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DOE OSTI2022

Parametric dynamic mode decomposition for reduced order modeling

Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by singular value decomposition of the temporal data sets. For parameter-dependent models, as found in many multi-query applications such as uncertainty quantification or design optimization, the only parametric DMD technique developed was a stacked approach, with data sets at multiple parameter values were aggregated together, increasing the computational work needed to devise low-rank dynamical reduced-order models. Here in this paper, we present two novel approach to carry out parametric DMD: one based on the interpolation of the reduced-order DMD eigen-pair and the other based on the interpolation of the reduced DMD (Koopman) operator. Numerical results are presented for diffusion-dominated nonlinear dynamical problems, including a multiphysics radiative transfer example. All three parametric DMD approaches are compared.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Wearable Sensors Measure Ankle Joint Changes of Patients with Parkinson’s Disease before and after Acute Levodopa Challenge

Background . Previous studies found levodopa could improve the activity of the ankle joints of patients with Parkinson’s disease (PD). But ankle joint movement is composed of four motion ranges. The specific changes of four motion ranges in PD remain unknown. Objective . The purpose of this study was to decompose the complex ankle joint movement, measure ankle joint changes before and after the acute levodopa challenge test (ALCT), and investigate the effects of these parameters on gait performance. Methods . 29 PD patients and 30 healthy control subjects (HC) completed the Instrumented Stand and Walk (ISAW) test and gait parameters were collected by the JiBuEn gait analysis system. The percentage of improvement of gait data and the UPDRS III in the on-drug condition (ON) were determined with respect to the off-drug condition (OFF). Results . We observed a reduction in the heel strike angle (HS), 3-plantarflexion (3-PF) angle, and 4-dorsiflexion (4-DF) angle of ankle joints. We did not find significant difference in the toe-off angle (TO), 1-plantarflexion (1-PF) angle, and 2-dorsiflexion (2-DF) angle among three groups. Stride length improvement rate was significantly correlated with HS ( r s = 0.616, P < 0.001 ) and 3-PF ( r s = 0.639, P < 0.001 ) improvement rates. The improvement in the sum of rigidity items (UPDRS motor subsection item 22) was also correlated with HS ( r s = 0.389, P = 0.037 ) and 3-PF ( r s = 0.373, P = 0.046 ) improvement rates. Conclusions . Exogenous levodopa supplementation can significantly reduce the rigidity of patients with PD, improve their 3-PF and 4-DF of ankle joint kinematic parameters, and ultimately enhance their gait.

Wu, Zhuang↗

DOE OSTI2020

Influence of physical and chemical hydrology on bioremediation of a U-contaminated aquifer informed by reactive transport modeling incorporating 238 U/ 235 U ratios

Microbially-catalyzed reductive immobilization of aqueous uranium (U) as a solid phase has been proposed as a U remediation technique. Both laboratory and field experiments have demonstrated that this reduction reaction alters the 238 U/ 235 U ratio, producing a 238 U-enriched U(IV) solid. In contrast, other major U reactive transport processes fractionate these isotopes much less. This suggests the potential to quantify the extent of bioreduction occurring in groundwater containing U using the 238 U/ 235 U ratio, which would substantially improve upon current practices largely relying on U concentration measurements alone. Current reactive transport models for uranium dynamics include only concentration measurements, which are strongly influenced by highly coupled reactive transformation and aqueous transport processes. The complex physical and chemical behavior of U potentially compromises such quantitative analysis of U storage and release. Here we report the first numerical reactive transport model which explicitly incorporates variations in the 238 U/ 235 U ratio of U and demonstrates improved interpretation of the principal chemical reactions and groundwater transport processes affecting the subsurface mobility and distribution of this widespread contaminant. Recent U bioreduction studies performed in a contaminated aquifer in Rifle, Colorado, USA applied Rayleigh distillation models to interpret U stable isotope fractionation observed as a result of acetate amendment. These simplified models were unable to resolve the spatiotemporal pattern of U isotope fractionation recorded in the aqueous solutes. Here, we employ the multi-component, isotope-enabled CrunchTope reactive transport software to interpret these measured U isotope ratios, and demonstrate accurate reproduction of observed trends in both geochemistry and 238 U/ 235 U ratios for two consecutive years of field experiments. Overall, our results indicate that accurately modeling both the U concentration and isotope ratio distributions greatly constrains the parameter space of the model. We find that the transport properties of U in the Rifle aquifer are governed by the presence of low-permeability regions, which the isotopes are uniquely sensitive to. When U reduction is spatially constrained by these low-permeability regions, the shift in the 238 U/ 235 U ratio becomes more muted. Accurate modeling of observed U isotope ratios thus provides a powerful means to better understand bioremediation, and the current study serves to advance the application of this novel method.

238U/235U↗

NASA NTRS2006

Effect of Trailing Edge Flow Injection on Fan Noise and Aerodynamic Performance

An experimental investigation using trailing edge blowing for reducing fan rotor/guide vane wake interaction noise was completed in the NASA Glenn 9- by 15-foot Low Speed Wind Tunnel. Data were acquired to measure noise, aerodynamic performance, and flow features for a 22" tip diameter fan representative of modern turbofan technology. The fan was designed to use trailing edge blowing to reduce the fan blade wake momentum deficit. The test objective was to quantify noise reductions, measure impacts on fan aerodynamic performance, and document the flow field using hot-film anemometry. Measurements concentrated on approach, cutback, and takeoff rotational speeds as those are the primary conditions of acoustic interest. Data are presented for a 2% (relative to overall fan flow) trailing edge injection rate and show a 2 dB reduction in Overall Sound Power Level (OAPWL) at all fan test speeds. The reduction in broadband noise is nearly constant and is approximately 1.5 dB up to 20 kHz at all fan speeds. Measurements of tone noise show significant variation, as evidenced by reductions of up to 6 dB in the 2 BPF tone at 6700 rpm.: and increases of nearly 2 dB for the 4 BPF tone at approach speed. Aerodynamic performance measurements show the fan with 2 % injection has an overall efficiency that is comparable to the baseline fan and operates, as intended, with nearly the same pressure ratio and mass flow parameters. Hot-film measurements obtained at the approach operating condition indicate that mean blade wake filling in the tip region was not as significant as expected. This suggests that additional acoustic benefits could be realized if the trailing edge blowing could be modified to provide better filling of the wake momentum deficit. Nevertheless, the hot-film measurements indicate that the trailing edge blowing provided significant reductions in blade wake turbulence. Overall, these results indicate that further work may be required to fully understand the proper implementation of injecting flow at/near the trailing edge as a wake filling strategy. However, data do support the notion that noise reductions can be realized not only for tones but perhaps more importantly, also for broadband. Furthermore, the technique can be implemented without adversely effecting overall fan aerodynamic performance.

Fite, E. Brian↗

DOE OSTI2021

Transfer learning of memory kernels for transferable coarse-graining of polymer dynamics

The present work concerns the transferability of coarse-grained (CG) modeling in reproducing the dynamic properties of the reference atomistic systems across a range of parameters. In particular, we focus on implicit-solvent CG modeling of polymer solutions. The CG model is based on the generalized Langevin equation, where the memory kernel plays the critical role in determining the dynamics in all time scales. Thus, we propose methods for transfer learning of memory kernels. The key ingredient of our methods is Gaussian process regression. By integration with the model order reduction via proper orthogonal decomposition and the active learning technique, the transfer learning can be practically efficient and requires minimum training data. Through two example polymer solution systems, we demonstrate the accuracy and efficiency of the proposed transfer learning methods in the construction of transferable memory kernels. The transferability allows for out-of-sample predictions, even in the extrapolated domain of parameters. Built on the transferable memory kernels, the CG models can reproduce the dynamic properties of polymers in all time scales at different thermodynamic conditions (such as temperature and solvent viscosity) and for different systems with varying concentrations and lengths of polymers.

Ma, Zhan↗

DOE OSTI2022

Grassland productivity responds unexpectedly to dynamic light and soil water environments induced by photovoltaic arrays

Abstract Agrivoltaic (AV) systems are designed to coproduce photovoltaic (PV) energy on lands simultaneously supporting agriculture (food/forage production). PV infrastructure in agroecosystems alters resources critical for plant growth, and water‐limited agroecosystems such as grasslands are likely to be particularly sensitive to the unique spatial and temporal patterns of incident sunlight and soil water inherent within AV systems. However, the impact of resource alteration on forage production, the primary ecosystem service from managed grasslands, is poorly resolved. Here, we evaluated seasonal patterns of soil moisture (SM) and diurnal variation in incident sunlight (photosynthetic photon flux density [PPFD]) in a single‐axis‐tracking AV system established in a formerly managed semiarid C 3 grassland in Colorado. Our goals were to (1) quantify dynamic patterns of PPFD and SM within a 1.2 MW PV array in a perennial grassland, and (2) determine how aboveground net primary production (ANPP) and photosynthetic parameters responded to the resource patterns created by the PV array. We hypothesized that spatial variability in ANPP would be strongly related to SM patterns, typical of most grasslands. We measured significant reductions in ANPP directly beneath PV panels, where SM and PPFD were both low. However, in locations with significantly increased SM from the shedding and redistribution of precipitation by PV panels, ANPP was not increased. Instead, ANPP was greatest in locations where plants were shaded in the afternoon but received high levels of PPFD in the morning hours, when air temperatures and vapor pressure deficits were relatively low. Thus, contrary to expectations, we found relatively weak relationships between SM and ANPP despite significant spatial variability in both. Further, there was little evidence that light‐saturated photosynthesis ( A sat ) and quantum yield of CO 2 assimilation (ϕCO 2 ) differed for plants growing directly beneath (lowest PPFD) versus between (highest PPFD) PV panels. Overall, the AV system established in this semiarid managed grassland did not alter patterns of ANPP in ways predictable from past studies of controls of ANPP in open grasslands. However, our results suggest that the diurnal timing of low versus high periods of PPFD incident on plants is an important determinant of productivity patterns in grasslands.

14 SOLAR ENERGY↗

DOE OSTI2020

Microbially mediated iron redox cycling of subsurface sediments from Hanford Site, Washington State, USA

Iron-bearing clay minerals are predominant in soils and sediments, and they undergo oxidation-reduction cycles as a result of natural processes such as wetting/drying cycles and plant root respiration. However, the kinetics and mechanisms of multiple redox cycles of iron in clay-rich sediments and consequences of such cycling on sediment properties are poorly understood. The objective of this study was to understand how multiple redox cycles of Fe in clay-rich sediment affect the rate and extent of Fe bioreduction and the physicochemical properties of the sediment. A natural sediment sample containing Fe-bearing montmorillonite from Hanford, Washington, USA was size-fractionated [2.0 to 0.5 μm (Hanford-C) and 0.5 to 0.02 μm (Hanford-F)] and redox-cycled for four times. Bioreduction was achieved utilizing Geobacter sulfurreducens and re-oxidization was performed with sparged air. Time-course change of total Fe (II) was monitored to measure the rate and extent of Fe (III) bioreduction. Redox-cycled sediments were characterized to determine the physicochemical changes. Both the initial rate and extent of bioreduction fluctuated across the four redox cycles, but they ultimately decreased from 5.3 μmol g -1 h -1 and 22.9% to nearly zero by the fourth cycle. These fluctuation patterns were likely due to a combined effect of reductive dissolution of small/poorly crystalline clay particles (by 3–5%) and clay mineral structural changes, as evidenced by redox induced changes of aqueous chemistry, surface area, cation exchange capacity, mineralogy, and Mössbauer parameters. Once these small/poorly crystalline clay particles were dissolved, structural Fe in residual larger and more crystalline clay particles was largely reversible across additional redox cycles, as revealed by Mössbauer spectroscopy through the first three cycles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Calibrating hypersonic turbulence flow models with the HIFiRE-1 experiment using data-driven machine-learned models.

In this paper we study the efficacy of combining machine-learning methods with projection-based model reduction techniques for creating data-driven surrogate models of computationally expensive, high-fidelity physics models. Such surrogate models are essential for many-query applications e.g., engineering design optimization and parameter estimation, where it is necessary to invoke the high-fidelity model sequentially, many times. Surrogate models are usually constructed for individual scalar quantities. However there are scenarios where a spatially varying field needs to be modeled as a function of the model’s input parameters. Here we develop a method to do so, using projections to represent spatial variability while a machine-learned model captures the dependence of the model’s response on the inputs. The method is demonstrated on modeling the heat flux and pressure on the surface of the HIFiRE-1 geometry in a Mach 7.16 turbulent flow. The surrogate model is then used to perform Bayesian estimation of freestream conditions and parameters of the SST (Shear Stress Transport) turbulence model embedded in the high-fidelity (Reynolds-Averaged Navier–Stokes) flow simulator, using shock-tunnel data. The paper provides the first-ever Bayesian calibration of a turbulence model for complex hypersonic turbulent flows. We find that the primary issues in estimating the SST model parameters are the limited information content of the heat flux and pressure measurements and the large model-form error encountered in a certain part of the flow.

42 ENGINEERING↗

DOE OSTI2024

Experimental investigation into coal wettability changes caused by reactions with scCO 2 -H 2 O

Geological CO 2 sequestration (GCS) can help mitigate global warming and enhance methane recovery from coal beds. However, few studies have linked the effects of CO 2 to surface chemistry changes controlling wetting behavior in deep coal beds. Contact angles (CAs) of CO 2 /N 2 -high volatile bituminous coal-water systems were measured under different temperatures and pressures. The surface chemistry and physical structure of coals were characterized to investigate changes in physicochemical properties and their relations with wettability after reactions. For N 2 treatment, the time-dependence of static and dynamic CAs were insignificant, ranging within 4°. For gaseous CO 2 treatment, the static CAs and the average advancing angles increased slightly. With supercritical (sc) CO 2 , both the static and dynamic CAs increased significantly, and θ adv changed to intermediate-wet (92°). Reactions with minerals exposed to scCO 2 resulted in greater surface roughness and heterogeneity, greater contact angle hysteresis and more surface sites occupied by scCO 2 rather than H 2 O. Increases in hydrophobic functional groups and decreases in hydrophilicity were shown by FTIR spectra, reflecting the shedding of polar oxygen-containing functional groups, reduction of hydrogen bonds, and increasing percentage of hydrocarbons. XRD patterns obtained following scCO 2 -treatment showed that crystallite growth and molecular polymerization were higher toward graphite-like. The calculated structural parameters of functional groups and crystallites both showed elevated coal rank. Changes in crystallite structure, notably higher carbon content and decreased negative surface charge, are unfavorable for water-wetting. Finally, this study contributes to understanding surface chemistry changes responsible for decreased wettability during CO 2 -enhanced coal bed methane recovery and GCS in coal reservoirs.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2020

Distributed Aerodynamic Control using Active Trailing-Edge Flaps for Large Wind Turbines

This work presents a numerical framework to investigate distributed aerodynamic control devices for application in large wind turbines. Tool capabilities were extended to facilitate multiple aerodynamic polar tables. The airfoil aerodynamics characteristics were automatically determined, and blade-pitch, generator-torque, and trailing-edge-flap controllers were tuned in-the-loop according to a specific blade design. This automated workflow allows analysis and optimization of trailing-edge flaps, enabling codesign studies. Results targeted reductions of root-flap-bending moment derivatives. The applied trailing-edge-flap control reduced the standard deviation of root-flap-bending moments by more than 6% and benefit related parameters, e.g., reduce blade-tip deflections, by up to 8%. Because of varying thrust distributions along the blade span, different flap designs have nonlinear characteristics in terms of the control objective and show best performance when located at the radial position with maximum thrust. In general, larger flaps provide a greater influence to reduce the target control objective.

17 WIND ENERGY↗

DOE OSTI2026

Primordial black hole dark matter: A quantitative parameter sensitivity comparison across formation mechanisms and particle candidates

Primordial black holes (PBHs) in the asteroid-mass window ( 10 17 – 10 22 g ) can account for all of the dark matter without violating any observational constraint, yet are routinely dismissed as fine-tuned. I put that dismissal to the test by applying three complementary sensitivity measures uniformly across a broad landscape: three noninflationary PBH production mechanisms, six classes of inflationary PBH models, and seven particle dark matter benchmarks, all evaluated against the same observable target. Three distinct naturalness universality classes emerge, determined entirely by the analytic structure of the abundance map rather than by the nature of the dark matter candidate. Biased-domain-wall PBHs, in their least model-dependent (free- V b ) form, have the same low sensitivity, Δ = 4.5 , as off-resonance weakly interacting massive particles and freeze-in particles ( Δ = 2 ), a sensitivity that, because it is constant over the entire parameter space of the construction, also coincides trivially with its own Wilson-normalized average within that parameter space (Section Definition and conventions), an equivalence that concerns only the space over which Δ is computed and is not a naturalness statement about the construction as a whole; a further reduction to Δ = 2 is possible only under the additional, independently motivated but not required, assumption that the domain-wall bias is generated by Planck-suppressed operators; early matter-domination PBHs occupy an intermediate tier alongside coannihilating weakly interacting massive particles (WIMPs), unified by a structural identity in which the sensitivity measure equals the logarithm of the ratio of the formation scale to the matter–radiation equality scale; first-order phase transition PBHs, once the more accurate super-exponential collapse probability is used in place of the single-exponential approximation, instead belong to the same highly sensitive tier as resonant WIMP annihilation and single-field inflationary collapse, for a structurally distinct reason; single-field ultraslow-roll inflationary collapse is severely tuned for a distinct reason: a double exponential in which the power spectrum amplitude is itself exponentially sensitive to the inflaton potential coefficients, on top of the exponential collapse sensitivity of the abundance map. My main conclusion is that the claim that PBH dark matter is generically fine-tuned conflates the worst case with a landscape spanning every naturalness tier. The Barbieri-Giudice sensitivity computed here and the Wilson-normalized measure of Iovino and Riotto answer distinct and mutually consistent questions about the same construction, a distinction I clarify within the two-layer decomposition.

Profumo, Stefano [University of California, Santa ↗

DOE OSTI2021

Algal Biomass Production via Open Pond Algae Farm Cultivation: 2020 State of Technology and Future Research

The annual State of Technology (SOT) assessment is an essential activity for platform research conducted under the Bioenergy Technologies Office. It allows for the impact of research progress to be quantified in terms of economic improvements in the overall biofuel production process for a particular biomass processing pathway, whether based on terrestrial or algal biomass feedstocks. As such, initial benchmarks can be established for currently demonstrated performance, and progress can be tracked towards out-year goals to ultimately demonstrate economically viable biofuel technologies. NREL's algae state of technology benchmarking efforts focus both on front-end algal biomass production and separately on back-end conversion to fuels through NREL's "combined algae processing" (CAP) pathway. The production model is based on outdoor long-term cultivation data, enabled by comprehensive algal biomass production trials conducted under Development of Integrated Screening, Cultivar Optimization, and Verification Research (DISCOVR) consortium efforts, driven by data furnished by Arizona State University (ASU) at the Arizona Center for Algae Technology and Innovation (AzCATI) testbed site. The CAP model is based on experimental efforts conducted under NREL research and development projects. This report focuses on front-end algal biomass production, documenting the pertinent algal biomass cultivation parameters that were input to the NREL open pond algae farm model based on the latest DISCOVR cultivation performance data. Relative to prior 2019 benchmarks, the 2020 algae farm SOT achieved further reductions in modeled minimum biomass selling price of approximately $70/ton (roughly 10%), primarily attributable to a 16% demonstrated improvement in annual average cultivation productivity rates.

09 BIOMASS FUELS↗

DOE OSTI2020

Dimensionality Reduction of SDSS Spectra with Variational Autoencoders

High-resolution galaxy spectra contain much information about galactic physics, but the high dimensionality of these spectra makes it difficult to fully utilize the information they contain. We apply variational autoencoders (VAEs), a nonlinear dimensionality reduction technique, to a sample of spectra from the Sloan Digital Sky Survey (SDSS). In contrast to principal component analysis (PCA), a widely used technique, VAEs can capture nonlinear relationships between latent parameters and the data. We find that a VAE can reconstruct the SDSS spectra well with only six latent parameters, outperforming PCA with the same number of components. Different galaxy classes are naturally separated in this latent space, without class labels having been given to the VAE. The VAE latent space is interpretable because the VAE can be used to make synthetic spectra at any point in latent space. For example, making synthetic spectra along tracks in latent space yields sequences of realistic spectra that interpolate between two different types of galaxies. Using the latent space to find outliers may yield interesting spectra: in our small sample, we immediately find unusual data artifacts and stars misclassified as galaxies. In this exploratory work, we show that VAEs create compact, interpretable latent spaces that capture nonlinear features of the data. While a VAE takes substantial time to train (≈1 day for 48,000 spectra), once trained, VAEs can enable the fast exploration of large astronomical data sets.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Assimilation of multiple datasets results in large differences in regional- to global-scale NEE and GPP budgets simulated by a terrestrial biosphere model

In spite of the importance of land ecosystems in offsetting carbon dioxide emissions released by anthropogenic activities into the atmosphere, the spatiotemporal dynamics of terrestrial carbon fluxes remain largely uncertain at regional to global scales. Over the past decade, data assimilation (DA) techniques have grown in importance for improving these fluxes simulated by terrestrial biosphere models (TBMs), by optimizing model parameter values while also pinpointing possible parameterization deficiencies. Although the joint assimilation of multiple data streams is expected to constrain a wider range of model processes, their actual benefits in terms of reduction in model uncertainty are still under-researched, also given the technical challenges. In this study, we investigated with a consistent DA framework and the ORCHIDEE-LMDz TBM–atmosphere model how the assimilation of different combinations of data streams may result in different regional to global carbon budgets. To do so, we performed comprehensive DA experiments where three datasets (in situ measurements of net carbon exchange and latent heat fluxes, spaceborne estimates of the normalized difference vegetation index, and atmospheric CO 2 concentration data measured at stations) were assimilated alone or simultaneously. We thus evaluated their complementarity and usefulness to constrain net and gross C land fluxes. We found that a major challenge in improving the spatial distribution of the land C sinks and sources with atmospheric CO 2 data relates to the correction of the soil carbon imbalance.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1972

Methods for reducing blade passing frequency noise generated by rotor-wake - stator interaction

A theoretical model for the generation of blade-passage noise caused by the interaction of rotor wakes with the downstream stator blades in a fan stage has been compiled. This model has combined a description of the rotor wake based on existing experimental correlations with an existing theory for the response of the stator blades to those wakes. This model of the interaction-caused blade-passage noise has been used to examine some effects of blade geometry and flow conditions on the noise generated. A set of significant parameters has been identified to reduce this interaction-caused blade-passage frequency noise. A redesign of an existing fan with the use of these concepts has produced a theoretical noise reduction of more than 7 decibels.

Dittmar, J. H.↗

NASA NTRS1979

The scatter of mechanical values of carbon fiber composites and its causes

The scatter of experimental data obtained in an investigation of the parameters of structural components was investigated. Strength parameters which are determined by the resin or the adhesion between fiber and resin were included. The statistical characteristics of the mechanical parameters of carbon fiber composites, and the possibilities which exist to reduce this scatter were emphasized. It is found that quality control tests of fiber and resin are important for such a reduction.

Roth, S.↗

NASA NTRS1979

Multistage variable probability forest volume inventory

An inventory scheme based on the use of computer processed LANDSAT MSS data was developed. Output from the inventory scheme provides an estimate of the standing net saw timber volume of a major timber species on a selected forested area of the Navajo Nation. Such estimates are based on the values of parameters currently used for scaled sawlog conversion to mill output. The multistage variable probability sampling appears capable of producing estimates which compare favorably with those produced using conventional techniques. In addition, the reduction in time, manpower, and overall costs lend it to numerous applications.

Anderson, J. E.↗

NASA NTRS1988

Ocean Drifter Project

Four drifting buoys were fabricated from mostly local hardware plus animal locating transmitters. The first two working models were dropped from a Wallops aircraft, to test the mechanical integrity and to test the ability of the whole system to withstand the drop and provide usable data. There are two temperature sensors on board, one to measure sea surface temperature and the other to measure air temperature. An onboard computer controls the transmissions, sending three water temperature readings for each air temperature reading in order to differentiate one from the other after data reduction. Guidelines for the development and test of optical drifting buoys include: air deployable and expendable, reasonable cost for multiple deployment, 1 year lifetime, use of existing technology and a minimal validation parameter set.

Mason, C. D.↗