperatures. The relative abundances of FeO, SiO2 and MgO in the mantle vary significantly between planetary growth models, and the mantle abundances of these elements can be used to provide important constraints on Earth’s accretion. To match Earth’s core mass and mantle composition, Earth’s building blocks must have been enriched in Fe and depleted in Si compared with CI chondrites. Finally, too little Mg, Si and O are partitioned into the core for precipitation of oxides to be a major source of energy for the geodynamo. In contrast, several ppb of U can be partitioned into the core at high temperatures, and this energy source must be accounted for in thermal evolution models.

dynamo↗

High Performance Computing Based Parallel HIearchical Modal Association Clustering (HPAR HMAC)

For many applications, clustering is a crucial step in order to gain insight into the makeup of a dataset. The best approach to a given problem often depends on a variety of factors, such as the size of the dataset, time restrictions, and soft clustering requirements. The HMAC algorithm seeks to combine the strengths of 2 particular clustering approaches: model-based and linkage-based clustering. One particular weakness of HMAC is its computational complexity. HMAC is not practical for mega-scale data clustering. For high-definition imagery, a user would have to wait months or years for a result; for a 16-megapixel image, the estimated runtime skyrockets to over a decade! To improve the execution time of HMAC, it is reasonable to consider an multi-core implementation that utilizes available system resources. An existing imple-mentation (Ray and Cheng 2014) divides the dataset into N partitions - one for each thread prior to executing the HMAC algorithm. This implementation benefits from 2 types of optimization: parallelization and divide-and-conquer. By running each partition in parallel, the program is able to accelerate computation by utilizing more system resources. Although the parallel implementation provides considerable improvement over the serial HMAC, it still suffers from poor computational complexity, O(N2). Once the maximum number of cores on a system is exhausted, the program exhibits slower behavior. We now consider a modification to HMAC that involves a recursive partitioning scheme. Our modification aims to exploit divide-and-conquer benefits seen by the parallel HMAC implementation. At each level in the recursion tree, partitions are divided into 2 sub-partitions until a threshold size is reached. When the partition can no longer be divided without falling below threshold size, the base HMAC algorithm is applied. This results in a significant speedup over the parallel HMAC.

Patlolla, Dilip R↗

An Element-Based Concurrent Partitioner for Unstructured Finite Element Meshes

A concurrent partitioner for partitioning unstructured finite element meshes on distributed memory architectures is developed. The partitioner uses an element-based partitioning strategy. Its main advantage over the more conventional node-based partitioning strategy is its modular programming approach to the development of parallel applications. The partitioner first partitions element centroids using a recursive inertial bisection algorithm. Elements and nodes then migrate according to the partitioned centroids, using a data request communication template for unpredictable incoming messages. Our scalable implementation is contrasted to a non-scalable implementation which is a straightforward parallelization of a sequential partitioner.

concurrent partitioner finite element meshes distr↗

The relationship between leaf area growth and biomass accumulation in Arabidopsis thaliana

Leaf area growth determines the light interception capacity of a crop and is often used as a surrogate for plant growth in high-throughput phenotyping systems. The relationship between leaf area growth and growth in terms of mass will depend on how carbon is partitioned among new leaf area, leaf mass, root mass, reproduction, and respiration. A model of leaf area growth in terms of photosynthetic rate and carbon partitioning to different plant organs was developed and tested with Arabidopsis thaliana L. Heynh. ecotype Columbia (Col-0) and a mutant line, gigantea-2 (gi-2), which develops very large rosettes. Data obtained from growth analysis and gas exchange measurements was used to train a genetic programming algorithm to parameterize and test the above model. The relationship between leaf area and plant biomass was found to be non-linear and variable depending on carbon partitioning. The model output was sensitive to the rate of photosynthesis but more sensitive to the amount of carbon partitioned to growing thicker leaves. The large rosette size of gi-2 relative to that of Col-0 resulted from relatively small differences in partitioning to new leaf area vs. leaf thickness.

carbon partitioning↗

Activity model for 36 elements in Fe-Ni-Si-S-C liquids with application to terrestrial planet accretion and mantle geochemistry: New data for Ru, Re, Pt, Os, Ti, Nb, and Ta

Understanding siderophile element partitioning between metal and silicate melts under diverse conditions can be used to place important constraints on the materials and conditions of planetary accretion and core formation, as well as post core formation processes. However, the effects of Si on the partitioning and activity coefficients for these elements are not well known, despite Si likely being one of the dominant light elements in Earth’s core. To address this gap in understanding, we have undertaken a systematic study of the highly siderophile elements Re, Pt, Os, and Ru, and the refractory lithophile elements Nb, Ta and Ti at 1600 °C and 1 GPa, to derive epsilon interaction parameters for these elements in FeSi metallic liquids. Positive epsilon interaction parameters were measured for Nb, Ta, Ti, Ru, Re, Pt, and Os, indicating that dissolved Si in Fe liquids causes a decrease in their metal/silicate partition coefficients (or ‘silicophobic’ behavior). Furthermore, ε$_{Re, Os, or Ru}^{Si}$ > ε$_{Re, Os, or Ru}^{S}$ which means Si causes a larger decrease in D(metal/silicate) than S, and the chalcophile behavior expected from some elements will be completely masked by the presence of Si in a metallic liquid. The new parameters are used to update an activity model that now includes 36 siderophile elements in Fe-Ni-Si-S-C liquids (27 trace elements considered here). Systematic assessment of these 27 elements shows which have the strongest affinity for Si, C, and S, and also how activity coefficients for these elements would vary during accretion and core formation in Earth, Mars, and Mercury of widely differing fO 2 and core compositional conditions. The activity model is combined with new partitioning expressions for Mo, W, Cr, Re Ru, Pt, and Os and applied to aspects of post core formation mantle geochemistry of Earth, Mars, and Mercury. Our updated expressions show that the BSE Mo/W ratio can easily be achieved with metal/silicate partitioning during growth of the Earth, whereas Re, Os and Ru become lower than and highly fractionated compared with BSE values during core formation and accretion, and thus nearly 99% of their BSE abundances are likely contributed by late accretion. Ru isotopes should be a very good indicator of the source material for the late accretion. The high Pt/Os and Re/Os developed in a deepening magma ocean during the growth of the Earth, indicates 186 Os and 187 Os isotopes could be coupled if this ancient material remained isolated and subsequently became entrained in mantle plumes and measured in surficial lavas. The extent to which this occurred will be limited by the low Os content of this ancient material, thus requiring mixing as a major component in plume sources. Martian mantle Hf/W ratio stays low during accretion and core formation modelling, suggesting that W isotope anomalies are more likely due to solid/liquid silicate fractionation than to core formation. Finally, Ti contents measured by MESSENGER at Mercury’s surface can be explained by segregation of either a metallic core (IW-6 to -8) or metallic core + sulfide (IW-4 to -7.5) followed by mantle melting.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Volatility Basis Set Distributions and Viscosity of Organic Aerosol Mixtures: Insights from Chemical Characterization Using Temperature-Programmed Desorption–Direct Analysis in Real-Time High-Resolution Mass Spectrometry

Quantitative assessment of gas-particle partitioning of individual components within complex atmospheric organic aerosols (OA) mixtures is critical for predicting and comprehending the formation and evolution of OA particles in the atmosphere. This investigation leverages previously documented data obtained through a temperature programmed desorption - direct analysis in real time – high resolution mass spectrometry (TPD-DART-HRMS) platform. This methodology facilitates the bottom-up construction of volatility basis set (VBS) distributions for constituents found in three biogenic secondary organic aerosol (SOA) mixtures produced through the ozonolysis of a-pinene, limonene, and ocimene. The apparent enthalpies (ΔH*, kJ mol -1 ) and saturated vapor mass concentrations (C T *, µg∙m -3 ) of individual SOA components, determined as a function of temperature (T, K), facilitated an assessment of changes in VBS distributions and gas-particle partitioning with respect to T and atmospheric total organic mass loadings (tOM, µg∙m -3 ). Further, the VBS distributions reveal distinct differences in volatilities among monomers, dimers, and trimers, enabling their categorization into separate volatility bins. At the ambient temperature of T = 298 K, only monomers efficiently partition between gas and particle phases across a broad range of atmospherically relevant total organic mass loadings (tOM) values of 1–100 µg∙m -3 . Partitioning of dimers and trimers becomes notable only at T > 360 K and T > 420 K, respectively. The viscosity of SOA mixtures is assessed using a bottom-up calculation approach, incorporating the input of elemental formulas, ΔH*, C T *, and particle-phase mass fractions of the SOA components. Through this approach, we are able to accurately estimate the variations in SOA viscosity that result from the evaporation of its components. These variations are, in turn, influenced by atmospherically relevant changes in tOM and T. Comparison of the calculated SOA viscosity and diffusivity values with literature reported experimental results shows close agreement, thereby validating the employed calculation approach. These findings underscore the significant potential for TPD-DART-HRMS measurements in enabling the untargeted analysis of organic molecules within OA mixtures. This approach facilitates quantitative assessment of their gas-particle partitioning and allows for the estimation of their viscosity and condensed-phase diffusion, thereby contributing valuable insights to atmospheric models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Engineering lipid structure for recognition of the liquid ordered membrane phase

The selective partitioning of lipid components in phase-separated membranes is essential for domain formation involved in cellular processes. Identifying and tracking the movement of lipids in cellular systems would be improved if we understood how to achieve selective affinity between fluorophore-labeled lipids and membrane assemblies. Furthermore, we investigated the structure and chemistry of membrane lipids to evaluate lipid designs that partition to the liquid ordered (L o ) phase. A range of fluorophores at the headgroup position and lengths of PEG spacer between the lipid backbone and fluorophore were examined. On a lipid body with saturated palmityl or palmitoyl tails, we found that although the lipid tails can direct selective partitioning to the L o phase through favorable packing interactions, headgroup hydrophobicity can override the partitioning behavior and direct the lipid to the disordered membrane phase (L d ). The PEG spacer can serve as a buffer to mute headgroup–membrane interactions and thus improve L o phase partitioning, but its effect is limited with strongly hydrophobic fluorophore headgroups. We present a series of lipid designs leading to the development of novel fluorescently labeled lipids with selective affinity for the L o phase.

59 BASIC BIOLOGICAL SCIENCES↗

Even-handed subsystem selection in projection-based embedding

Projection-based embedding offers a simple framework for embedding correlated wavefunction methods in density functional theory. Partitioning between the correlated wavefunction and density functional subsystems is performed in the space of localized molecular orbitals. However, during a large geometry change—such as a chemical reaction—the nature of these localized molecular orbitals, as well as their partitioning into the two subsystems, can change dramatically. This can lead to unphysical cusps and even discontinuities in the potential energy surface. In this work, we present an even-handed framework for localized orbital partitioning that ensures consistent subsystems across a set of molecular geometries. We illustrate this problem and the even-handed solution with a simple example of an S N 2 reaction. Applications to a nitrogen umbrella flip in a cobalt-based CO 2 reduction catalyst and to the binding of CO to Cu clusters are presented. In both cases, we find that even-handed partitioning enables chemically accurate embedding with modestly sized embedded regions for systems in which previous partitioning strategies are problematic.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

SU-E-J-71: Spatially Preserving Prior Knowledge-Based Treatment Planning

Purpose: Prior knowledge-based treatment planning is impeded by the use of a single dose volume histogram (DVH) curve. Critical spatial information is lost from collapsing the dose distribution into a histogram. Even similar patients possess geometric variations that becomes inaccessible in the form of a single DVH. We propose a simple prior knowledge-based planning scheme that extracts features from prior dose distribution while still preserving the spatial information. Methods: A prior patient plan is not used as a mere starting point for a new patient but rather stopping criteria are constructed. Each structure from the prior patient is partitioned into multiple shells. For instance, the PTV is partitioned into an inner, middle, and outer shell. Prior dose statistics are then extracted for each shell and translated into the appropriate Dmin and Dmax parameters for the new patient. Results: The partitioned dose information from a prior case has been applied onto 14 2-D prostate cases. Using prior case yielded final DVHs that was comparable to manual planning, even though the DVH for the prior case was different from the DVH for the 14 cases. Solely using a single DVH for the entire organ was also performed for comparison but showed a much poorer performance. Different ways of translating the prior dose statistics into parameters for the new patient was also tested. Conclusion: Prior knowledge-based treatment planning need to salvage the spatial information without transforming the patients on a voxel to voxel basis. An efficient balance between the anatomy and dose domain is gained through partitioning the organs into multiple shells. The use of prior knowledge not only serves as a starting point for a new case but the information extracted from the partitioned shells are also translated into stopping criteria for the optimization problem at hand.

60 APPLIED LIFE SCIENCES↗

Profiling the BLAST bioinformatics application for load balancing on high-performance computing clusters

Abstract Background The Basic Local Alignment Search Tool (BLAST) is a suite of commonly used algorithms for identifying matches between biological sequences. The user supplies a database file and query file of sequences for BLAST to find identical sequences between the two. The typical millions of database and query sequences make BLAST computationally challenging but also well suited for parallelization on high-performance computing clusters. The efficacy of parallelization depends on the data partitioning, where the optimal data partitioning relies on an accurate performance model. In previous studies, a BLAST job was sped up by 27 times by partitioning the database and query among thousands of processor nodes. However, the optimality of the partitioning method was not studied. Unlike BLAST performance models proposed in the literature that usually have problem size and hardware configuration as the only variables, the execution time of a BLAST job is a function of database size, query size, and hardware capability. In this work, the nucleotide BLAST application BLASTN was profiled using three methods: shell-level profiling with the Unix “time” command, code-level profiling with the built-in “profiler” module, and system-level profiling with the Unix “gprof” program. The runtimes were measured for six node types, using six different database files and 15 query files, on a heterogeneous HPC cluster with 500+ nodes. The empirical measurement data were fitted with quadratic functions to develop performance models that were used to guide the data parallelization for BLASTN jobs. Results Profiling results showed that BLASTN contains more than 34,500 different functions, but a single function, RunMTBySplitDB, takes 99.12% of the total runtime. Among its 53 child functions, five core functions were identified to make up 92.12% of the overall BLASTN runtime. Based on the performance models, static load balancing algorithms can be applied to the BLASTN input data to minimize the runtime of the longest job on an HPC cluster. Four test cases being run on homogeneous and heterogeneous clusters were tested. Experiment results showed that the runtime can be reduced by 81% on a homogeneous cluster and by 20% on a heterogeneous cluster by re-distributing the workload. Discussion Optimal data partitioning can improve BLASTN’s overall runtime 5.4-fold in comparison with dividing the database and query into the same number of fragments. The proposed methodology can be used in the other applications in the BLAST+ suite or any other application as long as source code is available.

59 BASIC BIOLOGICAL SCIENCES↗

An efficient approach for treating composition-dependent diffusion within organic particles

Mounting evidence demonstrates that under certain conditions the rate of component partitioning between the gas and particle phase in atmospheric organic aerosol is limited by particle-phase diffusion. To date, however, particle-phase diffusion has not been incorporated into regional atmospheric models. An analytical rather than numerical solution to diffusion through organic particulate matter is desirable because of its comparatively small computational expense in regional models. Current analytical models assume diffusion to be independent of composition and therefore use a constant diffusion coefficient. To realistically model diffusion, however, it should be composition-dependent (e.g. due to the partitioning of components that plasticise, vitrify or solidify). This study assesses the modelling capability of an analytical solution to diffusion corrected to account for composition dependence against a numerical solution. Results show reasonable agreement when the gas-phase saturation ratio of a partitioning component is constant and particle-phase diffusion limits partitioning rate (<10% discrepancy in estimated radius change). However, when the saturation ratio of the partitioning component varies, a generally applicable correction cannot be found, indicating that existing methodologies are incapable of deriving a general solution. Until such time as a general solution is found, caution should be given to sensitivity studies that assume constant diffusivity. Furthermore, the correction was implemented in the polydisperse, multi-process Model for Simulating Aerosol Interactions and Chemistry (MOSAIC) and is used to illustrate how the evolution of number size distribution may be accelerated by condensation of a plasticising component onto viscous organic particles.

54 ENVIRONMENTAL SCIENCES↗

NLR HPC Kestrel Jobs Data

Overview: Anonymized job-level records from the Kestrel HPC system at the National Laboratory of the Rockies (NLR). Each record represents a Slurm batch job with scheduling metadata, resource requests, utilization, energy estimates, and efficiency metrics. Sensitive fields (user, account, job name, submit line, working directory, submit script, and job type) are replaced with 7-character cryptographic hashes. System & Timeframe: Kestrel is located at the NLR campus. Standard compute nodes have 104 cores and 256 GB RAM; bigmem nodes have 2,000 GB. GPU nodes (gpu-h100 partition) use NVIDIA H100 GPUs. Data covers jobs submitted August 2023 through December 2025. Funding provided by the U.S. Department of Energy, EERE. Files: esif.hpc.kestrel.job-anon.zip — Anonymized job records (Hive-partitioned Parquet) datacard.md — Full dataset documentation ~11 million rows, 50 variables. Readable with PyArrow, pandas, DuckDB, Apache Spark, or any Parquet-compatible tool. Data Collection: Jobs collected via sacct with timezone-aware export (SLURM_TIME_FORMAT="%Y-%m-%dT%H:%M:%S%z"), loaded into PostgreSQL. Calculated columns updated via database triggers and batch functions. All timestamps use timestamptz and correctly handle DST transitions. Preprocessing: Anonymization of name, user, account, submit_line, work_dir, submit_script, and job_type via 7-char hex hashes Derived columns: queue_wait, cpu_eff, max/min/avg_mem_eff, energy estimates Simplified job state mapping (e.g., "CANCELLED by 132357" → "CANCELLED") Boolean flags: python_job, reframe_job Temporal decomposition: year, month, day, day_of_week, hour, minute from submit_time Shared node tracking: shared_job_count, nodes_shared, jobs_shared Key Variables: Scheduling: job_id, partition, state_simple, submit_time, start_time, end_time, queue_wait Resources: nodes_req/used, processors_req/used, memory_req, wallclock_req/used, gpus_requested Efficiency: cpu_eff, max/min/avg_mem_eff Energy: cpu_energy_tdp_estimated_max/used_watt_hours, consumed_energy_raw_joules, consumed_energy_raw_watt_hours Sharing: shared_job_count, nodes_shared, jobs_shared Partitions: short, standard, debug, gpu-h100 Job States: CANCELLED, COMPLETED, FAILED, PENDING, RUNNING QoS Levels: normal, high Important Notes: Timestamps include timezone offsets; DST transitions are handled correctly, though adding intervals across DST boundaries requires offset adjustment shared_job_count reflects physical node co-residency, not use of the shared partition Job step records and raw Slurm JSONB fields are excluded Do not attempt to re-identify individuals from hashed fields

97 MATHEMATICS AND COMPUTING↗

Extraction and classification of objects in multispectral images

Presented here is an algorithm that partitions a digitized multispectral image into parts that correspond to objects in the scene being sensed. The algorithm partitions an image into successively smaller rectangles and produces a partition that tends to minimize a criterion function. Supervised and unsupervised classification techniques can be applied to partitioned images. This partition-then-classify approach is used to process images sensed from aircraft and the ERTS-1 satellite, and the method is shown to give relatively accurate results in classifying agricultural areas and extracting urban areas.

Robertson, T. V.↗

Alkali element depletion by core formation and vaporization on the early Earth

The depletion of Na, K, Rb, and Cs in the Earth's upper mantle and crust relative to their abundances in chondrites is a long standing problem in geochemistry. Here we consider two commonly invoked mechanisms, namely core formation, and vaporization, for producing the observed depletions. Our models predict that a significant percentage of the Earth's bulk alkali element inventory is in the core (30 percent for Na, 52 percent for K, 74 percent for Rb, and 92 percent for Cs). These predictions agree with independent estimates from nebular volatility trends and (for K) from terrestrial heat flow data. Our models also predict that vaporization and thermal escape during planetary accretion are unlikely to produce the observed alkali element depletion pattern. However, loss during the putative giant impact which formed the Moon cannot be ruled out. Experimental, observational, and theoretical tests of our predictions are also described. Alkali element partitioning into the Earth's core was modeled by assuming that alkali element partitioning during core formation on the aubrite parent body (APB) is analogous to that on the early Earth. The analogy is reasonable for three reasons. First, the enstatite meteorites are the only known meteorites with the same oxygen isotope systematics as the Earth-Moon system. Second, the large core size of the Earth and the V depletion in the mantle requires accretion from planetesimals as reduced as the enstatite chondrites. Third, experimental studies of K partitioning between silicate and metal plus sulfide show that more K goes into the metal plus sulfide at higher pressures than at one atmosphere pressure. Thus partitioning in the relatively low pressure natural laboratory of the APB is a good guide to alkali elemental partitioning during the growth of the Earth.

Lodders, K.↗

Algorithms for parallel flow solvers on message passing architectures

The purpose of this project has been to identify and test suitable technologies for implementation of fluid flow solvers -- possibly coupled with structures and heat equation solvers -- on MIMD parallel computers. In the course of this investigation much attention has been paid to efficient domain decomposition strategies for ADI-type algorithms. Multi-partitioning derives its efficiency from the assignment of several blocks of grid points to each processor in the parallel computer. A coarse-grain parallelism is obtained, and a near-perfect load balance results. In uni-partitioning every processor receives responsibility for exactly one block of grid points instead of several. This necessitates fine-grain pipelined program execution in order to obtain a reasonable load balance. Although fine-grain parallelism is less desirable on many systems, especially high-latency networks of workstations, uni-partition methods are still in wide use in production codes for flow problems. Consequently, it remains important to achieve good efficiency with this technique that has essentially been superseded by multi-partitioning for parallel ADI-type algorithms. Another reason for the concentration on improving the performance of pipeline methods is their applicability in other types of flow solver kernels with stronger implied data dependence. Analytical expressions can be derived for the size of the dynamic load imbalance incurred in traditional pipelines. From these it can be determined what is the optimal first-processor retardation that leads to the shortest total completion time for the pipeline process. Theoretical predictions of pipeline performance with and without optimization match experimental observations on the iPSC/860 very well. Analysis of pipeline performance also highlights the effect of uncareful grid partitioning in flow solvers that employ pipeline algorithms. If grid blocks at boundaries are not at least as large in the wall-normal direction as those immediately adjacent to them, then the first processor in the pipeline will receive a computational load that is less than that of subsequent processors, magnifying the pipeline slowdown effect. Extra compensation is needed for grid boundary effects, even if all grid blocks are equally sized.

Vanderwijngaart, Rob F.↗

A Parallel Pipelined Renderer for the Time-Varying Volume Data

This paper presents a strategy for efficiently rendering time-varying volume data sets on a distributed-memory parallel computer. Time-varying volume data take large storage space and visualizing them requires reading large files continuously or periodically throughout the course of the visualization process. Instead of using all the processors to collectively render one volume at a time, a pipelined rendering process is formed by partitioning processors into groups to render multiple volumes concurrently. In this way, the overall rendering time may be greatly reduced because the pipelined rendering tasks are overlapped with the I/O required to load each volume into a group of processors; moreover, parallelization overhead may be reduced as a result of partitioning the processors. We modify an existing parallel volume renderer to exploit various levels of rendering parallelism and to study how the partitioning of processors may lead to optimal rendering performance. Two factors which are important to the overall execution time are re-source utilization efficiency and pipeline startup latency. The optimal partitioning configuration is the one that balances these two factors. Tests on Intel Paragon computers show that in general optimal partitionings do exist for a given rendering task and result in 40-50% saving in overall rendering time.

Chiueh, Tzi-Cker↗

Three-Dimensional High-Order Spectral Finite Volume Method for Unstructured Grids

Many areas require a very high-order accurate numerical solution of conservation laws for complex shapes. This paper deals with the extension to three dimensions of the Spectral Finite Volume (SV) method for unstructured grids, which was developed to solve such problems. We first summarize the limitations of traditional methods such as finite-difference, and finite-volume for both structured and unstructured grids. We then describe the basic formulation of the spectral finite volume method. What distinguishes the SV method from conventional high-order finite-volume methods for unstructured triangular or tetrahedral grids is the data reconstruction. Instead of using a large stencil of neighboring cells to perform a high-order reconstruction, the stencil is constructed by partitioning each grid cell, called a spectral volume (SV), into 'structured' sub-cells, called control volumes (CVs). One can show that if all the SV cells are partitioned into polygonal or polyhedral CV sub-cells in a geometrically similar manner, the reconstructions for all the SVs become universal, irrespective of their shapes, sizes, orientations, or locations. It follows that the reconstruction is reduced to a weighted sum of unknowns involving just a few simple adds and multiplies, and those weights are universal and can be pre-determined once for all. The method is thus very efficient, accurate, and yet geometrically flexible. The most critical part of the SV method is the partitioning of the SV into CVs. In this paper we present the partitioning of a tetrahedral SV into polyhedral CVs with one free parameter for polynomial reconstructions up to degree of precision five. (Note that the order of accuracy of the method is one order higher than the reconstruction degree of precision.) The free parameter will be determined by minimizing the Lebesgue constant of the reconstruction matrix or similar criteria to obtain optimized partitions. The details of an efficient, parallelizable code to solve three-dimensional problems for any order of accuracy are then presented. Important aspects of the data structure are discussed. Comparisons with the Discontinuous Galerkin (DG) method are made. Numerical examples for wave propagation problems are presented.

Liu, Yen↗

Evidence for Dry Carbonatite Metasomatism in the Oceanic Lithosphere from Peridotite Xenoliths of Samoa and Lanzarote

Water in Earth’s mantle affects processes like magmatism and plate tectonics. Experiments show that CO2-rich fluids lower the water solubility in olivine, implying that CO2-rich melts/fluids may dehydrate the lithosphere during metasomatism. To test this hypothesis, we report water concentrations (by polarized FTIR) of olivines, orthopyroxenes (OPX) and clinopyroxenes (CPX) from Savai’i (Samoa) and Lanzarote (Canary Islands) peridotite xenoliths with evidence of carbonatite metasomatism. Savai’i peridotites are highly depleted harzburgites and dunites with spinel Cr# (Cr/(Cr+Al)) ranging from 0.4 to 0.76 (estimated degree of melting: 191.5%). Strong Light Rare Earth Element (LREE) enrichments with Ti and Zr depletions in OPX and CO2-rich fluid inclusions (via Raman spectroscopy) are consistent with carbonatite metasomatism. Olivine, OPX and reconstructed bulk rock water concentrations (0.67-3.8, 17-89 and 4-26 ppm H2O, respectively) are low and show no apparent relationship with extent of carbonatite metasomatism. Calculated water concentrations of melts in equilibrium with Savai’i OPX (OPX/melt partitioning of water 0.0063 to 0.011) are, on average (0.540.32 wt% H2O), lower than host Samoan lavas (0.63 to 1.5 wt% H2O), despite the LREE enrichments in OPX. Lanzarote peridotites are also highly depleted (degree of melting from spinel Cr#: 171.8%).Water concentrations are low in olivines (1.7-5.3 ppm H2O) and variable in pyroxenes (OPX: 42-103 ppm H2O; CPX: 105-301 ppm H2O), and show no apparent correlation with indicators of carbonatite metasomatism. Both Savai’i and Lanzarote peridotites show negative correlations between water and degree of melting (i.e. Mg/(Mg+Fe), Cr#), suggesting melt depletion rather than metasomatism may have influenced their water concentrations. Calculated water concentrations of melts in equilibrium with Lanzarote CPX (average 1.90.75 wt% H2O; CPX/melt partitioning of water 0.011 to 0.012) are similar to those for Western Canaries lavas (average 1.80.31 wt%; CPX/melt partitioning of water 0.016 to 0.021) inferred from their CPX phenocrysts. However, calculated Ce concentrations in such melts (352 to 378 ppm; CPX/melt partitioning of Ce 0.07) are an order of magnitude greater than the lavas, and similar to carbonatites. This leads to H2O/Ce to be an order of magnitude lower in the inferred melts (26 to 57) than estimates for Western Canary lavas (280150). These low H2O/Ce ratios may suggest H2O loss from CPX during ascent, but the lack of strong water diffusion gradients in Lanzarote minerals does not support this. Instead we hypothesize that carbonatite metasomatism resulted in greater enrichment of Ce over H2O. Assuming carbonatite magmas are water rich, this implies a lower partitioning of water between minerals and melts during metasomatism, as suggested by experiments. Our data suggests carbonatite metasomatism does not result in significant re-hydration of the lithosphere, in contrast to silicate metasomatism as previously observed in Hawaiian peridotites.

Ashley, Aaron↗