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At least 343 records · Page 19

Accelerating Large-Format Metal Additive Manufacturing: How Controls R&D is Driving Speed, Scale, and Efficiency

This article highlights work at Oak Ridge National Laboratory’s Manufacturing Demonstration Facility to develop closed-loop, feedback control for laser-wire based Directed Energy Deposition, a form of metal Big Area Additive Manufacturing (m-BAAM), a process being developed in partnership with GKN Aerospace specifically for the production of Ti-6Al-4V pre-forms for aerospace components. A large-scale structural demonstrator component is presented as a case-study in which not just control, but the entire 3D printing workflow for m-BAAM is discussed in detail, including design principles for large-format metal AM, toolpath generation, parameter development, process control, and system operation, as well as post-print net-shape geometric analysis and finish machining. In terms of control, a multi-sensor approach has been utilized to measure both layer height and melt pool size, and multiple modes of closed-loop control have been developed to manipulate process parameters (laser power, print speed, deposition rate) to control these variables. Layer height control and melt pool size control have yielded excellent local (intralayer) and global (component-level) geometry control, and the impact of melt pool size control in particular on thermal gradients and material properties is the subject of continuing research. Further, these modes of control have allowed the process to advance to higher deposition rates (exceeding 7.5 lb/hr), larger parts (1-meter scale), shorter build times, and higher overall efficiency. The control modes are examined individually, highlighting their development, demonstration, and lessons learned, and it is shown how they operate concurrently to enable the printing of a large-scale, near net shape Ti-6Al-4V component.

Gibson, Brian↗

Mitigating the noise of DESI mocks using analytic control variates

In order to address fundamental questions related to the expansion history of the Universe and its primordial nature with the next generation of galaxy experiments, we need to model reliably large-scale structure observables such as the correlation function and the power spectrum. Cosmological N-body simulations provide a reference through which we can test our models, but their output suffers from sample variance on large scales. Fortunately, this is the regime where accurate analytic approximations exist. To reduce the variance, which is key to making optimal use of these simulations, we can leverage the accuracy and precision of such analytic descriptions using Control Variates (CV). The power of control variates stems from utilizing inexpensive but highly correlated surrogates of the statistics one wishes to measure. The stronger the correlation between the surrogate and the statistic of interest, the larger the variance reduction delivered by the method. We apply two control variate formulations to mock catalogs generated in anticipation of upcoming data from the Dark Energy Spectroscopic Instrument (DESI) to test the robustness of its analysis pipeline. Our CV-reduced measurements offer a factor of 5-10 improvement in the measurement error compared with the raw measurements. We explore the relevant properties of the galaxy samples that dictate this reduction and comment on the improvements we find on some of the derived quantities relevant to Baryon Acoustic Oscillation (BAO) analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

The S-PLUS Fifth Data Release: Over 4500 Square Degrees of the Southern Sky and a Multicolor View of the Hydra and Antlia Galaxy Clusters

Abstract We present the fifth data release (DR5) of the Southern Photometric Local Universe Survey (S-PLUS), covering 4592 deg 2 across 2491 fields. Observations were conducted with the T80-South, a Brazilian robotic telescope equipped with the Javalambre 12-filter system, containing five broadband and seven narrowband filters. Data products feature FITS images and extensive catalogs containing fluxes, magnitudes, and shape parameters for over 113 million detections. In addition, several value-added catalogs are provided, offering photometric redshifts (photo- zs ), object classifications, masks, and extinction coefficients. For the first time, this release includes coverage of 110 deg 2 along the Galactic disk, facilitating new research into Galactic structure and stellar populations. The release also provides full coverage of the Hydra Supercluster and numerous other nearby clusters with improved data reduction and calibration, enhancing photo- z accuracy, which is vital for large-scale structure studies. A preliminary analysis of the Hydra and Antlia galaxy clusters up to 5 × R 200 yields an updated catalog of 1706 cluster members based on both spectroscopic and high-quality photo- zs . Our photometric data shows that both clusters have a similar proportion of galaxies with an H α excess relative to their clustercentric distance, though Hydra has a higher fraction near its center. Additionally, the spatial distribution of all objects in our sample highlights a bridge connecting both clusters. We verify that S-PLUS DR5 provides a solid foundation for future scientific investigations, ranging from solar system studies to cosmology.

Vinicius Rodrigues de Lima, Erik [Universidade de ↗

Mirror dark sector solution of the Hubble tension with time-varying fine-structure constant

Here we explore a model introduced by Cyr-Racine et al. that resolves the Hubble tension by invoking a “mirror world” dark sector with energy density a fixed fraction of the “ordinary” sector of Λ+ cold dark matter. Although it reconciles cosmic microwave background and large-scale structure observations with local measurements of the Hubble constant, H 0 , the model requires a value of the primordial helium mass fraction, Y p = 0.170 ± 0.025, that is discrepant with observations and with the predictions of big bang nucleosynthesis. We consider a variant of the model with standard helium mass fraction but with the value of the electromagnetic fine-structure constant, α, slightly different during photon decoupling from its present value. If α at that epoch is lower than its current value by Δα ≃ -2 x 10 -5 , then we can achieve the same Hubble tension resolution as in the work by Cyr-Racine et al. but with consistent helium abundance. As an example of such time evolution of α, we consider a toy model of an ultralight scalar field, with mass m < 4 x 10 -29 eV, coupled to electromagnetism, which evolves after photon decoupling at redshift z ≃ 10 3 , and that with appropriate coupling appears to be consistent with late-time constraints on α variation and the weak equivalence principle.

79 ASTRONOMY AND ASTROPHYSICS↗

The Tianlai Cylinder Pathfinder Array: System Functions and Basic Performance Analysis

The Tianlai Cylinder Pathfinder is a radio interferometer array designed to test techniques for 21 cm intensity mapping in the post-reionization Universe, with the ultimate aim of mapping the large scale structure of the Universe and measuring cosmological parameters such as the dark energy equation of state. Each of its three parallel cylinder reflectors are oriented in the north-south direction, and the array has a large field of view. As the Earth rotates, the northern sky is observed by drift scanning. The array is located in Hongliuxia, a radio quiet site in Xinjiang, and saw its first light in September 2016. In this first paper on the data analysis of the Tianlai cylinder array, we describe the system functions of the array, the commissioning observations during 2016- 2018, and present its basic performance characteristics. We show examples of the interferometric visibility data, then using the observational data, we derive the actual beam profile in the east-west direction, the bandpass response, and calibrate the complex gains for the array elements either with a strong astronomical point source, or with an artificial calibrator source. Based on the preliminary analysis of the data, we derive the system temperature and sensitivity of the array.

79 ASTRONOMY AND ASTROPHYSICS↗

ThinCurr: An open-source 3D thin-wall eddy current modeling code for the analysis of large-scale systems of conducting structures

In this paper we present a new thin-wall eddy current modeling code, ThinCurr, for studying inductively-coupled currents in 3D conducting structures -- with primary application focused on the interaction between currents flowing in coils, plasma, and conducting structures of magnetically-confined plasma devices. The code utilizes a boundary finite element method on an unstructured, triangular grid to accurately capture device structures. The new code, part of the broader Open FUSION Toolkit, is open-source and designed for ease of use without sacrificing capability and speed through a combination of Python, Fortran, and C/C++ components. Scalability to large models is enabled through use of hierarchical off-diagonal low-rank compression of the inductance matrix, which is otherwise dense. Ease of handling large models of complicated geometry is further supported by automatic determination of supplemental elements through a greedy homology approach. Here, a detailed description of the numerical methods of the code and verification of the implementation of those methods using cross-code comparisons against the VALEN code and Ansys commercial analysis software is shown.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Continental-Scale Controls on Hyporheic Respiration Revealed by Knowledge-Guided Machine Learning

Hyporheic zone sediments regulate organic matter turnover and in-stream respiration, yet controls on sediment respiration remain poorly constrained across heterogeneous river networks, limiting prediction of stream metabolism and carbon processing at continental scales. Here, we integrate observations from ~90 river corridors across the United States in the WHONDRS consortium with a knowledge-guided machine learning (KGML) framework that couples thermodynamic rate theory with machine learning to identify dominant controls on hyporheic respiration. Diagnostic analyses show that organic matter concentration and thermodynamic favorability define an upper bound on respiration potential, whereas biological catalytic capacity and physical accessibility jointly govern realized respiration rates through interaction effects. To represent unmeasurable accessibility constraints, we use the mechanistic model as a scaffold for KGML, allowing machine learning to target residual structure not explained by process theory. This hybrid framework improves predictive skill relative to both the mechanistic model alone and fully data-driven models while preserving interpretability. These results indicate that variability in hyporheic respiration is largely mechanistically structured and demonstrate how integrating process theory with explainable AI enhances predictive performance while enabling scalable synthesis of river corridor observations.

Zheng, Jianqiu↗

Spectroscopy-guided discovery of three-dimensional structures of disordered materials with diffusion models

Spectroscopy techniques such as x-ray absorption near edge structure (XANES) provide valuable insights into the atomic structures of materials, yet the inverse prediction of precise structures from spectroscopic data remains a formidable challenge. In this study, we introduce a framework that combines generative artificial intelligence models with XANES spectroscopy to predict three-dimensional atomic structures of disordered systems, using amorphous carbon (a-C) as a model system. In this work, we introduce a new framework based on the diffusion model, a recent generative machine learning method, to predict 3D structures of disordered materials from a target property. For demonstration, we apply the model to identify the atomic structures of a-C as a representative material system from the target XANES spectra. We show that conditional generation guided by XANES spectra reproduces key features of the target structures. Furthermore, we show that our model can steer the generative process to tailor atomic arrangements for a specific XANES spectrum. Finally, our generative model exhibits a remarkable scale-agnostic property, thereby enabling generation of realistic, large-scale structures through learning from a small-scale dataset (i.e. with small unit cells). Our work represents a significant stride in bridging the gap between materials characterization and atomic structure determination; in addition, it can be leveraged for materials discovery in exploring various material properties as targeted.

36 MATERIALS SCIENCE↗

Selection of high-redshift Lyman-Break Galaxies from broadband and wide photometric surveys

In this paper, we investigate the possibility of selecting high-redshift Lyman-Break Galaxies (LBG) using current and future broadband wide photometric surveys, such as the Ultraviolet Near Infrared Optical Northern Survey (UNIONS) or the Vera C. Rubin Legacy Survey of Space and Time (LSST), using a Random Forest algorithm. This work is conducted in the context of future large-scale structure spectroscopic surveys like DESI-II, the next phase of the Dark Energy Spectroscopic Instrument (DESI), which will start around 2029.We use deep imaging data from the Hyper Suprime Camera (HSC) and the Canada-France-Hawaii Telescope Large Area U-band Deep Survey (CLAUDS) on the COSMOS and XMM-LSS fields. To predict the selection performance of LBGs with image quality similar to UNIONS, we degrade the u,g,r,i and z bands to UNIONS depth.The Random Forest algorithm is trained with the u,g,r,i and z bands to classify LBGs in the 2.5 < z < 3.5 range.We find that fixing a target density budget of 1,100 deg$^{-2}$, the Random Forest approach gives a density of z > 2 targets of 873 deg$^{-2}$, and a density of 493 deg$^{-2}$ of confirmed LBGs after spectroscopic confirmation with DESI. This UNIONS-like selection was tested in a dedicated spectroscopic observation campaign of 1,000 targets with DESI on the COSMOS field, providing a safe spectroscopic sample with a mean redshift of 3. This sample is used to derive forecasts for DESI-II, assuming a sky coverage of 5,000 deg$^{2}$. We predict uncertainties on Alcock-Paczynski parameters α$_{⊥}$ and α$_{∥}$ to be 0.7% and 1% for 2.6 < z < 3.2, resulting in a potential 2% measurement of the dark energy fraction at high redshift. Additionally, we estimate the uncertainty in local non-Gaussianity and predict σ$_{fNL}$ ≈ 7, which would be comparable to the current best precision achieved by Planck. The latter forecast suggests that achieving the precision required to place stringent constraints on inflationary models (σ$_{fNL}$ ≈ 1) using spectroscopic galaxy surveys necessitates the development of a next-generation (Stage V) spectroscopic survey.

79 ASTRONOMY AND ASTROPHYSICS↗

A computationally efficient algorithm for computing convex hull prices

Electricity markets worldwide allow participants to bid non-convex production offers. While non-convex offers can more accurately reflect a resource's capabilities, they create challenges for market clearing processes. For example, system operators may be required to execute side payments to participants whose costs are not covered through energy sales as determined via traditional locational marginal pricing schemes. Convex hull pricing minimizes this and other types of side payments while providing uniform (i.e., locationally and temporally consistent) prices. Computing convex hull prices involves solving either a large-scale linear program or the Lagrangian dual of the corresponding non-convex scheduling problem. Further, the former approach requires explicit descriptions of market participants' convex hulls. While linear programs for computing convex hull prices are large, their structure is naturally decomposable by generators. Here, in this work, we propose and empirically analyze a Benders decomposition approach to computing convex hull prices that leverages recent advances in convex hull formulations for thermal generating units. We demonstrate across a large set of test instances that our decomposition approach only requires modest computational effort, obtaining solutions at least an order of magnitude faster than the equivalent large-scale linear programming approach. Overall, we provide a computationally feasible method for computing convex hull prices for industrial scale market clearing problems, enabling the possibility of practical adoption of this advanced pricing mechanism.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Surface structure of mass-selected niobium oxide nanoclusters on Au(111)

The structures formed by the deposition of mass-selected niobium oxide clusters, Nb 3 O y ( y = 5, 6, 7), onto Au(111) were studied by scanning tunneling microscopy. The as-deposited Nb 3 O 7 clusters assemble into large dendritic structures that grow on the terraces as well as extend from the top and bottom of step edges. The Nb 3 O 6 cluster also forms dendritic assemblies but they are generally much smaller in size. The assemblies are composed of smaller discrete structures (<1 nm) which are likely to be single clusters. Furthermore, the dendritic assemblies for both the Nb 3 O 7 and Nb 3 O 6 clusters have fractal dimensions of about 1.7 which is very close to that expected for simple diffusion limited aggregation. Annealing the Nb 3 O 7,6 /Au(111) surfaces up to 550 K results in changes in assembly sizes and increases in heights, while heating to 700 results in the disruption of the assemblies into smaller structures. By contrast, the as-deposited Nb 3 O 5 /Au(111) surface at RT exhibits compact cluster structures which become 3D nanoparticles when annealed above 550 K. Differences in the observed surface structures and thermal stability are attributed to differences in metal-oxygen stoichiometry which can influence cluster binding energies, mobility and inter-cluster interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Selection of high-redshift Lyman-Break Galaxies from broadband and wide photometric surveys

Here, in this paper, we investigate the possibility of selecting high-redshift Lyman-Break Galaxies (LBG) using current and future broadband wide photometric surveys, such as the Ultraviolet Near Infrared Optical Northern Survey (UNIONS) or the Vera C. Rubin Legacy Survey of Space and Time (LSST), using a Random Forest algorithm. This work is conducted in the context of future large-scale structure spectroscopic surveys like DESI-II, the next phase of the Dark Energy Spectroscopic Instrument (DESI), which will start around 2029. We use deep imaging data from the Hyper Suprime Camera (HSC) and the Canada-France-Hawaii Telescope Large Area U-band Deep Survey (CLAUDS) on the COSMOS and XMM-LSS fields. To predict the selection performance of LBGs with image quality similar to UNIONS, we degrade the u,g,r,i and z bands to UNIONS depth. The Random Forest algorithm is trained with the u,g,r,i and z bands to classify LBGs in the 2.5 < z < 3.5 range. We find that fixing a target density budget of 1,100 deg -2 , the Random Forest approach gives a density of z > 2 targets of 873 deg -2 , and a density of 493 deg -2 of confirmed LBGs after spectroscopic confirmation with DESI. This UNIONS-like selection was tested in a dedicated spectroscopic observation campaign of 1,000 targets with DESI on the COSMOS field, providing a safe spectroscopic sample with a mean redshift of 3. This sample is used to derive forecasts for DESI-II, assuming a sky coverage of 5,000 deg 2 . We predict uncertainties on Alcock-Paczynski parameters α ⊥ and α ∥ to be 0.7% and 1% for 2.6 < z < 3.2, resulting in a potential 2% measurement of the dark energy fraction at high redshift. Additionally, we estimate the uncertainty in local non-Gaussianity and predict σ fNL ≈ 7, which would be comparable to the current best precision achieved by Planck. The latter forecast suggests that achieving the precision required to place stringent constraints on inflationary models (σ fNL ≈ 1) using spectroscopic galaxy surveys necessitates the development of a next-generation (Stage V) spectroscopic survey.

cosmological parameters from LSS↗

Conceptual monopile and tower sizing for the IEA Wind Task 37 Borssele reference wind farm

This paper explores the preliminary design of the support structures for the IEA Wind Task 37 reference wind farm at the Borssele site III and IV. The study looks at two different design methods that might be used within larger wind farm system design optimization (i.e. lay-out, electrical systems, etc.). The first consists of a scaling tool that scales a detailed design according to the rated power, water depth, hub height and rotor diameter. The second is a physics-based optimization approach that relies on the WISDEM® design tool. This research compares the results of these two methods for the design of both the tower and monopile of the IEA 10-MW and 15-MW reference wind turbines at a range of sea depths (25 m, 30 m, 35 m, 40 m). The two tools yield very similar results in terms of monopile base diameter, support structure natural frequency and mass. WISDEM is then used to also investigate the sensitivity of the design to the tower top forces, wave conditions and the soil conditions. It is shown that tower top forces dominate the design. In general, large diameter structures can carry additional costs associated with manufacturing and transportation requirements. Thus, the paper is concluded with a trade-off study between mass and diameter that quantifies the effect of the reduction in monopile diameter with the increase in structural mass.

WIND ENERGY↗

Target selection for the DESI Peculiar Velocity Survey

ABSTRACT We describe the target selection and characteristics of the DESI Peculiar Velocity Survey, the largest survey of peculiar velocities (PVs) using both the fundamental plane (FP) and the Tully–Fisher (TF) relationship planned to date. We detail how we identify suitable early-type galaxies (ETGs) for the FP and suitable late-type galaxies (LTGs) for the TF relation using the photometric data provided by the DESI Legacy Imaging Survey DR9. Subsequently, we provide targets for 373 533 ETGs and 118 637 LTGs within the Dark Energy Spectroscopic Instrument (DESI) 5-yr footprint. We validate these photometric selections using existing morphological classifications. Furthermore, we demonstrate using survey validation data that DESI is able to measure the spectroscopic properties to sufficient precision to obtain PVs for our targets. Based on realistic DESI fibre assignment simulations and spectroscopic success rates, we predict the final DESI PV Survey will obtain ∼133 000 FP-based and ∼53 000 TF-based PV measurements over an area of 14 000 deg2. We forecast the ability of using these data to measure the clustering of galaxy positions and PVs from the combined DESI PV and Bright Galaxy Surveys (BGS), which allows for cancellation of cosmic variance at low redshifts. With these forecasts, we anticipate a 4 per cent statistical measurement on the growth rate of structure at z < 0.15. This is over two times better than achievable with redshifts from the BGS alone. The combined DESI PV and BGS will enable the most precise tests to date of the time and scale dependence of large-scale structure growth at z < 0.15.

79 ASTRONOMY AND ASTROPHYSICS↗

Unfolding Structure Formation in the Dark Universe via Weak Gravitational Lensing: from Pixels to Cosmology in the Dark Energy Survey and Roman Space Telescope

Weak gravitational lensing (deflection of light from distant galaxies due to the gravitational potential of intervening mass) is one of the most exciting probes in cosmology as it is sensitive both to the growth of the large-scale structure and the expansion history of the Universe. We can measure the coherent distortion of galaxy shapes (which we call cosmic shear) and infer the matter distribution. With next-generation imaging surveys such as the Vera C. Rubin Observatory Legacy Survey of Space and Time (Rubin LSST) and the Nancy G. Roman Space Telescope (Roman), there is immense new promise in understanding the fundamental nature of dark matter and dark energy. With datasets from current experiments like the Dark Energy Survey (DES), we see apparent cosmological tensions between experiments that may either be real and indicate new physics or new systematics we do not yet understand. LSST and Roman will increase the number of galaxies we have observed by an order of magnitude, leading to improved constraints on our cosmological model by up to 300%. These experiments will have the potential to prove if these cosmological tensions are real. However, our control of systematic uncertainties must also improve by similar levels to achieve the promise of what these missions can deliver. To achieve these scientific outcomes, the challenges of determining galaxy shapes and redshifts and modeling the impact of astrophysical effects must be solved. My PhD has focused on enabling weak lensing science in DES and Roman. I co-led the shear analysis teams in DES to produce the largest weak lensing galaxy sample, as well as the final DES cosmological analysis of cosmic shear. For Roman, I have led two papers characterizing and mitigating shear-related systematics with image simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DECADE+ DES Y3 Weak Lensing Mass Map: A 13,000 deg $\^{} 2$ View of Cosmic Structure from 270 Million Galaxies

We present the largest galaxy weak lensing mass map of the late-time Universe, reconstructed from 270 million galaxies in the DECADE and DES Year 3 datasets, covering 13,000 square degrees. We validate the map through systematic tests against observational conditions (depth, seeing, etc.), finding the map is statistically consistent with no contamination. The large area covered by the mass map makes it a well-suited tool for cosmological analyses, cross-correlation studies and the identification of large-scale structure features. We demonstrate its potential by detecting cosmic filaments directly from the mass map for the first time and validating them through their association with galaxy clusters selected using the Sunyaev-Zeldovich effect from Planck and ACT DR6.

Gatti, M.↗

DECADE+DES Y3 Weak Lensing Mass Map: A 13,000 deg$^2$ View of Cosmic Structure from 270 Million Galaxies

We present the largest galaxy weak lensing mass map of the late-time Universe, reconstructed from 270 million galaxies in the DECADE and DES Year 3 datasets, covering 13,000 square degrees. We validate the map through systematic tests against observational conditions (depth, seeing, etc.), finding the map is statistically consistent with no contamination. The large area covered by the mass map makes it a well-suited tool for cosmological analyses, cross-correlation studies and the identification of large-scale structure features. We demonstrate its potential by detecting cosmic filaments directly from the mass map for the first time and validating them through their association with galaxy clusters selected using the Sunyaev-Zeldovich effect from Planck and ACT DR6.

Gatti, M. [Chicago U., KICP] (ORCID:00000001613487↗

Bulk Glassy GeTe 2 : A Missing Member of the Tetrahedral GeX 2 Family and a Precursor for the Next Generation of Phase-Change Materials

Vitreous germanium disulfide GeS 2 and diselenide GeSe 2 belong to canonical chalcogenide glasses extensively studied over the past half century. Their high-temperature orthorhombic polymorphs are congruently melting compounds, and the tetrahedral crystal and glass structure is largely preserved in the melt. In contrast, the ditelluride counterpart is absent in the Ge-Te phase diagram, which shows only a single compound, monotelluride GeTe. Phase-change materials based on GeTe have become a technologically important class of solids, and their structure and properties are also widely studied. Surprisingly, very scarce information is available for alloys having GeTe 2 stoichiometry. Using a fast quenching procedure in silica capillaries, high-energy X-ray diffraction, and Raman spectroscopy supported by first-principles simulations, we show that bulk glassy GeTe 2 differs substantially from the lighter GeX 2 members, revealing 46% of trigonal germanium, 31% of three-fold coordinated tellurium, and only 20% of edge-sharing tetrahedra or pyramids. The fraction of homopolar Ge-Ge bonds is low; however, the population of dominant Te-Te dimers and Te n oligomers, n <= 10, appears to be significant. The complex structural and chemical topology of g-GeTe 2 is directly related to the thermodynamic metastability of germanium ditelluride, schematically represented by the following reaction: GeTe 2 $\rightleftarrows$ GeTe + Te. Disproportionation is complete above liquidus in the temperature range of semiconductor-metal transition, and the dense metallic GeTe 2 liquid, mostly consisting of five-fold coordinated Ge species, exhibits high fluidity, strong fragility (m = 99 ± 5), and presumably a fast structural transformation rate combined with low atomic mobility in the vicinity of the glass transition temperature, favorable for reliable long-term data retention in nonvolatile memories. The observed and predicted characteristic features make GeTe 2 a promising precursor for the next generation of phase-change materials, especially coupled with additional metal doping, depolymerizing the tetrahedral interconnected glass network and accelerating (sub)nanosecond crystallization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗