Magnitude Of Fractionation Research Articles

Application of selenium isotopes to define selenium bioreduction in coal waste rock: Elk Valley, British Columbia

Anthropogenic sources of selenium (Se), including coal mining, can release Se to the environment and raise Se concentrations in receiving waters above drinking water and aquatic limits. Selenium bioreduction can be an important control to reduce dissolved selenate concentrations. This extensive study investigated the application of Se stable isotope ratios (δ82Se) of dissolved selenate to identify Se bioreduction in saturated and unsaturated mine rock piles (MRPs) located in the Elk Valley, Canada. The study included in situ and laboratory column experiments, where methanol was added to promote bioreduction. Results showed that selenate concentrations often are not reliable indicators of bioreduction. However, elevation of δ82Se relative to the selenate sources in all environments provided a robust indicator of widespread selenate bioreduction. Native microbes were shown to use both methanol and natural carbon sources as an electron donor for selenate bioreduction. Variability in the magnitude of apparent isotopic fractionation in column experiments was attributed to physical and microbiological heterogeneity, while variability in apparent isotopic fractionation from in situ experiments was attributed to the entrainment of small masses of background selenate into the experiment. Due to the uncertainty in apparent epsilon values, the extent of bioreduction can only be estimated with limited confidence. Despite uncertainties, however, the application of δ82Se is valuable in guiding the management of Se in mine environments.

Simulation of Somatic Evolution Through the Introduction of Random Mutation to the Rules of Conway’s Game of Life

Abstract Introduction Conway’s Game of Life (GOL), and related cellular automata (CA) models, have served as interesting simulations of complex behaviors resulting from simple rules of interactions between neighboring cells, that sometime resemble the growth and reproduction of living things. Thus, CA has been applied towards understanding the interaction and reproduction of single-cell organisms, and the growth of larger, disorganized tissues such as tumors. Surprisingly, however, there have been few attempts to adapt simple CA models to recreate the evolution of either new species, or subclones within a multicellular, tumor-like tissue. Methods In this article, I present a modified form of the classic Conway’s GOL simulation, in which the three integer thresholds that define GOL (number of neighboring cells, below which a cell will “die of loneliness”; number of neighboring cells, above which a cell will die of overcrowding; and number of neighboring cells that will result in spontaneous birth of a new cell within an empty lattice location) are occasionally altered with a randomized mutation of fractional magnitude during new “cell birth” events. Newly born cells “inherit” the current mutation state of a neighboring parent cell, and over the course of 10,000 generations these mutations tend to accumulate until they impact the behaviors of individual cells, causing them to transition from the sparse, small patterns of live cells characteristic of GOL into a more dense, unregulated growth resembling a connected tumor tissue. Results The mutation rate and mutation magnitude were systematically varied in repeated randomized simulation runs, and it was determined that the most important mutated rule for the transition to unregulated, tumor-like growth was the overcrowding threshold, with the spontaneous birth and loneliness thresholds being of secondary importance. Spatial maps of the different “subclones” of cells that spontaneously develop during a typical simulation trial reveal that cells with greater fitness will overgrow the lattice and proliferate while the less fit, “wildtype” GOL cells die out and are replaced with mutant cells. Conclusions This simple modeling approach can be easily modified to add complexity and more realistic biological details, and may yield new understanding of cancer and somatic evolution.

Isotopic Fractionation during Sublimation of Low Porosity Ice

The magnitude of isotopic fractionation during sublimation of ice remains poorly constrained. Field and laboratory studies that span decades have persistently shown conflicting results. A better understanding of fractionation during sublimation is needed to improve interpretation of alpine hydrology, glaciology, paleoclimate and planetary histories that rely on stable isotopic records stored in icy reservoirs. At the core of the problem is the question of whether sublimation occurs as a layer-by-layer process with no fractionation or whether diffusion within the ice and vapor-ice exchange generate fractionation. We present results from an experiment where we suspended ice spheres in temperatures ranging from -25 to -10 °C in an unsaturated atmosphere and used aRayleigh distillation model to estimate fractionation of the spheres. A small, yet statistically significant and repeatable, isotope fractionation (103lnα18O of ∼ −0.6 ‰ and 103lnα2H between −3.0 and − 4.0 ‰ or α = 0.999, α = 0.9940 to 0.9970, respectively) was found during the sublimation of ice. The results indicate the presence of fractionation yet the values are an order of magnitude smaller than would be predicted for equilibrium fractionation at this temperature. By assuming a porosity for the ice of 0.0005 % - which is typical for ice frozen under these conditions, we estimate an increase in diffusivity relative to solid ice consistent with the observed fractionation values. The results help to reconcile how fractionation estimates during sublimation could vary between experimental and observational studies where porosity is not controlled for and can vary substantially across a continuum from porous firn layers to low porosity ice deep in glaciers.

Quantifying mass-dependent isotope fractionation and nuclear field shift effects for the light rare Earth elements in hydrous systems

The improving sensitivity of mass-spectrometers has opened the potential of using stable isotope signatures of the rare Earth elements (REE) as geochemical tracers. However, thus far only limited studies have utilised REE stable isotopes, despite resolvable variations having been observed in a range of systems. An interesting but poorly explored area remains variations in aqueous environments across a range of temperatures including seawater, marine sediments, ion adsorption deposits or hydrothermal systems. Furthermore, the magnitudes and competing effects of mass-dependent isotope fractionation and mass-independent nuclear field shift effects, which can be significant factor for heavy elements especially at high temperatures, remain poorly understood.To contribute to a holistic understanding of REE isotope signatures, we calculated reduced partition function ratios (as 103lnβ) for mass-dependent and nuclear field shift effects for aqueous La, Ce, and Nd complexes from first principles. Theoretical calculations were compared with experimental data, and this demonstrates that calculations involving a combination of two explicit hydration shells and additional implicit solvation effects are required to accurately describe the coordination and molecular vibrations of aqueous complexes. This data was then combined with speciation modelling of seawater and hydrothermal fluids to assess isotope fractionation in hydrous systems. The predicted magnitude of isotope fractionation is significant in low (T = 25 °C) temperature systems (Δ139/138LaMax-Min = 0.20 ‰, Δ142/140CeMax-Min = 0.33 ‰, Δ146/144NdMax-Min = 0.34 ‰) and remains above currently achievable analytical uncertainties even at high (T = 500 °C) temperatures (±0.015 ‰ for δ146/144Nd; ±0.040 ‰ for δ142/140Ce). Unless oxidation occurs, which is only relevant for Ce in terrestrial environments, nuclear field shift effects are negligible even at temperatures up to 500 °C. The large difference in nuclear charge radius between 140Ce and 142Ce strongly enriches the lighter Ce isotope in the higher oxidation state (103lnβCe(IV)-Ce(III) = −0.45 at 25 °C) which almost completely cancels out the opposing mass-dependent effect (103lnβCe(IV)-Ce(III) = +0.46 at 25 °C). This means that variations in δ142/140Ce isotope signatures cannot easily be related to oxidation in ancient or recent environments.

Investigation of Oxide Layer Development of X6CrNiNb18-10 Stainless Steel Exposed to High-Temperature Water.

The oxide layer development of X6CrNiNb18-10 (AISI 347) during exposure to high-temperature water has been investigated. Stainless steels are known to form a dual oxide layer in corrosive environments. The secondary Fe-rich oxide layer has no significant protective effect. In contrast, the primary Cr-rich oxide layer is known to reach a stabilized state, protecting the base metal from further oxidation. This study's purpose was to determine the development of oxide layer dimensions over exposure time using SEM, TEM and EDX line scans. While a parabolic development of Cr in the protective primary layer and Fe in the secondary layer was observed, the dimensions of the Ni layer remained constant. Ni required the presence of a pronounced Fe-rich secondary layer before being able to reside on the outer secondary layer. With increasing immersion time, the Ni element fraction surpassed the Cr element fraction in the secondary layer. Oxide growth on the secondary layer could be observed. After 480 h, nearly the entire surface was covered by the outer oxide layer. In the metal matrix, no depletion of Cr or Ni could be observed over time; however, an increased presence of Cr and Ni in the primary layer was found at the expense of Fe content. The Nb-stabilized stainless steel was subject to the formation of Niobium pentoxide (Nb2O5), with the quantity and magnitude of element fraction increasing over exposure time.

A holistic investigation of fraction learning: examining the hierarchy of fraction skills, misconceptions, mathematics anxiety and response confidence

ABSTRACT This study aimed to holistically investigate fraction knowledge by considering pupils’ fraction performance on various tasks (i.e. mapping, equivalence, comparison, and arithmetic) and in relation to whole number arithmetic, fraction misconceptions, mathematics anxiety, and confidence in responses. Northern Irish pupils (N = 123; 77 girls; M age = 11.1 years) demonstrated a strong understanding of fraction magnitudes with few pupils showcasing misconceptions across magnitude tasks. In contrast, fraction arithmetic knowledge, which was uniquely predicted by whole number arithmetic and fraction comparison, was still developing with many pupils incorrectly applying whole number strategies to arithmetic problems. Mathematics anxiety was low, but negatively correlated with performance, and confidence reports were more closely aligned with performance on whole number arithmetic compared to fraction tasks. Overall, researchers and educators need to consider not just fraction performance, but also foundational skills, the presence of misconceptions, and pupils’ feelings and beliefs to better understand fraction learning.

Experimental constraints on barium isotope fractionation during adsorption–desorption reactions: Implications for weathering and erosion tracer applications

Constraining the processes that fractionate barium isotopes is essential for utilising barium isotope ratios as environmental tracers. Barium concentration measurements from soils, rivers, and estuaries demonstrate that adsorption–desorption reactions significantly influence the distribution of fluid–mobile barium at the Earth’s surface, potentially driving isotopic fractionation. To quantify the direction and magnitude of isotopic fractionation resulting from these reactions, a riverine and an estuarine series of batch experiments were conducted using environmentally important adsorbent minerals and surface waters. Himalayan river sediment and water samples were used to validate the experimental results.Adsorption–desorption reactions were found to be rapid, relative to the average transit time of sediment and water in catchments, and largely reversible. The direction and magnitude of isotopic fractionation in the riverine experiment series were consistent with the riverine field samples (preferential adsorption of the lighter isotopes). The reaction rate, reversibility, and magnitude of isotopic fractionation were found to depend primarily on the mineral. Experiments performed with iron oxyhydroxides (goethite and ferrihydrite) resulted in a greater degree of fractionation compared to clay minerals (kaolinite and montmorillonite). Estuarine experiments, designed to simulate sediment passage through a salinity gradient, demonstrated a high degree of reversibility, with 77% to 94% of adsorbed barium desorbed upon the addition of seawater to freshwater-equilibrated clay minerals.The results of the estuarine experiments suggest that barium isotope ratios measured in marine paleo-archives (e.g., corals) will reflect both the adsorbed and dissolved freshwater barium inputs to the ocean. The combined findings of this study indicate that the chemical and isotopic behaviour of barium differs from more conventional group 1 and 2 metal isotope systems due to a significant proportion of barium released from bedrock dissolution partitioning to mineral surfaces, rapid reaction rates between fluid–mobile phases, and a high degree of reaction reversibility. Consequently, riverine barium isotope ratios are likely to provide unique insights into the complex array of terrestrial weathering and erosion processes that sustain life on Earth.

Exploration of melting heat transfer and entropy generation in a magnetized hybrid nanoliquid over an extending sheet of varying thickness

The analysis of melting heat transfer over an expansive sheet of variable thickness is of the utmost importance in various industrial and engineering sectors, such as injection molding of polymers and composites, cooling of nuclear reactors, hot rolling, etc. Thus, the current work examines the flow dynamics, melting heat transport, and entropy generation of a magneto-hybrid nanofluid over a stretching device with variable thickness in porous media. A water-based hybridized nanofluid is formed using copper (Cu) and aluminium oxide (Al2O3) nanoparticles in the presence of thermal radiation, viscous dissipation, and Joulean heating. The transport partial derivatives were transmuted to ordinary derivatives using appropriate similarity quantities. These equations were numerically solved through shooting techniques combined with the Runge–Kutta–Fehlberg (RKF) method. Diverse figures and tables are sketched to illustrate the outcomes of the various parameters involved in the study. The investigation reveals an enlargement in the heat-bounding surface with an escalation in the magnitude of volume fraction, melting heat transfer, and magnetic field terms. In contrast, the momentum-bounding surface depletes with these parameters. Furthermore, as thermal radiation and Eckert numbers rise, the thermal gradient increases. The entropy generation increases with higher Brikman number and porosity term, but the melting heat parameter causes a decline in the entropy profiles.

Cadmium Isotope Fractionation during Adsorption onto Edge Sites and Vacancies in Phyllomanganate.

Cadmium (Cd) geochemical behavior is strongly influenced by its adsorption onto natural phyllomanganates, which contain both layer edge sites and vacancies; however, Cd isotope fractionation mechanisms at these sites have not yet been addressed. In the present work, Cd isotope fractionation during adsorption onto hexagonal (containing both types of sites) and triclinic birnessite (almost only edge sites) was investigated using a combination of batch adsorption experiments, extended X-ray absorption fine structure (EXAFS) spectroscopy, surface complexation modeling, and density functional theory (DFT) calculations. Light Cd isotopes are preferentially enriched on solid surfaces, and the isotope fractionation induced by Cd2+ adsorption on edge sites (Δ114/110Cdedge-solution = -1.54 ± 0.11‰) is smaller than that on vacancies (Δ114/110Cdvacancy-solution = -0.71 ± 0.21‰), independent of surface coverage or pH. Both Cd K-edge EXAFS and DFT results indicate the formation of double corner-sharing complexes on layer edge sites and mainly triple cornering-sharing complexes on vacancies. The distortion of both complexes results in the negative isotope fractionation onto the solids, and the slightly longer first Cd-O distances and a smaller number of nearest Mn atoms around Cd at edge sites probably account for the larger fractionation magnitude compared to that of vacancies. These results provide deep insights into Cd isotope fractionation mechanisms during interactions with phyllomanganates.

Thin Au/Ag/Cu-Water Nanoliquid Film Flow Over a Porous Unsteady Stretchable Cylinder

Most of the previous works on the thin nanoliquid-film (NLF) flow on a stretchable horizontal cylinder are limited to the boundary-layer flow (BLF) of infinite depth liquid. In this article, we have removed the above restrictions to examine the unsteady thin NLF flow on a porous stretchable cylinder by considering full momentum equations under the influence of thermal radiation and suction/injection. The implicit finite difference technique is utilized to obtain the numerical solutions to the problem. The present numerical solution is validated with the analytical solution obtained by Maity et al.41 for the isothermal case. It is found that the film thickness for Au/water nanoliquid is higher in comparison with Ag/water and Cu/water nanoliquids, respectively. The film thickness of nanoliquid enhances for rising magnitude of nanoparticle volume fraction (φ), porosity parameter (β), and Hartmann number (Mn). The film thickness of the nanoliquid increases or decreases as injection or suction (V) takes place through the surface of the cylinder. Furthermore, the sign of temperature gradient θR changes inside the nanoliquid depending on the values of other parameters. The percentage of changes in the film height is presented with the different parameters of the flow problem.

How do people compare visualizations of fraction magnitudes? Evidence from adults’ and children’s eye movements with continuous and discretized tape diagrams

Adults and children are able to compare visually represented fractions. Past studies show that people are more efficient with continuous visualizations than with discretized ones, but the specific reasons are unclear. Presumably, continuous visualizations highlight magnitudes more directly, while discretized ones encourage less efficient strategies such as counting. In two experiments, adults and children compared the magnitudes of continuous and discretized tape diagrams of fractions. In both experiments, participants answered more accurately, faster, and with fewer eye saccades when the visualizations were continuous rather than discretized. Sequences of saccades indicated that participants used counting strategies less often with continuous than discretized diagrams. The results suggest that adults and children are more efficient with continuous than discretized visualizations because they use more efficient, magnitude-based strategies with continuous visualizations. The findings indicate that integrating continuous visualizations in classroom teaching more frequently could be beneficial for supporting students in developing fraction magnitude concepts.

In-silico research on the effects of variable voltage pulse protocols on the cell survival and permeabilization fractions in electroporated cancerous tissues

Reversible electroporation is used to increase the cell membrane permeability by the application of short duration, high voltage electric pulses with electrodes strategically positioned to induce localized drug concentration in the tumor tissue. However, inadequate selection of pulses’ characteristics can lead to relevant loss of cell viability or lack of cell permeabilization, affecting aversively the results of the therapy. Accordingly, the balance between cell membrane electro-permeabilization and cell death is crucial, and the recursive modification of electroporation parameters can favor this balance to increase the drug uptake into viable cells. Particularly, the controlled diminution of the voltage level as the number of pulses increases can reduce the cell damage without compromising the membrane electro-permeabilization. In this work, a previously developed in-silico tool, based on the Global Method of Approximate Particular Solutions (GMAPS), is calibrated, validated, and used to study the differences between constant voltage and variable voltage pulse protocols (CVP and VVP) in terms of the magnitude and distribution of cell survival and permeabilization fractions along the tissue domain, and the internalization efficiency of the therapy. In VVP protocols, the reduction of the applied voltage with the number of pulses is numerically estimated to reach a target volume-averaged survival fraction in the most sensitive zone of the tissue. Numerical results indicate that differences between the pulse protocol types (CVP and VVP) depend on the initial voltage level ∅0 and number of pulses K, with the VVP protocol bringing about superior results for the larger values of ∅0 and K considered here.

Antimony isotopic fractionation induced by Sb(V) adsorption on β-MnO2

Antimony (Sb) isotopes hold immense promise for unraveling Sb biogeochemical cycling in environmental systems. Mn oxides help control the fate of Sb via adsorption reactions, yet the behavior and mechanisms of Sb isotopic fractionation on Mn oxides are poorly understood. In this study, we examine the Sb isotopic fractionation induced by adsorption on β-MnO2 in different experiments (kinetic, isothermal, effect of pH). We observe that adsorption on β-MnO2 surfaces preferentially enriches lighter Sb isotopes through equilibrium fractionation, with Δ123Sbaqueous-adsorbed of 0.55–0.79 ‰. Neither the pH or surface coverage affects the fractionation magnitude. The analysis of extended X-ray absorption fine structure (EXAFS) demonstrates that the enrichment of light isotope results from the adsorption of inner-sphere complexation on solids. Our finding of this study enhances our comprehension of the impact of β-MnO2 on Sb isotopic fractionation behavior and mechanism and facilitate the applicability of Sb isotopes as effective tracers to elucidate the origins and pathways of Sb contamination in environmental systems, as well as provide a new insight into forecasting the isotopic fractionation of other similar metals adsorbed by manganese oxides.

A thermodynamically consistent phase transformation model for multiphase alloys: application to Ti6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_6$$\\end{document}Al4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_4$$\\end{document}V in laser powder bed fusion processes

Titan aluminium alloys belong to the group of α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}–β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-alloys, which are used for many applications in industry due to their advantageous mechanical properties, e.g. for laser powder bed fusion (PBF-LB) processes. However, the composition of the crystal structure and the respective magnitude of the solid fraction highly influences the material properties of titan aluminium alloys. Specifically, the thermal history, i.e. the cooling rate, determines the phase composition and microstructure for example during heat treatment and PBF-LB processes. For that reason, the present work introduces a phase transformation framework based, amongst others, on energy densities and thermodynamically consistent evolution equations, which is able to capture the different material compositions resulting from cooling and heating rates. The evolution of the underlying phases is governed by a specifically designed dissipation function, the coefficients of which are determined by a parameter identification process based on available continuous cooling temperature (CCT) diagrams. In order to calibrate the model and its preparation for further applications such as the simulation of additive manufacturing processes, these CCT diagrams are computationally reconstructed. In contrast to empirical formulations, the developed thermodynamically consistent and physically sound model can straightforwardly be extended to further phase fractions and different materials. With this formulation, it is possible to predict not only the microstructure evolution during processes with high temperature gradients, as occurring in e.g. PBF-LB processes, but also the evolving strains during and at the end of the process.

Energy flux couples sulfur isotope fractionation to proteomic and metabolite profiles in Desulfovibrio vulgaris.

Microbial sulfate reduction is central to the global carbon cycle and the redox evolution of Earth's surface. Tracking the activity of sulfate reducing microorganisms over space and time relies on a nuanced understanding of stable sulfur isotope fractionation in the context of the biochemical machinery of the metabolism. Here, we link the magnitude of stable sulfur isotopic fractionation to proteomic and metabolite profiles under different cellular energetic regimes. When energy availability is limited, cell-specific sulfate respiration rates and net sulfur isotope fractionation inversely covary. Beyond net S isotope fractionation values, we also quantified shifts in protein expression, abundances and isotopic composition of intracellular S metabolites, and lipid structures and lipid/water H isotope fractionation values. These coupled approaches reveal which protein abundances shift directly as a function of energy flux, those that vary minimally, and those that may vary independent of energy flux and likely do not contribute to shifts in S-isotope fractionation. By coupling the bulk S-isotope observations with quantitative proteomics, we provide novel constraints for metabolic isotope models. Together, these results lay the foundation for more predictive metabolic fractionation models, alongside interpretations of environmental sulfur and sulfate reducer lipid-H isotope data.

From integers to fractions: The role of analogy in transfer and long-term learning

Fractions are the gatekeepers to advanced mathematics but are difficult to learn. One powerful learning mechanism is analogy, which builds fraction understanding on a pre-existing foundation of integer knowledge. Indeed, a short intervention that aligned fractions and integers on number lines improved children’s estimates of fractions (Yu et al., 2022). The breadth and durability of such gains, however, are unknown, and analogies to other sources (such as percentages) may be equally powerful. To investigate this issue, we randomly assigned 109 fourth and fifth graders to one of three experimental conditions with different analogical sources (integers, percentages, or fractions) or a control condition. During training, children in the experimental conditions solved pairs of aligned fraction number line problems and proportionally-equivalent problems expressed in integers, percentages, or fractions (e.g., 3/8 on a 0–1 number line aligned with 3 on a 0–8 number line). Children in the control group solved fraction number-line problems sequentially. At pretest and a two-week delayed posttest, children completed a broad fraction knowledge battery, including estimation, comparison, categorization, ordering, and arithmetic. Results showed that aligning integers and fractions on number lines facilitated better estimation of fractional magnitudes, and the training effect transferred to novel fraction problems after two weeks. Similar gains were not observed for analogies using percentages. These findings highlight the importance of building new mathematical knowledge through analogies to familiar, similar sources.

Fractionation of Methane Isotopologues during Preparation for Analysis from Ambient Air.

Preconcentration of methane (CH4) from air is a critical sampling step in the measurement of singly and doubly substituted isotopologue ratios. We demonstrate the potential for isotope fractionation during preconcentration onto and elution from the common trapping material HayeSep-D and investigate its significance in laser spectroscopy measurements. By altering the trapping temperature for adsorption, the flow direction of CH4 through the trap and the time at which CH4 is eluted during a desorption temperature ramp, we explain the mechanisms behind fractionation affecting δ13C(CH4) and δ2H(CH4). The results highlight that carbon isotope fractionation is driven by advection and diffusion, while hydrogen isotope fractionation is driven by the interaction of CH4 with the adsorbing material (tending to smaller isotopic effects at higher temperatures). We have compared the difference between the measured isotope ratio of sample gases (compressed whole air and a synthetic mixture of CH4 at ambient amount fraction in an N2 matrix) and their known isotopic composition. An open-system Rayleigh model is used to quantify the magnitude of isotopic fractionation affecting measured δ13C(CH4) and δ2H(CH4), which can be used to calculate the possible magnitude of isotopic fractionation given the recovery percentage. These results provide a quantitative understanding of isotopic fractionation during the sample preparation of CH4 from ambient air. The results also provide valuable insights applicable to other cryogenic preconcentration systems, such as those for measurements that probe the distribution of rarer isotopologues.

Cross-notation knowledge of rational numbers predicts fraction arithmetic.

Recent research showed that cross-notation magnitude knowledge of fractions and decimals was related to better performance in fraction arithmetic, but it remains unclear whether it made an independent contribution to fraction arithmetic longitudinally when other cognitive variables are considered. To examine the extent to which children's earlier knowledge of cross-notation magnitude predicted subsequent performance in fraction addition and subtraction as well as fraction multiplication and division longitudinally. Three hundred and fifty-four Chinese children (Mage = 112.1 months). During the first wave of assessment, a range of cognitive abilities of children were measured, including within-notation fraction and decimal magnitude comparisons, whole-number arithmetic fluency, non-verbal intelligence, attentive behaviours, counting recall, word-level reading, and phonological awareness. Twelve months later, the same children were assessed again with two tasks of fraction arithmetic: fraction addition and subtraction as well as fraction multiplication and division. Multiple linear regressions showed that within-notation fraction and decimal magnitude knowledge predicted fraction addition and subtraction longitudinally, after the effects of working memory, nonverbal intelligence, language skills, attentive behaviour, and whole-number arithmetic were controlled. Cross-notation magnitude knowledge made independent contributions to fraction addition and subtraction longitudinally beyond the influence of within-notation fraction and decimal magnitude knowledge and other covariates. However, within-notation fraction and decimal magnitude knowledge were not associated with fraction multiplication and division, whereas cross-notation magnitude knowledge remained a unique predictor. These findings suggest that it may be useful to incorporate cross-notation knowledge in the assessments of children's mathematics abilities and teaching.

Partitioning of highly siderophile elements between monosulfide solid solution and sulfide melt at high pressures

Base metal sulfides (Fe–Ni–Cu–S) are ubiquitous phases in mantle and subduction-related lithologies. Sulfides in the mantle often melt incongruently, which leads to the production of a Cu–Ni-rich sulfide melt and a solid residue called monosulfide solid solution (mss). Even though peridotite-hosted sulfides, which tend to be more Ni-rich, are likely completely molten at mantle potential temperatures, the same is not true for eclogite-hosted Ni-poor, Fe-rich sulfides. Because of this, solid crystalline mss may persist at higher pressures and equilibrate with co-existing sulfide melt along colder geotherms, like those associated with subduction zones. Because highly siderophile elements (HSE—Pt, Pd, Rh, Ru, Os, Ir, and Re) are known to fractionate as a result of mss/sulfide-melt equilibrium, the persistence of an mss/sulfide-melt assemblage to higher pressures may lead to the fractionation of these elements during the subduction process. In this contribution, we carried out an experimental investigation of the partitioning behavior of the HSE, as well as Cu and Ni, between mss and sulfide melt over a pressure and temperature range relevant to equilibration between Earth’s surface and transition zone depths (0.1 MPa to 14 GPa; 930–1530 ∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\circ }$$\\end{document}C), and variable Ni contents in sulfide. Results show that at higher pressures, the HSE are considerably less fractionated as a result of mss and sulfide melt equilibrium compared to lower pressure conditions. This is exemplified by a lowering of the Dimss/melt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{i}^\\mathrm{mss/melt}$$\\end{document} for the more compatible HSE (Ru, Os, Ir, Rh and Re) from around 10 at 0.1 MPa to just above or below unity at 14 GPa. Moreover, the higher the Ni content of the bulk sulfide assemblage, the larger the degree of change in the magnitude of HSE fractionation seen over the pressure range studied. The exchange coefficient (KDRu-Pt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K_D^{\ extrm{Ru}-\ extrm{Pt}}$$\\end{document}) between highly compatible HSE (Ru) and less compatible Pt illustrates a notable contrast. In the Ni-poor composition (E1), KDRu-Pt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K_D^{\ extrm{Ru}-\ extrm{Pt}}$$\\end{document} changes from 27 at 0.1 MPa to 6 at 14 GPa. In contrast, the Ni-rich composition exhibits a broader range, with KDRu-Pt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K_D^{\ extrm{Ru}-\ extrm{Pt}}$$\\end{document} ranging from 150 to 17 across the same pressure interval. Our results highlight key differences between experimental data obtained at lower and higher pressure, and how composition, namely the Ni content of sulfide, affects HSE partitioning behavior.

Unpacking the Connections Between Fractions and Algebra: The Importance of Fraction Schemes and Units Coordination

ABSTRACT Researchers from multiple disciplines have found that fractions and algebra knowledge are linked. One major strand of research has identified children’s units coordination structures as crucial for success with fractions and algebra via multiplicative reasoning, whereas a second strand of research points to magnitude knowledge as a central conceptual structure supporting fractions and algebra knowledge. In an online study with 59 eighth graders, we compared the associations of these two foundational factors with fractions and algebra knowledge by assessing students’ units coordination skills, magnitude knowledge, and several general cognitive skills alongside multiple aspects of fractions and algebra knowledge. In regression models controlling for math anxiety and general cognitive skills, units coordination and fraction schemes were better predictors of students’ algebra knowledge than were fraction magnitude or fraction arithmetic skills. We replicated findings from previous studies that showed units coordination and fraction schemes were closely related and showed for the first time that units coordination was significantly associated with fraction number line estimation and fraction arithmetic scores, even after accounting for general cognitive skills. We emphasize the need for interdisciplinary teams to continue investigating relations among these constructs to further our understanding and ultimately support student learning of fractions and algebra.