Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “consistent discretization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6

Towards a NEAMS-based high-fidelity model of the MARVEL reactor

This report outlines the progress of Idaho National Laboratory in developing a high-fidelity and high-resolution model of the Microreactor Applications Research Validation and Evaluation reactor. The model was developed under the Nuclear Energy Advanced Modeling and Simulation microreactor application driver at Idaho National Laboratory. The overarching objective of this activity is the development of a high-fidelity multiphysics MARVEL model using NEAMS tools, and to verify and validate NEAMS tools against MARVEL reference simulation and experimental data, respectively. This is a unique opportunity to conduct multiphysics analysis on a soon-to-be-deployed microreactor. This multiphysics model developed under the NEAMS-funded INL microreactor application driver leverages three single-physics models coupled via the MOOSE’s MultiApp and Transfer systems. The latter systems enable in-memory data transfer between MOOSE-based and MOOSE-wrapped applications. The first single-physics model, that functions as main application, leverages Griffin to model the neutron transport in the core through the discontinuous finite element (DFEM) discrete ordinates solver (SN). Several optimization flags that were developed by the Griffin developer team were beta-tested to enhance the solver’s performance. These include the combined use of using_average_xs and update_averaged_xs_on that enable to avoid expensive on-the-fly cross sections evaluations at each linear iterations in favor of evaluations of the macroscopic cross sections at each Picard iteration. The second single-physics model uses BISON to handle solid heat transfer and asymptotic hydrogen redistribution analysis in the fuel. While the model returns consistent results for the temperature and hydrogen distribution in the fuel, a mismatch was noticed in the calculated temperature in the reflector due to the value of the gap conductance used in our model. Ongoing investigations are being performed to assess the origin of this discrepancy. Finally, the System Analysis Module (SAM) was used to model the flow of the sodium-potassium eutectic in the primary loop. A first verification was also performed showing good agreement in terms of mass flow rate and inlet temperature. All mesh files were generated using the MOOSE Reactor module, removing the need for external meshing tools. Notably, this workscope represents one of the initial applications of the MOOSE Reactor module for modeling highly irregular geometries. The use of the reactor module significantly streamlined the mesh generation process. The full multiphysics mode, that combines all the single physics models, was leveraged to conduct initial steady-state multiphysics simulations to compute power, and temperature distribution in the reactor. Initial testing was performed for transient simulations as well. In this case, the new checkpoint restart capability for eigenvalue calculations was tested showing the capability for streamlined restart of transient calculations. Future work will focus on improving the fidelity of the model by performing comprehensive code-to-code comparisons. For instance, the full-core Griffin neutronics model will be benchmarked against MCNP reference results, that were provided by the MARVEL design team. Additionally, the SAM T/H model will be verified against reference RELAP-5 results for selected accident scenarios. Besides code-to-code verification exercises, the model fidelity will be improved by replacing the single-channel SAM model with a more complex SAM-Pronghorn coupled model, in which the sub-channel capability is deployed to obtain radial temperature resolution in the coolant. This model will be developed in synergy with the NEAMS thermal hydraulics team.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Time-Resolved Stochastic Dynamics of Quantum Thermal Machines

Steady-state quantum thermal machines are typically characterized by a continuous flow of heat between different reservoirs. However, at the level of discrete stochastic realizations, heat flow is unraveled as a series of abrupt quantum jumps, each representing an exchange of finite quanta with the environment. Here, in this work, we present a framework that resolves the dynamics of quantum thermal machines into cycles classified as enginelike, coolinglike, or idle. We analyze the statistics of individual cycle types and their durations, enabling us to determine both the fraction of cycles useful for thermodynamic tasks and the average waiting time between cycles of a given type. Central to our analysis is the notion of intermittency, which captures the operational consistency of the machine by assessing the frequency and distribution of idle cycles. Our framework offers a novel approach to characterizing thermal machines, with significant relevance to experiments involving mesoscopic transport through quantum dots.

full counting statistics↗

Parallel-in-Time Solution of Hyperbolic PDE Systems via Characteristic-Variable Block Preconditioning

We consider the parallel-in-time solution of both linear and nonlinear hyperbolic partial differential equation (PDE) systems in one spatial dimension. In the nonlinear setting, the discretized equations are solved with a preconditioned residual iteration based on a global linearization. The linear(ized) equation systems are approximately solved parallel-in-time using a block preconditioner applied in the characteristic variables of the underlying linear(ized) hyperbolic PDE. This change of variables is motivated by the observation that intervariable coupling between characteristic variables is weak, at least locally where spatio-temporal variations in the eigenvectors of the associated flux Jacobian are sufficiently small, while that between the original variables is not. For an ℓ-dimensional system of PDEs, applying the preconditioner consists of solving a sequence of ℓ scalar linear(ized)-advection-like problems, each associated with a different characteristic wave-speed in the underlying linear(ized) PDE. Furthermore, we approximately solve these linear advection problems using multigrid reduction-in-time (MGRIT); however, any other suitable parallel-in-time method could be used. Numerical examples are shown for the (linear) acoustics equations in heterogeneous media and for the (nonlinear) shallow water equations and Euler equations of gas dynamics with shocks and rarefactions. For many test problems, the solver converges in just a handful of iterations and with mesh-independent convergence rates.

97 MATHEMATICS AND COMPUTING↗

Robotics for Energy Infrastructure Construction on Earth and Beyond: Pilot Study Exploring Level 3-4 Semi-Autonomous Installation of a Reduced-Scale Photovoltaic Power Plant Prototype: Preprint

There is a growing need to build energy infrastructure at massive scale on both Earth and in space. On Earth, increasing electricity demand from applications such as AI data centers is driving rapid expansion of power systems, while in space, long-duration missions such as lunar operations require reliable and resilient energy infrastructure that can be deployed quickly. These needs outpace the capabilities of conventional construction methods. Robotic construction offers a path to faster, lower-cost, and more consistent deployment, yet most existing approaches focus on automating individual tasks rather than end-to-end assembly. The Industrialized Construction Innovation (ICI) team at the National Laboratory of the Rockies (NLR), in collaboration with the Colorado School of Mines, has been investigating robotics and automation strategies for rapid end-to-end energy infrastructure construction. This paper presents a pilot study demonstrating level 3-4 semi-autonomous, end-to-end robotic assembly of a reduced-scale photovoltaic power plant prototype under terrestrial conditions. The approach combines hardware redesign of photovoltaic components for robotic compatibility, discrete-event and physics-based robotic simulations in synthetic environments, and sim-to-real deployment to execute end-to-end robotic assembly of[NM1.1][NM1.2] tracking components, structural members, photovoltaic modules, and embedded electrical connections. The pilot identifies key limitations like tolerance management, perception and localization, end effector capability, fastening methods, and multi-physics simulation fidelity, that must be addressed to enable end-to-end robotic assembly of full-scale energy infrastructure. The study highlights how these insights inform scaling strategies for terrestrial energy infrastructure and adaptation to unstructured and extreme environments, including off-world scenarios such as robotic assembly of vertical tall lunar towers.

14 SOLAR ENERGY↗

Cardinal: Seismic and Geoacoustic Array Processing

Data collected via seismic and infrasound array deployments are leveraged in the geosciences to detect and characterize a myriad of natural and anthropogenic sources. These deployments consist of numerous sensors placed in a predetermined configuration to amplify signal strength and improve the efficacy of array processing techniques used to measure signal directionality and waveform coherence. High‐fidelity feature extraction is often predicated on interstation distance as well as the frequency content and wavelength of an incident signal. Numerous array processing softwares analyze data in sequential frequency bands to obtain a more detailed characterization of a signal. However, current algorithms are limited in their ability to determine optimal array configuration for each band. We introduce an open‐source Python code, called Cardinal, to process seismic and infrasound array data in discretized time–frequency space with the option of applying an adaptive array design to determine optimal subarray configuration for each frequency band. To reduce computational time, the array processing step can be run in parallel using multithreading. Furthermore, the software has the capability to aggregate array processing results from different time–frequency pixels to produce separate sets of detections, or families, with added utility via the application of an adaptive semblance threshold, which aids in isolating signals‐of‐interest from coherent background noise. Upon appropriate configuration, Cardinal exhibits the potential to combine distinct seismic and infrasound phases into separate families.

Adaptive Array↗

Forward modeling approach to nuclear reaction cross sections: Applications in neutron inelastic scattering

The development of nuclear reaction models for the production of evaluated nuclear data has traditionally been performed by comparing measured cross sections with predictions from reaction model codes whose physical input parameters are adjusted to obtain the best agreement between measured and modeled results. To more directly probe reaction model inputs, this work introduces a forward modeling approach to experimental reaction cross-section determination, where the most important physical input parameters to reaction model calculations are obtained via 𝜒 2 minimization between measured and calculated observables. This was demonstrated using data collected by the Gamma Energy Neutron Energy Spectrometer for Inelastic Scattering (GENESIS) at the 88-inch cyclotron at Lawrence Berkeley National Laboratory, a detection array consisting of organic liquid scintillators and high-purity germanium (HPGe) detectors. Using a broad-spectrum neutron beam and a 99.98%-enriched 56 Fe target, GENESIS was used to perform a simultaneous measurement of 56 Fe 𝛾-ray production cross sections and secondary neutron energy and angle distributions. The results of the forward modeling approach to the determination of energy-differential 𝛾-ray production cross sections for the yrast 4 + → 2 + and 6 + → 4 + transitions, as well as eight other off-yrast transitions, were compared against those obtained using conventional techniques, and the results are in good agreement. In addition to discrete 𝛾-ray yield total scattered neutron energy-angular distributions as a function of incident neutron energy were also obtained using forward modeling and found to agree with evaluated data, with the exception of elastic scattering at small angles. The fitted reaction model parameters obtained through forward modeling were also used to calculate the cross section for the unobserved (𝑛, 2⁢𝑛) reaction; excellent agreement with the current evaluation was obtained, providing a validation of the predictive capabilities of the forward model approach. This work bridges the gap between nuclear data experiment and evaluation by providing a new means for extracting inelastic neutron-scattering cross sections and neutron-induced 𝛾-ray production data while directly probing reaction model physics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Anion Data for the East River Watershed, Colorado (2014-2025)

The anion data for the East River Watershed, Colorado, consist of fluoride, chloride, sulfate, nitrate, and phosphate concentrations collected at multiple, long-term monitoring sites that include stream, groundwater, and spring sampling locations. These locations represent important and/or unique end-member locations for which solute concentrations can be diagnostic of the connection between terrestrial and aquatic systems. Such locations include drainages underlined entirely or largely by shale bedrock, land covered dominated by conifers, aspens, or meadows, and drainages impacted by historic mining activity and the presence of naturally mineralized rock. Developing a long-term record of solute concentrations from a diversity of environments is a critical component of quantifying the impacts of both climate change and discrete climate perturbations, such as drought, forest mortality, and wildfire, on the riverine export of multiple anionic species. Such data may be combined with stream gauging stations co-located at each monitoring site to directly quantify the seasonal and annual mass flux of these anionic species out of the watershed. This data package contains (1) a zip file (anion_data_2014_2025.zip) containing a total of 386 files: 387 data files of anion data from across the Lawrence Berkeley National Laboratory (LBNL) Watershed Function Scientific Focus Area (SFA) which is reported in .csv files per location and a locations.csv (1 file) with latitude and longitude for each location; (2) a file-level metadata (v7_20260901_flmd.csv) file that lists each file contained in the dataset with associated metadata; (3) a data dictionary (v7_20260901_dd.csv) file that contains terms/column_headers used throughout the files along with a definition, units, and data type; and (4) a anion MDL fact sheet (anion_MDLs_202608 in PDF and docx formats). Missing values within the anion data files are noted as either "-9999" or "0.0" for not detectable (N.D.) data. There are a total of 47 locations containing anion data. Update on 2022-06-10: versioned updates to this dataset was made along with these changes: (1) updated anion data for all locations up to 2021-12-31, (2) removal of units from column headers in datafiles, (3) added row underneath headers to contain units of variables, (4) restructure of units to comply with CSV reporting format requirements, and (5) the addition of the file-level metadata (flmd.csv) and data dictionary (dd.csv) were added to comply with the File-Level Metadata Reporting Format. Update on 2022-09-09: Updates were made to reporting format specific files (file-level metadata and data dictionary) to correct swapped file names, add additional details on metadata descriptions on both files, add a header_row column to enable parsing, and add version number and date to file names (v2_20220909_flmd.csv and v2_20220909_dd.csv). Update on 2022-12-20: Updates were made to both the data files and reporting format specific files. Conversion issues affecting ER-PLM locations for anion data was resolved for the data files. Additionally, the flmd and dd files were updated to reflect the updated versions of these files. Available data was added up until 2022-03-14. Update on 2023-08-08: Updates were made to both the data files and reporting format specific files. New available anion data was added, up until 2023-05-19. The file level metadata and data dictionary files were updated to reflect the additional data added. Update on 2024-03-11: Updates were made to both the data files and reporting format specific files. New available anion data was added, up until 2023-09-11. Further, revisions to the data files were made to remove incorrect data points (from 1970 and 2001). The reporting format specific files were updated to reflect the additional data added. Update on 2025-05-15: Updates were made to both the data files and reporting format specific files. New available anion data was added, up until the end of WY2024 (September 30, 2024). International Generic Sample Numbers (IGSNs), when registered, were added to the data files. The reporting format specific files were updated to reflect the additional data added. Update on 2026-09-01: Updates were made to both the data files and reporting format specific files. New available anion data was added, up until the end of WY2025 (September 30, 2025). An anion MDL document was included in this update.

54 ENVIRONMENTAL SCIENCES↗

On the predictability of turbulent fluxes from land: PLUMBER2 MIP experimental description and preliminary results

Accurate representation of the turbulent exchange of carbon, water, and heat between the land surface and the atmosphere is critical for modelling global energy, water, and carbon cycles in both future climate projections and weather forecasts. Evaluation of models' ability to do this is performed in a wide range of simulation environments, often without explicit consideration of the degree of observational constraint or uncertainty and typically without quantification of benchmark performance expectations. We describe a Model Intercomparison Project (MIP) that attempts to resolve these shortcomings, comparing the surface turbulent heat flux predictions of around 20 different land models provided with in situ meteorological forcing evaluated with measured surface fluxes using quality-controlled data from 170 eddy-covariance-based flux tower sites. Predictions from seven out-of-sample empirical models are used to quantify the information available to land models in their forcing data and so the potential for land model performance improvement. Sites with unusual behaviour, complicated processes, poor data quality, or uncommon flux magnitude are more difficult to predict for both mechanistic and empirical models, providing a means of fairer assessment of land model performance. When examining observational uncertainty, model performance does not appear to improve in low-turbulence periods or with energy-balance-corrected flux tower data, and indeed some results raise questions about whether the energy balance correction process itself is appropriate. In all cases the results are broadly consistent, with simple out-of-sample empirical models, including linear regression, comfortably outperforming mechanistic land models. In all but two cases, latent heat flux and net ecosystem exchange of CO 2 are better predicted by land models than sensible heat flux, despite it seeming to have fewer physical controlling processes. Land models that are implemented in Earth system models also appear to perform notably better than stand-alone ecosystem (including demographic) models, at least in terms of the fluxes examined here. The approach we outline enables isolation of the locations and conditions under which model developers can know that a land model can improve, allowing information pathways and discrete parameterisations in models to be identified and targeted for future model development.

54 ENVIRONMENTAL SCIENCES↗

Entanglement maximization and mirror symmetry in two-Higgs-doublet models

We consider 2-to-2 scatterings of Higgs bosons in a CP-conserving two-Higgs-doublet model (2HDM) and study the implication of maximizing the entanglement in the flavor space, where the two doublets Φ a , a = 1, 2, can be viewed as a qubit: Φ 1 = |0⟩ and Φ 2 = |1⟩. More specifically, we compute the scattering amplitudes for Φ a Φ b → Φ c Φ d and require the outgoing flavor entanglement to be maximal for a full product basis such as the computational basis, which consists of {|00⟩, |01⟩, |10⟩, |11⟩}. In the unbroken phase and turning off the gauge interactions, entanglement maximization results in the appearance of an U(2) × U(2) global symmetry among the quartic couplings, which in general is broken softly by the mass terms. Interestingly, once the Higgs bosons acquire vacuum expectation values, maximal entanglement enforces an exact U(2) × U(2) symmetry, which is spontaneously broken to U(1) × U(1). As a byproduct, this gives rise to Higgs alignment as well as to the existence of 6 massless Nambu-Goldstone bosons. The U(2) × U(2) symmetry can be gauged to lift the massless Goldstones, while maintaining maximal entanglement demands the presence of a discrete Z 2 symmetry interchanging the two gauge sectors. The model is custodially invariant in the scalar sector, and the inclusion of fermions requires a mirror dark sector, related to the standard one by the Z 2 symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A segmented approach to modeling building height: Delineating high-rise and low-rise buildings for enhanced height estimation

Understanding building height is imperative to the overall study of energy efficiency, population distribution, urban morphologies, emergency response, among others. Currently, existing approaches for modeling building height at scale are hindered by two pervasive issues. First, there is no consistent approach to quantify what a high-rise building is at a macro scale, leaving researchers unable to accurately compare results across geographies and domains. Second, high-rise buildings represent a small fraction of the built environment, implying data imbalance challenges that negatively affect current approaches. This is a problem of practical relevance since information on high-rise buildings is important for studies on urban heat islands, population dynamics, and pollution dispersion. Here, we introduce a novel approach to map building height which first identifies two distinct distributions within the built environment, with one being composed of low-rise buildings and one composed of high-rise buildings. We then develop an ensemble scheme where discrete specialist models are trained for each subset of low-rise buildings and high-rise buildings to infer building height from morphology features. For experiments mapping heights of 4.85 million buildings in Japan, we show an increase of 34 % in accuracy within 3m error when compared to the current state-of-the-art when modeling high-rise buildings, which based on KNN experimentation we define as any building > 12m . Our findings show that such an ensemble framework outperforms the current state-of-the-art approaches, which is especially relevant in relation to inferring height for high-rise buildings, a prominent issue of existing approaches for mapping the built environment.

97 MATHEMATICS AND COMPUTING↗

Mineralized sclerites in the gorgonian coral Leptogorgia chilensis as a natural jamming system

The soft corals (Cnidaria, Octocorallia), a diverse group of colonial marine invertebrates, can reversibly tune their body stiffness in response to external stimuli. This capability is attributed to their dynamic skeletal systems, which consist of thousands of mineralized skeletal elements, called sclerites, embedded within a gel-like matrix that swells/deswells and unjams/jams the sclerites, thus modulating skeletal stiffness. While sclerite morphology is widely used for species identification, its role in the mechanical performance of a soft coral’s skeletal system is largely unknown. Here, we investigated structure-jamming relationships in sclerite-based skeletal architectures using the red gorgonian octocoral Leptogorgia chilensis as a model system. The sclerites of L. chilensis exhibit a shaft-like geometry with two axial branches and two sets of triradiate side branches, which are aligned with the crystallographic symmetry of the constituent magnesium-containing calcite. By combining multiscale three-dimensional (3D) structural characterization, parametric geometrical modeling, 3D printing, mechanical testing, and discrete element simulations, we demonstrate how sclerite geometry achieves a balanced jamming performance in terms of stiffness, weight, strength, and fracture resistance in comparison to alternative geometries parametrically modified from the native sclerites (e.g., changes in the length and number of side branches). Here, we also found that these performance metrics are achieved through the effective interlocking among side and axial branches, which is further enhanced by the fractal-like microscopic spikes on the branch tips. The findings in this natural jamming system offer insights for designing synthetic mechanotunable material architectures for a wide range of applications, from soft robotics to mechanical dampeners.

36 MATERIALS SCIENCE↗

Thermal Management for Planar Package Power Electronics (CRADA Final Report)

The National Renewable Energy Laboratory (NREL) and John Deere Electronic Solutions (JDES) collaborated to develop and evaluate computer models and simulations related to the thermal performance of semiconductor device packaging for an inverter of an off-road vehicle ("Semiconductor Packaging"). The objective of the research was for NREL and JDES to develop a two or three-dimensional computer-aided design model of the Semiconductor Packaging ("Computer Model") for thermal performance evaluation in a simulation. The project developed computer models of a Semiconductor Package of silicon-carbide semiconductor devices with appropriate thermal dissipation via one or more of the following thermal features: a double-sided planar cooling configuration, an air-cooled configuration, a liquid-cooled configuration for off-road inverter applications in a relevant simulated operating environment. It is noted that surface area and prototype product embodiment consisting of air-cooled and liquid-cooled configurations may and may not be in direct contact with power semiconductor chips. The idea was to explore and develop packaging and thermal management technology for power semiconductors that was most effective in the performance yet had least burden in overall product cost for a given application.

33 ADVANCED PROPULSION SYSTEMS↗

Stable Water Isotope Data for the East River Watershed, Colorado (2014-2025)

The stable water isotope data for the East River Watershed, Colorado, consists of delta2H (hydrogen) and delta18O (oxygen) values from samples collected at multiple, long-term monitoring sites including streams, groundwater wells, springs, and a precipitation collector used to establish a local meteoric water line (LMWL) for the watershed. These locations represent important and/or unique end-member locations for which stable isotope values can be diagnostic of the connection between precipitation inputs as snow and rain and riverine export. Such locations include drainages underline entirely or largely by shale bedrock, land covered dominated by conifers, aspens, or meadows, and drainages impacted by historic mining activity and the presence of naturally mineralized rock. Developing a long-term record of water isotope values from a diversity of environments is a critical component of quantifying the impacts of both climate change and discrete climate perturbations, such as drought, forest mortality, and wildfire, on water export. Such data may be combined with stream gaging stations co-located at each surface water monitoring site to relate seasonal variations in water export to their stable isotopic signature. Data for liquid water delta2H and delta18O values are reported in units of parts per thousand (per-mil; ‰). This data package contains (1) a zip file (isotope_data_2014-2025.zip) containing a total of 95 files: 96 data files of isotope data from across the Lawrence Berkeley National Laboratory (LBNL) Watershed Function Scientific Focus Area (SFA) which is reported in .csv files per location and a locations.csv (1 file) with latitude and longitude for each location; (2) a file-level metadata (v6_20260901_flmd.csv) file that lists each file contained in the dataset with associated metadata; and (3) a data dictionary (v6_20260901_dd.csv) file that contains terms/column_headers used throughout the files along with a definition, units, and data type. Missing values within the anion data files are noted as either "-9999" or "0.0" for not detectable (N.D.) data. There are a total of 43 locations containing isotope data. Update on 2022-06-10: versioned updates to this dataset was made along with these changes: (1) updated isotope data for all locations up to 2021-12-31 and (2) the addition of the file-level metadata (flmd.csv) and data dictionary (dd.csv) were added to comply with the File-Level Metadata Reporting Format. Update on 2022-09-09: Updates were made to reporting format specific files (file-level metadata and data dictionary) to correct swapped file names, add additional details on metadata descriptions on both files, add a header_row column to enable parsing, and add version number and date to file names (v2_20220909_flmd.csv and v2_20220909_dd.csv). Update on 2023-08-08: Updates were made to both the data files and reporting format specific files. New available anion data was added, up until 2023-03-13. The file level metadata and data dictionary files were updated to reflect the additional data added. Update on 2024-03-11: Updates were made to both the data files and reporting format specific files. New available anion data was added, up until 2024-02-19. Further, revisions to the data files were made to remove incorrect data points (from 1970 and 2001). The reporting format specific files were updated to reflect the additional data added. Update on 2025-05-15: Updates were made to both the data files and reporting format specific files. New available isotope data was added, up until the end of WY2024 (September 30, 2024). International Generic Sample Numbers (IGSNs), when registered, were added to the data files. The reporting format specific files were updated to reflect the additional data added. Update on 2026-09-01: Updates were made to both the data files and reporting format specific files. New available isotope data was added, up until the end of WY2025 (September 30, 2025).

54 ENVIRONMENTAL SCIENCES↗

Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm

In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential applications in specialized areas such as segmented inverse beta decay neutrino detectors, astronomy, machine learning, and more. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.

Physics↗

Scientific machine learning for closure models in multiscale problems: A review

Here, closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have been proposed as a way to tackle the closure problem, combining traditional (physics-based) modeling with data-driven (machine-learned) techniques, typically through enriching differential equations with neural networks. This paper reviews the different reduced model forms, distinguished by the degree to which they include known physics, and the different objectives of a priori and a posteriori learning. The importance of adhering to physical laws (such as symmetries and conservation laws) in choosing the reduced model form and choosing the learning method is discussed. The effect of spatial and temporal discretization and recent trends toward discretization-invariant models are reviewed. In addition, we make the connections between closure problems and several other research disciplines: inverse problems, Mori-Zwanzig theory, and multi-fidelity methods. In conclusion, much progress has been made with scientific machine learning approaches for solving closure problems, but many challenges remain. In particular, the generalizability and interpretability of learned models is a major issue that needs to be addressed further.

97 MATHEMATICS AND COMPUTING↗

Reproducibility of Radiokrypton in Deep Desert Aquifers: Insights from a Decade of Research

Great technical advances have been achieved since the first atom-trap trace analysis (ATTA) -based radiokrypton application in Egypt, where 1 Myr old groundwater was discovered. Beyond advances in ATTA measurement capabilities, including reduction in sample size, analysis duration, and analytical uncertainty, major progress has been achieved over the past two decades in the sample collection and preparation techniques. These advances paved the expansion of ATTA-based noble gas applications to many other aquifers worldwide, illuminating the nature and flow pattern of deep groundwater systems. While the potential of this new analytical technique for old groundwater dating is well recognized, another important aspect yet to be examined is the reproducibility of radiokrypton in aquifers over time, i.e., how representative is a discrete groundwater sample, collected at a specific time and location, for the natural groundwater system? The likelihood of a negative answer is increased by flow-field disturbance in aquifers following massive groundwater abstraction. Here, in this work, we present repeated 81 Kr sampling and measurements in twenty-one sites over Israel, mostly of deep (up to 1 km) wells tapping confined aquifers in the arid to hyperarid Negev desert. The results demonstrate that radiokrypton measurements are indeed reproducible, even in cases where samples were collected as long as nine years apart and from highly productive (∼1 Mm 3 /yr order) pumping wells. Furthermore, many of the repeated measurements in this study (17 out of the 21 sites) were conducted with different ATTA Instruments in two different laboratories using slightly different sampling, preparation, and analysis techniques, yet with an overall good agreement. The consistency in the ATTA-based 81 Kr-dating results over time highlights the robustness of this state-of-the-art technique as a tool to unravel groundwater flow patterns and encourages further applications to many other yet-to-be-explored deep aquifers.

atom-trap trace analysis↗

Digital quantum magnetism on a trapped-ion quantum computer

Digital quantum matter—realized when discrete quantum gates approximate continuous time evolution—is susceptible to heating into chaotic, structureless states. If digitization errors are adequately suppressed, a long-lived transient regime of approximately energy-conserving dynamics can be observed on gate-based quantum computers. Conservation of energy, in turn, enables the exploration of a wide variety of complex behaviours observed in equilibrium systems, ranging from the non-trivial microscopic origins of thermalization itself to the stabilization of effective models hosting exotic emergent properties. Here we use Quantinuum’s H2 quantum computer to simulate digitized dynamics of the quantum Ising model, suppressing digitization errors well enough to observe thermalization on timescales that severely challenge classical simulation methods. Relaxation of an inhomogeneous state reveals an emergent hydrodynamics owing to approximate energy conservation and we compute the associated diffusion constant. By reprogramming our simulations to take place on a triangular lattice with periodic boundary conditions, we observe thermalization consistent with emergent gauge and topological constraints resulting from lattice frustration. Furthermore, our results were enabled by continued advances in two-qubit gate quality (native partial entangler fidelities of 99.94(1)%) and establish digital quantum computers as powerful tools for studying (effectively) continuous-time dynamics.

Information theory and computation↗

Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm

In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential for specialized applications in segmented inverse beta decay (IBD) neutrino detectors, astronomy, machine learning, and more. Although this method may easily extend to 3D scalar fields, our focus here is on 2D real-valued fields as it directly applies to directionality. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.

Data Analysis, Statistics and Probability (physics↗