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DOE OSTI2026

Design of monolithic piezoelectric bimorph mirrors made from lithium niobate

Recent advances in deformable mirrors based on monolithic piezoelectric substrates, such as lithium niobate, have the potential to improve the image quality of X-ray optical systems on synchrotron and free-electron laser beamlines and microscopes. However, the quantitative relationship between design parameters and the deformed shape has not been readily available in the literature. We present an analytical model, validated through finite element analysis, enabling calculation of tangential and sagittal curvatures based on mirror dimensions, crystallographic orientation, and applied voltage. We demonstrate that through the selection of material orientation, it is possible to achieve different deformed shapes (sphere, cylinder, or hyperbolic paraboloid). This methodology can be generalized to other piezoelectric materials and substrate-integrated actuator systems.

Marzari, Francesco [University of Trento (Italy); ↗

DOE OSTI2026

Diacylglycerol enantiomer selectivity of diacylglycerol acyltransferases highlights metabolic specialization in triacylglycerol synthesis across the tree of life

Triacylglycerols are the major energy storage lipids in plants, animals, and microorganisms, and are predominantly produced by acyl-CoA:diacylglycerol (DAG) acyltransferases (DGATs). Two enantiomers of the DAG substrate, sn -1,2 and sn -2,3, can be produced by different biological mechanisms; however, little is known about which species produce each enantiomer, the selectivity of DGAT isoforms for either enantiomer, or whether DGAT enantiomer selectivity varies across organisms. Here, DAG enantiomer selectivity of DGAT1 and DGAT2 was measured from eight seed plants, two mammals, one oleaginous yeast, and one photosynthetic microalga using enantiomer-specific in vitro DGAT assays. Across most plants, DGAT1 favored sn -1,2-DAG, whereas DGAT2 preferentially utilized sn -2,3-DAG. However, there were several exceptions. Mammalian DGAT1, DGAT2, and microbial DGAT1s efficiently used both DAG enantiomers, while microbial DGAT2s had unique selectivity. The selectivity of several DGATs for combined acyl-CoA and DAG enantiomer molecular species were also evaluated for biotechnical applications. Therefore, DGAT DAG enantiomer selectivity is common yet strongly dependent on lineage and isoform and likely shaped in part by species-specific metabolic context of triacylglycerol synthesis, turnover, and remodeling. This work expands our understanding of DGAT function and establishes a foundation for leveraging enantiomer-selective acyltransferases in metabolic engineering of tailored lipid products.

Arabidopsis thaliana↗

DOE OSTI2026

Hund's coupling governed orbital-selective superconductivity in Ba 1−𝑥 ⁢K 𝑥⁢ Fe 2 ⁢As 2

Understanding how strong electronic correlations shape superconductivity remains a central challenge in quantum materials. In multiorbital systems, correlations driven by Hund's coupling can differentiate the behavior of individual orbitals, producing the so-called Hund's metal state. How such orbital-selectivity also governs superconducting pairing, however, has remained largely unexplored experimentally. Here, in this study, we use high-resolution angle-resolved photoemission spectroscopy to systematically map the superconducting gap structure across the phase diagram of the representative iron-based superconductor Ba 1−x K x Fe 2 As 2 . We find that superconductivity evolves in a strongly orbital-dependent manner: the gap associated with the d xy orbital collapses beyond optimal doping while pairing on the d xz /d yz orbitals persists. This behavior mirrors the orbital-selective correlations observed in the normal state and reveals a direct connection between Hund's metal physics and the superconducting pairing landscape. Our results demonstrate that superconducting gaps themselves can serve as a sensitive probe of orbital-dependent correlations and suggest that Hund's coupling plays a central role in shaping pairing in multiorbital superconductors.

Corbae, Elena [SLAC National Accelerator Laborator↗

DOE OSTI2023

Selective and Scalable Control of Spin Quantum Memories in a Photonic Circuit

A central goal in many quantum information processing applications is a network of quantum memories that can be entangled with each other while being individually controlled and measured with high fidelity. This goal has motivated the development of programmable photonic integrated circuits (PICs) with integrated spin quantum memories using diamond color center spin-photon interfaces. However, this approach introduces a challenge into the microwave control of individual spins within closely packed registers. Here, we present a quantum memory-integrated photonics platform capable of (i) the integration of multiple diamond color center spins into a cryogenically compatible, high-speed programmable PIC platform, (ii) selective manipulation of individual spin qubits addressed via tunable magnetic field gradients, and (iii) simultaneous control of qubits using numerically optimized microwave pulse shaping. The combination of localized optical control, enabled by the PIC platform, together with selective spin manipulation opens the path to scalable quantum networks on intrachip and interchip platforms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2017

Inviscid/Boundary-Layer Aeroheating Approach for Integrated Vehicle Design

A typical entry vehicle design depends on the synthesis of many essential subsystems, including thermal protection system (TPS), structures, payload, avionics, and propulsion, among others. The ability to incorporate aerothermodynamic considerations and TPS design into the early design phase is crucial, as both are closely coupled to the vehicle's aerodynamics, shape and mass. In the preliminary design stage, reasonably accurate results with rapid turn-representative entry envelope was explored. Initial results suggest that for Mach numbers ranging from 9-20, a few inviscid solutions could reasonably sup- port surface heating predictions at Mach numbers variation of +/-2, altitudes variation of +/-10 to 20 kft, and angle-of-attack variation of +/- 5. Agreement with Navier-Stokes solutions was generally found to be within 10-15% for Mach number and altitude, and 20% for angle of attack. A smaller angle-of-attack increment than the 5 deg around times for parametric studies and quickly evolving configurations are necessary to steer design decisions. This investigation considers the use of an unstructured 3D inviscid code in conjunction with an integral boundary-layer method; the former providing the flow field solution and the latter the surface heating. Sensitivity studies for Mach number, angle of attack, and altitude, examine the feasibility of using this approach to populate a representative entry flight envelope based on a limited set of inviscid solutions. Each inviscid solution is used to generate surface heating over the nearby trajectory space. A subset of a considered in this study is recommended. Results of the angle-of-attack sensitivity studies show that smaller increments may be needed for better heating predictions. The approach is well suited for application to conceptual multidisciplinary design and analysis studies where transient aeroheating environments are critical for vehicle TPS and thermal design. Concurrent prediction of aeroheating environments, coupled with the use of unstructured methods, is considered enabling for TPS material selection and design in conceptual studies where vehicle mission, shape, and entry strategies evolve rapidly.

Lee, Esther↗

NASA NTRS2014

Application of Adjoint Methodology in Various Aspects of Sonic Boom Design

One of the advances in computational design has been the development of adjoint methods allowing efficient calculation of sensitivities in gradient-based shape optimization. This paper discusses two new applications of adjoint methodology that have been developed to aid in sonic boom mitigation exercises. In the first, equivalent area targets are generated using adjoint sensitivities of selected boom metrics. These targets may then be used to drive the vehicle shape during optimization. The second application is the computation of adjoint sensitivities of boom metrics on the ground with respect to parameters such as flight conditions, propagation sampling rate, and selected inputs to the propagation algorithms. These sensitivities enable the designer to make more informed selections of flight conditions at which the chosen cost functionals are less sensitive.

Rallabhandi, Sriram K.↗

DOE OSTI2020

Atomically Precise Membranes for the Separation of Gases

Industrial separations require enormous amounts of energy, accounting for approximately half the industrial energy use and 10–15% of the total energy consumption. Distillation alone accounts for about half the energy demand for industrial separations. If these processes could be replaced by an energy-efficient membrane separation process, this energy demand could be reduced by 90%. However, although some membrane processes have made inroads into thermal distillation, for membrane-based separations to replace the distillation process to a far more significant and practical level, new membranes with higher robustness, selectivity, and flux still need be developed. In this membrane development program, we leveraged Temple University’s prior work in spiroligomers to develop robust membrane structures. These structures can be formed into atomically precise pores by controlling the chemical synthesis and the oligomer building blocks to first build precisely controlled macrocycles and then subsequently crosslinking these macrocycles to produce a membrane. Furthermore, through the highly controllable chemistry of our molecular building blocks, not only can we integrate pores with highly controllable and reproducible size and morphology, but we can also target internal functionalization. By using a range of scalable membrane synthesis approaches, combined with control of each and every pores internal chemistry and molecular conformation we can achieve membrane structures that can display the ultimate in high selectivity and permeance. The Mainstream-Temple University membranes can be designed to achieve ultra-selective separations based on the key factors of molecular size, shape, and functionality. In our approach to fabricate scalable atomically precise membranes, we used our molecular Lego nanostructures. We demonstrated an approach to create atomically precise pores within the membrane with pores that are the dimensions of the molecule we are trying to separate. Moreover, in addition to controlling the morphology of the membrane structure by controlling the size of every pore, we can also decorate every pore with precisely targeted and placed functional groups. These accurately placed functional groups can provide selective binding to molecules and provide enhanced selectivity via a facilitated transport mechanism. In Phase II, the Mainstream-Temple University team demonstrated the scalable synthesis of oligomers and the ability to control the pore internal and external functionality, or chemistry, to allow the fabrication of a thin-film membrane. The initial steps of the spiroligomer synthesis to produce the two key bis-amino enantiomer building blocks were scaled from the gram scale to the kilogram scale, obtaining 25 kg of the materials by transferring the procedure to a toll manufacturer. Finally, we successfully optimized the fabrication of these macrocycles into robust membranes. We successfully transitioned from a laboratory based, hard-to-scale Langmuir trough synthesis to a highly scalable, roll-to-roll applicable, interfacial polymerization process. During this Phase II program, we established a platform of atomically precise membranes where our highly controllable, atomically precise macrocycles served as a scaffold with precisely and uniformly controlled pores. Furthermore, this layer can be tailored to accommodate a diverse range of functional groups, which both further controlled the pore size to enhance the sieving effect as well as imparting precisely controlled targeted selectivity through biomimetic molecular interactions. In this Phase II, we established and scaled up a platform approach to both tune the pore size and chemistry as well as scale it to produce membranes that can be applied to a wide range of industries. In future development, the project team expects to scale up both the macrocycle building block production and interfacial polymerization process to produce the atomically precise membrane with targeted pore sizes and pore chemistries.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Evolution of AISI 304L stainless steel part properties due to powder recycling in laser powder-bed fusion

Selective laser melting (SLM) is a powder-bed fusion process in Additive Manufacturing (AM) that uses a laser beam to selectively fuse layers of powder into near net-shape components with little porosity. However, inconsistencies in the part properties due to the presence of defects in as-built components has hindered the widespread adoption of SLM for industrial applications forcing researchers to study the sources of variation for quality control purposes. A critical area suspected of creating variation in the part properties is the feedstock, where batch-to-batch differences as well as changes in the powder properties with reuse have the potential to affect performance. During processing, laser spatter and condensate eject from the melt pool and deposit into the powder-bed surrounding the parts. These particulates, more commonly known as ejecta, differ morphologically and chemically from the virgin powder compromising its reusability. In this study, 304L stainless steel powder was recycled for a total of 5 times through a systematic approach aimed at accelerating powder degradation to reveal the influence on both the tensile and impact toughness properties. Through analysis of variance (ANOVA), it was found that tensile properties did not change with reuse, while the impact toughness showed a steady decline illustrating the differences in static and dynamic part properties due to powder recycling.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Tectonic and geological setting influence hot spring microbiology

Hydrothermal systems form at divergent and convergent boundaries of lithospheric plates and within plates due to weakened crust and mantle plumes, playing host to diverse microbial ecosystems. Little is known of how differences in tectonic setting influence the geochemical and microbial compositions of these hydrothermal ecosystems. Here, for this work, coordinated geochemical and microbial community analyses were conducted on 87 high-temperature (>65°C) water and sediment samples from hot springs in Yellowstone National Park, Wyoming, USA ( n = 41; mantle plume setting), Iceland ( n = 41, divergent boundary), and Japan ( n = 5; convergent boundary). Region-specific variation in geochemistry and sediment-associated 16S rRNA gene amplicon sequence variant (ASV) composition was observed, with 16S rRNA gene assemblages being nearly completely distinguished by region and pH being the most explanatory parameter within regions. Several low abundance ASVs exhibited cosmopolitan distributions across regions, while most high-abundance ASVs were only identified in specific regions. The presence of some cosmopolitan ASVs across regions argues against dispersal limitation primarily shaping the distribution of taxa among regions. Rather, the results point to local tectonic and geologic characteristics shaping the geochemistry of continental hydrothermal systems that then select for distinct microbial assemblages. These results provide new insights into the co-evolution of hydrothermal systems and their microbial communities.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Estimation of elastic properties of an additively manufactured lattice using resonant ultrasound spectroscopy

Development of improved approaches in the characterization of additively manufactured structures continues to be a topic of interest for the advanced manufacturing community. This article will investigate an approach using resonant ultrasound spectroscopy (RUS) to determine the effective elastic constants of an orthotropic lattice structure. The evaluation is performed on a cube shaped 316 L stainless steel test specimen, constructed using selective laser melting techniques. The approach uses RUS techniques in conjunction with the assumption that in the frequency regime of interest, the wavelength of the diagnostic ultrasound is greater than the discrete structural features of the unit cell of the lattice; thus, the AM structure can be treated as an anisotropic continuum with effective material properties and symmetry inherited from the unit cell. The RUS analysis estimates the nine elastic coefficients associated with orthotropic sample symmetry, which, in turn, are used to determine the elastic moduli and Poisson ratios. Current results show good agreement between experiments and modeled data. Comparisons to published results are also in good agreement, indicating the potential applicability of this characterization technique for estimating the linear elastic properties of innovative additive manufactured metal lattice structures.

36 MATERIALS SCIENCE↗

DOE OSTI2026

GridPIQ Reference Data

GridPIQ uses dozens of publicly available datasets to provide context for a user's grid project, as well as defaults for users to choose from. Users can choose to import their own data to better customize their analysis or use GridPIQ-supplied defaults. This allows users to get up and running with an analysis very quickly without having to spend significant time pulling together input data. To run an electric vehicle (EV) smart charging project, a user will need to provide or select from prepopulated values for the regional load profile shape and peak load, region of interest and closest weather station, EV charging profile, number of EVs to add for the analysis, maximum EV charging power, location of chargers relative to grid infrastructure, and allowable charging times (for coordinated charging mode). The outputs of the analysis are changes in air quality, EV energy consumption, EV peak demand, and EV hourly consumption profile—before and after project implementation." For a detailed description of the tool methodology, including all the publicly available datasets used by the tool, see the [GridPIQ documentation](https://gridpiq.pnnl.gov/v2-beta/doc/).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Energy Northwest - Horn Rapids Solar and Storage: An Assessment of Battery Technical Performance

Chartered in 1957 as a joint action agency of the state, Energy Northwest (ENW) is a consortium of 27 public utility districts and municipalities across Washington state. ENW takes advantage of economies of scale and shared services to help utilities run their operations more efficiently and at lower cost, to the benefit of more than 1.5 million customers. ENW develops, owns, and operates a diverse mix of electricity generating resources, including hydro, solar, and wind projects – and the Northwest’s only active nuclear energy facility. These projects provide enough reliable, affordable, and environmentally responsible energy to power more than a million homes each year, and that carbon-free electricity is provided at the cost of generation. The agency continually explores new generation projects to meet its members’ needs. In 2017, as part of the second round of funding from the Washington state Clean Energy Fund, the Washington State Department of Commerce granted up to $3 million in matching funds to develop an estimated $6.5 million project that deployed a 4-MW, 20-acre solar generating array of photovoltaic (PV) panels coupled with a 1 MW/5.5 MWh lithium-iron-phosphate battery energy storage system (BESS) in Richland, Washington. The combination of PV and BESS will provide a predictable, renewable generating source and will also serve as a training ground for solar and battery technicians throughout the nation. The City of Richland will purchase the power from the project and utilize the benefits of the energy storage. The project provides Washington state with its first opportunity to integrate a large-scale solar and storage facility into its clean mix of hydro, nuclear, and wind resources. This first-of-its-kind facility combines solar generation with battery storage and technician training. In 2019, Pacific Northwest National Laboratory (PNNL) worked with ENW to assess the integrated PV and BESS in representative use cases that could benefit the City of Richland. Between March and May 2022, extensive testing was conducted, and the results were used to assess the technical performance of the BESS subjected to actual field operations. Both reference performance and use case tests were performed: (A) Reference performance tests assess the general technical capabilities of the BESS, such as energy capacity, round-trip efficiency (RTE), ramp rate, and signal tracking capability. These are the first tests performed (baseline), and they are repeated after use case tests (post cycle). A standardized U.S. Department of Energy (DOE) energy storage performance protocol was used to characterize the BESS, including representative duty cycle profiles, test procedure guidance, and calculation guidance for determining key characteristics. (B) Use case tests examine the performance of the BESS for specific use cases using duty cycles developed by PNNL in collaboration with ENW. Five use cases were selected for testing: 1) demand charge reduction, 2) load shaping, 3) transmission charge reduction, 4) Volt-VAR service, and 5) outage mitigation. The use case duty cycles were developed based on utility and site-specific characteristics in addition to the technical characteristics and physical capabilities of the BESS. Use case tests were performed between the baseline and post cycle tests. This report describes the BESS and its components, presents testing and performance analysis results, and shares key insights and lessons learned from this project. Outcomes of the tests and analyses will help ENW understand the performance of the Horn Rapids BESS in its current state and design appropriate operational strategies for this and other BESSs over the long term.

14 SOLAR ENERGY↗

DOE OSTI2022

OPALCO - Decatur Island Solar and Energy Storage Project: An Assessment of Battery Technical Performance

Orcas Power & Light Cooperative (OPALCO) is a member-owned, nonprofit cooperative utility that provides energy services to approximately 11,200 customers across 20 islands in San Juan County, Washington. OPALCO’s mostly hydroelectric power is generated by Bonneville Power Administration and delivered to the islands by submarine cables. In 2016, as part of the second round of funding from the Washington state Clean Energy Fund, OPALCO received a $1 million matching grant to support a project that deployed a 504-kW LG community photovoltaic (PV) system in combination with a 1 MW/2 MWh lithium-iron-phosphate battery energy storage system (BESS) on Decatur Island, Washington. The Decatur Island Substation is essential to ensuring reliable energy for the residents of the San Juan Islands as it is the point of interconnection with the mainland transmission system. The BESS, in combination with the community solar array, will deliver an innovative method to both defer the costly upgrade of the transmission system and allow for other high-value applications intended to benefit the utility and its customers. In 2018, Pacific Northwest National Laboratory (PNNL) completed a preliminary economic assessment for several identified use cases in collaboration with OPALCO. Between August 2021 and May 2022, extensive testing was conducted, and the results were used to assess the technical performance of the BESS subjected to actual field operations. Both reference performance and use case tests were performed: (a) Reference performance tests assess the general technical capabilities of the BESS, such as energy capacity, round-trip efficiency (RTE), ramp rate, and signal tracking capability. These are the first tests performed (baseline) and are repeated after use case tests (post cycle). A standardized U.S. Department of Energy (DOE) energy storage performance protocol was used to characterize the BESS, including representative duty cycle profiles, test procedure guidance, and calculation guidance for determining key characteristics. (b) Use case tests examine the performance of the BESS for specific use cases using duty cycles developed by PNNL in collaboration with OPALCO. Four use cases were selected for testing: 1) demand charge reduction, 2) load shaping, 3) outage mitigation, and 4) transmission deferral. The use case duty cycles were developed based on utility and site-specific characteristics in addition to the technical characteristics and physical capabilities of the BESS. Use case tests were performed between the baseline and post cycle tests. This report describes the BESS and its components, presents testing and performance analysis results, and shares key insights and lessons learned from this project. Outcomes of the tests and analyses will help OPALCO understand the performance of the Decatur Island BESS in its current state and design appropriate operational strategies for this and other BESSs over the long term.

14 SOLAR ENERGY↗

NASA NTRS1972

Design and development of pressure and repressurization purge system for reusable space shuttle multilayer insulation system

The experimental determination of purge bag materials properties, development of purge bag manufacturing techniques, experimental evaluation of a subscale purge bag under simulated operating conditions and the experimental evaluation of the purge pin concept for MLI purging are discussed. The basic purge bag material, epoxy fiberglass bounded by skins of FEP Teflon, showed no significant permeability to helium flow under normal operating conditions. Purge bag small scale manufacturing tests were conducted to develop tooling and fabrication techniques for use in full scale bag manufacture. A purge bag material layup technique was developed whereby the two plys of epoxy fiberglass enclosed between skins of FEP Teflon are vacuum bag cured in an oven in a single operation. The material is cured on a tool with the shape of a purge bag half. Plastic tooling was selected for use in bag fabrication. A model purge bag 0.6 m in diameter was fabricated and subjected to a series of structural and environmental tests simulating various flight type environments. Pressure cycling tests at high (450 K) and low (200 K) temperature as well as acoustic loading tests were performed. The purge bag concept proved to be structurally sound and was used for the full scale bag detailed design model.

Source record↗

NASA NTRS1975

Analytical displacements and vibrations of cantilevered unsymmetric fiber composite laminates

A fiber composite flat cantilever plate that has symmetric and nonsymmetric laminate configurations is theoretically investigated to determine its static and dynamic structural response. The finite element analysis method used includes a unique triangular finite element developed at Lewis for the analysis of fiber composite airfoils. The various responses investigated include tip displacements, natural frequencies, and fundamental mode shapes. The results show that laminate configurations may be selected for a cantilever such that when the tip at the leading edge is loaded normal to the plane of the plate, the tip at the trailing edge can (1) deflect in the opposite direction, (2) deflect about the same, or (3) deflect more than the tip at the leading edge. This variation in response can be utilized to provide built-in structural damping to resist flutter.

Minich, M. D.↗

NASA NTRS1976

A spectral reflectance estimation technique using multispectral data from the Viking lander camera

A technique is formulated for constructing spectral reflectance curve estimates from multispectral data obtained with the Viking lander camera. The multispectral data are limited to six spectral channels in the wavelength range from 0.4 to 1.1 micrometers and most of these channels exhibit appreciable out-of-band response. The output of each channel is expressed as a linear (integral) function of the (known) solar irradiance, atmospheric transmittance, and camera spectral responsivity and the (unknown) spectral responsivity and the (unknown) spectral reflectance. This produces six equations which are used to determine the coefficients in a representation of the spectral reflectance as a linear combination of known basis functions. Natural cubic spline reflectance estimates are produced for a variety of materials that can be reasonably expected to occur on Mars. In each case the dominant reflectance features are accurately reproduced, but small period features are lost due to the limited number of channels. This technique may be a valuable aid in selecting the number of spectral channels and their responsivity shapes when designing a multispectral imaging system.

Park, S. K.↗

NASA NTRS1981

Large modal survey testing using the Ibrahim time domain /ITD/ identification technique

The ability of the ITD identification algorithm in identifying a complete set of structural modal parameters using a large number of free-response time histories simultaneously in one analysis, assuming a math model with a high number of degrees-of-freedom, has been studied. Identification results using simulated free responses of a uniform rectangular plate, with 225 measurement stations, and experimental responses from a ground vibration test of the Long Duration Exposure Facility (LDEF) Space Shuttle payload, with 142 measurement stations, are presented. As many as 300 degrees-of-freedom were allowed in analyzing these data. In general, the use of a significantly oversized math model in the identification process was found to maintain or increase identification accuracy and to identify modes of low response level that are not identified with smaller math model sizes. The concept of a Mode Shape Correlation Constant is introduced for use when more than one identification analysis of the same structure are conducted. This constant quantifies the degree of correlation between any two sets of complex mode shapes identified using different excitation conditions, different user-selectable algorithm constants, or overlapping sets of measurements.

Ibrahim, S. R.↗

NASA NTRS1982

Modal vector estimation for closely spaced frequency modes

Techniques for obtaining improved modal vector estimates for systems with closely spaced frequency modes are discussed. In describing the dynamical behavior of a complex structure modal parameters are often analyzed: undamped natural frequency, mode shape, modal mass, modal stiffness and modal damping. From both an analytical standpoint and an experimental standpoint, identification of modal parameters is more difficult if the system has repeated frequencies or even closely spaced frequencies. The more complex the structure, the more likely it is to have closely spaced frequencies. This makes it difficult to determine valid mode shapes using single shaker test methods. By employing band selectable analysis (zoom) techniques and by employing Kennedy-Pancu circle fitting or some multiple degree of freedom (MDOF) curve fit procedure, the usefulness of the single shaker approach can be extended.

Craig, R. R., Jr.↗