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At least 1,243 records · Page 69

Reducing spurious mesh motion in Lagrangian finite volume and discontinuous Galerkin hydrodynamic methods

The Lagrangian finite volume (FV) cell-centered hydrodynamic (CCH) method and the Lagrangian discontinuous Galerkin (DG) CCH method have been demonstrated to be quite stable and capable of producing very accurate solutions on many mesh topologies. However, some challenges can arise with higher-order elements and polygonal elements that have many deformational degrees of freedom. With these types of meshes, elements can deform in unphysical ways and the mesh can tangle. In this study, we present methods for obtaining more robust Lagrangian solutions on polygonal and higher-order elements. The robustness is achieved by (1) incorporating a new iterative method that modifies the velocity reconstructions in the corners of the elements, and (2) a new multidirectional approximate Riemann solver that, when coupled with the iterative method, reduces spurious mesh motion. Lastly, the details of the numerical methods are discussed and their utility is demonstrated on a diverse suite of test problems using higher-order and polygonal elements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A massively-parallel, unstructured overset method to simulate moving bodies in turbulent flows

An unstructured overset method capable of performing direct numerical simulation (DNS) and large eddy simulation (LES) of many (O(10 5 )) moving bodies, utilizing many computational cores (O(10 5 )), in turbulent, incompressible fluid flow is presented. Unstructured meshes are attached to bodies and placed within a fixed background domain. Body meshes are allowed to arbitrarily overlap and move throughout the domain. Within each mesh a high resolution, unstructured, non-dissipative finite volume method is used to solve for the flow field. Boundary conditions for each mesh are provided by interpolation from flow solutions on overlapping meshes. When many unstructured meshes of different resolution overlap, care is required in the connection between the different flow solutions. An interpolant is created which seeks to preserve volume conservation of flow quantities between meshes regardless of overlapping mesh differences. An implicit fractional step method is used for time advancement, requiring the calculation of a predicted fluid velocity and corrector pressure field. For the predictor step, the resulting interpolation is directly introduced into the implicit equations for the predicted flow field. For the corrected pressure field, the continuity between meshes is weakly enforced using a penalty formulation. The pressure formulation is symmetric, positive-definite and non-singular resulting in a formulation which is readily solvable using traditional iterative matrix inversion techniques. An Arbitrary Euler-Lagrangian (ALE) method coupled to a 6 degrees of freedom rigid body equation system (6-DOF) is used for body motion. For rotation, a quaternion representation is used to solve Euler's equations of rigid body motion. A linear spring damper model, which uses geometry information readily available from the overset assembly process, is used for collisions. Validation of the method for canonical flow fields is presented including assessment of order of accuracy and kinetic energy conservation properties. Particle-resolved direct numerical simulation (PR-DNS) of single particles in various flow fields are presented for validation. PR-DNS results of 50,000 spherical particles freely moving within turbulent channel flow are shown as a demonstration of the method at full scale. LES results of a marine propeller under crashback conditions are shown to demonstrate the ability to simulate highly unsteady turbulent flows over complex, moving geometries.

97 MATHEMATICS AND COMPUTING↗

A mass conservative, well balanced, tangency preserving and energy decaying method for the shallow water equations on a sphere

Here a fully discrete surface finite element method is proposed for solving the viscous shallow water equations in a bounded Lipschitz domain on the sphere based on a general triangular mesh. The method consists of a modified Crank–Nicolson method in time and a Galerkin surface finite element method in space for the fluid thickness H and the fluid velocity u. A finite element space tangential to the sphere at all finite element nodes is proposed to approximate the fluid velocity u. The proposed method has second-order accuracy in time and first-order accuracy in space, and preserves mass conservation, well balancedness, tangency of velocity to the sphere, and energy decay. Numerical experiments are presented to illustrate the accuracy of the proposed method and the preservation of the physical properties, including mass conservation, well balancedness, and energy decay. A numerical simulation of ocean mesoscale activity on a circular basin with a continental shelf is provided.

97 MATHEMATICS AND COMPUTING↗

Conservative DG method for the micro-macro decomposition of the Vlasov–Poisson–Lenard–Bernstein model

The micro-macro (mM) decomposition approach is considered for the numerical solution of the Vlasov– Poisson–Lenard–Bernstein (VPLB) system, which is relevant for plasma physics applications. In the mM approach, the kinetic distribution function is decomposed as $f$ = $\mathscr{E}$[$ρ_f$] + g , where $\mathscr{E}$ is a local equilibrium distribution, depending on the macroscopic moments $ρ_f$ = $∫_{\mathbb{R}}$ $efdv$ = $\langle$$ef$$\rangle$$_{\mathbb{R}}$, where e = (1, $v$, $\frac{1}{2}$ $v^2$) T , and $g$, the microscopic distribution, is defined such that $\langle$$eg$$\rangle$$_{\mathbb{R}}$ = 0. We aim to design numerical methods for the mM decomposition of the VPLB system, which consists of coupled equations for $ρ_f$ and $g$. To this end, we use the discontinuous Galerkin (DG) method for phase-space discretization, and implicit-explicit (IMEX) time integration, where the phase-space advection terms are integrated explicitly and the collision operator is integrated implicitly. We give special consideration to ensure that the resulting mM method maintains the $\langle$$eg$$\rangle$$_{\mathbb{R}}$ = 0 constraint, which may be necessary for obtaining (i) satisfactory results in the collision dominated regime with coarse velocity resolution, and (ii) unambiguous conservation properties. The constraint-preserving property is achieved through a consistent discretization of the equations governing the micro and macro components. Here, we present numerical results that demonstrate the performance of the mM method. The mM method is also compared against a corresponding DG-IMEX method solving directly for $f$.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons

Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with traditional methods. However, quantifying errors and uncertainties in NN-based inference is more complicated than in traditional methods. This is because in addition to aleatoric uncertainty associated with noisy data, there is also uncertainty due to limited data, but also due to NN hyperparameters, overparametrization, optimization and sampling errors as well as model misspecification. Although there are some recent works on uncertainty quantification (UQ) in NNs, there is no systematic investigation of suitable methods towards quantifying the total uncertainty effectively and efficiently even for function approximation, and there is even less work on solving partial differential equations and learning operator mappings between infinite-dimensional function spaces using NNs. In this work, we present a comprehensive framework that includes uncertainty modeling, new and existing solution methods, as well as evaluation metrics and post-hoc improvement approaches. Further, to demonstrate the applicability and reliability of our framework, we present an extensive comparative study in which various methods are tested on prototype problems, including problems with mixed input-output data, and stochastic problems in high dimensions. In the Appendix, we include a comprehensive description of all the UQ methods employed. Further, to help facilitate the deployment of UQ in Scientific Machine Learning research and practice, we present and develop in [1] an open-source Python library (github.com/Crunch-UQ4MI/neuraluq), termed NeuralUQ, that is accompanied by an educational tutorial and additional computational experiments.

11 physics-informed neural networks↗

An iterative phase-space explicit discontinuous Galerkin method for stellar radiative transfer in extended atmospheres

In this work, a phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region, and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equation and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicular to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiation intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiation intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The influence of synthesis method on the microstructure and catalytic performance of Y0.07Sr0.93Ti0.8Fe0.2O3-δ in synthetic biogas operated solid oxide fuel cells

Highlights: • Fabrication method leads to differences in phase composition and chemical stability. • Grain size and their distribution in a catalytic layer were different. • The best long-term stability in biogas showed a Pechini-method fabricated material. - Abstract: The Y{sub 0.07}Sr{sub 0.93}Ti{sub 0.8}Fe{sub 0.2}O{sub 3-δ} (YSTF) material was fabricated using three different synthesis methods: modified polymer precursor method (MPP), Pechini method and a solid state reaction method. It was applied as an anode catalytic material for biogas reforming in solid oxide fuel cells. Clear differences in the microstructure of fabricated catalytic layers were found, mainly with respect to a grain size and distribution of grains. This led to some differences in biogas diffusion through the layer as well as in an amount of active sites for a biogas reforming. Also different chemical stability of each compound was observed in the fuel cell operating conditions. The best long-term stability in biogas was found for a fuel cell with the YSTF{sub P}echini catalytic layer (sintered in air at 1100 °C for 2 h) and the lowest one for a fuel cell with the YSTF{sub M}PP layer.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A review of regulatory standard test methods for residential wood heaters and recommendations for their advancement

In many regions, residential wood heaters are a leading source of harmful air pollution but only satisfy a small portion of local heating demands. In response, standardized laboratory test methods have been developed to characterize and limit wood heater emissions. While these test methods are a key tool for advancing both wood heater technology and environmental regulations, many of the experimental procedures are outdated and provide few actionable insights for improving heater performance. Furthermore, these test methods vary widely around the world and may not adequately capture the performance of wood heaters operating in residences. This study presents a comprehensive review of standardized wood heater test methods to identify fundamental experimental objectives and regulated performance metrics. Using the results of this review, recommendations are provided to make the test methods more accessible and representative of residential performance, while generating actionable data to motivate heater design improvements. This study elucidates the current state of standard test methods, and the developments needed to advance clean wood heater technologies and public policies.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

An ICP-OES method for the precise and accurate quantification of rare earth elements in natural water: A comparative study from mine waste sites in New Mexico, USA

Inductively coupled plasma techniques such as ICP-OES and ICP-MS are routinely used to determine the concentrations of rare earth elements (REE) in water samples. However, their performance for the determination of REE concentration in mine drainage waters from epithermal vein and porphyry copper mining districts has not been evaluated extensively. In this work, we develop an REE analysis method on an Agilent 5900 ICP-OES instrument and assess the accuracy and precision for the quantification of REE in the natural waters collected from mine adits and an acid seep of mine sites in the Steeple Rock and Hillsboro mining districts, New Mexico, USA. The total REE concentrations in the water samples were measured using the methods we developed for both ICP-OES and ICP-MS. The power of the new ICP-OES method lies in routine analysis of μg/L level concentrations normally analyzed using ICP-MS, including a U.S. Geological Survey standard reference sample, laboratory blank samples spiked with a National Institute of Standards and Technology traceable standard, and surface water samples from mine waste sites. This ICP-OES method achieves low quantification limits ranging from 0.2 to 5 μg/L and excellent analytical accuracy and precision for REE analysis. The precision of light (La-Gd) and heavy (Tb-Lu) REE analysis using this method are better than 5% at average concentrations above 5 ± 4 μg/L and 3 ± 2 μg/L, respectively, and 3% at average concentrations above 10 ± 9 μg/L and 5 ± 4 μg/L, respectively. This method also shows excellent sensitivity and reproducibility for our laboratory and field samples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Isolating organic carbon fractions with varying turnover rates in temperate agricultural soils – A comprehensive method comparison

Fractionation of soil organic carbon (SOC) is crucial for mechanistic understanding and modeling of soil organic matter decomposition and stabilization processes. It is often aimed at separating the bulk SOC into fractions with varying turnover rates, but a comprehensive comparison of methods to achieve this is lacking. In this study, a total of 20 different SOC fractionation methods were tested by participating laboratories for their suitability to isolate fractions with varying turnover rates, using agricultural soils from three experimental sites with vegetation change from C3 to C4 22–36 years ago. Enrichment of C4-derived carbon was traced and used as a proxy for turnover rates in the fractions. Methods that apply a combination of physical (density, size) and chemical (oxidation, extraction) fractionation were identified as most effective in separating SOC into fractions with distinct turnover rates. Coarse light SOC separated by density fractionation was the most C4-carbon enriched fraction, while oxidation-resistant SOC left after extraction with NaOCl was the least C4-carbon enriched fraction. Surprisingly, even after 36 years of C4 crop cultivation in a temperate climate, no method was able to isolate a fraction with more than 76% turnover, which challenges the link to the most active plant-derived carbon pools in models. Particles with density >2.8 g cm -3 showed similar C4-carbon enrichment as oxidation-resistant SOC, highlighting the importance of sesquioxides for SOC stabilization. The importance of clay and silt-sized particles (<50 μm) for SOC stabilization was also confirmed. Particle size fractionation significantly outperformed aggregate size fractionation, due to the fact that larger aggregates contain smaller aggregates and organic matter particles of various sizes with different turnover rates. An evaluation scheme comprising different criteria was used to identify the most suitable methods for isolating fractions with distinct turnover rates, and potential benefits and trade-offs associated with a specific choice. The study's findings can be of great help to select the appropriate method(s) for fractionation of agricultural soils.

59 BASIC BIOLOGICAL SCIENCES↗

Efficient Calculation of NMR Shielding Constants Using Composite Method Approximations and Locally Dense Basis Sets

This paper presents a systematic study of applying composite method approximations with locally dense basis sets (LDBS) to efficiently calculate NMR shielding constants in small and medium-sized molecules. The pcSseg-n series of basis sets are shown to have similar accuracy to the pcS-n series when n ≥ 1 and can slightly reduce computational costs. We identify two different LDBS partition schemes that perform very effectively for density functional calculations. Here, we select a large subset of the recent NS372 database containing 290 H, C, N, and O shielding values evaluated by reference methods on 106 molecules to carefully assess methods of the high, medium, and low computational costs to make practical recommendations. Our assessment covers conventional electronic structure methods (density functional theory and wave function) with global basis calculations, as well as their use in one of the satisfactory LDBS approaches, and a range of composite approaches, also with and without LDBS. Altogether 99 methods are evaluated. On this basis, we recommend different methods to reach three different levels of accuracy and time requirements across the four nuclei considered.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Spin–Orbit Coupling via Four-Component Multireference Methods: Benchmarking on p-Block Elements and Tentative Recommendations

Within current electronic structure theory methods, fully relativistic four-component (4c) approaches based on the Dirac Hamiltonian treat spin–orbit coupling with the most rigor. The spin treatment arises naturally from the formulation and does not need to be included ad hoc. Spin–orbit splittings can provide insightful benchmark criteria for the assessment of 4c methods; however, there have not been extensive studies in this respect. Spin–orbit splittings of the p-block elements B–I were computed using the 4c-CASSCF, 4c-CASPT2, and 4c-MR-CISD+Q methods, as recently implemented in BAGEL, with uncontracted Dunning basis sets. Comparison with experiment reveals that the four-component methods yield good results, with most of the computed splittings falling within 15% of the experimental values. A large basis set is needed to obtain accurate splittings of the light elements B–F, while splittings of heavier elements show little basis dependence. The 4c-MR-CISD+Q method gave the best splittings for light elements, while 4c-CASSCF showed the best splittings for elements beyond fluorine. In conclusion, the 4c-CASPT2 method gave the best splittings for group 13 atoms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Unimolecular Reaction Pathways of a γ-Ketohydroperoxide from Combined Application of Automated Reaction Discovery Methods

Ketohydroperoxides are important in liquid-phase autoxidation and in gas-phase partial oxidation and pre-ignition chemistry, but because of their low concentration, instability, and various analytical chemistry limitations, it has been challenging to experimentally determine their reactivity, and only a few pathways are known. In the present work, 75 elementary-step unimolecular reactions of the simplest γ-ketohydroperoxide, 3-hydroperoxypropanal, were discovered by a combination of density functional theory with several automated transition-state search algorithms: the Berny algorithm coupled with the freezing string method, single- and double-ended growing string methods, the heuristic KinBot algorithm, and the single-component artificial force induced reaction method (SC-AFIR). The present joint approach significantly outperforms previous manual and automated transition-state searches – 68 of the reactions of γ-ketohydroperoxide discovered here were previously unknown and completely unexpected. All of the methods found the lowest-energy transition state, which corresponds to the first step of the Korcek mechanism, but each algorithm except for SC-AFIR detected several reactions not found by any of the other methods. We show that the low-barrier chemical reactions involve promising new chemistry that may be relevant in atmospheric and combustion systems. Our study highlights the complexity of chemical space exploration and the advantage of combined application of several approaches. Altogether, the present work demonstrates both the power and the weaknesses of existing fully automated approaches for reaction discovery which suggest possible directions for further method development and assessment in order to enable reliable discovery of all important reactions of any specified reactant(s).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Advancing density functional tight-binding method for large organic molecules through equivariant neural networks

Semi-empirical quantum-mechanical (QM) methods have become valuable tools for studying complex (bio)molecular systems due to their balance between computational efficiency and accuracy. A key aspect of these methods is their parameterization, which not only governs the reliability of the results but also provides an opportunity to enhance their overall performance. In our previous work [J. Phys. Chem. Lett., 2021, 11, 16], we advanced the third-order semi-empirical density functional tight-binding (DFTB3) method for computing multiple properties of small molecules by developing the machine learning (ML) potential NN rep to bridge the gap between DFTB3 electronic components and those of the hybrid DFT-PBE0 functional. To overcome the limitations of NN rep , we introduce the EquiDTB framework, which leverages physics-inspired equivariant neural networks (NN) to parameterize scalable and transferable many-body Δ TB potentials, replacing the standard pairwise DFTB repulsive potential. This advancement extends the applicability of our ML-corrected DFTB approach to larger molecules and non-covalent systems (including only C, N, O, and H atoms), going beyond the chemical space represented in the training QM datasets. The enhanced performance of EquiDTB over the standard TB methods is demonstrated by the accurate computation of the atomic forces of S66x8 molecular dimers, as well as their interaction energies. Moreover, EquiDTB can be effectively employed to explore the potential energy surfaces of large and flexible drug-like molecules—for example, to determine the minimum energy path between isomers, analyze structural transitions during dynamical simulations, compute vibrational modes, and investigate energetic rankings. The performance for single molecules slightly decreases when the DFTB electronic energy is reduced to first-order but remains superior to standard TB methods. Our work thus demonstrates that an optimal integration of an equivariant NN with QM datasets can advance the DFTB method while maintaining high efficiency, paving the way for reliable (bio)molecular simulations.

Medrano Sandonas, Leonardo [Technische Universität↗

Refinement of Fread s Method for improved tracking of stream discharges during unsteady flows

There are a plethora of analytical approaches to account for the effect of unsteady flow (a.k.a. hysteretic behavior) on the conventionally-built steady rating curves (RCs) used to continuously estimate discharges in open channel flow. One of the most complete correction methods is Fread s method (Fread, 1975) which is based on fully dynamic one-dimensional wave equation. Proposed herein is a modified Fread s method which is adjusted to account for the actual geometry of the cross section. This method improves the accuracy associated with the estimation of conveyance factor and energy slope, so it is particularly useful for small to mid-size streams/rivers where the original method s assumption does not properly hold. The modified Fread s method is tested for the sites in Clear Creek (Iowa, USA) and Ebro River (Spain) to illustrate the significance of its improvement in discharge estimation. While the degree of improvement is apparent for the conveyance factor because the hydraulic depth is replaced by hydraulic radius, that for the energy slope term specifically depends on the site and event conditions.

54 ENVIRONMENTAL SCIENCES↗

A comparative study of different methods for calculating electronic transition rates

We present a comprehensive comparison of the following mixed quantum-classical methods for calculating electronic transition rates: (1) nonequilibrium Fermi’s golden rule, (2) mixed quantum-classical Liouville method, (3) mean-field (Ehrenfest) mixed quantum-classical method, and (4) fewest switches surface-hopping method (in diabatic and adiabatic representations). The comparison is performed on the Garg-Onuchic-Ambegaokar benchmark charge-transfer model, over a broad range of temperatures and electronic coupling strengths, with different nonequilibrium initial states, in the normal and inverted regimes. Under weak to moderate electronic coupling, the nonequilibrium Fermi’s golden rule rates are found to be in good agreement with the rates obtained via the mixed quantum-classical Liouville method that coincides with the fully quantum-mechanically exact results for the model system under study. Furthermore our results suggest that the nonequilibrium Fermi’s golden rule can serve as an inexpensive yet accurate alternative to Ehrenfest and the fewest switches surface-hopping methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A simulation method for the phase diagram of complex fluid mixtures

We present that the phase behavior of complex fluid mixtures is of continuing interest, but obtaining the phase diagram from computer simulations can be challenging. In the Gibbs ensemble method, for example, each of the coexisting phases is simulated in a different cell, and ensuring the equality of chemical potentials of all components requires the transfer of molecules from one cell to the other. For complex fluids such as polymers, successful insertions are rare. An alternative method is to simulate both coexisting phases in a single simulation cell, with an interface between them. The challenge here is that the interface position moves during the simulation, making it difficult to determine the concentration profile and coexisting concentrations. In this work, we propose a new method for single cell simulations that uses a spatial concentration autocorrelation function to (spatially) align instantaneous concentration profiles from different snapshots. This allows one to obtain average concentration profiles and hence the coexisting concentrations. We test the method by calculating the phase diagrams of two systems: the Widom-Rowlinson model and the symmetric blends of freely jointed polymer molecules for which phase diagrams from conventional methods are available. Excellent agreement is found, except in the neighborhood of the critical point where the interface is broad and finite size effects are important. Finally, the method is easy to implement and readily applied to any mixture of complex fluids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

X-ray analysis methods for sources from self-modulated laser wakefield acceleration driven by picosecond lasers

A versatile set of methods for analyzing x-ray energy spectra and photon flux has been developed for laser plasma accelerator experiments driven by picosecond lasers. Forward fit provides extrapolated broad energy spectrum measurements, while Ross pair and differential average transmission analysis provide directly measured data points using a particular diagnostic. Combining these methods allows the measurement of x-ray energy spectra with improved confidence. We apply here the methods to three diagnostics (filter wheel, stacked image plate spectrometer, and step wedge), each sensitive to a different region of x-ray energies (<40 keV, 35–100 keV, and 60–1000 keV, respectively), to characterize the analysis methods using laser-driven bremsstrahlung x-rays. We then apply the methods to measure three x-ray mechanisms, betatron, inverse Compton scattering, and bremsstrahlung, driven by a laser plasma accelerator. The analysis results in the measurement of x-ray energy spectra ranging from 10 keV to 1 MeV with peak flux greater than 10 10 photons/keV/Sr. The combined analysis methods provide a robust tool to accurately measure broadband x-ray sources (keV to MeV) driven by laser plasma acceleration with picosecond, kilojoule-class lasers.

47 OTHER INSTRUMENTATION↗