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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Far-from-equilibrium search for the QCD critical point

Initial conditions for relativistic heavy-ion collisions may be far from equilibrium (i.e., there are large initial contributions from the shear stress tensor and bulk pressure) but it is expected that on very short time scales the dynamics converge to a universal attractor that defines hydrodynamic behavior. Thus far, studies of this nature have only considered an idealized situation at LHC energies (high temperatures T and vanishing baryon chemical potential µ B = 0) but, in this work, we investigate for the first time how far-from-equilibrium effects may influence experimentally driven searches for the Quantum Chromodynamic critical point at RHIC. We find that the path to the critical point is heavily influenced by far from equilibrium initial conditions where viscous effects lead to dramatically different {T, µ B } trajectories through the QCD phase diagram. We compare hydrodynamic equations of motion with shear and bulk coupled together at finite µB for both DNMR and phenomenological Israel-Stewart equations of motion and discuss their influence on potential attractors at finite µ B and their corresponding {T, µ B } trajectories.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Dynamical Aspects of the Quark Gluon Plasma

Shortly after the Big Bang the entire universe was filled with a nearly perfect fluid known as the Quark Gluon Plasma. Relativistic heavy ion collisions can now reproduce this fluid in the laboratory where the Quark Gluon Plasma exhibits a rapid but smooth cross-over phase transition into hadrons at vanishing net-baryon densities. Recent experiments plan to explore finite baryon densities where a critical point is expected. If found, this would mark the first discovery of a critical point in a relativistic system described by a fundamental theory of nature, which would have far-reaching consequences for high-energy nuclear physics and nuclear astrophysics (such as in neutron star mergers). Characteristic temperatures of equilibrium (e.g. the inflection point of the entropy density) and transport coefficients (e.g. minimum of the shear viscosity over entropy density) vary widely at a cross-over phase transition but converge at a critical point, and extracting the behavior of these characteristic temperatures is a major focal point of this research. Specifically, the interplay between strange and light hadrons is exploited to study the flavor hierarchy in the cross-over region. To investigate this, a viscous relativistic hydrodynamics framework with two conserved charges is being developed into a new open-source code along with initial conditions that contain baryon number and strangeness. Flow observables sensitive to the equation of state and transport coefficients are calculated across beam energies. New techniques are being developed to study this flavor hierarchy from first principles and to extract the characteristic temperatures from experimental data. Through this new dynamical framework, this project provides essential guidance to the Beam Energy Scan II runs at Relativistic Heavy-Ion Collider and the future Facility for Antiproton and Ion Research facility in the search for the Quantum Chromodynamic critical point and subsequent investigation of the baryon-rich Quark Gluon Plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1986

The role of latent heat in kinetic energy conversions of South Pacific cyclones

The four-dimensional behavior of cyclone systems in the South Pacific Convergence Zone (SPCZ) is analyzed. Three cyclone systems, which occurred during the period from January 10-16, 1979, are examined using the data collected during the first special observing period of the FGGE. The effects of latent heating on the life cycles of the cyclones are investigated. Particular attention is given to the conversions of eddy available potential energy to eddy kinetic energy and of mean kinetic energy to eddy kinetic energy. The net radiation profile, sensible heat flux, total field of vertical motion, and latent heat component were computed. The life cycles of the cyclones are described. It is observed that the latent heating component accounts for nearly all the conversion in the three cyclones, and latent heating within the SPCZ is the major source of eddy kinetic energy for the cyclones.

Kann, Deirdre M.↗
NASA NTRS2012

Advances in the RXTE Proportional Counter Array Calibration: Nearing the Statistical Limit

During its 16 years of service Rossi X-ray Timing Explorer (RXTE) mission has provided an extensive archive of data, which will serve as a primary source of high cadence observation of variable X-ray sources for fast timing studies. It is, therefore, very important to have the most reliable calibration of RXTE instruments. The Proportional Counter Array (PCA) is the primary instrument on-board RXTE which provides data in 2-50 keY with higher than millisecond time resolution in up to 256 energy channels. In 2009 RXTE team revised the response residual minimization method used to derive the parameters of the PCA physical model. The procedure is now based on the residual minimization between the model spectrum for Crab nebula emission and a calibration data set consisting of a number of spectra from the Crab and the on-board Am241 calibration source, uniformly covering a whole RXTE span. The new method led to a much more effective model convergence and allowed for better understanding of the behavior of the PCA energy-to-channel relationship. It greatly improved the response matrix performance. We describe the new version of the RXTE/PCA response generator PCARMF vll.7 along with the corresponding energy-to-channel conversion table (version e05v04) and their difference from the previous releases of PCA calibration. The new PCA response adequately represents the spectrum of the calibration sources and successfully predicts the energy of the narrow iron emission line in Cas-A throughout the RXTE mission.

Shaposhnikov, Nikolai↗
NASA NTRS2023

Implementation, Realization and an Effective Solver of Two-Equation Turbulence Models

Currently, when the Reynolds-Averaged Navier-Stokes (RANS) equations are solved using turbulence modeling, most often the one-equation model of Spalart and Allmaras is used. Then, it is only necessary to solve the RANS equations in conjunction with a single transport equation for modeling turbulence. For this model, considerable assessment and analysis has been performed, allowing the possibility of a reliable solution method for an eddy viscosity required to compute the Reynolds stresses in the RANS equations. Such evaluation along with analysis has not been achieved to realize similar performance with two-equation models of the k-w type. The primary objective of this paper is to present and discuss the components of an effective numerical algorithm for solving the RANS equations and the two transport equations of k-w type turbulence models. All the important details of the turbulence model as actually implemented are given, which is sometimes not done in various papers considering such modeling. The viability and effectiveness of this solution algorithm are demonstrated by solving both two-dimensional and three-dimensional aerodynamic flows. In all applications, a linear rate of convergence without oscillations or other evidence of unstable behavior is observed. This behavior is also particularly true when the proposed algorithm is applied to systematically renewed mesh sequences, which is generally not observed with algorithms solving more than one transport equation. Thus, numerical integration errors are systematically reduced, allowing for a significantly more reliable assessment of the effectiveness of the turbulence model. Additionally, in this paper, analysis of the solution algorithm, including linear stability, is also performed for a particular flow problem.

Turbulence↗
NASA NTRS1995

Convergence properties of finite-difference hydrodynamics schemes in the presence of shocks

We investigate the asymptotic convergence of finite-difference schemes for the Euler equations when the limiting solution contains shocks. The Lax-Wendroff theorem guarantees that certain conservative schemes converge to correct, physically valid solutions. We focus on two one-dimensional operator-split schemes with explicit artificial-viscosity terms. One, an internal-energy scheme, does not satisfy the assumptions of Lax-Wendroff; the other, a conservative total-energy scheme, does. With viscous lengths chosen proportional to the grid size, we find that both schemes converge to their zero-grid-size limits at the theoretically expected rate, but only the conversative scheme converges toward correct solutions of the inviscid fluid equations. We show that the difference in their behaviors results directly from the presence of shocks in the limiting solution. Empirically, we find that when the viscous lenghts tend toward zero more slowly than the grid size, however the nonconservative scheme also converges toward correct solutions. We characterize the asymptotic behavior of the total-energy scheme in a particular problem in which a shock forms. As the grid is refined, a Cauchy error approaches the expected rate of change slowly. We show that the changes in the artificial viscosity alter the diffusion of small-amplitude waves. The differences associated with such waves make the dominant contribution to the Cauchy error. We formulate an analytic model to relate the rate of approach to the effect of varying diffusion in waves and find quantitative agreement with our numerical results.

Kimoto, Paul A.↗
DOE OSTI2024

Hutchinson Trace Estimation for high-dimensional and high-order Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) have proven effective in solving partial differential equations (PDEs), especially when some data are available by seamlessly blending data and physics. However, extending PINNs to high-dimensional and even high-order PDEs encounters significant challenges due to the computational cost associated with automatic differentiation in the residual loss function calculation. Herein, we address the limitations of PINNs in handling high-dimensional and high-order PDEs by introducing the Hutchinson Trace Estimation (HTE) method. Starting with the second-order high-dimensional PDEs, which are ubiquitous in scientific computing, HTE is applied to transform the calculation of the entire Hessian matrix into a Hessian vector product (HVP). This approach not only alleviates the computational bottleneck via Taylor-mode automatic differentiation but also significantly reduces memory consumption from the Hessian matrix to an HVP’s scalar output. We further showcase HTE’s convergence to the original PINN loss and its unbiased behavior under specific conditions. Comparisons with the Stochastic Dimension Gradient Descent (SDGD) highlight the distinct advantages of HTE, particularly in scenarios with significant variability and variance among dimensions. We further extend the application of HTE to higher-order and higher-dimensional PDEs, specifically addressing the biharmonic equation. By employing tensor-vector products (TVP), HTE efficiently computes the colossal tensor associated with the fourth-order high-dimensional biharmonic equation, saving memory and enabling rapid computation. The effectiveness of HTE is illustrated through experimental setups, demonstrating comparable convergence rates with SDGD under memory and speed constraints. Additionally, HTE proves valuable in accelerating the Gradient-Enhanced PINN (gPINN) version as well as the Biharmonic equation. Overall, HTE opens up a new capability in scientific machine learning for tackling high-order and high-dimensional PDEs.

Curse of dimensionality↗
NASA NTRS2018

The Fusion Driven Rocket: Nuclear Propulsion through Direct Conversion of Fusion Energy

The future of manned space exploration and development of space depends critically on the creation of a dramatically more efficient propulsion architecture for in-space transportation. A very persuasive reason for investigating the applicability of nuclear power in rockets is the vast energy density gain of nuclear fuel when compared to chemical combustion energy. The Fusion Driven rocket (FDR) represents a revolutionary approach to fusion propulsion where the power source releases its energy directly into the propellant, not requiring conversion to electricity. It employs a solid lithium propellant that requires no significant tankage mass. The propellant is rapidly heated and accelerated to high exhaust velocity (> 30 km/s), while having no substantial physical interaction with the spacecraft thereby avoiding damage to the rocket and limiting both the thermal heat load and radiator mass. The key to achieving this stems from research at MSNW and the UW on the magnetically driven implosion of metal foils onto a magnetized plasma target to obtain fusion conditions. A logical extension of this work leads to a method that utilizes these metal shells (or liners) to not only achieve fusion conditions, but to serve as the propellant as well. Several low-mass, magnetically driven metal liners are inductively driven to converge radially and axially and form a thick blanket surrounding the target plasmoid and compress the plasmoid to fusion conditions. Virtually all of the radiant, neutron and particle energy from the plasma is absorbed by the encapsulating, thick metal blanket thereby isolating the spacecraft from the fusion. This energy, in addition to the intense Ohmic heating at peak magnetic field compression, is adequate to vaporize and ionize the metal blanket. The expansion of this hot, ionized metal propellant through a magnetically insulated nozzle produces high thrust at the optimal Isp. The energy from the fusion process, along with the waste heat, is thus utilized at very high efficiency. The basic scheme for FDR is illustrated and described in the report (see Fig. 2) The two most critical issues in meeting challenges introduced employing magneto-inertial fusion as the power source is driver efficiency and “stand-off” – the ability to isolate and protect fusion and thruster from the resultant fusion energy. By employing metal shells for compression, it is possible to produce the desired convergent motion inductively by inserting the metal sheets along the inner surface of cylindrical or conically tapered coils. Both stand-off and energy efficiency issues are solved by this arrangement. 3 This two year effort focused on achieving three key criteria for the Fusion Driven Rocket to move forward for technological development: (1) the physics of the FDR must be fully understood and validated, (2) the design and technology development for the FDR required for its implementation in space must be fully characterized, and (3) an in-depth analysis of the rocket design and spacecraft integration as well as mission architectures enabled by the FDR need to be performed. A subscale, laboratory liner compression test facility was assembled at the University of Washington Plasma Dynamics Laboratory with sufficient liner kinetic energy (~ 0.5 MJ) to reach conditions required for fusion breakeven conditions. Detailed experimental studies of the dynamic behavior of the driven liners as well as liner convergence and magnetic compression were performed. The development of both the 1D liner dynamics code and the full 3D ANSYS® liner calculations was achieved. The characterization of both the FDR and spacecraft as well as a design architecture analysis was conducted that included an examination of a wide range of mission architectures and destinations for which this fusion propulsion system would be enabling or critical. In particular a rapid, single launch manned Mars mission was developed.

Energy↗
NASA NTRS2000

Spatiotemporal processing of linear acceleration: primary afferent and central vestibular neuron responses

Spatiotemporal convergence and two-dimensional (2-D) neural tuning have been proposed as a major neural mechanism in the signal processing of linear acceleration. To examine this hypothesis, we studied the firing properties of primary otolith afferents and central otolith neurons that respond exclusively to horizontal linear accelerations of the head (0.16-10 Hz) in alert rhesus monkeys. Unlike primary afferents, the majority of central otolith neurons exhibited 2-D spatial tuning to linear acceleration. As a result, central otolith dynamics vary as a function of movement direction. During movement along the maximum sensitivity direction, the dynamics of all central otolith neurons differed significantly from those observed for the primary afferent population. Specifically at low frequencies (</=0.5 Hz), the firing rate of the majority of central otolith neurons peaked in phase with linear velocity, in contrast to primary afferents that peaked in phase with linear acceleration. At least three different groups of central response dynamics were described according to the properties observed for motion along the maximum sensitivity direction. "High-pass" neurons exhibited increasing gains and phase values as a function of frequency. "Flat" neurons were characterized by relatively flat gains and constant phase lags (approximately 20-55 degrees ). A few neurons ("low-pass") were characterized by decreasing gain and phase as a function of frequency. The response dynamics of central otolith neurons suggest that the approximately 90 degrees phase lags observed at low frequencies are not the result of a neural integration but rather the effect of nonminimum phase behavior, which could arise at least partly through spatiotemporal convergence. Neither afferent nor central otolith neurons discriminated between gravitational and inertial components of linear acceleration. Thus response sensitivity was indistinguishable during 0.5-Hz pitch oscillations and fore-aft movements. The fact that otolith-only central neurons with "high-pass" filter properties exhibit semicircular canal-like dynamics during head tilts might have important consequences for the conclusions of previous studies of sensory convergence and sensorimotor transformations in central vestibular neurons.

NASA Discipline Neuroscience↗
DOE OSTI2021

Elastic distributed training with fast convergence and efficient resource utilization

Distributed learning is now routinely conducted on cloud as well as dedicated clusters. Training with elastic resources brings new challenges and design choices. Prior studies focus on runtime performance and assume a static algorithmic behavior. In this work, by analyzing the impact of of resource scaling on convergence, we introduce schedules for synchronous stochastic gradient descent that proactively adapt the number of learners to reduce training time and improve convergence. Our approach no longer assumes a constant number of processors throughout training. In our experiment, distributed stochastic gradient descent with dynamic schedules and reduction momentum achieves better convergence and significant speedups over prior static ones. Numerous distributed training jobs running on cloud may benefit from our approach.

Cong, Guojing↗
DOE OSTI2025

Using ARM Observations to Evaluate Process-Interactions in MCS Simulations Across Scales (Final Progress Report)

This project, funded by DOE Atmospheric System Research (DE-SC0020050), focused on improving the representation of mesoscale convective systems (MCSs) in numerical weather and climate models by leveraging high-resolution observations from the DOE Atmospheric Radiation Measurement (ARM) program. The research aimed to evaluate model sensitivities to grid spacing, microphysics, and planetary boundary layer (PBL) schemes, with a particular emphasis on improving convection parameterization for high-resolution modeling. Findings from this work highlight several key advancements. Model validation against ARM radar wind profiler data from the Southern Great Plains (SGP) and Manaus (MAO) sites revealed systematic biases in simulated convective mass flux profiles, leading to the development of an observationally constrained evaluation framework for diagnosing and improving model performance. Sensitivity analyses demonstrated that the representation of Amazonian MCSs was highly dependent on PBL scheme selection, while mid-latitude MCSs were more strongly influenced by microphysics parameterizations. A series of high-resolution WRF simulations, ranging from 4 km to 125 m grid spacing, provided insight into the behavior of convective drafts across scales. While updraft properties converged at sub-kilometer resolutions, biases in downdraft intensity persisted even at the finest resolution tested, emphasizing the need for further refinements in model physics. Additionally, comparisons of MCS vertical structures between mid-latitude and tropical environments revealed stronger updrafts and larger mass flux in mid-latitude MCSs, providing critical insights for improving climate model representations of storm-scale dynamics. The project’s findings have already contributed to advancing numerical modeling capabilities, particularly in WRF, MPAS, ICON, and DOE’s SCREAM model, by refining how convective processes are represented in high-resolution climate simulations. Results were disseminated through peer-reviewed publications, conference presentations, and ARM/ASR Research Highlights, engaging the broader scientific community. The project also provided valuable training opportunities for two postdoctoral researchers, who played central roles in model development, analysis, and dissemination of results. Their work contributed to several publications and conference presentations, helping prepare them for careers in atmospheric modeling. By improving the simulation of MCSs, this research directly supports the development of next-generation climate models capable of more accurately representing extreme precipitation and convective processes. The insights gained will inform future improvements in convective parameterization and guide the design of high-resolution weather and climate simulations, ultimately enhancing the reliability of climate projections and weather forecasts.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1992

Practical aspects of spatially high accurate methods

The computational qualities of high order spatially accurate methods for the finite volume solution of the Euler equations are presented. Two dimensional essentially non-oscillatory (ENO), k-exact, and 'dimension by dimension' ENO reconstruction operators are discussed and compared in terms of reconstruction and solution accuracy, computational cost and oscillatory behavior in supersonic flows with shocks. Inherent steady state convergence difficulties are demonstrated for adaptive stencil algorithms. An exact solution to the heat equation is used to determine reconstruction error, and the computational intensity is reflected in operation counts. Standard MUSCL differencing is included for comparison. Numerical experiments presented include the Ringleb flow for numerical accuracy and a shock reflection problem. A vortex-shock interaction demonstrates the ability of the ENO scheme to excel in simulating unsteady high-frequency flow physics.

Godfrey, Andrew G.↗
NASA NTRS1992

Development of simplified ecosystem models for applications in Earth system studies: The Century experience

During the past decade, a growing need to conduct regional assessments of long-term trends of ecosystem behavior and the technology to meet this need have converged. The Century model is the product of research efforts initially intended to develop a general model of plant-soil ecosystem dynamics for the North American central grasslands. This model is now being used to simulate plant production, nutrient cycling, and soil organic matter dynamics for grassland, crop, forest, and shrub ecosystems in various regions of the world, including temperate and tropical ecosystems. This paper will focus on the philosophical approach used to develop the structure of Century. The steps included were model simplification, parameterization, and testing. In addition, the importance of acquiring regional data bases for model testing and the present regional application of Century in the Great Plains, which focus on regional ecosystem dynamics and the effect of altering environmental conditions, are discussed.

Parton, William J.↗
NASA NTRS2005

Quantifying Exact Motions Along Lineaments on Europa

Evaluating the precise motions along lineaments on the surface of Jupiter's icy moon, Europa, is a valuable tool for interpreting the development and history of lineaments of various morphologies. Such morphologies include strike-slip faults, dilational bands, ridges, and convergence zones. However, the exact mode of origin and kinematic behavior of these various lineaments are not obvious based on morphology alone. In fact, the apparent motions implied by displaced crosscut features can provide misleading indications of true motions along lineaments. Identifying the precise motions (combinations of sliding and opening/closing) is critical to the accurate characterization and interpretation of each of these lineament types. Lineaments of interest (i.e., those having displaced relatively older features in some manner) are identified on Galileo spacecraft images and measurements are made of the total offset, the separation, and relative orientations of crosscut features with respect to the lineament of interest. Specifically, by using these measured quantities and a series of trigonometric equations, the precise motions (i.e., dilation, convergence, strike-slip, or a combination of strike-slip and dilation or convergence) can be determined. These measurements are, however, limited by the resolution of the available images. This study focuses on motion analysis techniques for Europan lineaments and the precise characterization of fault-orthogonal and/or strike-slip motion along lineaments of varying morphologies. We highlight potential pitfalls of cursory analyses of motion indicators. For example, lineaments with obvious lateral offsets have typically been identified simply as strike-slip faults. This assumption may actually be incorrect, as fault-orthogonal motions may contribute to apparent lateral displacements (offsets or separations). Also, variability in the amount of fault motion along the trace length should theoretically be identifiable using the outlined technique. Strike-slip faults on Europa have conventionally been presumed to have a constant slip magnitude along their lengths; however, we posit that variable distributions of slip may be common, as is typical along terrestrial strike-slip faults.

Vetter, J. C.↗
NASA NTRS1995

Analysis and Development of Finite Element Methods for the Study of Nonlinear Thermomechanical Behavior of Structural Components

Underintegrated methods are investigated with respect to their stability and convergence properties. The focus was on identifying regions where they work and regions where techniques such as hourglass viscosity and hourglass control can be used. Results obtained show that underintegrated methods typically lead to finite element stiffness with spurious modes in the solution. However, problems exist (scalar elliptic boundary value problems) where underintegrated with hourglass control yield convergent solutions. Also, stress averaging in underintegrated stiffness calculations does not necessarily lead to stable or convergent stress states.

Oden, J. Tinsley↗
DOE OSTI2021

Relationship between the contact force strength and numerical inaccuracies in piecewise-smooth systems

This work studies the different types of behavior and inaccuracies that can occur when contact is not adequately accounted for in a dynamical system with freeplay, as the strength of the contact stiffness increases. The MATLAB® ode45 time integration solver, with the built-in Event Location capability, is first validated using past experimental data from a forced Duffing oscillator with freeplay. Next, numerical results utilizing event location are compared to results neglecting event location in order to highlight possible numerical errors and effects on multistable dynamical responses. Inaccuracies tend to occur in two different ways. First, neglecting event location can affect the boundaries between basins of attraction. Second, neglecting event location has little effect on the behaviors of the attractor solutions themselves besides merely resembling poorly converged solutions. Errors are less pronounced at the limits of soft or hard contact stiffness. Finally, this study shows the importance of accurately solving piecewise-smooth systems and the existing correlation between the strength of the contact force and possible numerical inaccuracies.

42 ENGINEERING↗
DOE OSTI2020

Non-local model for surface tension in fluid-fluid simulations

We propose a non-local model for surface tension obtained in the form of an integral of a molecular-force-like function with support 3.5e added to the Navier-Stokes momentum conservation equation. We demonstrate analytically and numerically that with the non-local model interfaces with a radius of curvature larger than the support length behave macroscopically and microscopically, otherwise. For static droplets, the pressure difference Pe,in - Pe,out satisfies the Young-Laplace law for droplet radius greater than 3.5e and other- wise deviates from the Young-Laplace law. The latter indicates that the surface tension in the proposed model decreases with decreasing radius of curvature, which agrees with molecular dynamics and experimental studies of nanodroplets. Using the non-local model we perform numerical simulations of droplets under dynamic conditions, including a rising droplet, a droplet in shear flow, and two colliding droplets in shear flow, and compare results with a standard Navier-Stokes model subject to the Young-Laplace boundary condition at the fluid-fluid interface implemented via the Conservative Level Set (CLS) method. We find good agreement with existing numerical methods and analytical results for a rising macroscopic droplet and a droplet in a shear flow. For colliding droplets in shear flow, the non- local model converges (with respect to the grid size) to the correct behavior, including sliding, coalescence, and merging and breaking of two droplets depending on the capillary number. In contrast, we find that the results of the CLS model are highly grid-size dependent.

Howard, Amanda A.↗
DOE OSTI2025

HighDimMixedModels.jl: Robust high-dimensional mixed-effects models across omics data

High-dimensional mixed-effects models are an increasingly important form of regression in which the number of covariates rivals or exceeds the number of samples, which are collected in groups or clusters. The penalized likelihood approach to fitting these models relies on a coordinate descent algorithm that lacks guarantees of convergence to a global optimum. Here, we empirically study the behavior of this algorithm on simulated and real examples of three types of data that are common in modern biology: transcriptome, genome-wide association, and microbiome data. Our simulations provide new insights into the algorithm’s behavior in these settings, and, comparing the performance of two popular penalties, we demonstrate that the smoothly clipped absolute deviation (SCAD) penalty consistently outperforms the least absolute shrinkage and selection operator (LASSO) penalty in terms of both variable selection and estimation accuracy across omics data. To empower researchers in biology and other fields to fit models with the SCAD penalty, we implement the algorithm in a Julia package, HighDimMixedModels.jl .

Gorstein, Evan↗