A thermal-gradient approach to variable-temperature measurements resolved in space
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In a thin section, grains that were approximately spherical in situ appear circular in cross section, and the distribution of apparent diameters frequently assumed to be their size distribution. Scanning ion imaging by secondary ion mass spectrometry (SIMS) is capable of providing precise (< 1‰) stable isotope ratio measurements of such grains, but, importantly, also registers their rate of evolution in apparent size as they are ablated by the primary beam. By assessing rates of radius change with depth, the described methodology enables the ‘true’ size of grains to be estimated, as well as the distance of the sectioned surface from the original grain centre. Transects in three dimensions are made possible, and this capability enables better identification (and thus separation) of both inter‐grain chemical signatures as a function of grain size, and intra‐grain radial trends. In this example, we highlight the specific application to pyrite (FeS 2 ) minerals, which are frequently analysed by SIMS to determine their inter‐grain and intra‐grain geochemical variations, particularly in their sulfur stable isotopic ratios (δ 34 S). Benefits of the new methodology over the Faraday cup ‘spot mode’ are described. Data correction algorithms and precision considerations are discussed.
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Comparison of wind farm layout optimization results with simulations or wind tunnel tests is important because the models used during optimization use simplifying assumptions that can alter the design space. Some of the characteristics of the simple models may negatively influence the resulting layouts. In this paper we perform wind farm layout optimization and compare the resulting improvements to large eddy simulation (LES) results. We begin by describing the models used, including changes specific for use with gradient-based optimization. We then compare our version of the models with the original versions and large eddy simulation LES) data from previous publications. Using the models described, we performed gradient-based wind farm layout optimization, using exact gradients, and compare the results to LES simulations. The models predicted an improvement in annual energy production (AEP) of 7.4%, while the LES reported an AEP improvement of 9:9%. We conclude that the improvements found by optimizing with the simple models are not just an artifact of the models, but are real improvements.
Here we propose a class of novel fractional-order optimization algorithms. We define a fractional-order gradient via the Caputo fractional derivatives that generalizes integer-order gradient. We refer it to as the Caputo fractional-based gradient, and develop an efficient implementation to compute it. A general class of fractional-order optimization methods is then obtained by replacing integer-order gradients with the Caputo fractional-based gradients. To give concrete algorithms, we consider gradient descent (GD) and Adam, and extend them to the Caputo fractional GD (CfGD) and the Caputo fractional Adam (CfAdam). We demonstrate the superiority of CfGD and CfAdam on several large scale optimization problems that arise from scientific machine learning applications, such as ill-conditioned least squares problem on real-world data and the training of neural networks involving non-convex objective functions. Numerical examples show that both CfGD and CfAdam result in acceleration over GD and Adam, respectively. We also derive error bounds of CfGD for quadratic functions, which further indicate that CfGD could mitigate the dependence on the condition number in the rate of convergence and results in significant acceleration over GD.
ABSTRACT This is the second paper of the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) Dynamics and stellar Population (DynPop) series, which analyses the global stellar population, radial gradients, and non-parametric star-formation history of ∼10K galaxies from the MaNGA Survey final data release 17 and relates them with dynamical properties of galaxies. We confirm the correlation between the stellar population properties and the stellar velocity dispersion σe, but also find that younger galaxies are more metal-poor at fixed σe. Stellar age, metallicity, and mass-to-light ratio (M*/L) all decrease with increasing galaxy rotation, while their radial gradients become more negative (i.e. lower value at the outskirts). The exception is the slow rotators, which also appear to have significantly negative metallicity gradients, confirming the mass–metallicity gradient correlation. Massive disc galaxies in the green valley, on the $(\sigma _{\rm e},\rm age)$ plane, show the most negative age and metallicity gradients, consistent with their old central bulges surrounded by young star-forming discs and metal-poor gas accretion. Galaxies with high σe, steep total mass-density slope, low dark matter fraction, high M*/L, and high metallicity have the highest star-formation rate at earlier times, and are currently quenched. We also discover a population of low-mass star-forming galaxies with low rotation but physically distinct from the massive slow rotators. A catalogue of these stellar population properties is provided publicly.
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Non-structural carbohydrates (NSCs) are essential for maintenance of plant metabolism, and may be sensitive to both short- and long-term climatic variation. The NSC variation in NSCs in moist tropical forests has only rarely been studied, however, so regulation of NSCs in these systems is poorly understood. We measured foliar and branch NSC content in 23 tree species at three sites located across a large precipitation gradient in Panama during the 2015-2016 El Niño to examine how short- and long-term climatic variation impacts carbohydrate dynamics. Across all sites, leaf NSCs increased over diurnal time-periods. There was no significant difference in total NSCs over as the progression of the drought progressed (leaf p=0.32, branch p=0.30), nor across the rainfall gradient (leaf p=0.91, branch p=0.96). The Foliar soluble sugars decreased while starch increased :starch ratio did decrease over the duration of the dry period, suggesting greater partitioning of NSCs to storage than metabolism or transport as drought progressed. There was large variation across species at all sites, but total foliar NSCs were positively correlated with leaf mass per area, while branch sugars were positively related to leaf temperature and negatively correlated with daily photosynthesis and wood density. The NSC homeostasis across a wide range of conditions suggests that NSCs are an allocation priority in moist tropical forests.
The $O(3)$ non-linear sigma model (NLSM) is a prototypical field theory for QCD and ferromagnetism, featuring topological qualities. Though the topological susceptibility should vanish in physical theories, lattice simulations of the NLSM find that the topological susceptibility diverges in the continuum limit. We introduce a $\theta$-term and analyze the topological charge as a function of $\theta$ under the gradient flow. Our results show that divergence persists in the presence of the flow, even at non-zero $\theta$.
As an important Markov chain Monte Carlo (MCMC) method, the stochastic gradient Langevin dynamics (SGLD) algorithm has achieved great success in Bayesian learning and posterior sampling. Furthermore, SGLD typically suffers from a slow convergence rate due to its large variance caused by the stochastic gradient. In order to alleviate these drawbacks, we leverage the recently developed Laplacian smoothing technique and propose a Laplacian smoothing stochastic gradient Langevin dynamics (LS-SGLD) algorithm. We prove that for sampling from both log-concave and non-log-concave densities, LS-SGLD achieves strictly smaller discretization error in 2-Wasserstein distance, although its mixing rate can be slightly slower. Experiments on both synthetic and real datasets verify our theoretical results and demonstrate the superior performance of LS-SGLD on different machine learning tasks including posterior sampling, Bayesian logistic regression, and training Bayesian convolutional neural networks.
We report on a subpercent scale determination using the omega baryon mass and gradient-flow methods. The calculations are performed on 22 ensembles of 𝑁 𝑓 =2 +1 +1 highly improved, rooted staggered sea-quark configurations generated by the MILC and CalLat Collaborations. The valence quark action used is Möbius domain wall fermions solved on these configurations after a gradient-flow smearing is applied with a flowtime of 𝑡 gf = 1 in lattice units. The ensembles span four lattice spacings in the range 0.06 ≲ 𝑎 ≲0.15 fm, six pion masses in the range 130 ≲ 𝑚 𝜋 ≲ 400 MeV and multiple lattice volumes. On each ensemble, the gradient-flow scales 𝑡 0 /𝑎 2 and 𝑤 0 /𝑎 and the omega baryon mass 𝑎𝑚 Ω are computed. The dimensionless product of these quantities is then extrapolated to the continuum and infinite volume limits and interpolated to the physical light, strange and charm quark mass point in the isospin limit, resulting in the determination of $\sqrt{t}_0$ = 0.1422(14) fm and 𝑤 0 = 0.1709(11) fm with all sources of statistical and systematic uncertainty accounted for. The dominant uncertainty in both results is the stochastic uncertainty, though for $\sqrt{t}_0$ there are comparable continuum extrapolation uncertainties. For 𝑤 0 , there is a clear path for a few-per-mille uncertainty just through improved stochastic precision, as recently obtained by the Budapest-Marseille-Wuppertal Collaboration.
The high diversity of soil bacteria is attributed to the spatial complexity of soil systems, where habitat heterogeneity promotes niche partitioning among bacterial taxa. This premise remains challenging to test, however, as it requires quantifying the traits of closely related soil bacteria and relating these traits to bacterial abundances and geographic distributions. In this work, we sought to investigate whether the widespread soil taxon Curtobacterium consists of multiple coexisting ecotypes with differential geographic distributions. We isolated Curtobacterium strains from six sites along a climate gradient and assayed four functional traits that may contribute to niche partitioning in leaf litter, the top layer of soil. Our results revealed that cultured isolates separated into fine-scale genetic clusters that reflected distinct suites of phenotypic traits, denoting the existence of multiple ecotypes. We then quantified the distribution of Curtobacterium by analysing metagenomic data collected across the gradient over 18 months. Six abundant ecotypes were observed with differential abundances along the gradient, suggesting fine-scale niche partitioning. However, we could not clearly explain observed geographic distributions of ecotypes by relating their traits to environmental variables. Thus, while we can resolve soil bacterial ecotypes, the traits delineating their distinct niches in the environment remain unclear.
Tensor decomposition is a well-known tool for multiway data analysis. This work proposes using stochastic gradients for efficient generalized canonical polyadic (GCP) tensor decomposition of large-scale tensors. GCP tensor decomposition is a recently proposed version of tensor decomposition that allows for a variety of loss functions such as Bernoulli loss for binary data or Huber loss for robust estimation. Here, the stochastic gradient is formed from randomly sampled elements of the tensor and is efficient because it can be computed using the sparse matricized-tensor times Khatri--Rao product tensor kernel. For dense tensors, we simply use uniform sampling. For sparse tensors, we propose two types of stratified sampling that give precedence to sampling nonzeros. Numerical results demonstrate the advantages of the proposed approach and its scalability to large-scale problems.
Thin‐film solid‐state metal dealloying (thin‐film SSMD) is a promising method for fabricating nanostructures with controlled morphology and efficiency, offering advantages over conventional bulk materials processing methods for integration into practical applications. Although machine learning (ML) has facilitated the design of dealloying systems, the selection of key thermal treatment parameters for nanostructure formation remains largely unknown and dependent on experimental trial and error. To overcome this challenge, a workflow enabling high‐throughput characterization of thermal treatment parameters is demonstrated using a laser‐based thermal treatment to create temperature gradients on single thin‐film samples of Nb‐Al/Sc and Nb‐Al/Cu. This continuous thermal space enables observation of dealloying transitions and the resulting nanostructures of interest. Through synchrotron X‐ray multimodal and high‐throughput characterization, critical transitions and nanostructures can be rapidly captured and subsequently verified using electron microscopy. The key temperatures driving chemical reactions and morphological evolutions are clearly identified. While the oxidation may influence nanostructure formation during thin‐film treatment, the dealloying process at the dealloying front involves interactions solely between the dealloying elements, highlighting the availability and viability of the selected systems. Further, this approach enables efficient exploration of the dealloying process and validation of ML predictions, thereby accelerating the discovery of thin‐film SSMD systems with targeted nanostructures.
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Here, pulsed field gradient nuclear magnetic resonance (PFG-NMR) measurements were successfully applied to the 27 Al (I = 5/2) nucleus in concentrated electrolytes to investigate the diffusion of aluminate ions [Al(OH) 4 – ] in simulant high-level nuclear waste (3 M NaOH) between 25 and 85 °C. The temperature-dependent diffusion coefficients obtained from 1 H, 23 Na, and 27 Al PFG-NMR were well fit by a Vogel–Fulcher–Tammann model and a power law equation. Comparison of 27 Al diffusion coefficients of 0.1 M Al(OH) 4 – in ~3 M MOH (where M = Na + , K + , (CH 3 ) 4 N + ) at room temperature varied in agreement with the expected changes in solution viscosity via Stokes–Einstein relationship, confirming that the dominant Al species at these conditions are Al(OH) 4 – monomers. This 27 Al PFG-NMR study extends an established methodology to a previously unexplored nucleus enabling this experimental technique to be leverage for exploring ion transport, speciation, and solution structure in concentrated electrolytes.
Aim Intensified droughts are affecting tropical forests across the globe. However, the underlying mechanisms of tree drought response and mortality are poorly understood. Hydraulic traits and especially hydraulic safety margins (HSMs), i.e. the extent to which plants buffer themselves from thresholds of water stress, provide insights into species-specific drought vulnerability. Methods We investigated hydraulic traits during an intense drought triggered by the 2015-2016 El Niño on 27 canopy trees across three tropical forest sites with differing precipitation. We capitalized on the drought event as a time when plant water status might approach or exceed thresholds of water stress. We investigated the degree to which these traits varied across the rainfall gradient, as well as relationships amongst hydraulic traits and species-specific optimal moisture and mortality rates. Results There were no differences among sites for any measured trait. There was strong coordination among traits, with a network analysis revealing two major groups of coordinated traits. In one group there were water potentials, turgor loss point, sapwood capacitance and density, HSMs, and mortality rate. In the second group there was leaf mass per area, leaf dry matter content, hydraulic architecture (leaf area to sapwood area ratio), and species-specific optimal moisture. Conclusion These results demonstrated that while species with greater safety from turgor loss had lower mortality rates, hydraulic architecture was the only trait that explained species’ moisture dependency. Species with a greater leaf area to sapwood area ratio were associated with drier sites and reduced their transpirational demand during the dry season via deciduousness.