Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Buffers”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Micro-tensile characteristics of As-fabricated and irradiated AGR-2 TRISO fuel particle buffer, IPyC, and buffer-IPyC interlayer regions

A recently developed micro-tensile sample preparation technique was implemented to evaluate the tensile strengths of the buffer, IPyC, and buffer-IPyC interlayer regions of the unirradiated and irradiated AGR-2 TRISO fuel particles. Understanding the mechanical properties of the buffer-IPyC interlayer is essential for developing thermomechanical models of buffer-IPyC separation, yet there is a lack of experimental data on its micro-tensile properties. TEM analysis was conducted on these regions to determine the microstructural changes relevant to the samples' tensile properties. In the unirradiated TRISO particle samples, the buffer layer demonstrated the weakest tensile strength, while the IPyC layer exhibited the highest. Conversely, in the irradiated TRISO particle samples, the buffer-IPyC interlayer region showed the lowest tensile strength, with the IPyC layer being the strongest. Fractures in the samples from the buffer-IPyC region predominantly occurred either in the buffer layer or at the buffer-IPyC interface. However, some buffer-IPyC interlayer samples displayed stress-strain and fracture behaviors more akin to the IPyC layer than the buffer layer. Analysis of diffraction patterns suggests that irradiation may have increased anisotropy in the three regions tested. Despite this suggested increase in anisotropy, there was no evidence that it affected the measured strengths. The irradiated TRISO particles demonstrated a considerable increase in void space and a decrease in ultimate tensile strength within the buffer-IPyC interlayer region due to the densification and contraction of the buffer layer. Minor variations in diffraction ring patterns were also observed. These changes, coupled with a significant reduction in the Weibull modulus/shape parameter, imply that irradiation-induced densification leads to tearing between the buffer and IPyC layers at locations of elevated porosity in the buffer-IPyC interlayer region.

Tristructural isotropic (TRISO)↗
NASA NTRS2013

The W-W02 Oxygen Fugacity Buffer at High Pressures and Temperatures: Implications for f02 Buffering and Metal-silicate Partitioning

Oxygen fugacity (fO2) controls multivalent phase equilibria and partitioning of redox-sensitive elements, and it is important to understand this thermodynamic parameter in experimental and natural systems. The coexistence of a metal and its oxide at equilibrium constitutes an oxygen buffer which can be used to control or calculate fO2 in high pressure experiments. Application of 1-bar buffers to high pressure conditions can lead to inaccuracies in fO2 calculations because of unconstrained pressure dependencies. Extending fO2 buffers to pressures and temperatures corresponding to the Earth's deep interior requires precise determinations of the difference in volume (Delta) V) between the buffer phases. Synchrotron x-ray diffraction data were obtained using diamond anvil cells (DAC) and a multi anvil press (MAP) to measure unit cell volumes of W and WO2 at pressures and temperatures up to 70 GPa and 2300 K. These data were fitted to Birch-Murnaghan 3rd-order thermal equations of state using a thermal pressure approach; parameters for W are KT = 306 GPa, KT' = 4.06, and αKT = 0.00417 GPa K-1. Two structural phase transitions were observed for WO2 at 4 and 32 GPa with structures in P21/c, Pnma and C2/c space groups. Equations of state were fitted for these phases over their respective pressure ranges yielding the parameters KT = 190, 213, 300 GPa, KT' = 4.24, 5.17, 4 (fixed), and αKT = 0.00506, 0.00419, 0.00467 GPa K-1 for the P21/c, Pnma and C2/c phases, respectively. The W-WO2 buffer (WWO) was extended to high pressure by inverting the W and WO2 equations of state to obtain phase volumes at discrete pressures (1-bar to 100 GPa, 1 GPa increments) along isotherms (300 to 3000K, 100 K increments). The slope of the absolute fO2 of the WWO buffer is positive with increasing temperature up to approximately 70 GPa and is negative above this pressure. The slope is positive along isotherms from 1000 to 3000K with increasing pressure up to at least 100 GPa. The WWO buffer is at a higher fO2 than the IW buffer at pressures lower than 40 GPa, and the magnitude of this difference decreases at higher pressures. This qualitatively indicates an increasingly lithophile character for W at higher pressures. The WWO buffer was quantitatively applied to W metal-silicate partitioning by using the WWO-IW buffer difference in combination with literature data on W metal-silicate partitioning to model the exchange coefficient (KD) for the Fe-W exchange reaction. This approach captures the pressure dependence of W metal-silicate partitioning using the WWO-IW buffer difference and models the activities of the components in the silicate and metallic phases using an expression of the Gibbs excess energy of mixing. Calculation of KD along a peridotite liquidus predicts a decrease in W siderophility at higher pressures that supports the qualitative behavior predicted by the WWO-IW buffer difference, and agrees with findings of others. Comparing the competing effects of temperature and pressure on W metal-silicate partitioning, our results indicate that pressure exerts a greater effect.

Shofner, G. A.↗
NASA NTRS1982

Low noise buffer amplifiers and buffered phase comparators for precise time and frequency measurement and distribution

Extremely low noise, high performance, wideband buffer amplifiers and buffered phase comparators were developed. These buffer amplifiers are designed to distribute reference frequencies from 30 KHz to 45 MHz from a hydrogen maser without degrading the hydrogen maser's performance. The buffered phase comparators are designed to intercompare the phase of state of the art hydrogen masers without adding any significant measurement system noise. These devices have a 27 femtosecond phase stability floor and are stable to better than one picosecond for long periods of time. Their temperature coefficient is less than one picosecond per degree C, and they have shown virtually no voltage coefficients.

Eichinger, R. A.↗
DOE OSTI2025

Microstructural Characterization of AGR-2 TRISO-coated Particle Buffer, IPyC, and Buffer-IPyC Interfaces

Investigating the microstructural, mechanical, and chemical behaviors of Tristructural Isotropic (TRISO) fuel particles is vital for its qualification and use in advanced reactors. Central to the study of TRISO particles is understanding the silicon carbide (SiC) layer's ability to confine fission products, with failure mechanisms linked to chemical degradation following mechanical degradation of the buffer and IPyC layers. Research has been done to quantify the micro-tensile properties of the buffer, inner pyrolytic carbon (IPyC), and buffer-IPyC interlayer regions and their interactions within both irradiated and un-irradiated TRISO particles. Techniques such as atom probe tomography (APT) and transmission electron microscopy (TEM) have also been deployed to examine microstructural defects and fission product distribution in detail. The goal is to understand layer delamination, establish connections between microstructure and mechanical attributes, and inform computational predictions of fuel performance. This work may help refine predictive models of TRISO fuel behavior and facilitating its certification for use in advanced reactors.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2004

Cell buffer with built-in test

A cell buffer with built-in testing mechanism is provided. The cell buffer provides the ability to measure voltage provided by a power cell. The testing mechanism provides the ability to test whether the cell buffer is functioning properly and thus providing an accurate voltage measurement. The testing mechanism includes a test signal-provider to provide a test signal to the cell buffer. During normal operation, the test signal is disabled and the cell buffer operates normally. During testing, the test signal is enabled and changes the output of the cell buffer in a defined way. The change in the cell buffer output can then be monitored to determine if the cell buffer is functioning correctly. Specifically, if the voltage output of the cell buffer changes in a way that corresponds to the provided test signal, then the functioning of the cell buffer is confirmed. If the voltage output of the cell buffer does not change correctly, then the cell buffer is known not to be operating correctly. Thus, the built in testing mechanism provides the ability to quickly and accurately determine if the cell buffer is operating correctly. Furthermore, the testing mechanism provides this functionality without requiring excessive device size and complexity.

Ott, William E.↗
NASA NTRS1990

Free flow cell electrophoresis using zwitterionic buffer

Studies of a zwitterionic buffer formulated for cell electrophoresis were done using the McDonnell-Douglas Continuous Flow Electrophoresis System. Standard buffers were analyzed for their stability in the electrical field and the results showed that both buffers tested were inherently unstable. Further, titration studies showed that the standards buffers buffered poorly at the pH employed for electrophoresis. The zwitterionic buffer buffered well at its nominal pH and was shown to be stable in the electrical field. Comparative studies of the buffer with standard cell separation buffers using formalin fixed rabbit and goose red blood cells showed that the zwitterionic buffer gave better resolution of the fixed cells. Studies with viable hybridoma cells showed that buffer Q supported cell viability equal to Hank's Balanced Salt Solution and that hybridoma cells in different stages of the growth cycle demonstrated reproducible differences in electrophoretic mobility.

Rodkey, R. Scott↗
DOE OSTI2025

Assessment of buffer-IPyC thermomechanical debonding behavior using new experimental strength data in BISON

TRIstructural ISOtropic (TRISO) fuel is a nuclear fuel commonly used in High Temperature Gas-cooled Reactors (HTGRs). A single sub-millimeter-diameter TRISO fuel particle consists of a spherical fuel kernel surrounded by four coating layers: a low-density pyrocarbon buffer layer, an inner pyrolytic carbon (IPyC) layer, a silicon carbide (SiC) layer, and an outer pyrolytic carbon (OPyC) layer. The kernel is commonly made of UO2 or a mixture of uranium carbide and uranium oxide (UCO). During reactor operation, the TRISO coating layers are subjected to irradiation-induced dimensional changes and the associated thermomechanical behavior of each layer. One of the observed behaviors is gap formation between the buffer and IPyC layer due to the porous buffer’s irradiation-induced shrinkage exceeding that of the IPyC layer. Not all irradiated particles will experience buffer-IPyC gap formation. The debonding may be partial, or it may be nearly total. However, from post-irradiation examination of UCO TRISO fuels irradiated as part of the Advanced Gas Reactor (AGR) Fuel Development and Qualification Program, it was concluded that partial buffer-IPyC debonding was the most common type of buffer-IPyC interaction. To predict TRISO thermomechanical performance, multi-physics models have been built that are being continually updated and refined. The BISON code is a finite element-based nuclear fuel performance code that may be used for 1D, 2D, and 3D TRISO particle simulations. This code is used to calculate fuel temperature, kernel swelling, buffer densification, thermal and irradiation creep, fracture, and fission gas production and release. One of the recent additions to the BISON code is the ability to model the process of layer debonding. This paper will focus on the simulation results of the improved BISON debonding model that will utilize updated strengths measured from irradiated AGR TRISO fuel particles. The new experimental strength data from micromechanical tests of irradiated TRISO fuel samples were exercised in the BISON simulations and compared to baseline strength data to assess their applicability in the models. This also includes updated buffer-IPyC bond strengths to simulate layer delamination. Based on current experimental observations it is noted that the buffer-IPyC separation occurs not exactly at the junction of these two layers, but more on the side of the buffer layer. That observation is also implemented in the TRISO interface debonding model. This improved modeling approach using experimental strength data to characterize buffer-IPyC debonding and its potential subsequent cracking will be presented in the paper along with comparisons to available experimental observations.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1988

New MBE buffer for micron- and quarter-micron-gateGaAs MESFETs

A new buffer layer has been developed that eliminates backgating in GaAs MESFETs and substantially reduces short-channel effects in GaAs MESFETs with 0.27-micron-long gates. The new buffer is grown by molecular beam epitaxy (MBE) at a substrate temperature of 200 C using Ga and As sub 4 beam fluxes. The buffer is crystalline, highly resistive, optically inactive, and can be overgrown with high quality GaAs. GaAs MESFETs with a gate length of 0.27 microns that incorporate the new buffer show improved dc and RF properties in comparison with a similar MESFET with a thin undoped GaAs buffer. To demonstrate the backgating performance improvement afforded by the new buffer, MESFETs were fabricated using a number of different buffer layers and structures. A schematic cross section of the MESFET structure used in this study is shown. The measured gate length, gate width, and source-drain spacing of this device are 2,98, and 5.5 microns, respectively. An ohmic contact, isolated from the MESFET by mesa etching, served as the sidegate. The MESFETs were fabricated in MBE n-GaAs layers grown on the new buffer and also in MBE n-GaAs layers grown on buffer layers of undoped GaAs, AlGaAs, and GaAs/AlGaAs superlattices. All the buffer layers were grown by MBE and are 2 microns thick. The active layer is doped to approximately 2 x 10 to the 17th/cu cm with silicon and is 0.3 microns thick.

Source record↗
NASA NTRS1990

Damage tolerance of woven graphite-epoxy buffer strip panels

Graphite-epoxy panels with S glass buffer strips were tested in tension and shear to measure their residual strengths with crack-like damage. The buffer strips were regularly spaced narrow strips of continuous S glass. Panels were made with a uniweave graphite cloth where the S glass buffer material was woven directly into the cloth. Panels were made with different width and thickness buffer strips. The panels were loaded to failure while remote strain, strain at the end of the slit, and crack opening displacement were monitoring. The notched region and nearby buffer strips were radiographed periodically to reveal crack growth and damage. Except for panels with short slits, the buffer strips arrested the propagating crack. The strength (or failing strain) of the panels was significantly higher than the strength of all-graphite panels with the same length slit. Panels with wide, thick buffer strips were stronger than panels with thin, narrow buffer strips. A shear-lag model predicted the failing strength of tension panels with wide buffer strips accurately, but over-estimated the strength of the shear panels and the tension panels with narrow buffer strips.

Kennedy, John M.↗
NASA NTRS1981

An assessment of buffer strips for improving damage tolerance

Graphite/epoxy panels with buffer strips were tested in tension to measure their residual strength with crack-like damage. Panels were made with 45/0/-45/90(2S) and 45/0/450(2S) layups. The buffer strips were parallel to the loading directions. They were made by replacing narrow strips of the 0 deg graphite plies with strips of either 0 deg S-Glass/epoxy or Kevlar-49/epoxy on either a one for one or a two for one basis. In a third case, O deg graphite/epoxy was used as the buffer material and thin, perforated Mylar strips were placed between the 0 deg piles and the cross-plies to weaken the interfaces and thus to isolate the 0 deg plies. Some panels were made with buffer strips of different widths and spacings. The buffer strips arrested the cracks and increased the residual strengths significantly over those plain laminates without buffer strips. A shear-lag type stress analysis correctly predicted the effects of layups, buffer material, buffer strip width and spacing, and the number of plies of buffer material.

Poe, C. C., Jr.↗
NASA NTRS1980

An assessment of buffer strips for improving damage tolerance of composite laminates

Graphite/epoxy panels with buffer strips were tested in tension to measure their residual strength with crack-like damage. Panels were made with (45/0/-45/90)2S and (45/0/-45/0)2S layups. The buffer strips were parallel to the loading direction. They were made by replacing narrow strips of the 0 deg graphite plies with strips of either 0 deg S-Glass/epoxy or Kevlar-90/epoxy on either a one-for-one or a two-for-one basis. In a third case, 0 deg graphite/epoxy was used as the buffer material and thin, perforated Mylar strips were placed between the 0 deg plies and the cross-plies to weaken the interfaces and thus to isolate the 0 deg plies. Some panels were made with buffer strips of different width and spacings. The buffer strips arrested the cracks and increased the residual strengths significantly over those of plain laminates without buffer strips. A shear-lag type stress analysis correctly predicted the effects of layup, buffer material, buffer strip width and spacing, and the number of plies of buffer material

Poe, C. C., Jr.↗
NASA NTRS2000

The Effects of pH on the Growth and Aspect Ratio of Chicken Egg White Lysozyme Crystals Prepared in Different Buffers

We have measured the nucleation and aspect ratio of CEWL crystals grown by vapor diffusion in acetate, butyrate, carbonate, succinate, and phosphate buffers in a range of pH spanning the pK(sub a) of these buffers. The nucleation numbers drop off significantly in the vicinity of pK(sub a) for each of the buffers except the phosphate system, in which we used only the pH range around the second titration point(pK2). There is a concomitant increase in the sizes of the crystals. Some typical nucleation number results are shown. These data support and extend other observations. In addition, we have examined changes in aspect ratio which accompany the suppression of nucleation within each buffer system. The length of the face in the [001] direction was measured, and compared to the width of the (110) face in the [110] type directions. We find that while the aspect ratio of the crystals is affected by pH, it is dominated by a correlation with the size of the crystals. Small crystals are longer in the [0011 direction than crystals that are larger (higher pH within a buffer system). This relationship is found to hold independent of the choice of buffer. These results are consistent with those of Judge et al, who used a batch process which resulted in uniform sizing of crystals at each pH. In these experiments, we specifically avoid agitating the protein/salt buffer mixture when combining the two. This permits the formation of a range of sizes at a given pH. The results for a .05 M acetate 5% NaCl buffer are also shown. We will discuss these results in light of a growth model.

Gibson, U. J.↗
NASA NTRS1999

Buffer Effects in the Solubility, Nucleation and Growth of Chicken Egg White Lysozyme

The growth of protein crystals is important for determination of their three-dimensional structure, which relates to their biochemical functions and to the practical goal of designing pharmaceuticals to modify that function. While many proteins have been successfully crystallized by a variety of methods, there is still limited understanding of the process of nucleation and growth of even the simplest proteins. Chicken egg-white lysozyme (CEWL) is readily crystallized under a variety of conditions, and studies underway at MSFC are designed to elucidate the mechanisms by which the crystals nucleate and grow. We have investigated the effect of buffer choice on the solubility, nucleation and growth of CEWL. CEWL was purified by dialysis against a .05M phosphate buffer and chromatographic separation from contaminants in a sepharose column. Solubility studies were made as a function of buffer concentration for phosphate and formate buffers, and the nucleation and growth of crystals at 10 C was studied as a function of pH for oxalate, succinate, formate, butyrate, carbonate, phosphate and acetate buffer solutions. The solubility data support the conclusion that there is a solubility minimum as a function of buffer concentration for amphiphilic molecules, while no minimum is observed for a phosphate buffer. Nucleation is suppressed at pH greater than pKa for all buffers except phosphate. The aspect ratio of the (110) faces is shown to be a function of crystal size, rather than pH.

Gibson, Ursula J.↗
NASA NTRS2004

Buffer Gas Experiments in Mercury (Hg+) Ion Clock

We describe the results of the frequency shifts measured from various buffer gases that might be used as a buffer gas to increase the loading efficiency and cooling of ions trapped in a small mercury ion clock. The small mass, volume and power requirement of space clock precludes the use of turbo pumps. Hence, a hermetically sealed vacuum system, incorporating a suitable getter material with a fixed amount of inert buffer gas may be a practical alternative to the groundbased system. The collision shifts of 40,507,347.996xx Hz clock transition for helium, neon and argon buffer gases were measured in the ambient earth magnetic field. In addition to the above non-getterable inert gases we also measured the frequency shifts due to getterable, molecular hydrogen and nitrogen gases which may be used as buffer gases when incorporated with a miniature ion pump. We also examined the frequency shift due to the low methane gas partial pressure in a fixed higher pressure neon buffer gas environment. Methane gas interacted with mercury ions in a peculiar way as to preserve the ion number but to relax the population difference in the two hyperfine clock states and thereby reducing the clock resonance signal. The same population relaxation was also observed for other molecular buffer gases (N H ,) but at much reduced rate.

mercury ion clock↗
DOE OSTI2024

Biomass yield potential, feedstock quality, and nutrient removal of perennial buffer strips under continuous zero fertilizer application

Perennial-based buffer strips have been promoted as having the potential for improving ecosystem services from riparian areas while producing biomass as livestock feed or as a bioenergy feedstock. Both biomass production and nutrient removal of buffer strips are substantially influenced by the vegetation types for the multipurpose perennial buffers. In this 2016–2019 study in western Illinois, two perennial cropping systems, including forage crops composed of cool-season grass mixtures (forage system) and bioenergy crops made up of warm-season grass mixtures (bioenergy system), were used to establish buffer strips for assessing biomass production, feedstock quality, nutrient removal, and buffer longevity. Treatments for this study reflecting agronomic practices included (1) two harvests occurring in summer (at anthesis) and fall (after complete senescence) and (2) one harvest in fall for the forage system (two-cut vs. one-cut forage) and (3) one fall harvest for the bioenergy system (one-cut bioenergy). Successively harvesting without any fertilizer input resulted in a yield decline in forage biomass over 3 years by approximately 30 % (6.3 to 4.4 Mg DM ha –1 (dry matter) with a rate of 1.0 Mg ha –1 yr –1 ) in the two-cut forage and by 35 % (4.9 to 3.2 Mg DM ha –1 with a rate of 0.9 Mg ha –1 yr –1 ) in the one-cut forage systems. The feed quality also decreased over the years by showing declined rates of 12.9 (crucial protein), 0.9 (calcium), 0.7 (copper), and 1.3 g kg –1 DM yr –1 (zinc). Empirical models predicted enteric CH 4 emissions from cattle ranged from 225.7 to 242.6 g per cow per day based on the feed nutritive values. In contrast, bioenergy biomass yield increased by 27 % from 4.9 to 6.7 Mg DM ha –1 with a consistent quality (cellulose of ~ 397.9 g kg –1 ; hemicellulose of ~ 299.4 g kg –1 ), corresponding to the increased total theoretical ethanol yield from 1.8 × 10 3 to 2.4 × 10 3 L ha –1 (~ 33 % increase). Annual nutrient removals of N, P, K, Ca, and Mg were significantly higher in the forage systems (e.g., two-cut: 52.6–106.9 kg N ha –1 ; one-cut: 44.5–84.1 kg N ha –1 ) than those in the bioenergy system (e.g., 25.9–34.4 kg N ha –1 ); however, the removal rate declined rapidly over 3 years (e.g., ~ 49 % reduction) as the annual biomass yield declined in the forage systems. This on-farm field study demonstrated the potential of the perennial crop used as buffer strip options for biomass production and buffer sustainability at the edge of the field.

09 BIOMASS FUELS↗
NASA NTRS1981

An assessment of buffer strips for improving damage tolerance of composite laminates at elevated temperature

Buffer strips greatly improve the damage tolerance of graphite/epoxy laminates loaded in tension. Graphite/polyimide buffer strip panels were made and tested to determine their residual strength at ambient and elevated (177 C) temperature. Each panel was cut in the center to represent damage. Panels were radiographed and crack-opening displacements were recorded to indicate fracture, fracture arrest, and the extent of damage in the buffer strip after arrest. All panels had the same buffer strip spacing and width. The buffer strip material was 0 deg S-glass/PMR-15. The buffer strips were made by replacing narrow strips of the 0 deg graphite plies with strips of the 0 deg S-glass on either a one-for-one or a two-for-one basis. Half of the panels were heated to 177 + or - 3 C before and during the testing. Elevated temperature did not alter the fracture behavior of the buffer configuration.

Bigelow, C. A.↗
NASA NTRS1983

Leakage effects in n-GaAs MESFET with n-GaAs buffer layer

Whereas improvement of the interface between the active layer and the buffer layer has been demonstrated, the leakage effects can be important if the buffer layer resistivity is not sufficiently high and/or the buffer layer thickness is not sufficiently small. It was found that two buffer leakage currents exist from the channel under the gate to the source and from drain to the channel in addition to the buffer leakage resistance between drain and source. It is shown that for a 1 micron gate-length n-GaAs MESFET, if the buffer layer resistivity is 12 OHM-CM and the buffer layer thickness h is 2 microns, the performance of the device degrades drastically. It is suggested that h should be below 2 microns.

Wang, Y. C.↗
NASA NTRS1985

Electrophoretic mobilities of erythrocytes in various buffers

The calibration of space flight equipment depends on a source of standard test particles, this test particle of choice is the fixed erythrocyte. Erythrocytes from different species have different electrophoretic mobilities. Electrophoretic mobility depends upon zeta potential, which, in turn depends upon ionic strength. Zeta potential decreases with increasing ionic strength, so cells have high electrophoretic mobility in space electrophoresis buffers than in typical physiological buffers. The electrophoretic mobilities of fixed human, rat, and rabbit erythrocytes in 0.145 M salt and buffers of varying ionic strength, temperature, and composition, to assess the effects of some of the unique combinations used in space buffers were characterized. Several effects were assessed: glycerol or DMSO (dimethylsulfoxide) were considered for use as cryoprotectants. The effect of these substances on erythrocyte electrophoretic mobility was examined. The choice of buffer depended upon cell mobility. Primary experiments with kidney cells established the choice of buffer and cryoprotectant. A nonstandard temperature of EPM in the suitable buffer was determined. A loss of ionic strength control occurs in the course of preparing columns for flight, the effects of small increases in ionic strength over the expected low values need to be evaluated.

Plank, L. D.↗