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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Spectral scaling laws of solar wind fluctuations at 1 AU: Part 2

In-situ measurements of solar wind fluctuations at 1 AU show that the reduced energy spectrum, equal to the sum of the reduced kinetic plus magnetic energy spectra, is characterized by a power-law scaling k{sup -{alpha}} in the inertial range with an average spectral exponent {alpha} Asymptotically-Equal-To 3/2, a result confirmed by independent analyses using data from different spacecraft. Magnetic field and electron density spectra at kinetic scales {rho}{sup -1}{sub i} < k < {rho}{sup -1}{sub e} both have a spectral index of approximately 2.7. These and other recent observations of spectral scaling laws in the solar wind using single spacecraft measurements are briefly reviewed. The first part of this review, Part 1, is contained in a separate paper in these proceedings.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Scaling laws in jet classification

We demonstrate the emergence of scaling laws in the benchmark top versus QCD jet classification problem in collider physics. Six distinct physically-motivated classifiers exhibit power-law scaling of the binary cross-entropy test loss as a function of training set size, with distinct power law indices. This result highlights the importance of comparing classifiers as a function of dataset size rather than for a fixed training set, as the optimal classifier may change considerably as the dataset is scaled up. We speculate on the interpretation of our results in terms of previous models of scaling laws observed in natural language and image datasets.

Batson, Joshua↗
DOE OSTI2026

Neural Scaling Laws for Jet Generation

Recently observed empirical scaling laws describe the performance of foundation-type models as three independent key quantities -- dataset size, compute, and model parameters -- are modified. Extracting these scaling laws informs the training of large complex models for which the tuning of hyperparameters in traditional ways is not feasible. This work for the first time explores if scaling laws can also be observed for the task of particle jet generation -- both relevant as a pre-training objective for foundation models and as in-situ simulation by itself. We indeed replicate the key logarithmic scaling law behavior for model-size scaling. Beyond studying the next token prediction validation loss of the generative model, we also study the sliced Wasserstein distance of five physical quantities that are not immediately available to the model during training. Our study shows that this quantity is monotonically related to the next token prediction validation loss, meaning that this loss is indeed a good proxy for the physics performance. For the scaling with dataset size and compute, we observe substantially weaker scaling behavior of both the loss and the sliced Wasserstein distance. We analyze this behavior by introducing the concept of a learnable window, and argue that autoregressive next token prediction on jet constituents exhibits comparatively rapid saturation relative to language-model studies. We discuss possible origins of this behavior, including the stochastic nature of QCD radiation and differences between generative and supervised learning tasks in collider physics.

Amram, Oz [Fermilab]↗
DOE OSTI2026

Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study

Neural scaling laws play a pivotal role in the performance of deep neural networks and have been observed in a wide range of tasks. However, a complete theoretical framework for understanding these scaling laws remains underdeveloped. In this paper, we explore the neural scaling laws for deep operator networks, which involve learning mappings between function spaces, with a focus on the Chen and Chen style architecture. These approaches, which include the popular Deep Operator Network (DeepONet), approximate the output functions using a linear combination of learnable basis functions and coefficients that depend on the input functions. We establish a theoretical framework to quantify the neural scaling laws by analyzing its approximation and generalization errors. We articulate the relationship between the approximation and generalization errors of deep operator networks and key factors such as network model size and training data size. Moreover, we address cases where input functions exhibit low-dimensional structures, allowing us to derive tighter error bounds. These results also hold for deep ReLU networks and other similar structures. Our results offer a partial explanation of the neural scaling laws in operator learning and provide a theoretical foundation for their applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Scaling Law for Cloud-Rise Velocity vs. Scaled Height of Burst (SHOB)

The shockwave produced by a nuclear detonation leaves a low-density region in the vicinity of air zero (i.e., the point of detonation). As the shockwave degenerates into an acoustic wave, the buoyant force takes over and causes the low-density region to begin to rise at speeds that can reach as high as ~200-300 mph. The objective of this project was to find out if this initial cloud rise followed any scaling law, by stimulating a cloud rise for a 1 kiloton (kt) detonation and determining if a correlation existed between the scaled-height-of-burst (SHOB) and the scaled-cloud-rise velocity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Nonlinear modeling of the scaling law for the m/n = 3/2 error field penetration threshold

The scaling law for the m/n=3/2 error field (EF) penetration threshold is predicted numerically based on nonlinear single-fluid and two-fluid modeling using the TM1 code. The simulated penetration threshold of radial magnetic field b r at the plasma edge is scaled to the electron density n e , temperature T e , viscous time τ μ , toroidal field B t and the natural frequency ω in the form of b r /B t ∝n e αn T e αT τ μ αμ B t αB ω αω by scanning these parameters separately. Here, α n , α T , α μ , α B and α ω are the scaling coefficients on n e , T e , τ μ , B t and ω, respectively. Single-fluid modeling shows that the 3/2 EF threshold scales as b r /B t ∝n e 0.56 T e 0.6 τ μ -0.59 B t -1.15 ω, which is similar with the analytical scaling law in both the Rutherford and visco-resistive regimes. Yet, two-fluid modeling shows that the scaling law differs significantly in particular regarding the dependence on plasma rotation. In detail, the scaling coefficient α n on density decreases from 0.67 to 0.56 and α T on temperature decreases from 0.67 to 0.32, while α μ on viscous time is around -0.45 and α B on toroidal field decreases slightly from -1.15 to -1, when the ratio |ω E /ω *e | between plasma rotation frequency ω E and diamagnetic drift frequency ω *e varies from 0 to 10. Scans of the plasma rotation reveals that the penetration threshold linearly depends on the perpendicular rotation frequency (or natural frequency) ω ⊥e =ω E +ω *e , and there is a minimum in the required field amplitude when ω ⊥e 0. In addition, the enduring mystery of non-zero penetration threshold at zero plasma natural frequency in EF experiments is resolved by two-fluid simulations. We report that the very small island and smooth bifurcation in EF penetration near zero frequency is hard to detect in the experiment, leading to a finite penetration threshold within the capability of the experimental measurements.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

Scaling law for direct current field emission-driven microscale gas breakdown

The effects of field emission on direct current breakdown in microscale gaps filled with an ambient neutral gas are studied numerically and analytically. Fundamental numerical experiments using the particle-in-cell/Monte Carlo collisions method are used to systematically quantify microscale ionization and space-charge enhancement of field emission. The numerical experiments are then used to validate a scaling law for the modified Paschen curve that bridges field emission-driven breakdown with the macroscale Paschen law. Analytical expressions are derived for the increase in cathode electric field, total steady state current density, and the ion-enhancement coefficient including a new breakdown criterion. It also includes the effect of all key parameters such as pressure, operating gas, and field-enhancement factor providing a better predictive capability than existing microscale breakdown models. The field-enhancement factor is shown to be the most sensitive parameter with its increase leading to a significant drop in the threshold breakdown electric field and also to a gradual merging with the Paschen law. The proposed scaling law is also shown to agree well with two independent sets of experimental data for microscale breakdown in air. The ability to accurately describe not just the breakdown voltage but the entire pre-breakdown process for given operating conditions makes the proposed model a suitable candidate for the design and analysis of electrostatic microscale devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

MULTI-WAVELENGTH OBSERVATIONS OF THE SPATIO-TEMPORAL EVOLUTION OF SOLAR FLARES WITH AIA/SDO. II. HYDRODYNAMIC SCALING LAWS AND THERMAL ENERGIES

In this study we measure physical parameters of the same set of 155 M- and X-class solar flares observed with AIA/SDO as analyzed in Paper I, by performing a differential emission measure analysis to determine the flare peak emission measure EM{sub p} , peak temperature T{sub p} , electron density n{sub p} , and thermal energy E{sub th}, in addition to the spatial scales L, areas A, and volumes V measured in Paper I. The parameter ranges for M- and X-class flares are log (EM{sub p}) = 47.0-50.5, T{sub p} = 5.0-17.8 MK, n{sub p} = 4 × 10{sup 9}-9 × 10{sup 11} cm{sup –3}, and thermal energies of E{sub th} = 1.6 × 10{sup 28}-1.1 × 10{sup 32} erg. We find that these parameters obey the Rosner-Tucker-Vaiana (RTV) scaling law T{sub p}{sup 2}∝n{sub p} L and H∝T {sup 7/2} L {sup –2} during the peak time t{sub p} of the flare density n{sub p} , when energy balance between the heating rate H and the conductive and radiative loss rates is achieved for a short instant and thus enables the applicability of the RTV scaling law. The application of the RTV scaling law predicts power-law distributions for all physical parameters, which we demonstrate with numerical Monte Carlo simulations as well as with analytical calculations. A consequence of the RTV law is also that we can retrieve the size distribution of heating rates, for which we find N(H)∝H {sup –1.8}, which is consistent with the magnetic flux distribution N(Φ)∝Φ{sup –1.85} observed by Parnell et al. and the heating flux scaling law F{sub H} ∝HL∝B/L of Schrijver et al.. The fractal-diffusive self-organized criticality model in conjunction with the RTV scaling law reproduces the observed power-law distributions and their slopes for all geometrical and physical parameters and can be used to predict the size distributions for other flare data sets, instruments, and detection algorithms.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Towards Scaling Law Analysis For Spatiotemporal Weather Data

Compute-optimal scaling laws are relatively well studied for NLP and CV, where objectives are typically single-step and targets are comparatively homogeneous. Weather forecasting is harder to characterize in the same framework: autoregressive rollouts compound errors over long horizons, outputs couple many physical channels with disparate scales and predictability, and globally pooled test metrics can disagree sharply with per-channel, late-lead behavior implied by short-horizon training. We extend neural scaling analysis for autoregressive weather forecasting from single-step training loss to long rollouts and per-channel metrics. We quantify (1) how prediction error is distributed across channels and how its growth rate evolves with forecast horizon, (2) if power law scaling holds for test error, relative to rollout length when error is pooled globally, and (3) how that fit varies jointly with horizon and channel for parameter, data, and compute-based scaling axes. We find strong cross-channel and cross-horizon heterogeneity: pooled scaling can look favorable while many channels degrade at late leads. We discuss implications for weighted objectives, horizon-aware curricula, and resource allocation across outputs.

Kiefer Jr, Alexander [ORNL] (ORCID:000000025398874↗
DOE OSTI2024

Invariant regimes of Spencer scaling law for magnetic compression of rotating FRC plasma

Abstract The scaling laws for the magnetic compression of a toroidally rotating field reversed configuration (FRC) have been investigated in this work. The magnetohydrodynamics (MHD) simulations of the magnetic compression on rotating FRCs employing the NIMROD code (Sovinec et al 2004 J. Comput. Phys. 195 355), are compared with the Spencer’s one-dimensional (1D) theory (Spencer et al 1983 Phys. Fluids 26 1564) for a wide range of initial flow speeds and profiles. The toroidal flow can influence the scalings directly through the alteration of the compressional work as also evidenced in the 1D adiabatic model, and indirectly by reshaping the initial equilibrium. However, in comparison to the static initial FRC equilibrium cases, the pressure and the radius scalings remain invariant for the magnetic compression ratio B w 2 / B w 1 up to 6 in presence of the initial equilibrium flow, suggesting a broader applicable regime of the Spencer scaling law for FRC magnetic compression. The invariant scaling has been proven a natural consequence of the conservation of angular momentum of both fluid and magnetic field during the dynamic compression process.

Ma, Yiming↗
DOE OSTI2015

Entropy-scaling laws for diffusion coefficients in liquid metals under high pressures

Molecular dynamic simulations on the liquid copper and tungsten are used to investigate the empirical entropy-scaling laws D{sup *}=A exp(BS{sub ex}), proposed independently by Rosenfeld and Dzugutov for diffusion coefficient, under high pressure conditions. We show that the scaling laws hold rather well for them under high pressure conditions. Furthermore, both the original diffusion coefficients and the reduced diffusion coefficients exhibit an Arrhenius relationship D{sub M}=D{sub M}{sup 0} exp(−E{sub M}/K{sub B}T), (M=un,R,D) and the activation energy E{sub M} increases with increasing pressure, the diffusion pre-exponential factors (D{sub R}{sup 0} and D{sub D}{sup 0}) are nearly independent of the pressure and element. The pair correlation entropy, S{sub 2}, depends linearly on the reciprocal temperature S{sub 2}=−E{sub S}/T, and the activation energy, E{sub S}, increases with increasing pressure. In particular, the ratios of the activation energies (E{sub un}, E{sub R}, and E{sub D}) obtained from diffusion coefficients to the activation energy, E{sub S}, obtained from the entropy keep constants in the whole pressure range. Therefore, the entropy-scaling laws for the diffusion coefficients and the Arrhenius law are linked via the temperature dependence of entropy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Improved scaling law for the prediction of deuterium retention in beryllium co-deposits

Hydrogen isotope co-deposition with Be eroded from the first wall is expected to be the main fusion fuel retention mechanism in ITER. Since good fuel accounting is crucial for economic and safety reasons, reliable predictions of hydrogen isotope retention are needed. Furthermore, this study builds upon the well-established empirical De Temmerman scaling law that predicts D/Be ratios in co-deposited layers based on deposition temperature, deposition rate, and deuterium particle energy. Expanding the data used in the original development of the scaling law with an additional dataset obtained with more recent measurements using a different technique to the original De Temmerman approach, allows us to obtain new values for free parameters and improve the prediction capabilities of the new scaling law. In an effort to improve the model even further, scaling with D 2 background pressure was included and a new two-term model derived, describing D retention in low- and high-energy traps separately.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Scaling laws and deformation mechanisms of nanoporous copper under adiabatic uniaxial strain compression

A series of large-scale molecular dynamics simulations were conducted to investigate the scaling laws and the related atomistic deformation mechanisms of Cu monocrystal samples containing randomly placed nanovoids under adiabatic uniaxial strain compression. At onset of yielding, plastic deformation is accommodated by dislocations emitted from void surfaces as shear loops. The collapse of voids are observed by continuous emissions of dislocations from void surfaces and their interactions with further plastic deformation. The simulation results also suggest that the effect modulus, the yield stress and the energy aborption density of samples under uniaxial strain are linearly proportional to the relative density ρ. Moreover, the yield stress, the average flow stress and the energy aborption density of samples with the same relative density show a strong dependence on the void diameter d, expressed by exponential relations with decay coefficients much higher than -1/2. The corresponding atomistic mechanisms for scaling laws of the relative density and the void diameter were also presented. The present results should provide insights for understanding deformation mechanisms of nanoporous metals under extreme conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Size of the Atmospheric Blocking Events: Scaling Law and Response to Climate Change

Abstract Understanding the response of atmospheric blocking events to climate change has been of great interest in recent years. However, potential changes in the blocking area (size), which can affect the spatiotemporal characteristics of the resulting extreme events, have not received much attention. Using two large‐ensemble, fully coupled general circulation model (GCM) simulations, we show that the size of blocking events increases with climate change, particularly in the Northern Hemisphere (by as much as 17%). Using a two‐layer quasi‐geostrophic model and a dimensional analysis technique, we derive a scaling law for the size of blocking events, which shows that area mostly scales with width of the jet times the Kuo scale (i.e., the length of stationary Rossby waves). The scaling law is validated in a range of idealized GCM simulations. Predictions of this scaling law agree well with changes in blocking events' size under climate change in fully coupled GCMs in winters but not in summers.

Nabizadeh, Ebrahim↗
DOE OSTI2021

Comparative study with two reduced test facilities for air-cooled RCCS scaling law

Korea Atomic Energy Research Institute (KAERI) and Argonne National Laboratory (ANL) conducted steady-state tests at constant heat flux conditions to investigate the scale effect on heat removal behavior of the air-cooled Reactor Cavity Cooling System (RCCS). Two differently scaled-down test facilities were used in this study, KAERI’s ¼ scale with 4.0-m cavity height, and ANL’s ½ scale with 6.8-m cavity height. Two scaling laws were proposed to simulate the radiation across the cavity and the buoyancy-driven duct flow in the riser, respectively. The test matrix for KAERI and ANL test facilities focused on the scaling effect of the heated riser length with constant heat flux at the PMR200 RCCS design. The test results showed that mixed convection in the riser duct is an important factor for accurately extrapolating the thermo-fluid behavior in the prototype from the test results in the scale-down facilities. The system analysis code, GAMMA+, with improved heat transfer models predicted fairly well the air-cooled RCCS test data from two facilities. GAMMA+ analysis results showed that the predicted radiation fractions on the heated plate in the scale-down test conditions were larger than those on the reactor vessel in the prototype. The scaling law for air-cooled RCCS was improved by considering the mixed convection in the riser duct and the same radiation fraction on the heated plate. The mixed convection effect was calculated by the height ratio. The same radiation fraction provided a conservative extrapolation from the scale-down test results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Superdiffusion of quantized vortices uncovering scaling laws in quantum turbulence

Significance Quantum turbulence (QT) can appear in the presence of a chaotic tangle of quantized vortices in various quantum-fluid systems, including atomic Bose–Einstein condensates, superfluid helium, superfluid neutron stars, etc. Insights into the generic scaling behaviors of tangled vortices are crucial in developing an advanced statistical model of QT. By tracking tracer particles trapped on vortices in superfluid 4 He, we report the observation of an apparent superdiffusion of the vortices in QT. Our analysis shows that this superdiffusion is not due to Lévy flights, i.e., long-distance hops that are responsible for superdiffusion of random walkers. Instead, a power-law scaling of the vortex–velocity correlation is identified as the cause. This finding may motivate extensive future research on hidden scaling laws in QT.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗