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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Construction of Fractal Order and Phase Transition with Rydberg Atoms

We propose the construction of a many-body phase of matter with fractal structure using arrays of Rydberg atoms. The degenerate low energy excited states of this phase form a self-similar fractal structure. This phase is analogous to the so-called “type-II fracton topological states.” The main challenge in realizing fractonlike models in standard condensed matter platforms is the creation of multispin interactions, since realistic systems are typically dominated by two-body interactions. In this work, we demonstrate that the van der Waals interaction and experimental tunability of Rydberg-based platforms enable the simulation of exotic phases of matter with fractal structures, and the study of a quantum phase transition involving a fractal ordered phase.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Thermalization of Gauge Theories from their Entanglement Spectrum

Using dual theories embedded into a larger unphysical Hilbert space along entanglement cuts, we study the entanglement structure of Z 2 lattice gauge theory in (2 + 1) spacetime dimensions. Here we demonstrate Li and Haldane’s conjecture, and show consistency of the entanglement Hamiltonian with the Bisognano-Wichmann theorem. Studying nonequilibrium dynamics after a quench, we provide an extensive description of thermalization in Z 2 gauge theory which proceeds in a characteristic sequence: Maximization of the Schmidt rank and spreading of level repulsion at early times, self-similar evolution with scaling coefficients α = 0.8 ± 0.2 and β = 0.0 ± 0.1 at intermediate times, and finally thermal saturation of the von Neumann entropy.

2-dimensional systems↗
DOE OSTI2023

Hindered segmental dynamics in associative protein hydrogels studied by neutron spin-echo spectroscopy

Transient binding between associating macromolecules can cause qualitative changes to chain dynamics, including modes of conformational relaxation and diffusion, through tethering effects imparted by long-range connectivity. Here, in this work, the role of binding on short-time segmental dynamics in associative polymer gels is investigated by neutron spin-echo (NSE) measurements on a class of model artificial coiled-coil proteins with a systematically varied architecture, probing timescales of 0.1–130 ns, and length scales close to the molecular radius of gyration. The results illustrate effects of transient cross-linking on chain dynamics on different timescales, manifested in changes in segmental relaxation behavior with variations in strand length, chain concentration, and sticker distribution (endblock- vs midblock-functionalized). In all gels, a short-time cooperative diffusion mode is seen over all wave vectors, analogous to a semidilute solution, with no transitions seen at any known structural length scale. However, the diffusion coefficients are found to decrease with increasing junction density across all gels, with the strand length and number of stickers per chain in each gel appearing to play a relatively minor role. The slowing of cooperative diffusion with junction density contrasts with classical predictions of a greater restoring force for fluctuation dissipation due to the increased elasticity, suggesting additional effects of the coiled-coil junctions such as an enhancement in local viscosity that slows dynamics. Notably, the relaxation rates for all gels can be rescaled by the interjunction spacing inferred from small-angle neutron scattering, where they collapse onto a master curve suggestive of self-similar dynamics even in networks with different strand lengths and chain architectures. On long timescales (but shorter than the junction exchange time), a slowing of network relaxation is observed, resulting in a nondecaying plateau in the spin-echo amplitude attributed to a freezing of chain dynamics due to tethering. A characteristic length scale corresponding to the extent of dynamic fluctuations is estimated for each gel, which appears to be smaller than the interjunction spacing but similar to the correlation blob size of the overlapping strands. The results indicate an important role of transient binding on molecular-scale dynamics in associative polymer gels, even on timescales shorter than the junction exchange time, in addition to its effects on long-range self-diffusion previously observed.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Global cascade of kinetic energy in the ocean and the atmospheric imprint

Here, we present an estimate for the ocean's global scale transfer of kinetic energy (KE), across scales from 10 to 40,000 km. Oceanic KE transfer between gyre scales and mesoscales is induced by the atmosphere’s Hadley, Ferrel, and polar cells, and the intertropical convergence zone induces an intense downscale KE transfer. Upscale transfer peaks at 300 gigawatts across mesoscales of 120 km in size, roughly one-third the energy input by winds into the oceanic general circulation. Nearly three quarters of this “cascade” occurs south of 15°S and penetrates almost the entire water column. The mesoscale cascade has a self-similar seasonal cycle with characteristic lag time of ≈27 days per octave of length scales; transfer across 50 km peaks in spring, while transfer across 500 km peaks in summer. KE of those mesoscales follows the same cycle but peaks ≈40 days after the peak cascade, suggesting that energy transferred across a scale is primarily deposited at a scale four times larger.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Explicit Monotone Stable Super-Time-stepping Methods for Finite Time Singularities

We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge–Kutta–Legendre (RKL) and Runge–Kutta–Gegenbauer (RKG) super-time-stepping methods were originally developed for nonlinear complex physics problems with diffusion. These are multistage single step second-order, forward-in-time methods with no implicit solves. The advantage is that the time-step size for stability scales with stage number 𝑠 as $\mathcal{O}$⁡(𝑠 2 ). Many interesting nonlinear PDEs have finite-time singularities, and the presence of diffusion often limits one to using implicit or semi-implicit time-step methods for stability constraints. Finite-time singularities are particularly challenging due to the large range of scales that one desires to resolve, often with adaptive spatial grids and adaptive time steps. Here, in this study, we show two examples of nonlinear PDEs for which the self-similar singularity structure has time and space scales that are resolvable using the RKL and RKG methods, without forcing even smaller time steps. Compared to commonly used implicit numerical methods, we achieve a significantly smaller run time while maintaining comparable accuracy. We also prove numerical monotonicity for both the RKL and RKG methods under their linear stability conditions for the constant coefficient heat equation, in the case of infinite domain and periodic boundary condition, leading to a theoretical guarantee of the superiority of the RKL and RKG methods over traditional super-time-stepping methods, such as the Runge-Kutta-Chebyshev and the orthogonal Runge-Kutta-Chebyshev methods. Code can be found at https://github.com/ZT220501/SRK-Singularity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

High-speed fiber-coupled terahertz time-domain spectroscopy system using a bias-free plasmonic source

We demonstrate a high-speed fiber-coupled terahertz time-domain spectroscopy (THz-TDS) system using a bias-free plasmonic terahertz source. The system is powered by a compact, low-power femtosecond fiber laser oscillator that drives a dual-branch fiber amplifier to pump and probe a plasmonic terahertz source and detector, respectively. A polarization-maintaining, fiber-coupled optical delay line is employed to precisely control the temporal offset between the pump and probe beams through a compact, robust platform. Operating in the self-similar amplification regime, the fiber amplifiers are engineered to mitigate nonlinear pulse distortion and dispersion while delivering robust, high-energy pulses at a 1560-nm wavelength, with an output power exceeding 326 mW. In reflection mode, the THz-TDS system achieves a peak dynamic range of 81 dB and a bandwidth greater than 3.5 THz at a scan rate of 3.75 Hz. The utility of the system for rapid sensing is further demonstrated by quantifying the porosity and density of pharmaceutical tablets through measurements of their physical thickness and effective refractive index.

Jiang, Xinghe [University of California, Los Angel↗
DOE OSTI2022

Taylor wave solution for a general equation of state

This document describes a solution procedure for calculating the Taylor wave behind an unsupported Chapman–Jouguet (CJ) detonation in planar, cylindrical, and spherical geometries given a general equation of state. The resulting semi-analytic solution can be utilized to examine new equation of state models for detonation products and during the verification of hydrodynamic codes. The governing partial differential equations are reduced to ordinary differential equations in both characteristic and self-similar forms. The first-order systems corresponding to each geometry are amenable to solution numerically using commonly available methods. A difficulty arises at the CJ point in radial coordinates where the similarity equations become singular. Two separate strategies are proposed to integrate the first-order system. The first one uses an asymptotic approximation near the CJ point that can be used to perturb the boundary conditions. The second one applies a change of variables which removes the singularity at the expense of an additional equation to be integrated. A test problem is provided for the Davis products equation of state to illustrate the qualitative features of the Taylor wave in each geometric configuration and compared with a Lagrangian hydrodynamics research code. A Python code listing gives an implementation using the SciPy library to assists users in generating the results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Stress Birth and Death: Disruptive Computational Mechanics and Novel Diagnostics for Fluid-to-Solid Transitions

Many materials of interest to Sandia transition from fluid to solid or have regions of both phases coexisting simultaneously. Currently there are, unfortunately, no material models that can accurately predict this material response. This is relevant to applications that "birth stress" related to geoscience, nuclear safety, manufacturing, energy production and bioscience. Accurately capturing solidification and residual stress enables fully predictive simulations of the evolving front shape or final product. Accurately resolving flow of proppants or blood could reduce environmental impact or lead to better treatments for heart attacks, thrombosis, or aneurism. We will address a science question in this proposal: When does residual stress develop during the critical transition from liquid to solid and how does it affect material deformation? Our hypothesis is that these early phases of stress development are critical to predictive simulation of material performance, net shape, and aging. In this project, we use advanced constitutive models with yield stress to represent both fluid and solid behavior simultaneously. The report provides an abbreviated description of the results from our LDRD "Stress Birth and Death: Disruptive Computational Mechanics and Novel Diagnostics for Fluid-to-Solid Transitions," since we have written four papers that document the work in detail and which we reference. We give highlights of the work and describe the gravitationally driven flow visualization experiment on a model yield stress fluid, Carbopol, at various concentrations and flow rates. We were able to collapse the data on a single master curve by showing it was self-similar. We also describe the Carbopol rheology and the constitutive equations of interest including the Bingham-Carreau-Yasuda model, the Saramito model, and the HB-Saramito model including parameter estimation for the shear and oscillatory rheology. We present several computational models including the 3D moving mesh simulations of both the Saramito models and Bingham-Carreau-Yasuda (BCY) model. We also show results from the BCY model using a 3D level set method and two different ways of handling reduced order Hele-Shaw modeling for generalized Newtonian fluids. We present some first ever two-dimensional results for the modified Jeffries Kamani-Donley-Rogers constitutive equation developed during this project. We include some recent results with a successful Saramito-level set coupling that allows us to tackle problems with complex geometries like mold filling in a thin gap with an obstacle, without the need for remeshing or remapping. We report on some experiments for curing systems where fluorescent particles are used to track material flow. These experiments were carried out in an oven on Sylgard 184 as a model polymerizing system. We conclude the report with a summary of accomplishments and some thoughts on follow-on work.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A Scaling Analysis of Post-Detonation Mixing With Detailed Chemical Kinetics

This report documents a scaling study of hemispherical pentaerythritol tetranitrate explosives detonated in ambient air. The focus is on the mixing layer and evolution of the chemical species. The HyBurn code developed at the University of Florida is used to simulate center initiated 12, 38, 120, and 1200 mm diameter charges. The results show blast structures commonly found in the literature. Azimuthal averaging is used to radially average the flow variables to get mean values. The charges exhibit self-similar behavior at early times in a primarily gas dynamic regime, but discrepancies between the scales form at later times due to the finite rate chemistry. The turbulent mixing layer is calculated and used to define a region to conditionally average by mixture fraction. The results of the conditional averages imply a transition from a kinetic-limited regime to a mixing-limited regime with increasing scale. The scaling of the total heat release rate confirms an early time gas dynamic regime, and a later time regime where mixing and chemistry becomes impactful.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Experimental Measurements of Soot and Soot Precursors of Sustainable Aviation Fuels

Sustainable Aviation Fuels (SAFs) are promising for decarbonizing the challenging-to-electrify aerospace sector and reducing yearly greenhouse gas emissions by thousands of tons. Developing predictive detailed chemical kinetic models for SAF (and traditional) fuel mixtures necessitates a robust experimental database to elucidate the intricate pyrolysis and oxidation chemistry of SAF fuel blend components. Two critical components of SAF surrogate mixtures are iso-dodecane isomers and trans-decalin. This report characterizes the structure of three slightly sooting, laminar, non-premixed, nitrogen-diluted Planar Mixing Layer Flames (PMLFs) fueled by either pure ethylene, ethylene doped with 1500ppm of either 2,2,4,6,6-pentamethyl-heptane or trans-decalin. The flames have the same stoichiometric mixture fraction and total mole fraction of fuels in the fuel stream (X F,F = X C2H4,F + X Dopant,F = 0.26), resulting in approximately the same maximum temperature (T max ≈ 1800 K) to highlight the effect of doping on soot and its gaseous precursors. The PMLF is unconfined and established between adjacent planar jets of the fuel and oxidizer streams surrounded by annular shielding nitrogen. The flow is stabilized by exhausting the hot buoyant flame products through a slot in a downstream plate onto which the cold flow impinges. Importantly, any horizontal cross-section of the PMLF has a self-similar thermochemical structure of a reactive boundary layer that grows at increasing Height Above the Burner (HAB). Therefore, the horizontal cross-sections of a PMLF can be modeled as a One-Dimensional Counterflow Flame (1D-CF) with very low strain rates which are unachievable in traditional CFs and yield a structure that is several millimeters thick. In brief, the PMLF is ideal for performing spatially resolved measurements with minimal effects of the sampling-induced perturbations, to develop and validate detailed chemical kinetic models on time scales of a few tens of milliseconds that are relevant in aviation applications. The horizontal profiles of C0-C18 gaseous species at HAB = 50 mm and soot volume fraction at 25 and 50 mm are measured using capillary sampling followed by GC-MS analyses and Laser Induced Emission Spectroscopy (LIES), respectively. Additionally, the Elastic Laser Light Scattering (E-LLS) coefficient is measured at HAB = 50 mm and 25 mm to determine the strain rates of the 1D-CFs equivalent to the characterized PMLF horizontal cross sections and the profile of the E-LLS equivalent diameter of soot. The comparison of the results in the base PMLF fueled only by ethylene with those in either doped PMLF in which 1500 ppm of ethylene are replaced with 2,2,4,6,6-pentamethyl-heptane or trans-decalin, reveals that the doping increases the mole fraction of several Polycyclic Aromatic Hydrocarbons (PAHs) at both HABs by a factor of approximately 2.5, and the soot volume fraction at both HABs by factors of ~1.5 for 2,2,4,6,6-pentamethyl-heptane and ~1.25 for trans-decalin doping, respectively. Conversely, doping causes a near doubling of the soot equivalent diameter only at HAB = 50 mm, without significant effects at 25 mm. The experimental results partially validate the tested state-of-the-art detailed chemical kinetic model and also point toward the further improvement of its predictive capabilities.

10 SYNTHETIC FUELS↗
DOE OSTI2023

Symphony: Cosmological Zoom-in Simulation Suites over Four Decades of Host Halo Mass

Abstract We present Symphony, a compilation of 262 cosmological, cold-dark-matter-only zoom-in simulations spanning four decades of host halo mass, from 10 11 –10 15 M ⊙ . This compilation includes three existing simulation suites at the cluster and Milky Way–mass scales, and two new suites: 39 Large Magellanic Cloud-mass (10 11 M ⊙ ) and 49 strong-lens-analog (10 13 M ⊙ ) group-mass hosts. Across the entire host halo mass range, the highest-resolution regions in these simulations are resolved with a dark matter particle mass of ≈3 × 10 −7 times the host virial mass and a Plummer-equivalent gravitational softening length of ≈9 × 10 −4 times the host virial radius, on average. We measure correlations between subhalo abundance and host concentration, formation time, and maximum subhalo mass, all of which peak at the Milky Way host halo mass scale. Subhalo abundances are ≈50% higher in clusters than in lower-mass hosts at fixed sub-to-host halo mass ratios. Subhalo radial distributions are approximately self-similar as a function of host mass and are less concentrated than hosts’ underlying dark matter distributions. We compare our results to the semianalytic model Galacticus , which predicts subhalo mass functions with a higher normalization at the low-mass end and radial distributions that are slightly more concentrated than Symphony. We use UniverseMachine to model halo and subhalo star formation histories in Symphony, and we demonstrate that these predictions resolve the formation histories of the halos that host nearly all currently observable satellite galaxies in the universe. To promote open use of Symphony, data products are publicly available at http://web.stanford.edu/group/gfc/symphony .

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

A Generative Model for Realistic Galaxy Cluster X-Ray Morphologies

Abstract The X-ray morphologies of clusters of galaxies display significant variations, reflecting their dynamical histories and the nonlinear dependence of X-ray emissivity on the density of the intracluster gas. Qualitative and quantitative assessments of X-ray morphology have long been considered a proxy for determining whether clusters are dynamically active or “relaxed.” Conversely, the use of circularly or elliptically symmetric models for cluster emission can be complicated by the variety of complex features realized in nature, spanning scales from megaparsecs down to the resolution limit of current X-ray observatories. In this work, we use mock X-ray images from simulated clusters from The Three Hundred project to define a basis set of cluster image features. We take advantage of the clusters’ approximate self-similarity to minimize the differences between images before encoding the remaining diversity through a distribution of high-order polynomial coefficients. Principal component analysis then provides an orthogonal basis for this distribution, corresponding to natural perturbations from an average model. This representation allows novel, realistically complex X-ray cluster images to be easily generated, and we provide code to do so. The approach provides a simple way to generate training data for cluster image analysis algorithms and could be straightforwardly adapted to generate clusters displaying specific types of features or selected by physical characteristics available in the original simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Simulating Hydrodynamics in Cosmology with CRK-HACC

Abstract We introduce CRK-HACC, an extension of the Hardware/Hybrid Accelerated Cosmology Code (HACC), to resolve gas hydrodynamics in large-scale structure formation simulations of the universe. The new framework couples the HACC gravitational N -body solver with a modern smoothed-particle hydrodynamics (SPH) approach called conservative reproducing kernel SPH (CRKSPH). CRKSPH utilizes smoothing functions that exactly interpolate linear fields while manifestly preserving conservation laws (momentum, mass, and energy). The CRKSPH method has been incorporated to accurately model baryonic effects in cosmology simulations—an important addition targeting the generation of precise synthetic sky predictions for upcoming observational surveys. CRK-HACC inherits the codesign strategies of the HACC solver and is built to run on modern GPU-accelerated supercomputers. In this work, we summarize the primary solver components and present a number of standard validation tests to demonstrate code accuracy, including idealized hydrodynamic and cosmological setups, as well as self-similarity measurements.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Electromagnetic Fireworks: Fast Radio Bursts from Rapid Reconnection in the Compressed Magnetar Wind

One scenario for the generation of fast radio bursts (FRBs) is magnetic reconnection in a current sheet of the magnetar wind. Compressed by a strong magnetic pulse induced by a magnetar flare, the current sheet fragments into a self-similar chain of magnetic islands. Time-dependent plasma currents at their interfaces produce coherent radiation during their hierarchical coalescence. We investigate this scenario using 2D radiative relativistic particle-in-cell simulations to compute the efficiency of the coherent emission and to obtain frequency scalings. Consistent with expectations, a fraction of the reconnected magnetic field energy, f ~ 0.002, is converted to packets of high-frequency fast magnetosonic waves, which can escape from the magnetar wind as radio emission. In agreement with analytical estimates, we find that magnetic pulses of 10 47 erg s –1 can trigger relatively narrowband GHz emission with luminosities of approximately 10 42 erg s –1 , sufficient to explain bright extragalactic FRBs. The mechanism provides a natural explanation for a downward frequency drift of burst signals, as well as the ~100 ns substructure recently detected in FRB 20200120E.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Constraints on Nonthermal Pressure at Galaxy Cluster Outskirts from a Joint SPT and XMM-Newton Analysis

We present joint South Pole Telescope and XMM-Newton observations of eight massive galaxy clusters (0.8–2 × 10$^{15}$ M$_{⊙}$) spanning a redshift range of 0.16–0.35. Employing a novel Sunyaev–Zel’dovich + X-ray fitting technique, we effectively constrain the thermodynamic properties of these clusters out to the virial radius. The resulting best-fit electron density, deprojected temperature, and deprojected pressure profiles are in good agreement with previous observations of massive clusters. For the majority of the cluster sample (five out of eight clusters), the entropy profiles exhibit a self-similar behavior near the virial radius. We further derive hydrostatic mass, gas mass, and gas fraction profiles for all clusters up to the virial radius. Comparing the enclosed gas fraction profiles with the universal gas fraction profile, we obtain nonthermal pressure fraction profiles for our cluster sample at >0.5R$_{500}$, demonstrating a steeper increase between R$_{500}$ and R$_{200}$ that is consistent with the hydrodynamical simulations. Our analysis yields nonthermal pressure fraction ranges of 8%–28% (median: 15% ± 11%) at R$_{500}$ and 21%–35% (median: 27% ± 12%) at R$_{200}$. Notably, weak-lensing mass measurements are available for only four clusters in our sample, and our recovered total cluster masses, after accounting for nonthermal pressure, are consistent with these measurements.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

High-fidelity Experiments of Turbulent Buoyant Jets from Simultaneous Particle Image Velocimetry and Laser Induced Fluorescence

Accurate models of turbulent buoyant flows are essential for the design of nuclear reactors thermal hydraulics and passive safety systems. However, available models fail to fully capture the physics of turbulent mixing when buoyancy becomes predominant with respect to momentum. Therefore, high-fidelity experiments of well-controlled fundamental flows are needed to develop and validate more accurate models. We performed experiments of positive and negative turbulent buoyant jets, both in uniform and stratified environments, with the aim of understanding the thermal hydraulics of turbulent mixing with variable density and providing high-fidelity data for the development and validation of turbulence models. Non-intrusive, simultaneous Particle Image Velocimetry and Laser Induced Fluorescence measurements were carried out to acquire instantaneous velocity and concentration fields on a vertical section parallel to the axis of a jet in the self-similar region. The Refractive Index Matching method was applied to measure high-resolution buoyant jets with up to 8.6% density difference. These data are free of the typical errors that characterize optical measurements of buoyancy driven flows (e.g., natural and mixed convection) where the refractive index of the fluid is inhomogeneous throughout the measurement domain. Turbulent statistics and entrainment of buoyant jets in uniform and stratified environments are presented. These data are compared with non-buoyant jets in uniform environment, as a reference to investigate the effects of buoyancy and stratification on turbulent mixing. The results will be used for the assessment of current turbulence models and as basis for the development of a new one that captures turbulent mixing.

42 ENGINEERING↗
DOE OSTI2023

A riming‐dependent parameterization of scattering by snowflakes using the self‐similar Rayleigh–Gans approximation

Abstract Riming is a key process of precipitation formation in ice‐containing clouds, but quantifying riming from observations is challenging, limiting our ability to evaluate the riming process in numerical weather models. One challenge for radar observations is that riming changes both the physical properties (mass, area cross‐section) and scattering properties of ice particles. These changes need to be implemented consistently as a function of riming in radar forward operators, which are required for retrievals and model evaluation in observation space. In this study, mass–size, cross‐section area–size, and backscattering cross‐section relations are developed as a function of the normalized rime mass for aggregates composed of various monomer types (columns, dendrites, needles, plates, and rosettes). The proposed framework allows us to simulate scattering properties of aggregated ice particles consistently as a function of riming in retrievals and radar forward operators. The parameterizations are developed from a large data set of simulated rimed aggregates of different sizes and monomer crystal types. The backscattering cross‐section parameterization (the “riming‐dependent parameterization”) is evaluated for radar frequencies of 35.6 and 94.0 GHz and is based on the Self‐Similar Rayleigh–Gans approximation (SSRGA), which is increasingly used to calculate microwave scattering of ice crystals and snowflakes. Compared with parameterizations from the literature that do not consider riming, the riming‐dependent parameterization leads to significantly smaller biases in terms of backscattering cross‐section. When using the particle masses and scattering properties of the individual particles simulated by the aggregation and riming model as a reference, the bias of our parameterization is below 1 dB when integrating over an exponential particle size distribution with sizes from 0.1–10 mm.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Seeing through noise in power laws

Despite widespread claims of power laws across the natural and social sciences, evidence in data is often equivocal. Modern data and statistical methods reject even classic power laws such as Pareto’s law of wealth and the Gutenberg–Richter law for earthquake magnitudes. We show that the maximum-likelihood estimators and Kolmogorov–Smirnov (K-S) statistics in widespread use are unexpectedly sensitive to ubiquitous errors in data such as measurement noise, quantization noise, heaping and censorship of small values. This sensitivity causes spurious rejection of power laws and biases parameter estimates even in arbitrarily large samples, which explains inconsistencies between theory and data. We show that logarithmic binning by powers of λ > 1 attenuates these errors in a manner analogous to noise averaging in normal statistics and that λ thereby tunes a trade-off between accuracy and precision in estimation. Binning also removes potentially misleading within-scale information while preserving information about the shape of a distribution over powers of λ, and we show that some amount of binning can improve sensitivity and specificity of K-S tests without any cost, while more extreme binning tunes a trade-off between sensitivity and specificity. We therefore advocate logarithmic binning as a simple essential step in power-law inference.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗