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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.

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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Verification of the Shafranov shift in free-boundary VMEC, DESC, and SPEC calculations with elliptical geometry

Here, given a set of current-carrying filaments that create a magnetic field with rotating elliptical flux surfaces, we present verification calculations using the VMEC, DESC, and SPEC free-boundary magnetohydrostatic equilibrium codes for both the “vacuum” equilibrium, for which there is no plasma pressure and no plasma currents, and for a non-zero pressure, zero toroidal current equilibrium. For the vacuum case, these codes are quantitatively compared to the magnetic field produced by the coils. For the non-zero pressure case, they are compared to each other. As the stepped pressure profile used in SPEC approaches the continuous profile used in VMEC and DESC, the SPEC magnetic axis approaches the VMEC and DESC axes. To within an error given by the difference between the pressure profiles, the VMEC, DESC, and SPEC calculations give the same pressure-induced geometric shift of the magnetic axis, known as the Shafranov shift.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Demonstration and performance testing of extreme-resolution simulations with static meshes on Summit (CPU & GPU) for a parked-turbine configuration and an actuator-line (mid-fidelity model) wind farm configuration (ECP-Q4 FY2020 Milestone Report)

The goal of the ExaWind project is to enable predictive simulations of wind farms comprised of many megawatt-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. The primary physics codes in the ExaWind simulation environment are Nalu-Wind, an unstructured-grid solver for the acoustically incompressible Navier-Stokes equations, AMR-Wind, a block-structured-grid solver with adaptive mesh refinement capabilities, and OpenFAST, a wind-turbine structural dynamics solver. The Nalu-Wind model consists of the mass-continuity Poisson-type equation for pressure and Helmholtz-type equations for transport of momentum and other scalars. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as reinitialization of matrices and recomputation of preconditioners is required at every time step. The choice of overset-mesh methodology to model the moving and non-moving parts of the computational domain introduces constraint equations in the elliptic pressure-Poisson solver. The presence of constraints greatly affects the performance of algebraic multigrid preconditioners.

17 WIND ENERGY↗
DOE OSTI2019

Flow Characterization of Compressed Woody Biomass

Global interest for using terrestrial biomass as an energy source has been increasing recently due to potentially significant socio-economic and environmental benefits relative to fossil energy. Thermochemical biomass processes converting biomass to fuels are relatively well developed, e.g. for direct combustion, gasification, and pyrolysis. However, critical problems often arise when attempting to feed biomass into commercial-scale reactors continuously and without interruption. Biomass particles, whether derived from woody or agricultural feedstock, vary greatly in size, shape, density, and moisture content. High cohesiveness, low bulk density, and poor material flow characteristics often prevent continuous feeding due to bridging, rat-hole formation, blockage, and seal failures. Among all different types of feeders utilized to feed biomass into reactors, screw feeding has received significant attention in recent years. Screw feeders are fuel-specific and require careful design to be reliable, efficient, and economical, especially for reactors operating at elevated pressures. In order to mimic the flow properties of compressed biomass inside a compression-screw feeder, rheological properties of three types of compressed lignocellulosic biomass were investigated using a co-rotating twin screw microcompounder. Experiments were conducted to find the impact of moisture content, particle size and type, and screw speed on rheological properties of forest residual particles as well as sawdust. Increasing moisture from 10 to 50% reduced the apparent viscosity of the compressed biomass. Also, higher screw speeds (10 to 90 rpm) led to a lower relative viscosity. At elevated screw speeds, significant temperature differences were measured between the initial and final states, which should be accounted for in equipment design and operation.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2024

Yet Another Sunshine Mystery: Unexpected Asymmetry in GeV Emission from the Solar Disk

The Sun is one of the most luminous γ-ray sources in the sky and continues to challenge our understanding of its high-energy emission mechanisms. This study provides an in-depth investigation of the solar disk γ-ray emission, using data from the Fermi Large Area Telescope spanning 2008 August to 2022 January. We focus on γ-ray events with energies exceeding 5 GeV, originating from 0°5 angular aperture centered on the Sun, and implement stringent time cuts to minimize potential sample contaminants. We use a helioprojection method to resolve the γ-ray events relative to the solar rotation axes and combine statistical tests to investigate the distribution of events over the solar disk. We found that integrating observations over large time windows may overlook relevant asymmetrical features, which we reveal in this work through a refined time-dependent morphological analysis. We describe significant anisotropic trends and confirm compelling evidence of energy-dependent asymmetry in the solar disk γ-ray emission. Intriguingly, the asymmetric signature coincides with the Sun's polar field flip during the cycle 24 solar maximum, around 2014 June. Our findings suggest that the Sun's magnetic configuration plays a significant role in shaping the resulting γ-ray signature, highlighting a potential link between the observed anisotropies, solar cycle, and the solar magnetic fields. These insights pose substantial challenges to established emission models, prompting fresh perspectives on high-energy solar astrophysics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Validation of Numerical Models of the Offshore Wind Turbine From the Alpha Ventus Wind Farm Against Full-Scale Measurements Within OC5 Phase III

The main objective of the Offshore Code Comparison Collaboration Continuation, with Correlation (OC5) project is validation of aero-hydro-servo-elastic simulation tools for offshore wind turbines (OWTs) through comparison of simulated results to the response data of physical systems. Phase III of the OC5 project validates OWT models against the measurements recorded on a Senvion 5M wind turbine supported by the OWEC Quattropod from the alpha ventus offshore wind farm. The following operating conditions of the wind turbine were chosen for the validation: (1) idling below the cut-in wind speed, (2) rotor-nacelle assembly (RNA) rotation maneuver below the cut-in wind speed, (3) power production below and above the rated wind speed, and (4) shutdown. A number of validation load cases were defined based on these operating conditions. The following measurements were used for validation: (1) strains and accelerations recorded on the support structure and (2) pitch, yaw, and azimuth angles, generator speed, and electrical power recorded from the RNA. Strains were not directly available from the majority of the OWT simulation tools; therefore, strains were calculated based on out-of-plane bending moments, axial forces, and cross-sectional properties of the structural members. The simulation results and measurements were compared in terms of time series, discrete Fourier transforms, power spectral densities, and probability density functions of strains and accelerometers. A good match was achieved between the measurements and models setup by OC5 Phase III participants.

17 WIND ENERGY↗
DOE OSTI2019

Validation of Numerical Models of the Offshore Wind Turbine From the Alpha Ventus Wind Farm Against Full-Scale Measurements Within OC5 Phase III

The main objective of the Offshore Code Comparison Collaboration Continuation, with Correlation (OC5) project is validation of aero-hydro-servo-elastic simulation tools for offshore wind turbines (OWTs) through comparison of simulated results to the response data of physical systems. Phase III of the OC5 project validates OWT models against the measurements recorded on a Senvion 5M wind turbine supported by the OWEC Quattropod from the alpha ventus offshore wind farm. The following operating conditions of the wind turbine were chosen for the validation: (1) Idling below the cut-in wind speed; (2) Rotor-nacelle assembly (RNA) rotation maneuver below the cut-in wind speed; (3) Power production below and above the rated wind speed; and (4) Shutdown. A number of validation load cases were defined based on these operating conditions. The following measurements were used for validation: (1) Strains and accelerations recorded on the support structure; (2) Pitch, yaw, and azimuth angles, generator speed, and electrical power recorded from the RNA. Strains were not directly available from the majority of the OWT simulation tools. Therefore, strains were calculated based on out-of-plane bending moments, axial forces, and cross-sectional properties of the structural members. Also, a number of issues arose during the validation: (1) The need for a thorough quality check of sensor measurements; (2) The sensitivity of the turbine loads to the controller and airfoil properties, which were only approximated in the modeling approach; (3) The importance of estimating and applying an appropriate damping value for the structure; and (4) The importance of wind characteristics beyond turbulence on the loads. The simulation results and measurements were compared in terms of time series, discrete Fourier transforms, power spectral densities, probability density functions of strains and accelerometers. A good match was achieved between the measurements and models set up by OC5 Phase III participants.

17 WIND ENERGY↗
DOE OSTI2023

The DESC stellarator code suite. Part 2. Perturbation and continuation methods

A new perturbation and continuation method is presented for computing and analysing stellarator equilibria. The method is formally derived from a series expansion about the equilibrium condition $\boldsymbol {F} \equiv \boldsymbol {J}\times \boldsymbol {B} - \boldsymbol {\nabla } p = 0$ , and an efficient algorithm for computing solutions to second- and third-order perturbations is developed. The method has been implemented in the DESC stellarator equilibrium code, using automatic differentiation to compute the required derivatives. Examples are shown demonstrating its use for computing complicated equilibria, perturbing a tokamak into a stellarator and performing parameter scans in pressure, rotational transform and boundary shape in a fraction of the time required for a full solution.

Conlin, Rory (ORCID:0000000183662111)↗
DOE OSTI2023

Effect of off-diagonal elements in the Wannier Hamiltonian on DFT + DMFT for low-symmetry materials: Study of Li 2 MnO 3

Here, we study the effect of the off-diagonal elements of the Wannier Hamiltonian on the electronic structure of the low-symmetry material Li 2 MnO 3 ( C2/m ), using dynamical mean field theory calculations with a continuous-time quantum Monte Carlo impurity solver. The presence of significant off-diagonal elements leads to a pronounced suppression of the energy gap. The off-diagonal elements are largest when the Wannier projection is used based on the global coordinate, and they remain substantial even with the projection using the local coordinate close to the direction of Mn-O bonds. We show that the energy gap is enhanced by the diagonalization of the Mn d block in the full p-d Hamiltonian with the application of a unitary rotation matrix. Additionally, the inclusion of small double counting energy is crucial for achieving the experimental gap by reducing p-d hybridization. Furthermore, we establish the efficiency of a low-energy (d-only basis) model for studying the electronic structure of Li 2 MnO 3 , as the Wannier basis represents a hybridized state of Mn d and O p orbitals. These findings suggest an appropriate approach for investigating low-symmetry materials using the density functional theory plus dynamical mean field theory (DFT + DMFT) method. We also find that the antiferromagnetic ground state $\Gamma$ 2u is stable with U ≤ 2 eV within density functional theory+$U$ calculations, which is much smaller than the widely used U = 5 eV.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

ROTA-CAP™: An Intensified Carbon Capture System Using Rotating Packed Beds (Final Scientific/Technical Report)

GTI Energy and Carbon Clean Solutions Limited successfully designed, constructed, and operated an integrated ROTA-CAP carbon capture skid. ROTA-CAP™ is a process intensification technology, applied for post-combustion carbon capture, which utilizes the centrifugal forces generated from rotation of rotating packed beds as well as advanced solvents to achieve increased mass transfer rates 1-2 orders of magnitude higher than conventional columns while substantially decreasing footprint. The test skid, which consisted of a dual stage RPB absorber with external interstage cooling and a single stage RPB regenerator, was operated at capacities up to 0.5 tonne/day of CO 2 capture with flue gas concentrations ranging from 4% to 22% CO 2 by vol. CO 2 removal rates greater than 95% were achieved, with CO 2 product purity also exceeding 95% by vol. Over 1,600 hours of operation were accumulated throughout the project, including over 1,000 hours of operation of the with real flue gas containing at least 9.8% CO 2 by vol. The skid was operated continuously for 24 hours per day and 7 days per week over the course of 7 long-term test campaigns, with the campaigns ranging from approximately 2-4 weeks per campaign. A techno-economic analysis was performed, and a cost of capture of $\$$41.18/tonne CO 2 was calculated for the ROTA-CAP process, compared to $\$$45.75/tonne for a Cansolv-based process. These results show a cost reduction of approximately 10% compared to the Cansolv-based process. Although this still exceeds the target cost of capture of $\$$30/tonne specified for this project, GTI expects that the cost of capture can be further reduced through further optimization of the design and technology. GTI also performed an engineering design review to determine the scale-up potential of the technology, with the results of the preliminary assessment indicating that it appears to be feasible to scale up the RPB technology to 4,000 TPD. It was also determined that both horizontal and vertical rotor orientations are feasible, though there are mechanical advantages to the vertical orientation.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2022

Fine resolution remote sensing spectra improves estimates of gross primary production of croplands

Gross primary production (GPP) is a fundamental measure of the terrestrial carbon cycle critical to our understanding of ecosystem function under the changing climate and land use. Remote sensing enables access to continuous spatial coverage, but remains challenged in heterogeneous croplands. Coarse resolution products, like MOD17A (500 m), may aggregate fragmented land cover types commonly found in heavily managed landscapes and misrepresent their respective contribution to carbon production. Consequently, this study demonstrates the capability of fine-resolution imagery (20-30 m) and available red-edge vegetation indices to characterize GPP across seven Midwest cropping systems. Four sites were established on a 22-year-old USDA Conservation Reserve Program (CRP); and the other three on land conventionally farmed with corn-soybean-wheat rotation (AGR). We compare in situ GPP estimates from eddy-covariance towers with ten satellite models: eight variants of the vegetation photosynthesis models (VPM), of which five include a red-edge vegetation index, as well as conventional products Landsat CONUS GPP (30 m) and MOD17A2H V6 (500 m). Daily and cumulative fine-resolution imagery integrated within VPM generally agreed with tower-based GPP in heterogeneous landscapes more than those from MODIS 500 m VPM or conventional GPP products from MOD17AH V6 or Landsat 8 CONUS. Here, replacing EVI2 with red-edge indices NDRE2, NDRE1, and MTCI in Sentinel 2 VPMs notably improved explanation of variance and estimation of cumulative GPP. While existing methods using MODIS- and Landsat-derived GPP are important baselines for regional and global studies, future research may benefit from the higher spatial, temporal, and radiometric resolution.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Identification of Grand-design and Flocculent spirals from SDSS using deep convolutional neural network

ABSTRACT Spiral galaxies can be classified into the Grand-designs and Flocculents based on the nature of their spiral arms. The Grand-designs exhibit almost continuous and high contrast spiral arms and are believed to be driven by stationary density waves, while the Flocculents have patchy and low-contrast spiral features and are primarily stochastic in origin. We train a deep convolutional neural network model to classify spirals into Grand-designs and Flocculents, with a testing accuracy of $\mathrm{97.2{{\ \rm per\ cent}}}$. We then use the above model for classifying 1354 spirals from the SDSS. Out of these, 721 were identified as Flocculents, and the rest as Grand-designs. Interestingly, we find the mean asymptotic rotational velocities of our newly classified Grand-designs and Flocculents are 218 ± 86 and 146 ± 67 km s−1, respectively, indicating that the Grand-designs are mostly the high-mass and the Flocculents the intermediate-mass spirals. This is further corroborated by the observation that the mean morphological indices of the Grand-designs and Flocculents are 2.6 ± 1.8 and 4.7 ± 1.9, respectively, implying that the Flocculents primarily consist of a late-type galaxy population in contrast to the Grand-designs. Finally, an almost equal fraction of bars ∼0.3 in both the classes of spiral galaxies reveals that the presence of a bar component does not regulate the type of spiral arm hosted by a galaxy. Our results may have important implications for formation and evolution of spiral arms in galaxies.

Astronomy & Astrophysics↗
DOE OSTI2025

Outflow Boundary Conditions for Turbine-Integrated Rotating Detonation Combustors

This study examines outflow boundary conditions (BCs) in computational fluid dynamics (CFD) simulations of a transition duct with and without guide vanes that converts supersonic flow exiting a rotating detonation combustor (RDC) to subsonic flow to drive a turbine. Since the flow exiting the transition duct has swirling shock waves with significant spatial and temporal variations in pressure, temperature, and Mach number, imposing proper BCs poses a challenge. To ensure all swirling shock waves exit the transition duct without creating non-physical reflected waves at its outlet, this study examined three outflow BCs: (1) the average pressure imposed at the duct’s outlet, (2) a nonreflecting BC (NRBC) with a specified average pressure imposed at the duct’s outlet, (3) the average pressure imposed at the outlet of an extension duct made up of a buffer layer and a sponge layer. This study is based on the three-dimensional, unsteady density-weighted-ensemble-averaged continuity, Navier–Stokes, and energy equations for a thermally perfect gas closed by the realizable k–ε model and “enhanced” wall functions. The results obtained show that imposing an average pressure at the transition duct’s outlet produces spurious waves that degrade the physical meaningfulness of the solution. When the NRBC was applied, swirling shock waves exited the duct’s outlet without creating spurious waves. However, its usage requires the gas to be thermally, as well as calorically, perfect, which this study shows could be a concern. By imposing the average pressure at the outlet of an extension duct, the gas does not need to be calorically perfect. The results obtained show the effects of the sponge layer’s length and coarsening ratio on damping nonuniformities in non-physical reflected waves to ensure the flow exiting the transition duct’s outlet can do so as if there are no boundaries present and has the desired average pressure—even though the BC is applied at the extension duct’s outlet.

gas turbines↗
DOE OSTI2025

3D Radio Frequency Mapping and Polarization Observations Show Lightning Flashes Were Ignited by Cosmic‐Ray Showers

Previous 2D radio frequency interferometric observations showed that lightning is commonly started with a positive fast discharge (+FD) before a normal negative leader continues from the origin of the +FD to the ensuing lightning flash. However, the inception and development of the +FD cannot be convincingly explained by existing discharge theories. With our new 3D broadband interferometric mapping and polarization system, we observed that the +FD was sometimes followed by an even faster and more extensive negative discharge (−FD) that propagated backward and overshoot the origin by a few hundred meters, as reported by an earlier 2D study. Surprisingly, the signal polarization, which measures the orientation of the discharge current, systematically slanted from the discharge propagation direction and rotated between the two opposite discharges, showing the +FD and −FD were driven by other storm-independent factors in addition to the storm electric field, or otherwise all would align in the same direction. Assuming a cosmic-ray shower (CRS) piercing through the cloud immediately before the +FD/−FD discharge, we found that their path is consistent with a pre-ionized path by the CRS, and the polarizations for the two opposite discharges are consistent with the respective deflected trajectories of high-energy positrons and electrons in the geomagnetic and an electric field. We further analyzed the more commonly observed +FD and showed that it is consistent with the CRS interpretation, suggesting these flashes in thunderstorms were ignited by cosmic-ray showers.

58 GEOSCIENCES↗
DOE OSTI2022

UAE6 - Wind Tunnel Tests Data - UAE6 - Sequence R - Raw Data

Sequence R: Step AOA, No Probes (P) This sequence was designed to quantify the effect of the five-hole probes on the 3-D blade static angle-of-attack response in the presence of rotational influences by repeating Sequence K without five-hole probes. This test sequence used an upwind, rigid turbine with a 0° cone angle. The wind speeds ranged from 6 m/s to 20 m/s, and data were collected at yaw angles of 0° and 30°. The rotor rotated at 72 RPM. Blade pressure measurements were collected. The five-hole probes were removed and the plugs were installed. Plastic tape 0.03-mm-thick was used to smooth the interface between the plugs and the blade. The teeter dampers were replaced with rigid links, and these two channels were flagged as not applicable by setting the measured values in the data file to –99999.99 Nm. The teeter link load cell was pre-tensioned to 40,000 N. During post-processing, the probe channels were set to read –99999.99. The blade pitch angle ramped continuously at 0.18°/s over a wide range of increasing and decreasing pitch angles. A step sequence was also performed. The blade pitch was stepped 5°; the flow was allowed to stabilize; and the pitch angle was held for 5 seconds. Then the pitch angle step was repeated. Again, a wide range of pitch angles was obtained, both increasing and decreasing. The file lengths for this sequence varied from 96 seconds to 6 minutes, depending on the pitch angle range. Some short points were collected at 0° yaw and 3° pitch to ascertain the functionality of the instrumentation and repeatability over time. The file name convention used the initial letter R, followed by two digits specifying wind speed, followed by two digits for yaw angle, followed by RU, RD, or ST, followed by the repetition digit. The angle of attack motion was differentiated by RU (ramp up), RD (ramp down), and ST (step down, then step up). This sequence is related to Sequences K and L.

17 WIND ENERGY↗
DOE OSTI2022

Characters, quasinormal modes, and Schwinger pairs in dS 2 with flux

An integral representation of the 1-loop partition function for charged scalars and spinors, minimally coupled to a uniform U(1) field on S 2 , is given in terms of SO(1, 2) Harish-Chandra group characters and evaluated exactly in terms of Hurwitz ζ-functions. Analytically continuing the U(1) field, we interpret the path integrals as quasicanonical partition functions in dS 2 with an electric field. The character itself is obtained as a trace over states living at the future boundary of de Sitter and has a quasinormal mode expansion. The imaginary part of the partition function captures Schwinger pair creation in the static patch at finite temperature. The thermal enhancement is most noticeable for scalar masses below Hubble and leads to non-monotonicity of the current as a function of the field. This parameter range, when dimensionally reducing from a charged or rotating Nariai spacetime, is excluded by Swampland-inspired bounds. Around the AdS 2 black hole, in contrast to dS 2 , there is a threshold to pair creation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Modulation of Tropical Convection-Circulation Interaction by Aerosol Indirect Effects in Convective Self-Aggregation Simulations of a Gray Zone Global Model

Disentangling the response of tropical convective updrafts to enhanced aerosol concentrations has been challenging. Leading theories for explaining the influence of aerosol concentrations on tropical convection are based on the dynamical response of convection to changes in cloud microphysics, neglecting possible changes in the environment. In recent years, global convection-permitting models (GCPM) have been developed to circumvent problems arising from imposing artificial scale separation on physical processes associated with deep convection. Here, we use a global model in the convective gray zone that partially simulates deep convection to investigate how enhanced concentrations of aerosols that act as cloud condensate nuclei (CCN) impact tropical convection features by modulating the convection-circulation interaction. Results from a pair of idealized non-rotating radiative-convective equilibrium simulations show that the enhanced CCN concentration leads to weaker large-scale circulation, the closeness of deep convective systems to the moist cluster edges, and more mid-level cloud water at an equilibrium state in which convective self-aggregation occurred. Correspondingly, the enhanced CCN concentration modulates how the physical processes that support or oppose convective aggregation maintain the aggregated state at equilibrium. Overall, the enhanced CCN concentration facilitates the development of deep convection in a drier environment but reduces mean precipitation. Our results emphasize the importance of allowing atmospheric phenomena to evolve continuously across spatial and temporal scales in simulations when investigating the response of tropical convection to changes in cloud microphysics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

High-resolution vibrational predissociation spectroscopy of I - ·H 2 O by single-mode CW infrared excitation in a 3D cryogenic ion trap

We describe the integration of a tunable, single-mode, continuous wave infrared laser into a cryogenic ion spectroscopy experiment to measure the rovibrational spectrum of the I - ∙H 2 O complex in the OH stretching region. These upper levels lie about 300 cm -1 above the dissociation threshold. The measurements are carried out by loading the ions in a radiofrequency ion trap at 10 Hz and cooling them to 5 K with pulsed He buffer gas. IR photodissociation (PD) of the I - ∙H 2 O complex is monitored by recording the I - product yield by time-of-flight mass spectrometry as a function of laser wavelength. Very narrow (Δν~75 MHz) rotational lines are observed throughout the spectrum, indicating long (ca. 2 ns) lifetimes for the excited metastable rovibrational levels. Rotational analysis of the band arising from the K”=1 to K’=2 transition of the free OH stretching fundamental yields the structure of the complex for the first time. Over 50% of the trapped ion ensemble in the trap can be photodissociated upon excitation of a single rotational line. This enables very high signal-to-noise in the PD spectrum, and is traced to a mechanism in which the ground state rotational levels are rapidly equilibrated by collisions with the buffer gas.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2026

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↗