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Near-Real-Time Material Tracking: Combining Vis–NIR Spectroscopy with Flow Sensing for Accurate Nd(III) Quantification

A fiber-optic visible–near-infrared (vis–NIR) absorption spectroscopy and flow sensor system has been developed for near-real-time tracking of Nd mass in the effluent stream from a column in a fume hood. The approach leverages two unique data streams and a partial least-squares regression (PLSR) model trained on vis–NIR absorption spectra of Nd(III) (0–1.5 M) in 1 M HNO 3 . In-line volumetric flow rate and vis–NIR spectra are measured in sequence after a chromatography column. The time stamps from each data stream are then synchronized, which allows integrated volumes to be combined with Nd(III) molarities predicted by a PLSR model to accurately calculate the Nd mass flowing through the column. This integrated measurement provides instantaneous mass flow and accumulates these data over time to obtain the total mass processed. The methodology developed in this study contributes critical technical infrastructure to improve monitoring capabilities to support chemical separations and the production of strategic materials and isotopes.

Irvine, Sawyer B. [Oak Ridge National Laboratory (

Elastic constants in monocrystalline tungsten under quasi-hydrostatic pressures to 11.3 GPa

Compressional (P) and shear (S) wave velocities of tungsten single crystals along the [100] and [110] directions were measured using ultrasonic interferometry at room temperature up to 11.3 GPa. Least-squares fitting of $V$$^{[100]}_{P}$, $V$$^{[100]}_{S}$, $V$$^{[110]}_{P}$, and pressure to finite strain (FS) equations yields the elastic constants: C 11 = 523.5(5) GPa, C 12 = 205.1(32) GPa, and C 44 = 160.8(4) GPa, along with their respective pressure derivatives: $C$$^{′}_{11}$ = 6.20(2), $C$$^{′}_{12}$ = 3.35(1), and $C$$^{′}_{44}$ = 1.65(6). Using the Voigt–Reuss–Hill approximation, the elastic moduli were derived as K S0 = 311.2(22) GPa and G 0 = 160.2(7)GPa, along with their respective pressure derivatives: $K$$^{′}_{S0}$ = 4.30(4) and $G$$^{′}_{0}$ = 1.56(1). The Debye temperature of tungsten was determined to be 380.7(8) K, showing good agreement with previous calorimetric measurements. The elastic anisotropy increases slightly from 1.01(1) at ambient pressure to 1.03(1) at 11.3 GPa, suggesting that tungsten remains nearly isotropic under compression. Poisson's ratio slightly increased from 0.281(3) to 0.288(3) with pressure. Additionally, Pugh's ratio decreased from 0.512(4) to 0.494(4), while Pettifor's ratio increased from 0.148(10) to 0.175(10) as pressure reached 11.3 GPa. These results suggest that tungsten is weakly ductile compared to the critical thresholds for ductile behavior (i.e., Pugh's ratio <0.6 and Pettifor's ratio >0, indicating ductile behavior), but that its ductility increases marginally under pressure.

Wang, Ran [Stony Brook University, NY (United Stat

4D beam matrix reconstruction in particle accelerators

Transverse beam parameters in particle accelerators are commonly described using the Twiss parameters, which are experimentally accessible yet inherently limited because they neglect correlations between different transverse coordinates. Such correlations frequently arise from uncompensated cathode magnetic fields or misaligned focusing quadrupoles, affecting beam quality and accelerator performance. To address this limitation, we propose and validate a novel diagnostic method for the complete four-dimensional (4D) transverse beam matrix. Our method involves passing the beam through a beamline comprising both conventional and skew quadrupole magnets, followed by downstream measurements of the resulting two-dimensional (2D) beam profiles. These measurements represent distinct 2D projections of the underlying 4D transverse phase–space distribution. By systematically varying quadrupole strengths, multiple independent projections of the beam phase space are obtained. We reconstruct the original 4D beam matrix from these measured projections using an optimization-based least-square fit, providing fast and robust reconstruction regardless of the specific beamline configuration. Through extensive numerical simulations and realistic particle-tracking studies, we demonstrate the diagnostic’s accuracy, robustness, and capability to achieve reconstruction uncertainties smaller than measurement errors, particularly when employing sufficient numbers of quadrupole scans. This method presents a powerful and flexible approach for comprehensive beam characterization and accelerator tuning.

43 PARTICLE ACCELERATORS

A framework for discrete optimization of stellarator coils

Designing magnets for three-dimensional plasma confinement is a key task for advancing the stellarator as a fusion reactor concept. Stellarator magnets must produce an accurate field while leaving adequate room for other components and being reasonably simple to construct and assemble. In this paper, a framework for coil design and optimization is introduced that enables the attainment of sparse magnet solutions with arbitrary restrictions on where coils may be located. The solution space is formulated as a 'wireframe' consisting of a mesh of interconnected wire segments enclosing the plasma. Two methods are developed for optimizing the current distribution on a wireframe: Regularized Constrained Least Squares, which uses a linear least-squares approach to optimize the currents in each segment, and Greedy Stellarator Coil Optimization, a fully discrete procedure in which loops of current are added to the mesh one by one to achieve the desired magnetic field on the plasma boundary. Examples are presented of solutions obtainable with each method, some of which achieve high field accuracy while obeying spatial constraints that permit easy assembly.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Detector alignment for X-ray crystallography using Millepede-II

I describe a method for accurately refining the geometrical parameters of segmented X-ray area detectors on the basis of serial crystallography data, using 'Millepede' – an algorithm created for a very similar problem in high-energy physics. The Millepede method for serial crystallography builds on the approach of Brewster et al. [Acta Cryst. (2018), D74, 877–894], in which the detector parameters are refined simultaneously with the parameters for each individual crystal. This accounts for the mutual dependency between the parameters and thereby avoids the bias and slow convergence problems that have afflicted older approaches in which the deviations between observed and calculated Bragg peak positions were taken directly as the updates for the detector panel positions. The Millepede method uses the special structure of the least-squares normal equations to reduce them to a much smaller form that can be solved very quickly, even compared with the sparse matrix methods used previously. This makes it practical to refine the detector geometry frequently and thereby maintain accurate calibration without specialized alignment campaigns. Tilts of detector panels out of the plane can be reliably refined, as can the overall distance of the detector in the beam direction. With a simulated test case, the new method produced panel shifts within 7% of the correct values with only one iteration, and produced almost exactly correct shifts after a second iteration. A simulated out-of-plane panel rotation was correctly determined to within 0.001°. Applied to experimental data from an X-ray free-electron laser, the method increased the indexable fraction of frames from 30% to 91% in a single iteration, and to 96% after two further iterations. Computing the geometry updates on the basis of 2060 crystals took only 0.819 s on desktop computing hardware, including the time taken to read the required data from disk. The scaling was found to be very close to linear for up to 100 980 sets of crystal parameters, which took only 78.2 s to process under the same conditions. The method has been applied as part of a real-time feedback system at a synchrotron radiation beamline, in which an out-of-plane detector tilt of 0.04° was detected and corrected. Possible further applications are also described here.

Millepede-II

How Much Reserve Fuel: Quantifying the Maximal Energy Cost of System Disturbances

Motivated by the design question of additional fuel needed to complete a task in an uncertain environment, this paper introduces metrics to quantify the maximal additional energy used by a control system in the presence of bounded disturbances, compared to a nominal, disturbance-free system. In particular, we consider the task of finite-time stabilization for a linear, time-invariant system. We compare the nominal energy required to achieve this task in the disturbance-free system to the worst-case energy over all feasible disturbances. Solving for the worst-case energy over all disturbances first leads to an optimal control problem with a least-squares solution, and then an infinite-dimensional optimization problem where we derive an upper bound on the solution. The comparison of energies is accomplished using additive and multiplicative metrics, for which we derive bounds. Simulation examples on an ADMIRE fighter jet model demonstrate the practicability of these metrics, and their variation with the distance of the initial condition from the origin and the task completion time.

koopman operator, resilience

Two-Level Sketching Alternating Anderson Acceleration for Complex Physics Applications

We present a novel two-level sketching extension of the Alternating Anderson–Picard (AAP) method for accelerating fixed-point iterations in challenging single- and multiphysics simulations governed by discretized PDEs. Our approach combines a static, physics-based projection that reduces the least-squares (LS) problem to the most informative field (e.g., via Schur-complement insight) with a dynamic, algebraic sketching stage driven by a backward stability analysis under Lipschitz continuity. We introduce inexpensive estimators for stability thresholds and cache-aware randomized selection strategies to balance computational cost against memory access overhead. The resulting algorithm solves reduced LS systems in place, minimizes memory footprints, and seamlessly alternates between low-cost Picard updates and Anderson mixing. Implemented in Julia, our two-level sketching AAP achieves up to 50% time-to-solution reductions compared to standard Anderson acceleration—without degrading convergence rates—on benchmark problems including Stokes, 𝑝-Laplacian, bidomain, and Navier–Stokes formulations at varying problem sizes. These results demonstrate the method’s robustness, scalability, and potential for integration into high-performance scientific computing frameworks. Our implementation is available open source in the AAP.jl library.

Barnafi, Nicolas [University of Chile, Santiago]

Single-shot picosecond pump coherent Rayleigh scattering thermometry

A single-shot coherent Rayleigh scattering (CRS) technique capable of measurement times less than 10 ns is presented. Here, the use of a mode-locked picosecond pump laser yields repeatable electrostrictive forcing compared to previous CRS experiments using unseeded nanosecond pump pulses, which are beset by shot-to-shot variations. Quantitative measurements are achieved by dispersing the CRS signal onto an EMCCD sensor using a virtually imaged phased array and comparing the experimental spectra to an existing kinetic model with a least-squares fitting routine. Measurements are demonstrated at ambient and low-pressure (2 Torr), low-temperature (100 K) conditions where the CRS measurement is within the collisionless regime. Single-shot statistics indicated precision and accuracy within 4% at ambient conditions and within 8% at low density and temperature conditions. This single-shot CRS technique is a powerful diagnostic tool with potential for multi-parameter measurements in complex flow environments, including high-speed aerodynamic ground test facilities.

Senior, William Charles Bowman [Sandia National La

RegularizedOptimization.jl: A Julia framework for regularized and nonsmooth optimization

RegularizedOptimization.jl is a Julia package that implements families of quadratic regularization and trust-region methods for solving the nonsmooth optimization problem $^{\textrm{minimize}}_{𝑥∈ℝ^𝑛}$ 𝑓(𝑥) + ℎ(𝑥) subject to 𝑐(𝑥) = 0, (1) where 𝑓 ∶ ℝ 𝑛 → ℝ and 𝑐 ∶ ℝ 𝑛 → ℝ 𝑚 are continuously differentiable, and ℎ ∶ ℝ 𝑛 → ℝ∪{+∞} is lower semi-continuous. The nonsmooth objective ℎ can be a regularizer, such as a sparsity inducing penalty, model simple constraints, such as 𝑥 belonging to a simple convex set, or can be a combination of both. All 𝑓, ℎ, and 𝑐 can be nonconvex. RegularizedOptimization.jl provides a modular and extensible framework for solving (1), and developing novel solvers. Currently, the following solvers are implemented: • Trust-region solvers TR and TRDH (Aravkin et al., 2022; Leconte & Orban, 2025) • Quadratic regularization solvers R2, R2DH and R2N (Aravkin et al., 2022; Diouane, Habiboullah, et al., 2024) • Levenberg-Marquardt solvers LM and LMTR (Aravkin et al., 2024) used when 𝑓 is a least-squares residual. • Augmented Lagrangian solver AL (De Marchi et al., 2023). All solvers rely on first derivatives of 𝑓 and 𝑐, and optionally on their second derivatives in the form of Hessian-vector products. If second derivatives are not available, quasi-Newton approximations can be used. In addition, the proximal mapping of the nonsmooth part ℎ, or adequate models thereof, must be evaluated. At each iteration, a step is computed by solving a subproblem of the form (1) inexactly, in which 𝑓, ℎ, and 𝑐 are replaced with appropriate models around the current iterate. The solvers R2, R2DH, and TRDH are particularly well suited to solve the subproblems, though they are general enough to solve (1). All solvers are allocation-free, so re-solves incur no additional allocations. To illustrate our claim of extensibility, a first version of the AL solver was implemented by an external contributor. Furthermore, a nonsmooth penalty approach, described in Diouane, Gollier, et al. (2024), is currently being developed, that relies on the library to efficiently solve the subproblems.

Gollier, Maxence [Polytechnique Montréal, QC (Cana

Neutron Positioning and Geometric Distortion Correction on the SNS SiPM Anger Camera

Neutron Anger cameras are scintillator-based thermal neutron detectors that utilize pixelated photosensors to read out visible light signals and position neutrons accurately They are versatile detectors that can cover large areas for diffraction instruments and offer high efficiency and sub-millimeter spatial resolution. Photomultiplier Tube (PMT) based cameras are installed on three instruments at Spallation Neutron Source (SNS). The next generation camera uses Silicon Photomultipliers (SiPMs) instead of PMTs, which allows for a more compact design and higher spatial resolution. In this report, the Gaussian least-squares position fitting method is described in detail, as well as the method used to correct for geometric distortions across the face of the camera. Results from neutron camera tests before and after the distortion correction are shown and the spatial resolution is quantified.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND

Estimation of Fission Product Transport Parameters for Cesium in the AGR-3/4 TRISO Fuel Experiment

A one-dimensional (1D) finite-element model of fission product transport in the AGR-3/4 experiment has been developed using the Multiphysics Object Oriented Simulation Environment (MOOSE) framework and implemented in the fuel performance code, BISON. The model resolves capsule-specific geometries, materials, and temperature histories and simulates radial migration of fission products from the fuel compact through the inner ring, outer ring, and into the sink ring. Model parameters governing diffusion and sorption were estimated for key fission products – cesium (Cs), and europium (Eu) – by simultaneously fitting modeled isotopic concentration profiles and total ring inventories to a post-irradiation experimental measurement. These data include gamma scanning, liquid scintillation for Sr-90, radial deconsolidation leach-burn-leach analysis, tomographic reconstructions, and destructive physical sampling. A mortar-based interfacial sorption framework was implemented to enforce physically consistent mass transfer and flux conservation across gas gaps. Two classes of parameter sets were derived: a least-squares best-fit, and a safety-oriented conservative-fit, what applies strong penalties for underprediction of sink inventories. Across all twelve capsules, the model successfully reproduces the dominant radial transport trends for Cs, Sr, with decreasing concentrations from the compact outward through successive rings. Cs behavior is captured most consistently, while strontium predictions reveal systematic trade-offs between compact accuracy and conservative sink-ring bounding. The results demonstrate that sink ring weighted calibration provides conservative, safety relevant bounds on low temperature fission product transport, but at the cost of underpredicting compact inventories for Sr isotopes. These discrepancies highlight the need for additional physics, including fast-slow diffusion model, incorporating trapping mechanism in the transport behavior. Overall, this work establishes a robust, capsule-specific modeling framework for AGR-3/4 fission product transport and provides a defensible basis for parameter selection in source-term and fuel performance analyses for high temperature gas-cooled reactors.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Gearbox bearing crack growth prognostics and uncertainty quantification with physics-informed machine learning

This paper introduces the extreme theory of functional connections (X-TFC), a physics-informed machine learning algorithm, and tailors it to estimate the remaining useful life (RUL) of wind turbine gearbox bearings experiencing fatigue crack growth. Unlike purely data-driven methods, X-TFC embeds a physics model, based on Head's theory in this work, into its training objective. The core of X-TFC is a random-projection single-layer neural network trained via an extreme learning machine, which requires only limited damage progression data and solves for output weights with a least-squares optimization algorithm. A composite loss function balances the network's fit to observed degradation data against the residuals of the governing crack growth differential equation, ensuring the learned damage trajectory remains physically plausible. When applied to a vibration-based health-index (HI) dataset measured during the growth of a crack on the inner ring of a high-speed bearing in a wind turbine gearbox (Bechhoefer and Dubé, 2020), X-TFC achieves near-zero prediction bias. Even when trained on only the first 10 %–20 % of the damage progression data, with sufficient physics weighting its predictions remain monotonic and smooth, delivering high prognosability and trendability. To quantify the epistemic uncertainty, we employ a Monte Carlo ensemble of independently initialized X-TFC models trained on noise-perturbed data, which yields confidence intervals around each RUL estimate and captures both model-parameter and epistemic uncertainty. In addition to a vibration-based HI, we demonstrate that the proposed framework can be directly applied to a supervisory control and data acquisition (SCADA) data-based HI (Eftekhari Milani et al., 2026) measured during similar wind turbine gearbox bearing crack faults, preserving its accuracy and interpretability. This extension shows the versatility of our approach, which is applicable to bearings of multiple gearbox manufacturers, models, and ratings using only SCADA data. By integrating domain knowledge with machine learning, X-TFC offers a rapid, reliable tool for crack prognostics. Its adaptability to other bearing failure modes, such as pitch bearing ring cracks, positions X-TFC as a powerful enabler of data-driven, physics-informed asset management in the wind energy sector and beyond.

17 WIND ENERGY

Satellite material contaminant optical properties

The Air Force Wright Research and Development Center and the Arnold Engineering Development Center are continuing a program for measuring optical effects of satellite material outgassing products on cryo-optic surfaces. Presented here are infrared (4000 to 700 cm(-1)) transmittance data for contaminant films condensed on a 77 K geranium window. From the transmittance data, the contaminant film refractive and absorptive indices (n, k) were derived using an analytical thin-film interference model with a nonlinear least-squares algorithm. To date 19 materials have been studied with the optical contents determined for 13 of those. The materials include adhesives, paints, composites, films, and lubricants. This program is continuing and properties for other materials will be available in the future.

Wood, B. E.

Air-Broadened Line Shapes in the 2n3 R Branch of 12ch4 Between 6014 and 6100 cm-1

Complete and accurate information on line shape parameters of 2?3 methane transitions for air broadening as a function of temperature is critical not only for the correct interpretation of the observed atmospheric spectra but also for the development of a reliable theoretical model. For this reason, we obtained a series of high-resolution, high S/N spectra of high-purity 12CH4 and 12CH4 broadened with dry air at temperatures in the 130 to 295 K range using the Bruker IFS 125HR Fourier transform spectrometer at JPL. Two absorption cells were used in the experiment, a White cell with path length of 13 m for room temperature spectra and a 21 m Herriott cella for cold sample spectra. The 15 spectra used in the analysis consisted of 3 low pressure (0.26 to 2.57 Torr) spectra with pure 12CH4 and 12 air-broadened spectra with total sample pressures of 79-805 Torr and volume mixing ratios of methane between 0.23 and 1%. A multispectrum least-squares fitting techniqueb was employed to fit all 15 spectra simultaneously. Preliminary results for select R(J) manifolds will be presented.

V Malathy Devi

Searches for New Physics With Muon Conversion at Fermilab and Triboson Production at the LHC

We report on several efforts to search for physics beyond the standard model of particle physics at broad energy scales. The Mu2e experiment at Fermilab will search for charged lepton flavor violation via the muon to electron conversion process, which is suppressed in the Standard Model. Mu2e will be operated at a low energy, yet can probe New Physics at very high mass scales (O(1e3 - 1e4 ) TeV). At high energies, the CMS experiment at the CERN LHC continues to deliver an impressive suite of Standard Model measurements and limits on a variety of New Physics signatures. Mu2e is under construction and slated to collect its first physics data in the coming years. This thesis describes work done during the construction phase of Mu2e and focuses on two critical areas: magnetic field modeling and statistical analysis. We describe a novel method for field modeling which we validate using a simulated dataset representing the expected magnetic field in the Detector Solenoid. This method blends a standard least-squares fitting technique that utilizes physically motivated analytical model functions with a novel physics informed network that is constructed to obey Maxwell’s equations. We show the technique can model the field with an accuracy of 10−7 despite the presence of injected noise in the pseudo-measurements at the 10−5 level. We then present preliminary results of the calibration of 3D Hall probes at the sub-10−4 level. These probes will be used to directly measure the Mu2e Detector Solenoid magnetic field on a sparse grid; these measurements serve as the input to the field model fitting. Finally, we describe the first implementation of both an unbinned shape analysis and a Bayesian interpretation applied to Mu2e pseudo-data. Up to 20% tighter limits can be set by the shape analysis compared to a standard cut & count analysis. The AlCap experiment collected data at PSI in 2015 to measure several important quantities related to nuclear muon capture on an aluminum target, which is a significant background process for Mu2e. The neutron emission from muon capture can introduce background hits in the Mu2e detectors and can increase radiation damage in various elements of the apparatus. We present measurements of the neutron group fluence and mean neutron multiplicity for muon capture on aluminum nuclei. Finally, we discuss an analysis of triboson production at CMS using an Effective Field Theory framework. Standard Model triboson production, which was first observed at CMS in 2020, has a relatively small cross section and provides direct access to both anomalous triple gauge couplings and quartic gauge couplings. These couplings, interpreted in the Standard Model Effective Field Theory, are studied in the present work. We target the boosted regime where the background rate is low and yields are enhanced when dimension-6 and dimension-8 Wilson coefficients are non-zero. We do not observe an excess in the data and therefore set bounds on the Wilson coefficients. For dimension-6 coefficients the tightest observed (expected) bounds are set on cW /Λ2 where Λ is the mass scale of new physics; the bounds are [−0.13, 0.12] TeV−2 ([−0.12, 0.12] TeV−2 ) at 95% CL. The tightest bounds in dimension-8 are set on fT,0 / Λ4 ; the observed (expected) bounds at 95% CL are [−0.63, 0.69] TeV−4 ([−0.54, 0.62] TeV−4 ). Additional results are presented which include scenarios where multiple Wilson coefficients are non-zero, the application of signal model clipping to address unitarity violation in Effective Field Theories, and a novel template fit developed for easier reinterpretation of our results.

Kampa, Cole Erik [Northwestern U. (main)] (ORCID:0

Measurement-informed Dynamic Aggregation of Distribution Systems

This paper proposes a measurement-informed dynamic aggregation methodology in order to create equivalent representations of distribution systems that are compatible with large-scale transmission analysis. By optimizing an equivalent feeder parameters using time-series measurements of active power, reactive power, and voltage at the Point of Interconnection (POI), the approach yields simplified yet dynamically accurate equivalents. Implemented in PSCAD with models of photovoltaic–battery systems, three-phase motors, and static loads, the method employs hybrid differential evolution and bounded least-squares optimization laying the foundation for for real-time state estimation and optimized sensor placement in distribution networks.

Ahmed, Kazi Ishrak [University of Tennessee, Knoxv

Tracking seasonal variability in plant traits from spaceborne PRISMA and NEON AOP across forest types and ecoregions

Plant traits serve as critical indicators of how plants adapt to environmental changes and influence ecosystem functions. While airborne hyperspectral remote sensing effectively maps plant traits through detailed reflectance properties, it is limited by cost and scale, making large-scale and temporal studies challenging. The recently launched spaceborne hyperspectral imager, PRecursore IperSpettrale della Missione Applicativa (PRISMA), offers frequent, large scale and high-fidelity observations on a spatial resolution of 30 m and a revisit time of around 29 days, making it suitable for large-scale seasonal trait mapping. However, their potential remains largely unexplored. This study developed a multi-stage framework by leveraging the PRISMA spaceborne hyperspectral data and National Ecological Observatory Network (NEON) Airborne Observation Platform (AOP) hyperspectral data to investigate the seasonal dynamics of four key plant traits — chlorophyll content, carotenoid content, equivalent water thickness, and nitrogen content — across eleven NEON sites representing diverse forest types and ecoregions in the contiguous U.S. Our results demonstrated that PRISMA hyperspectral data can reliably track seasonal variability in plant traits, achieving overall R 2 values ranging from 0.78 to 0.88 and normalized root mean square error (NRMSE) values ranging from 5.4% to 8.4% for the four traits. Seasonal patterns revealed bell-shaped trajectories for chlorophyll and carotenoids, while equivalent water thickness decreased steadily across most sites, driven by structural changes during leaf maturation and senescence. Nitrogen content exhibited less pronounced seasonal variation but followed expected nutrient resorption patterns. Analysis of environmental drivers showed that seasonal variability is primarily controlled by solar radiation and day length in northern sites, vapor pressure in semi-arid regions, and temperature in mid-southeastern sites. Spatial variability, meanwhile, was primarily driven by soil properties, particularly during the peak growing season. However, the influence of soil variables slightly declines toward the end of the season at several sites, as climatic factors become more prominent. This study highlights the capability of PRISMA, and potentially other similar spaceborne hyperspectral data for large-scale, time-series plant trait mapping and provides valuable insights into the interactions between plant traits and environmental factors. In conclusion, these findings contribute to advancing our understanding of plant functional ecology and improving predictions of ecosystem responses to environmental changes.

Environmental drivers

Framework for X-ray mirror surface shape fitting

For accurate characterization of grazing-incidence X-ray mirrors, we present a comprehensive framework to fit measured surface shapes (either slope or height) of X-ray mirrors used in synchrotron radiation and free-electron laser facilities. We summarize the closed-form expressions of some typical surface shapes of X-ray mirrors including elliptic cylinders, hyperbolic cylinders, ellipsoids, hyperboloids, and diaboloids. This framework is composed of four layers: definition of standard shapes with closed-form expressions, generation of theoretical surface with pose parameters (six degrees of freedom defining an object's position and orientation relative to a coordinate system), parameter optimization with the ability to select which parameters are fit and which are held constant, and the development of user-friendly fitting function wrappers for particular fitting tasks. A few practical fitting examples are demonstrated to verify the effectiveness of the proposed fitting framework. We discuss the physical meanings of the fitting parameters, and provide several examples using the elliptic cylinder and ellipsoid shapes to highlight some features of the framework. Moreover, we provide the presented framework as open-source codes (MATLAB and Python codes available at https://github.com/nsls2omf/xmf) to the community to encourage academic collaboration and further improvements.

36 MATERIALS SCIENCE