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Natively Periodic Fast Multipole Method: Approximating the Optimal Green’s Function
The fast multipole method (FMM) obeys periodic boundary conditions "natively" if it uses a periodic Green's function for computing the multipole expansion in the interaction zone of each FMM oct-tree node. One can define the "optimal" Green's function for such a method that results in the numerical solution that converges to the equivalent particle-mesh (PM) solution in the limit of sufficiently high order of multipoles. A discrete functional equation for the optimal Green's function can be derived, but is not practically useful as methods for its solution are not known. Instead, this paper presents an approximation for the optimal Green's function that is accurate to better than 10 -3 in ${L}_{\mathrm{MAX}}$ norm and 10 -4 in L 2 norm for practically useful multipole counts. Such an approximately optimal Green's function offers a practical way for implementing the FMM with periodic boundary conditions natively, without the need to compute lattice sums or to rely on hybrid FMM-PM approaches.
Early arrival waveform inversion using data uncertainties and matching filters with application to near-surface seismic refraction data
We develop an early arrival waveform inversion (EAWI) technique for high-resolution near-surface velocity estimation by iteratively updating the P-wave velocity model to minimize the difference between the observed and calculated seismic refraction data. Traditional EAWI uses a least-squares penalty function and an acoustic forward-modeling engine. Conventional least-squares error is sensitive to data with low signal-to-noise ratio (S/N) and iterations of EAWI stop at a local-minimum data misfit or at the preassigned maximum number of iterations. These stopping criteria can result in overfitting the data. In addition, fitting the elastic field data with an acoustic modeling engine can introduce artifacts in velocity estimation, especially in land data with significant elastic effects. To overcome these challenges, we develop a robust EAWI (REAWI) method by (1) incorporating the data uncertainties into the penalty function and (2) mitigating the elastic effects using a matching filter workflow. The data uncertainties are estimated from waveform reciprocal errors. When full-waveform reciprocity is not available, trace interpolation is applied. The proposed method prevents closely fitting data with low S/N, avoids overall overfitting by stopping the iterations when a normalized chi-square ([Formula: see text]) waveform misfit of one is achieved, and is less affected by elastic effects. Numerical examples and application to near-surface refraction data at a groundwater contamination site suggest that the final REAWI models are more accurate than the corresponding EAWI models, at the same level of misfit. This is the first known application of a matching filter workflow to real land data. The final REAWI models satisfy an appropriate misfit between the real data and predicted elastic P-wave data, making this approach in this respect equivalent to elastic waveform inversion. We also develop a method to analyze model constraint by examining the energy of the wavefield Fréchet derivative thereby avoiding the influence of the data residuals in traditional Fréchet kernels.
Fine structure of the isovector giant dipole resonance in Nd 142 – 150 and Sm 152
Inelastic proton scattering at energies of a few hundred MeV and very-forward scattering angles including 0° has been established as a tool for the study of electric-dipole strength distributions in nuclei. The present work reports a systematic investigation of the chain of stable even-mass Nd isotopes representing a transition from spherical to quadrupole-deformed nuclei. Extraction of the equivalent photo-absorption cross sections and analysis of their fine structure in the energy region of the isovector giant dipole resonance (IVGDR). Method: Proton inelastic scattering reactions of 200 MeV protons were measured at the iThemba Laboratory for Accelerator Based Sciences in Cape Town, South Africa. The scattering products were momentum-analyzed by the K600 magnetic spectrometer positioned at θ Lab = 0°. Using dispersion-matching techniques, energy resolutions of ΔE ≈ 40–50 keV (full width at half maximum) were obtained. After subtraction of background and contributions from other multipoles, the spectra were converted to photoabsorption cross sections using the equivalent virtual-photon method. Wavelet-analysis techniques are used to extract characteristic energy scales of the fine structure of the IVGDR from the experimental data. Fine structure of the IVGDR is observed even for the most deformed nuclei studied. Comparisons between the extracted experimental energy scales and those energy scales obtained from the quasiparticle-phonon model (QPM) and Skyrme separable random phase approximation (SSRPA) predictions provide insight into the role of different giant-resonance damping mechanisms. It can be seen that the scales in the spherical and most likely also in the deformed nuclei mainly result from the fragmentation of the one-particle-one-hole (1p1h) strength into several dominant transitions serving as doorway states. In cases where calculations beyond the 1p1h level are available, some impact of the spreading due to coupling of the two-particle-two-hole (2p2h) states to the 1p1h doorway states is observed. New virtual-photon absorption data for the chain of stable Nd isotopes and 152 Sm are presented, with a focus on the phenomenon of nonstatistical cross-section fluctuations, referred to as fine structure, in the energy region of the IVGDR. The wavelet-analysis techniques used allowed for the features of the fine structure to be quantified in the form of characteristic scales. Finally, comparisons between experimental results and model predictions indicate that Landau damping seems to be the main source of the fine structure in both the spherical and deformed nuclei, but calculations including 2p2h degrees of freedom would be beneficial to confirm this for the deformed cases.
A general approach to seismic inversion with automatic differentiation
Imaging Earth structure or seismic sources from seismic data involves minimizing a target misfit function, and is commonly solved through gradient-based optimization. The adjoint-state method has been developed to compute the gradient efficiently; however, its implementation can be time-consuming and difficult. We develop a general seismic inversion framework to calculate gradients using reverse-mode automatic differentiation. The central idea is that adjoint-state methods and reverse-mode automatic differentiation are mathematically equivalent. Here, the mapping between numerical PDE simulation and deep learning allows us to build a seismic inverse modeling library, ADSeismic, based on deep learning frameworks, which supports high performance reverse-mode automatic differentiation on CPUs and GPUs. We demonstrate the performance of ADSeismic on inverse problems related to velocity model estimation, rupture imaging, earthquake location, and source time function retrieval. ADSeismic has the potential to solve a wide variety of inverse modeling applications within a unified framework.
Atom Equivalent Energies for the Rapid Estimation of the Heat of Formation of Explosive Molecules from Density Functional Tight Binding Theory
Atom equivalent energies have been derived from which the gas-phase heat of formation of explosive molecules can be estimated from fast, semiempirical density functional tight binding total energy calculations. The root-mean-square deviation and maximum deviation of the heats of formation from the experimental values for the set of 45 energetic molecules compiled by Byrd and Rice [ J. Phys. Chem. A, 2006, 110, 1005–1013] are 10.4 and 25.5 kcal/mol, respectively, using 4 atom equivalent energies and 7.4 and 15.0 kcal/mol, respectively, using 7 atom equivalent energies. These errors are around a factor of 2–3 larger than those obtained from density functional theory calculations but are smaller than those obtained from other semiempirical electronic structure methods. Heats of formation calculated with density functional tight binding theory using the 4 and 7 atom equivalent energies, the Byrd and Rice scheme, and the atom pair contribution method for a new set of 531 energetic molecules that contain only carbon, hydrogen, nitrogen, and oxygen are provided.
A 24-channel ultra-low-noise preamplifier for dN/dx measurements with drift tube detectors
Cluster counting $(dN/dx)$ is a promising method to enhance particle identification for gaseous detectors, especially in next-generation collider experiments like the FCC-ee, where good $π/K$ separation over a broad momentum range is essential. However, its implementation in large-scale systems has been limited by the challenging requirements for high-resolution signal amplification and readout. This paper presents a 24-channel ultra-low-noise preamplifier board designed for drift tube detectors to enable $dN/dx$ measurements. The three-stage amplification topology employs SiGe transistors and integrates dedicated noise-minimization techniques, achieving a charge gain of 21.11 mV/fC from 0.3 fC to 50 fC, a bandwidth of 542 MHz, and a voltage gain of 47.8 dB. The measured voltage noise density is 0.35 nV/$\sqrt{\textrm{Hz}}$ , surpassing most of the state-of-the-art preamplifiers for gaseous and silicon detectors. Validation tests conducted on the sMDT chambers at the CERN Proton Synchrotron test beam facility demonstrate that the proposed design meets the stringent preamplifier requirements for implementing the $dN/dx$ method in drift-tube detector systems, achieving an equivalent noise charge of 0.14 fC and a signal-to-noise ratio of 73 when operated with a He:iC 4 H 10 (90:10) gas mixture. The design also shows promise for broader application in other gaseous or semiconductor detectors.
Ferroelectric HfO 2 and the importance of strain
Ferroelectric oxides based on HfO 2 show tremendous promise for the next generation of memory and logic devices. The ferroelectric polymorph is one of several that can be derived from the high symmetry cubic fluorite structure of HfO 2 . A single grain of HfO 2 may consist of a coherent mixture of multiple orientational and translational variants of different polymorphs. Here, we use symmetry-adapted strain-order parameters to elucidate the relationship between the different HfO 2 polymorphs and their symmetrically equivalent variants. We use first-principles electronic structure methods to identify minimum energy pathways and map them in subspaces of the symmetry-adapted strain order parameters. We next investigate the atomic structure of domain boundaries that separate coexisting variants of ferroelectric HfO 2 . Further, we rely on Gibbsian excess quantities and a precise specification of mechanical boundary conditions to describe the thermodynamic properties of domain boundaries. Our first-principles calculations show that the O and Hf shuffle arrangement within a domain boundary is closely related to the intermediate shuffle patterns of the homogeneous pathways between ferroelectric variants. Furthermore, the preferred structure within a boundary is very sensitive to local strain constraints imposed by the adjacent ferroelectric variants, leading to highly anisotropic domain boundary energies.
Effect of frequency and applied voltage of an atmospheric-pressure dielectric-barrier discharge on breakdown and hydroxyl-radical generation with a liquid electrode
This work examines the effect of the frequency and peak applied voltage on hydroxyl-radical generation in a dielectric-barrier plasma discharge between a metallic needle electrode and one electrode covered with dielectric. The authors examine a system that can expose up to 96 liquid samples in an automated fashion without human intervention beyond setting the initial software configuration. Then, hydroxylradical concentration, measured through coumarin fluorescence, was measured for 5 s plasma exposures generated under different highvoltage conditions with frequencies from 2 to 16 kHz and amplitudes from 4 to 9 kV. Their results show that an increase in frequency and/or applied voltage, within the range prescribed above and the limits of the high-voltage power supply, can yield up to a 150% increase in fluorescence with an equivalent hydroxyl-radical increase. Applications using typical previous methods, such as the Fenton Reaction, are limited in that they continuously generate hydroxyl radicals over millisecond and longer intervals. These results establish the electrical parameters that can now be applied to polymers, like proteins, which show three dimensional structures that are flexible and fluctuate on a microsecond and nanosecond time scale, with hydroxyl-radical generation on this time scale using this device. Additionally, plasma exposures may be optimized for a great variety of proteins, devices and techniques, where hydroxyl-radical generation is of utmost importance, reducing exposure time and potential subjection of samples to harmful side effects.
Asynchronous Truncated Multigrid-Reduction-in-Time
In this paper, we present the new “asynchronous truncated multigrid-reduction-in-time” (AT-MGRIT) algorithm for introducing time parallelism to the solution of discretized time-dependent problems. The new algorithm is based on the multigrid-reduction-in-time (MGRIT) approach, which, in certain settings, is equivalent to another common multilevel parallel-in-time method, Parareal. In contrast to Parareal and MGRIT that both consider a global temporal grid over the entire time interval on the coarsest level, the AT-MGRIT algorithm uses truncated local time grids on the coarsest level, each grid covering certain temporal subintervals. Further, these local grids can be solved completely in an independent way from each other, which reduces the sequential part of the algorithm and, thus, increases parallelism in the method. Here, we study the effect of using truncated local coarse grids on the convergence of the algorithm, both theoretically and numerically, and show, using challenging nonlinear problems, that the new algorithm consistently outperforms classical Parareal/MGRIT in terms of time to solution.
Polynomial Chaos Surrogate Construction for Random Fields with Parametric Uncertainty
Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many simulations for acceptable accuracy. Surrogate models provide a means of circumventing the high computational expense of sampling such complex models. In particular, polynomial chaos expansions (PCEs) have been successfully used for uncertainty quantification studies of deterministic models where the dominant source of uncertainty is parametric. We discuss an extension to conventional PCE surrogate modeling to enable surrogate construction for stochastic computational models that have intrinsic noise in addition to parametric uncertainty. We develop a PCE surrogate on a joint space of intrinsic and parametric uncertainty, enabled by Rosenblatt transformations, which are evaluated via kernel density estimation of the associated conditional cumulative distributions. Furthermore, we extend the construction to random field data via the Karhunen–Loève expansion. We then take advantage of closed-form solutions for computing PCE Sobol indices to perform a global sensitivity analysis of the model which quantifies the intrinsic noise contribution to the overall model output variance. Additionally, the resulting joint PCE is generative in the sense that it allows generating random realizations at any input parameter setting that are statistically approximately equivalent to realizations from the underlying stochastic model. The method is demonstrated on a chemical catalysis example model and a synthetic example controlled by a parameter that enables a switch from unimodal to bimodal response distributions.
TEMPI: An Interposed MPI Library with Canonical Representation of MPI Datatypes [Slides]
These points are covered in this presentation: Distributed GPU stencil, non-contiguous data; Equivalence of strided datatypes and minimal representation; GPU communication methods; Deploying on managed systems; Large messages and MPI datatypes; Translation and canonicalization; Automatic model-driven transfer method selection; and Interposed library implementation.
Extrapolation of the Rainflow-Counted Load Ranges for Fatigue Assessment of the Wind Turbine's Blades
Wind turbine design standards recommend the use of statistical modeling coupled with extrapolation of the short-term load data to long-term periods for fatigue reliability assessment. However, statistical error and computational expense can limit the accuracy of such approaches. In the case of wind turbine blades, the errors are more significant because of the high material fatigue exponent that makes the damage estimations more sensitive to variations. In addition, due to different excitation sources, the flapwise load range histogram is not unimodal, and thus its statistical modeling is complex. In the present work, we provide three methods for statistical modeling of the flapwise bending moment ranges including a novel approach based on frequency-based separation of the modes. The first two methods are simplified approaches for modeling the most crucial load ranges using unimodal distributions and the third method involves multimodal distribution fitting. The research is based on 3600 10-minute aeroelastic simulations of DTU 10MW case study wind turbine from which a benchmark damage equivalent load (DEL) is calculated. The DEL calculated by each of the three proposed methods is compared to this reference. The results show that the conventional approach based on using 6 seeds as well as using mixture models fitted on the limited data lead to under-conservative results with errors up to 23%. On the other hand, the simplified unimodal approaches provided in this work can provide conservative estimations of the fatigue damage with mean values 5% and 12% higher than the benchmark. However, the variability of the DEL estimates is higher when using unimodal extrapolation of the load ranges, and the data can be conservative by 17.5%. The proposed unimodal fits suggested for modeling and extrapolation of the blade's load ranges provide less errors relatively and most importantly conservative DEL estimations while maintaining computational efficiency.
Hybridized Discontinuous Galerkin Methods for Computational Fluid Dynamics
Hybridizable Discontinuous Galerkin (HDG) methods hold promise for any applications with significant advection character, including thermal hydraulics in light water reactors and advanced reactor concepts and fluid models of plasmas in magnetic confinement fusion. Its features include natural upwinding, local element conservation, and extensibility to arbitrarily high order accuracy. In the last fiscal year we have implemented HDG in the Multiphysics Object-Oriented Simulation Environment (MOOSE). We developed a first-of-its-kind automatic static condensation system in MOOSE’s underlying finite element library libMesh which can condense out arbitrarily many internal variables. Finally, we developed the first preconditioner for HDG discretizations of the Navier-Stokes equations which shows robust performance across a wide range of problem sizes and Reynolds numbers. This preconditioner yields solution times that are equivalent to the fastest developed for industry standard finite volume methods. Moreover, the arbitrarily high-order nature of HDG makes it a prime candidate for acceleration via graphical processing units (GPUs). We believe these developments will hold significant importance for future DOE Nuclear Energy (NE) and Fusion Energy Science (FES) programs.
Discrete fracture network model benchmarks developed and applied in a DECOVALEX-2023 repository performance assessment study
This study presents newly developed benchmarks for modeling flow and transport within discrete fracture networks (DFNs) and useful methods for analyzing the results. The new benchmarks are designed to test modeling approaches for use in probabilistic performance assessment models of deep geologic repositories in fractured rock. The benchmarks simulate flow and transport through a 1 km 3 block of fractured rock. The first simulates migration of a short pulse of tracer through a simple network of four intersecting fractures. The second adds 1089 stochastically generated fractures. The third changes the pulse to a continuous point source. Evaluation of model performance relies on moment analysis and comparison of the results of different models. The expected nondimensional first moment of the conservative tracer for each benchmark is 1. The benchmarks were simulated by teams from Canada, Czechia, Germany, Korea, Sweden, Taiwan, and the United States as part of a DECOVALEX-2023 study (decovalex.org). The teams used various approaches, including explicit DFN modeling, DFN upscaling to an equivalent continuous porous medium (ECPM), and a combination of both methods. Transport mechanisms are modeled using either the advection-dispersion equation or particle tracking. Results demonstrate strong agreement among the models in breakthrough behavior up to the 75th percentile. Significant deviations in first moments and well-clustered outputs led to the identification of inaccuracies in several models. Such findings exemplify the benefit of exercising these benchmarks and using the presented methods to test DFN flow and transport models.
Probing-Based Inertia Estimation Method Using Hybrid Power Plants
With the displacement of synchronous generation by inverter-based resources (IBRs), power systems could face the challenge of reduced inertia since IBRs do not inherently contribute to system inertia. Therefore, there is rising interest in monitoring system inertia in real-time applications for situational awareness. In addition, there is a growing number of IBRs that provide fast frequency responses (FFR) in the form of synthetic inertia and P-f droop. It is desirable to quantify the contribution of these FFR controls as equivalent inertia. This paper proposes a probing-based inertia estimation method using a PV-battery hybrid power plant in the Kauai island power system. The method is validated under different operating conditions.
Developing Equivalent Surface Heat Transfer Input Parameters for Updated Standard 140/BESTEST Thermal Fabric Test Cases
ANSI/ASHRAE Standard 140, Standard Method of Test for the Evaluation of Building Energy Analysis Computer Programs, is widely cited for evaluating software for use with performance-path energy efficiency analysis in conjunction with well-known energy-efficiency standards, including: ASHRAE Standard 90.1, the International Energy Conservation Code, and other international standards. This paper summarizes recent work to develop improved equivalent surface heat transfer input parameters for the building thermal fabric comparative test cases that comprise a portion of Standard 140. The software-to-software comparative test method allows comparison of simulation results from a wide variety of building energy simulation programs to each other. In this type of test method, it is of great importance to specify inputs that are as well-equivalenced as possible to accommodate a wide variety of input schemes for the tested programs, and thereby reduce the potential for disagreements among them in the tests. Results include new alternative constant surface coefficients that are appropriate to the test cases and demonstrate their ability to approximate the more detailed surface heat transfer models from which they are derived.
A preliminary investigation into the feasibility of laser ablation U–Pb isotope ratio measurement via all‐faraday cup detection with 10 11 ‐ and 10 13 ‐Ω amplifiers on the Neoma multicollector‐inductively coupled plasma‐mass spectrometer
Rationale Signal detection for uranium–lead (U–Pb) dating of zircon is typically performed via ion counters. Here, we develop a preliminary understanding of the strengths and limitations of faraday‐cup‐based detection. Methods A suite of zircon reference materials and the NIST‐610 glass were sampled using laser ablation followed by U–Pb isotope ratio measurement on a Neoma multicollector‐inductively coupled plasma‐mass spectrometer. Results We were able to produce geologically accurate 207 Pb/ 206 Pb, 206 Pb/ 238 U, and 207 Pb/ 235 U ratios for the NIST‐610 glass and the zircon standards, with ages ranging from ~2.5 Ga to ~337 Ma (TanBrown A, Oracle, 91550, Mud Tank, Temora, and Plešovice). Two of the younger zircon standards examined (94‐35, ~55.6 Ma, and Fish Canyon, 28.6 Ma) yielded accurate 206 Pb/ 238 U but not 207 Pb/ 235 U or 207 Pb/ 206 Pb ratios, whereas the youngest zircon standard (Penglai, ~4.4 Ma) failed for all three ratios of interest. The accuracy and precision of the all‐faraday method are directly tied to signal intensity, with reliable data capable of being produced even when both isotopes in a ratio have signals below ~0.001 V (equivalent to ~62 500 cps on an ion counter). Conclusion The all‐faraday cup multicollection method provides sufficient sensitivity to obtain geologically meaningful U–Pb data, with possible advantages being that laser pit depth‐dependent changes in the observed interelemental fractionation behavior may be easier to correct using a static collector configuration compared to when the ion beam is swept across a single detector while also removing the need for an interdetector‐type calibration. Further work is needed to refine the all‐faraday cup method (e.g., application of background subtraction and common Pb corrections, outlier removal, and interelement as well as down‐hole fractionation corrections), but our initial results demonstrate that the faraday detector method has sufficient sensitivity to warrant further study.