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DOE OSTI2024

Nonprompt direct-photon production in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV

The measurement of the direct-photon spectrum from Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV is presented by the PHENIX Collaboration using the external-photon-conversion technique for 0%–93% central collisions in a transverse-momentum (𝑝 𝑇 ) range of 0.8–10 GeV/𝑐. An excess of direct photons, above prompt-photon production from hard-scattering processes, is observed for 𝑝 𝑇 < 6 GeV/𝑐. Nonprompt direct photons are measured by subtracting the prompt component, which is estimated as 𝑁 coll -scaled direct photons from 𝑝 + 𝑝 collisions at 200 GeV, from the direct-photon spectrum. Results are obtained for 0.8 < 𝑝 𝑇 < 6.0 GeV/𝑐 and suggest that the spectrum has an increasing inverse slope from ≈0.2 to 0.4 GeV/𝑐 with increasing 𝑝 𝑇 , which indicates a possible sensitivity of the measurement to photons from earlier stages of the evolution of the collision. In addition, like the direct-photon production, the 𝑝 𝑇 -integrated nonprompt direct-photon yields also follow a power-law scaling behavior as a function of collision-system size. Finally, the exponent, 𝛼, for the nonprompt component is found to be consistent with 1.1 with no apparent 𝑝 𝑇 dependence.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Topological Singularity Induced Chiral Kohn Anomaly in a Weyl Semimetal

The electron-phonon interaction (EPI) is instrumental in a wide variety of phenomena in solid-state physics, such as electrical resistivity in metals, carrier mobility, optical transition, and polaron effects in semiconductors, lifetime of hot carriers, transition temperature in BCS superconductors, and even spin relaxation in diamond nitrogen-vacancy centers for quantum information processing. However, due to the weak EPI strength, most phenomena have focused on electronic properties rather than on phonon properties. One prominent exception is the Kohn anomaly, where phonon softening can emerge when the phonon wave vector nests the Fermi surface of metals. In this paper, we report a new class of Kohn anomaly in a topological Weyl semimetal (WSM), predicted by field-theoretical calculations, and experimentally observed through inelastic x-ray and neutron scattering on WSM tantalum phosphide. Compared to the conventional Kohn anomaly, the Fermi surface in a WSM exhibits multiple topological singularities of Weyl nodes, leading to a distinct nesting condition with chiral selection, a power-law divergence, and non-negligible dynamical effects. Our work brings the concept of the Kohn anomaly into WSMs and sheds light on elucidating the EPI mechanism in emergent topological materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1983

Polar cap electron densities from DE 1 plasma wave observations

Electric-field-spectum measurements from the plasma-wave instrument on the Dynamics Explorer 1 spacecraft are used to study the local electron density at high altitudes in the northern polar-cap region. The electron density is determined from the upper cutoff of whistler-mode radiation at the electron plasma frequency. Median density values over the polar cap at L greater than 10 are found to vary from 35.2 + or - 8.5 cu cm at 2.1 earth radii to 0.99 + or - 0.51 cu cm at 4.66 earth radii. The steady-state radial-outflow model is examined for consistency with the observed density profile. A power-law fit to the radial variation of the electron density yields an exponent of - 3.85 + or - 0.32, which for the radial-outflow model implies a flow velocity increasing nearly linearly with incresing radial distance. Comparison of the observed electron densities with theoretical polar-wind densities yields consistent results up to 2.8 earth radii. A comparison of the observed electron densities with low-altitude density profiles from the Alouette II and ISIS 1 spacecraft illustrates transitions in the slope of the profile at 1.16 earth radii and between 1.55 and 2.0 earth radii. The changes in the density profile suggest that changes occur in the basic radial-transport processes at these altitudes.

Persoon, A. M.↗

DOE OSTI2024

Asymmetric drift in MaNGA: mass and radially dependent stratification rates in galaxy discs

ABSTRACT We measure the age–velocity relationship from the lag between ionized gas and stellar tangential speeds in ∼500 nearby disc galaxies from MaNGA in Sloan Digital Sky Survey IV (SDSS-IV). Selected galaxies are kinematically axisymmetric. Velocity lags are asymmetric drift, seen in the Milky Way’s (MW) solar neighbourhood and other Local Group galaxies; their amplitude correlates with stellar population age. The trend is qualitatively consistent in rate ($\dot{\sigma }$) with a simple power-law model where σ ∝ tb that explains the dynamical phase-space stratification in the solar neighbourhood. The model is generalized based on disc dynamical times to other radii and other galaxies. We find in-plane radial stratification parameters σ0,r (dispersion of the youngest populations) in the range of 10–40 km s−1 and 0.2 < br < 0.5 for MaNGA galaxies. Overall, brincreases with galaxy mass, decreases with radius for galaxies above 10.4 dex (M⊙) in stellar mass, but is ∼constant with radius at lower mass. The measurement scatter indicates the stratification model is too simple to capture the complexity seen in the data, unsurprising given the many possible astrophysical processes that may lead to stellar population dynamical stratification. None the less, the data show dynamical stratification is broadly present in the galaxy population, with systematic trends in mass and density. The amplitude of the asymmetric drift signal is larger for the MaNGA sample than the MW, and better represented in the mean by what is observed in the discs of M31 and M33. Either typical discs have higher surface-density or, more likely, are dynamically hotter (hence thicker) than the MW.

Bershady, Matthew A. (ORCID:0000000231314374)↗

NASA NTRS2017

HMI Data Driven Magnetohydrodynamic Model Predicted Active Region Photospheric Heating Rates: Their Scale Invariant, Flare Like Power Law Distributions, and Their Possible Association With Flares

A data driven, near photospheric, 3 D, non-force free magnetohydrodynamic model pre- dicts time series of the complete current density, and the resistive heating rate Q at the photosphere in neutral line regions (NLRs) of 14 active regions (ARs). The model is driven by time series of the magnetic field B observed by the Helioseismic & Magnetic Imager on the Solar Dynamics Observatory (SDO) satellite. Spurious Doppler periods due to SDO orbital motion are filtered out of the time series for B in every AR pixel. Errors in B due to these periods can be significant. The number of occurrences N(q) of values of Q > or = q for each AR time series is found to be a scale invariant power law distribution, N(Q) / Q−s, above an AR dependent threshold value of Q, where 0.3952 < or = s < or = 0.5298 with mean and standard deviation of 0.4678 and 0.0454, indicating little variation between ARs. Observations show that the number of occurrences N(E) of coronal flares with a total energy released > or = E obeys the same type of distribution, N(E) / E−S, above an AR dependent threshold value of E, with 0.38 < or approx. S < or approx. 0.60, also with little variation among ARs. Within error margins the ranges of s and S are nearly identical. This strong similarity between N(Q) and N(E) suggests a fundamental connection between the process that drives coronal flares and the process that drives photospheric NLR heating rates in ARs. In addition, results suggest it is plausible that spikes in Q, several orders of magnitude above background values, are correlated with times of the subsequent occurrence of M or X flares.

Goodman, Michael L.↗

NASA NTRS2017

HMI Data Driven Magnetohydrodynamic Model Predicted Active Region Photospheric Heating Rates: Their Scale Invariant, Flare Like Power Law Distributions, and Their Possible Association With Flares

A data driven, near photospheric, 3 D, non-force free magnetohydrodynamic model predicts time series of the complete current density, and the resistive heating rate Q at the photosphere in neutral line regions (NLRs) of 14 active regions (ARs). The model is driven by time series of the magnetic field B observed by the Helioseismic and Magnetic Imager on the Solar Dynamics Observatory (SDO) satellite. Spurious Doppler periods due to SDO orbital motion are filtered out of the time series for B in every AR pixel. Errors in B due to these periods can be significant. The number of occurrences N(q) of values of Q > or = q for each AR time series is found to be a scale invariant power law distribution, N(Q) / Q−s, above an AR dependent threshold value of Q, where 0.3952 < or = s < or = 0.5298 with mean and standard deviation of 0.4678 and 0.0454, indicating little variation between ARs. Observations show that the number of occurrences N(E) of coronal flares with a total energy released > or = E obeys the same type of distribution, N(E) / E−S, above an AR dependent threshold value of E, with 0.38 < or approx. S < or approx. 0.60, also with little variation among ARs. Within error margins the ranges of s and S are nearly identical. This strong similarity between N(Q) and N(E) suggests a fundamental connection between the process that drives coronal flares and the process that drives photospheric NLR heating rates in ARs. In addition, results suggest it is plausible that spikes in Q, several orders of magnitude above background values, are correlated with times of the subsequent occurrence of M or X flares.

Goodman, Michael L.↗

DOE OSTI2022

The rapid destruction of toroidal magnetic surfaces

The operation of ITER will require reliable simulations in order to avoid major damage to the device from disruptions. Disruptions are the sudden breakup of magnetic surfaces across the plasma volume—a fast magnetic reconnection. This reconnection can be caused by the growth of perturbations outside of the plasma core causing an ideal perturbation to the core. This causes an increasing ratio of the maximum to the minimum separation, Δmax/Δmin, between neighboring magnetic surfaces. Magnetic reconnection becomes a dominant process when magnetic field lines can quickly interchange connections over a spatial scale ar. This occurs when Δmax/Δmin≳ar/Δd, where Δd is the scale over which non-ideal effects make magnetic field lines indistinguishable. Traditional reconnection theory is fundamentally different. It is a study of the steady-state cancelation of oppositely directed magnetic field components across a thin layer. During more than sixty years, mathematical implications of Faraday's law have been derived that clarify and constrain the physics of fast magnetic reconnection. These are reviewed because they are not commonly known but are needed to understand and to place in context how an ideal magnetic evolution can cause reconnection to quickly become a dominant process no matter how small Δd/ar may be.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Hyporheic Exchange Driven by Submerged Rigid Vegetation: A Modeling Study

Flow-vegetation interaction affects fluid flow hydraulics and associated material transport in river corridors. Concomitant changes in pressure within the flow field due to the presence of vegetation may act as a driver for the formation of hyporheic flow across the sediment-water interface. This potentially important process, however, has yet to be studied. In order to investigate vegetation-induced hyporheic exchange, a series of numerical models of interlinked surface-subsurface flow modified by plant stems was conducted. Periodically staggered plant stem arrays on a flat sediment bed were considered within a coupled multiphysics computational fluid dynamics approach. Plants were idealized as rigid cylinders and arranged in different streamwise and spanwise spacing distances. Each vegetation array was then subjected to a broad range of flow Reynolds Numbers (Re). The results showed that hyporheic flow occurs in all conditions with the presence of vegetation. The vegetation-induced hyporheic flux is found to be a function of Re via a power law. The flux increases with interstem space until the space reaches the distance that rigid stems no longer affect the flow structures in the vicinity of each other. Larger intervegetation distances lead to a larger hyporheic zone. A direct comparison with bedforminduced hyporheic flow showed that vegetation can induce higher hyporheic flux through relatively shallower exchange zones. The results of all the simulations were synthesized into predictive models for hyporheic flux, bulk residence time and exchange depth based on drag coefficient, vegetation density, and Reynolds Number.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Analysis of Two Models for the Angular Structure of the Outflows Producing the Swift/XRT “Larger-angle Emission” of Gamma-Ray Bursts

The quasi-instantaneous emission from a relativistic surface endowed with a Lorentz factor that decreases away from the outflow symmetry axis can naturally explain the three phases observed by Swift X-Ray Telescope (XRT) in gamma-ray bursts (GRBs) and their afterglows (GRB tail, afterglow plateau, and postplateau) based only on the angular change of the relativistic Doppler boost across the outflow surface. We develop further the analytical formalism of the “larger-angle emission” model for the case of “n-exponential” outflows (where the Lorentz factor Γ dependence of the angular location θ is Γ ~ exp{-(θ/θ c ) n }), and compare its ability to account for the X-ray emission of XRT afterglows relative to that of “power-law” outflows (Γ ∼ θ −g ). Power-law outflows yield longer afterglow plateaus, followed by slower postplateau flux decays than n-exponential outflows, features which may be used in identifying which type of angular structure is at work in a given afterglow. Identifying the Γ(θ) angular structure that accommodates XRT light curves is slightly complicated by the fact that the afterglow X-ray light curve is also determined by how two characteristics of the comoving-frame emission spectrum (peak energy $E'_p$ and peak intensity $i'_p$) change with the angular location or, equivalently, with the Lorentz factor. Here, we assume power-law Γ dependences of those spectral characteristics and find that, unlike power-law outflows, n-exponential outflows cannot account for plateaus with a temporal dynamical range larger than 100 (2 dex in logarithmic space). To capture all the information contained in XRT afterglow measurements (0.3–10 keV unabsorbed flux and effective spectral slope), we calculate 0.3 and 10 keV light curves using a broken-power-law emission spectrum of peak energy and low- and high-energy slopes that are derived from the effective slope measured by XRT. This economical peak energy determination is found to be consistent with the results of more expensive spectral fits. The angular distributions of the Lorentz factor, comoving frame peak energy, and peak intensity (Γ(θ), $E'_p$(θ), $i'_p$(θ)) constrain the (yet-to-be determined) convolution of various features of the production of relativistic jets by solar-mass black holes and of their propagation through the progenitor/circumburst medium, while the $E'_p$(Γ) and $i'_p$(Γ) dependences may constrain the GRB dissipation mechanism and the GRB emission process.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2012

Disentangling AGN and Star Formation in Soft X-Rays

We have explored the interplay of star formation and active galactic nucleus (AGN) activity in soft X-rays (0.5-2 keV) in two samples of Seyfert 2 galaxies (Sy2s). Using a combination of low-resolution CCD spectra from Chandra and XMM-Newton, we modeled the soft emission of 34 Sy2s using power-law and thermal models. For the 11 sources with high signal-to-noise Chandra imaging of the diffuse host galaxy emission, we estimate the luminosity due to star formation by removing the AGN, fitting the residual emission. The AGN and star formation contributions to the soft X-ray luminosity (i.e., L(sub x,AGN) and L(sub x,SF)) for the remaining 24 Sy2s were estimated from the power-law and thermal luminosities derived from spectral fitting. These luminosities were scaled based on a template derived from XSINGS analysis of normal star-forming galaxies. To account for errors in the luminosities derived from spectral fitting and the spread in the scaling factor, we estimated L(sub x,AGN) and L(sub x,SF))from Monte Carlo simulations. These simulated luminosities agree with L(sub x,AGN) and L(sub x,SF) derived from Chandra imaging analysis within a 3sigma confidence level. Using the infrared [Ne ii]12.8 micron and [O iv]26 micron lines as a proxy of star formation and AGN activity, respectively, we independently disentangle the contributions of these two processes to the total soft X-ray emission. This decomposition generally agrees with L(sub x,SF) and L(sub x,AGN) at the 3 sigma level. In the absence of resolvable nuclear emission, our decomposition method provides a reasonable estimate of emission due to star formation in galaxies hosting type 2 AGNs.

Disentangling↗

NASA NTRS1989

Monte Carlo simulation of particle acceleration at astrophysical shocks

A Monte Carlo code was developed for the simulation of particle acceleration at astrophysical shocks. The code is implemented in Turbo Pascal on a PC. It is modularized and structured in such a way that modification and maintenance are relatively painless. Monte Carlo simulations of particle acceleration at shocks follow the trajectories of individual particles as they scatter repeatedly across the shock front, gaining energy with each crossing. The particles are assumed to scatter from magnetohydrodynamic (MHD) turbulence on both sides of the shock. A scattering law is used which is related to the assumed form of the turbulence, and the particle and shock parameters. High energy cosmic ray spectra derived from Monte Carlo simulations have observed power law behavior just as the spectra derived from analytic calculations based on a diffusion equation. This high energy behavior is not sensitive to the scattering law used. In contrast with Monte Carlo calculations diffusive calculations rely on the initial injection of supra-thermal particles into the shock environment. Monte Carlo simulations are the only known way to describe the extraction of particles directly from the thermal pool. This was the triumph of the Monte Carlo approach. The question of acceleration efficiency is an important one in the shock acceleration game. The efficiency of shock waves efficient to account for the observed flux of high energy galactic cosmic rays was examined. The efficiency of the acceleration process depends on the thermal particle pick-up and hence the low energy scattering in detail. One of the goals is the self-consistent derivation of the accelerated particle spectra and the MHD turbulence spectra. Presumably the upstream turbulence, which scatters the particles so they can be accelerated, is excited by the streaming accelerated particles and the needed downstream turbulence is convected from the upstream region. The present code is to be modified to include a better description of particle scattering (pitch-angle instead of hard-sphere) and as iterative procedure for treating the self-excitation of the MHD turbulence.

Campbell, Roy K.↗

NASA NTRS1995

An intercomparison of plasma turbulence at three comets: Grigg-Skjellerup, Giacobini-Zinner, and Halley

The power laws are approximately f(exp -1.9), f(exp -1.9), and f(exp -2.1) respectively for the Grigg-Shjellerup (GS), Giacobini-Zinner (GZ), and Halley (H) comets. Other than similarities in the power spectra, the magnetic field turbulence is considerably different at the three comets. Phase steepening is demonstrated to occur at the trailing edges of the GS waves. This is probably due to nonlinear steepening plus dispersion of the left-hand mode components, i.e., the turbulence is whistler-mode. This too can be explained by nonlinear steepening plus dispersion of the magnetosonic waves. At the level of GS and GZ turbulence development when the spacecraft measurements were made, classical three-wave processes, such as the decay or modulation instabilities do not appear to play important roles. It is most likely that the nonlinear steepening and dispersive time scales are more rapid than three-wave processes, and the latter had not had time to develop for the relatively new turbulence. The wave turbulence at Halley is linearly polarized. The exact nature of this turbulence is still not well understood. Several possibilities are suggested, based on a preliminary analyses.

Tsurutani, Bruce T.↗

NASA NTRS2002

The Seyfert-Starburst Connection in X-rays: The Data - 1

We analyze X-ray spectra and images of a sample of Seyfert 2 galaxies that unambiguously contain starbursts, based on their optical and UV characteristics. Although all sample members contain active galactic nuclei (AGNs), supermassive black holes or other related processes at the galactic centers alone cannot account for the total X-ray emission in all instances. Eleven of the 12 observed galaxies are significantly resolved with the ROSAT High Resolution Imager, while six of the eight sources observed with the lower resolution Position Sensitive Proportional Counter also appear extended on larger scales. The X-ray emission is extended on physical scales of 10 kpc and greater, which we attribute to starburst-driven outflows and supernova heating of the interstellar medium. Spectrally, a physically motivated composite model of the X-ray emission that includes a heavily absorbed (N(sub H) greater than 10(exp 23)/sq cm) nuclear component (the AGN), power-law-like scattered AGN flux, and a thermal starburst describes this sample well. Half the sample exhibit iron K(alpha) lines, which are typical of AGNs.

Levenson, N. A.↗

NASA NTRS1991

Application of powder densification models to the consolidation processing of composites

Unidirectional fiber reinforced metal matrix composite tapes (containing a single layer of parallel fibers) can now be produced by plasma deposition. These tapes can be stacked and subjected to a thermomechanical treatment that results in a fully dense near net shape component. The mechanisms by which this consolidation step occurs are explored, and models to predict the effect of different thermomechanical conditions (during consolidation) upon the kinetics of densification are developed. The approach is based upon a methodology developed by Ashby and others for the simpler problem of HIP of spherical powders. The complex problem is devided into six, much simpler, subproblems, and then their predicted contributions are added to densification. The initial problem decomposition is to treat the two extreme geometries encountered (contact deformation occurring between foils and shrinkage of isolated, internal pores). Deformation of these two geometries is modelled for plastic, power law creep and diffusional flow. The results are reported in the form of a densification map.

Wadley, H. N. G.↗

DOE OSTI2022

Quantum criticality using a superconducting quantum processor

Quantum criticality emerges from the collective behavior of many interacting quantum particles, often at the transition between different phases of matter. It is one of the cornerstones of condensed matter physics, which we access on noisy intermediate-scale (NISQ) quantum devices by leveraging a dynamically driven phenomenon. Here we probe the critical properties of the one-dimensional quantum Ising model on a programmable superconducting quantum chip via a Kibble-Zurek process, obtain scaling laws, and estimate critical exponents despite inherent sources of errors on the hardware. In addition, we investigate how the improvement of NISQ computers (more qubits, less noise) will consolidate the computation of those universal physical properties. A one-parameter noise model captures the effect of imperfections and reproduces the experimental data. Its systematic study reveals that the noise, analogously to temperature, induces a new length scale in the system. We introduce and successfully verify modified scaling laws, directly accounting for the noise without any prior knowledge. It makes data analyses for extracting physical properties transparent to noise. By understanding how imperfect quantum hardware modifies the genuine properties of quantum states of matter, we enhance the power of NISQ processors considerably for addressing quantum criticality and potentially other phenomena and algorithms.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Impact of crowding on the diversity of expanding populations

Crowding effects critically impact the self-organization of densely packed cellular assemblies, such as biofilms, solid tumors, and developing tissues. When cells grow and divide, they push each other apart, remodeling the structure and extent of the population’s range. Recent work has shown that crowding has a strong impact on the strength of natural selection. However, the impact of crowding on neutral processes, which controls the fate of new variants as long as they are rare, remains unclear. Here, we quantify the genetic diversity of expanding microbial colonies and uncover signatures of crowding in the site frequency spectrum. By combining Luria–Delbrück fluctuation tests, lineage tracing in a novel microfluidic incubator, cell-based simulations, and theoretical modeling, we find that the majority of mutations arise behind the expanding frontier, giving rise to clones that are mechanically “pushed out” of the growing region by the proliferating cells in front. These excluded-volume interactions result in a clone-size distribution that solely depends on where the mutation first arose relative to the front and is characterized by a simple power law for low-frequency clones. Our model predicts that the distribution depends on a single parameter—the characteristic growth layer thickness—and hence allows estimation of the mutation rate in a variety of crowded cellular populations. Combined with previous studies on high-frequency mutations, our finding provides a unified picture of the genetic diversity in expanding populations over the whole frequency range and suggests a practical method to assess growth dynamics by sequencing populations across spatial scales.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2026

Molecular concentration field design using closed-form steady-state solutions

Control over spatial concentration fields represents a fundamental challenge in designing synthetic biological systems and programmable soft materials. While nature creates morphogen gradients that orchestrate complex developmental processes, synthetic approaches have largely relied on empirical optimization and computationally intensive simulations. Here, we present an analytical framework for steady-state concentration fields generated by finite-sized localized sources in diffusion–degradation systems and derive closed-form solutions for one-, two-, and three-dimensional geometries. By expressing these solutions in dimensionless form, we show that gradient steepness and spatial structure are organized by the Thiele modulus, which captures the competition between diffusion and degradation length scales. The analysis reveals distinct design regimes: in degradation-dominated systems, gradient shape is governed by exponential decay and becomes dimension-independent, whereas in diffusion-dominated systems, gradient magnitude and extent follow dimension-dependent power-law scaling. Building on these results, we introduce a quantitative design strategy that uses threshold-based criteria to program concentration ranges by tuning physically accessible parameters, most directly the production rate, while holding transport and degradation properties fixed. Comparisons with numerical solutions and reported experimental systems demonstrate consistency with the predicted scaling behavior. Together, this work provides a generalizable and physically transparent framework for designing steady-state concentration fields in synthetic biological and soft matter systems, enabling predictive control of gradient-mediated organization without reliance on extensive numerical optimization.

Kim, Dong Woo [Johns Hopkins University, Baltimore↗

NASA NTRS1988

Crater size estimates for large-body terrestrial impact

Calculating the effects of impacts leading to global catastrophes requires knowledge of the impact process at very large size scales. This information cannot be obtained directly but must be inferred from subscale physical simulations, numerical simulations, and scaling laws. Schmidt and Holsapple presented scaling laws based upon laboratory-scale impact experiments performed on a centrifuge (Schmidt, 1980 and Schmidt and Holsapple, 1980). These experiments were used to develop scaling laws which were among the first to include gravity dependence associated with increasing event size. At that time using the results of experiments in dry sand and in water to provide bounds on crater size, they recognized that more precise bounds on large-body impact crater formation could be obtained with additional centrifuge experiments conducted in other geological media. In that previous work, simple power-law formulae were developed to relate final crater diameter to impactor size and velocity. In addition, Schmidt (1980) and Holsapple and Schmidt (1982) recognized that the energy scaling exponent is not a universal constant but depends upon the target media. Recently, Holsapple and Schmidt (1987) includes results for non-porous materials and provides a basis for estimating crater formation kinematics and final crater size. A revised set of scaling relationships for all crater parameters of interest are presented. These include results for various target media and include the kinematics of formation. Particular attention is given to possible limits brought about by very large impactors.

Schmidt, Robert M.↗