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At least 775 records · Page 43

Root gravitropism: an experimental tool to investigate basic cellular and molecular processes underlying mechanosensing and signal transmission in plants

The ability of plant organs to use gravity as a guide for growth, named gravitropism, has been recognized for over two centuries. This growth response to the environment contributes significantly to the upward growth of shoots and the downward growth of roots commonly observed throughout the plant kingdom. Root gravitropism has received a great deal of attention because there is a physical separation between the primary site for gravity sensing, located in the root cap, and the site of differential growth response, located in the elongation zones (EZs). Hence, this system allows identification and characterization of different phases of gravitropism, including gravity perception, signal transduction, signal transmission, and curvature response. Recent studies support some aspects of an old model for gravity sensing, which postulates that root-cap columellar amyloplasts constitute the susceptors for gravity perception. Such studies have also allowed the identification of several molecules that appear to function as second messengers in gravity signal transduction and of potential signal transducers. Auxin has been implicated as a probable component of the signal that carries the gravitropic information between the gravity-sensing cap and the gravity-responding EZs. This has allowed the identification and characterization of important molecular processes underlying auxin transport and response in plants. New molecular models can be elaborated to explain how the gravity signal transduction pathway might regulate the polarity of auxin transport in roots. Further studies are required to test these models, as well as to study the molecular mechanisms underlying a poorly characterized phase of gravitropism that is independent of an auxin gradient.

Non-NASA Center↗

Geothermal Reservoir Characterization at Wattenberg Area in Denver Basin

The geothermal potential of the Denver-Julesburg (D-J) Basin is largely overlooked. This study focuses on characterizing the geothermal potential in the greater Wattenberg area within the Denver Basin, using available well data and subsurface information and gas wells drilled to above 2500 m deep. The review reveals that the main structures comprise ENE-trending wrench faults, along with NNE, N, and NNW trending normal faults. A thermal anomaly is present bonded by Lafayette and Longmont wrench faults and overlying vitrinite reflectance anomaly. The geometry of thermal anomaly suggests that it is influenced by Longmont wrench fault and Lafayette fault, as well as the basin margin fault. Bottom hole temperatures are of 160 Degrees Celsius, with thermal gradients of and 62 Degrees Celsius/km. Reservoir temperature estimates from thermal gradients suggest a range of >200 Degrees Celsius at depths of 3 km.

Denver basin↗

Photoelectron spectroscopy and computational investigations of the electronic structures and noncovalent interactions of cyclodextrin-closo-dodecaborate anion complexes x-CD·B12X122- (x = a, ß, y; X = H, F)

We report a joint negative ion photoelectron spectroscopy (NIPES) and computational study on the electronic structures and noncovalent interactions of a series of cyclodextrin-closo-dodecaborate dianion complexes, ?-CD·B12X122- (? = a, ß, ?; X = H, F). The measured vertical / adiabatic detachment energies (VDEs / ADEs) are 1.15/0.93, 3.55/3.20, 3.90/3.60, and 3.85/3.60 eV for B12H122- and its a-, ß-, ?-CD complexes, respectively; while the corresponding values are 1.90/1.70, 4.00/3.60, 4.33/3.95, and 4.30/3.85 eV for the X = F case. These results show that the inclusion of B12X122- into the CD cavities greatly increase the electronic stability of the dianions. The effect of electronic stabilization for ß-CD is roughly the same as for ?-CD, both being considerably stronger than that for a-CD. Density functional theory (DFT) based geometry optimization reveals that B12X122- are inserted into CDs increasingly deeper from a-CD to ?-CD. The calculated VDEs and ADEs agree with the experiments well, particularly, reproducing the electron binding energy (EBE) trends. The molecular orbital analyses indicate that the most loosely bound photodetached electrons origin from the guest B12X122- moieties. In addition to a shift of all signals to larger EBE, significant changes in the signal patterns are observed. At low EBE, this is due to the splitting of highly degenerate B12X122- orbitals, while at high EBE, photodetachment from CD oxygens contributes to the new bands. The guest B12X122- and host CD nocovalent, size-specific interaction based on the independent gradient model (IGM) and energy decomposition analysis (EDA), is dominated by electrostatic interactions. The analysis further unravels unambiguiously the existence of dihydrogen bonding and how it affects the total energy that stabilizes the host-guest complexes of CDs·B12H122- compared to the general hydrogen bonding interaction in CDs·B12F122-. This work clearly exhibits strong influences on the electronic structures of dodecaborates upon clustering with CDs, with both size (a-, ß-, ?-) and molecular (X = H or F) specificities, thus providing critical molecular-level information on the cyclodextrin-closo-dodecaborate interactions of interest to medical applications, e.g. Boron neutron capature therapy. The NIPES experiments done at PNNL were supported by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Bioscience (X.-B.W.) and was performed at the EMSL, a national scientific user facility sponsored by DOE’s Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. H.S. and Z.S. acknowledge the funding support of National Natural Science Foundation of China (Nos.11727810, 61720106009 and 21603074), the Science and Technology Commission of Shanghai Municipality (Nos. 19JC1412200), and the Program of Introducing Talents of Discipline to Universities 111 project (B12024). Z. L. thanks the China Scholarship Council (CSC) for financial support. We acknowledge the ECNU Multifunctional Platform for Innovation (001) and HPC Research Computing Team for providing computational and storage resources. J.W. acknowledges support from the Alexander von Humboldt foundation (Feodor Lynen Fellowship and Rückkehrerstipendium), a Freigeist fellowship of the Volkswagenfoundation and Prof. Vladimir A. Azov for helpful discussions.

Li, Zhipeng↗

Estimating Fine-Resolution Shortwave Broadband Albedo of Croplands from Harmonized Landsat and Sentinel-2 Data

Altered surface albedo due to land-cover conversions and management is a significant driver of global climate change. Albedo can be directly measured at ground stations, and remote sensing data can be used to scale-up albedo values to regional and global levels. Some previous studies have retrieved fine-resolution (10–30 m) instantaneous albedo and coarse-resolution (500–1000 m) daily mean albedo from remote sensing data, but they all required the input of Moderate Resolution Imaging Spectroradiometer (MODIS) albedo information at 500-m resolution, and none have assembled both instantaneous and daily albedo based exclusively on fine-resolution satellite data. Here, to address this issue, we compiled 387 instantaneous and 346 daily albedo records using field net radiometer measurements from the bioenergy croplands at the W. K. Kellogg Biological Station in southwest Michigan. We then connected these albedo records with a suite of variables derived from harmonized Landsat and Sentinel-2 data through two machine learning algorithms (random forest regression and extreme gradient boosting) to retrieve clear-sky instantaneous and daily shortwave broadband albedo. The performance statistics indicate reasonable accuracy of model results [root-mean-square error (RMSE)] around or below 0.03 except for snow-covered surfaces), suggesting that the retrieval of both instantaneous and daily albedo based exclusively on fine-resolution satellite data is promising. To facilitate the use of fine-resolution albedo products at the global level, future efforts need to include more albedo records of diverse surface cover types, as well as to accurately model daily albedo for cloudy days to address the “clear-sky bias.”

Harmonized Landsat and Sentinel-2↗

Remote sensing of coastal fronts and their effects on oil dispersion

The use of remote sensing techniques to determine the properties of coastal and estuarine fronts, which represent regions of discontinuities and high gradients in ocean physical parameters such as velocity and density, and to assess the influence of such fronts on oil pollutants is discussed. Results of an aircraft and boat verification study of an oil drift and spread model in Delaware Bay are indicated which illustrate the tendency of oil slicks to be attracted to frontal regions, where a denser fluid underlies a lighter fluid giving rise to an inclined interface with convergence zones. Landsat imagery of the bay acquired in order to incorporate frontal information into the interactive computer model is then presented which allows the locations of coastal fronts to be charted throughout a tidal cycle. It is noted that satellite observations of flood-associated fronts on the New Jersey side of the bay and ebb-associated fronts on the Delaware side agree with boat measurements and model predictions, and that the remote tracking of fronts by aircraft and satellites will aid in oil slick clean-up operations.

Klemas, V.↗

Air quality impacts from the development of unconventional oil and gas well pads: Air toxics and other volatile organic compounds

Unconventional oil and natural gas development (UOGD) has expanded rapidly across the United States in recent decades and raised concerns about associated air quality impacts. While significant effort has been made to quantify methane emissions, relatively few observations have been made of Volatile Organic Compounds (VOCs), especially during drilling and completion of new wells. Extensive air monitoring during development of several large, multi-well pads in Broomfield, Colorado, in the Denver-Julesburg Basin, provides a novel opportunity to examine changes in local air toxics and other VOC concentrations during well drilling and completions and production. These operations offer an especially useful case to study as several management practices were implemented to reduce emissions (e.g., electrified, grid-powered drill rigs and closed loop fluid handling systems to reduce truck traffic and limit fluid handling on the pad). With simultaneous measurements of methane and 50 VOCs from October 2018 to December 2022 at as many as 19 sites near well pads, in adjacent neighborhoods, and at a more distant reference location, we identify impacts from each phase of well development and production. Use of weekly, time-integrated canisters, a Proton Transfer Reaction Mass Spectrometer (PTR-MS), continuous photoionization detectors (PID) to trigger canister collection upon detection of VOC-rich plumes, and an instrumented vehicle, provided a powerful suite of measurements to characterize both transient plumes and longer-term changes in air quality. Prior to the start of well development, VOC gradients were small across Broomfield. Once drilling commenced, concentrations of oil and gas (O&G) related VOCs, including alkanes and aromatics, increased around active well pads. Concentration increases were clearly apparent during certain operations, including drilling, coil tubing/millout operations, and production tubing installation. Emissions of C 8 –C 10 n-alkanes during drilling operations highlighted the importance of VOC emissions from synthetic drilling mud chosen to reduce odor impacts. More than 90 samples were collected of transient plumes. Using composition measurements, meteorological data, and information about well pad activities, these plumes were connected with specific UOGD operations including drilling, flowback, and production equipment maintenance. The chemical signatures of these plumes differed by operation type (e.g., C 8 –C 10 n-alkanes constituted a larger fraction of measured VOCs in drilling-related plumes). Concentrations of individual, oil and gas-related VOCs in these plumes were often several orders of magnitude higher than in background air, with maximum ethane and benzene concentrations of 79,600 and 819 ppbv, respectively. Because these plumes typically impact a monitoring site for just several minutes, they are easily missed by slower-responding instruments. Study measurements highlight future emission mitigation opportunities during UOGD operations, including better control of emissions from shakers that separate drill cuttings from drilling mud, production separator maintenance operations, and periodic emptying of sand cans during flowback operations.

54 ENVIRONMENTAL SCIENCES↗

New tree-ring data from Canadian boreal and hemi-boreal forests provide insight for improving the climate sensitivity of terrestrial biosphere models

Understanding boreal/hemi-boreal forest growth sensitivity to seasonal variations in temperature and water availability provides important basis for projecting the potential impacts of climate change on the productivity of these ecosystems. Our best available information currently comes from a limited number of field experiments and terrestrial biosphere model (TBM) simulations of varying predictive accuracy. Here, we assessed the sensitivity of annual boreal/hemi-boreal forest growth in Canada to yearly fluctuations in seasonal climate variables using a large tree-ring dataset and compared this to the climate sensitivity of annual net primary productivity (NPP) estimates obtained from fourteen TBMs. We found that boreal/hemi-boreal forest growth sensitivity to fluctuations in seasonal temperature and precipitation variables changed along a southwestern to northeastern gradient, with growth limited almost entirely by temperature in the northeast and west and by water availability in the southwest. We also found a lag in growth climate sensitivity, with growth largely determined by the climate during the summer prior to ring formation. Analyses of NPP sensitivity to the same climate variables produced a similar southwest to northeast gradient in growth climate sensitivity for NPP estimates from all but three TBMs. However, analyses of growth from tree-ring data and analyses of NPP from TBMs produced contrasting evidence concerning the key climate variables limiting growth. While analyses of NPP primarily indicated a positive relationship between growth and seasonal temperature, tree-ring analyses indicated negative growth relationships to temperature. Also, the positive effect of precipitation on NPP derived from most TBMs was weaker than the positive effect of precipitation on tree-ring based growth: temperature had a more important limiting effect on NPP than tree-ring data indicated. These mismatches regarding the key climate variables limiting growth suggested that characterization of tree growth in TBMs might need revision, particularly regarding the effects of stomatal conductance and carbohydrate reserve dynamics.

54 ENVIRONMENTAL SCIENCES↗

Advancing attenuation estimation through integration of the Hessian in multiparameter viscoacoustic full-waveform inversion

Accurate seismic attenuation models of subsurface structures not only enhance subsequent migration processes by improving fidelity, resolution, and facilitating amplitude-compliant angle gather generation but also provide valuable constraints on subsurface physical properties. Leveraging full-wavefield information, multiparameter viscoacoustic full-waveform inversion ( Q-FWI) simultaneously estimates seismic velocity and attenuation ( Q) models. However, a major challenge in Q-FWI is the contamination of crosstalk artifacts, where inaccuracies in the velocity model are mistakenly mapped to the inverted attenuation model. While incorporating the Hessian is expected to mitigate these artifacts, the explicit implementation is prohibitively expensive due to its formidable computational cost. In this study, we formulate and develop a Q-FWI algorithm via the Newton-conjugate gradient (CG) framework, where the search direction at each iteration is determined through an internal CG loop. In particular, the Hessian is integrated into each CG step in a matrix-free fashion using the second-order adjoint-state method. We find through synthetic experiments that our Newton-CG Q-FWI significantly mitigates crosstalk artifacts compared with the limited-memory Broyden-Fletcher-Goldfarb-Shanno method and the CG method, albeit with a notable computational cost. In the discussion of several key implementation details, we also determine the significance of the approximate Gauss-Newton Hessian, the second-order adjoint-state method, and the two-stage inversion strategy.

Geochemistry & Geophysics↗

A review of the regional geophysics of the Arizona Transition Zone

A review of existing geophysical information and new data presented in this special section indicate that major changes in crustal properties between the Basin and Range and Colorado Plateau occur in, or directly adjacent to, the region defined as the Arizona Transition Zone. Although this region was designated on a physiographic basis, studies indicate that it is also the geophysical transition between adjoining provinces. The Transition Zone displays anomalous crustal and upper mantle seismic properties, shallow Curie isotherms, high heat flow, and steep down-to-the-plateau Bouguer gravity gradients. Seismic and gravity studies suggest that the change in crustal thickness, from thin crust in the Basin and Range to thick crust in the Colorado Plateau, may occur as a series of steps rather than a planar surface. Anomalous P wave velocities, high heat flow, shallow Curie isotherms, and results of gravity modeling suggest that the upper mantle is heterogeneous in this region. A relatively shallow asthenosphere beneath the Basin and Range and Transition Zone contrasted with a thick lithosphere beneath the Colorado Plateau would be one explanation that would satisfy these geophysical observations.

Hendricks, J. D.↗

Tropical Rainfall Analysis Using TRMM in Combination With Other Satellite Gauge Data: Comparison with Global Precipitation Climatology Project (GPCP) Results

This paper describes recent results of using Tropical Rainfall Measuring Mission (TRMM) information as the key calibration tool in a merged analysis on a 1 deg x 1 deg latitude/longitude monthly scale based on multiple satellite sources and raingauge analysis. The procedure used to produce the GPCP data set is a stepwise approach which first combines the satellite low-orbit microwave and geosynchronous IR observations into a "multi-satellite" product and than merges that result with the raingauge analysis. Preliminary results produced with the still-stabilizing TRMM algorithms indicate that TRMM shows tighter spatial gradients in tropical rain maxima with higher peaks in the center of the maxima. The TRMM analyses will be used to evaluate the evolution of the 1998 ENSO variations, again in comparison with the GPCP analyses.

Adler, Robert F.↗

AIVT: Inference of turbulent thermal convection from measured 3D velocity data by physics-informed Kolmogorov-Arnold networks

We propose the artificial intelligence velocimetry-thermometry (AIVT) method to reconstruct a continuous and differentiable representation of the temperature and velocity in turbulent convection from measured three-dimensional (3D) velocity data. AIVT is based on physics-informed Kolmogorov-Arnold networks and trained by optimizing a loss function that minimizes residuals of the velocity data, boundary conditions, and governing equations. We apply AIVT to a set of simultaneously measured 3D temperature and velocity data of Rayleigh-Bénard convection, obtained by combining particle image thermometry and Lagrangian particle tracking. This enables us to directly compare machine learning results to true volumetric, simultaneous temperature and velocity measurements. We demonstrate that AIVT can reconstruct and infer continuous, instantaneous velocity and temperature fields and their gradients from sparse experimental data at a high resolution, providing an additional approach for understanding thermal turbulence.

Science & Technology - Other Topics↗

Cosmic rays and the boundaries of the heliosphere

Anomalous cosmic rays (ACRs) are interstellar neutrals that drift into the heliosphere, become singly ionized, and are convected to the termination shock of the solar wind, where they are thought to be accelerated to hundreds of MeV. Because their effective origin is at the termination shock, studies of their gradients and spectral shape can reveal important clues about the shock's location, its strength, and the source flux of ACRs. Recently, such studies have predicted that one or more of the Voyager and Pioneer spacecraft may cross the termination shock in the next few years. In addition, there have been studies of galactic cosmic rays that shed new light on the location of the modulation boundary of these particles, which may be the heliopause region. In this talk, we will review these observations and the information they provide about the boundaries of the heliosphere.

Cummings, A. C.↗

Criterion for Identifying Vortices in High-Pressure Flows

A study of four previously published computational criteria for identifying vortices in high-pressure flows has led to the selection of one of them as the best. This development can be expected to contribute to understanding of high-pressure flows, which occur in diverse settings, including diesel, gas turbine, and rocket engines and the atmospheres of Jupiter and other large gaseous planets. Information on the atmospheres of gaseous planets consists mainly of visual and thermal images of the flows over the planets. Also, validation of recently proposed computational models of high-pressure flows entails comparison with measurements, which are mainly of visual nature. Heretofore, the interpretation of images of high-pressure flows to identify vortices has been based on experience with low-pressure flows. However, high-pressure flows have features distinct from those of low-pressure flows, particularly in regions of high pressure gradient magnitude caused by dynamic turbulent effects and by thermodynamic mixing of chemical species. Therefore, interpretations based on low-pressure behavior may lead to misidentification of vortices and other flow structures in high-pressure flows. The study reported here was performed in recognition of the need for one or more quantitative criteria for identifying coherent flow structures - especially vortices - from previously generated flow-field data, to complement or supersede the determination of flow structures by visual inspection of instantaneous fields or flow animations. The focus in the study was on correlating visible images of flow features with various quantities computed from flow-field data.

Bellan, Josette↗

Temperature Correction of Pressure-Sensitive Paints Simplified

Pressure-sensitive paint (PSP) has become a useful tool to augment conventional pressure taps in measuring the surface pressure distribution of aerodynamic components in wind tunnel testing. Although PSP offers the advantage of nonintrusive global mapping of the surface pressure, one prominent drawback to the accuracy of this technique is the inherent temperature sensitivity of PSP's luminescent intensity. Typical aerodynamic surface PSP tests rely on the coated surface to be both spatially and temporally isothermal, along with conventional instrumentation, to yield the highest accuracy pressure mappings. In some tests, however, spatial and temporal thermal gradients are generated by the nature of the test, as in a blowing jet impinging on a surface. In these cases, high accuracy and reliable data cannot be obtained unless the temperature variations on the painted surface are accounted for. A new temperature-correction technique was developed at the NASA Glenn Research Center at Lewis Field to collapse a "family" of PSP calibration curves to a single curve of intensity ratio versus pressure. This correction allows a streamlined procedure to be followed whether or not temperature information is used in the data reduction of the PSP.

Bencic, Timothy J.↗

On the feasibility of using physics-informed machine learning for underground reservoir pressure management

In this work, we evaluate the feasibility of using physics-informed machine learning (PIML) for underground energy-related pressure management. To this end, we develop a PIML framework to manage underground reservoir pressures by training neural networks to determine fluid extraction rates for dedicated extraction wells during fluid injection operations given a range of reservoir conditions (e.g., transmissivity and storativity). We implement an automatically-differentiable analytical physics model of fluid flow in porous media within the PIML framework as a proxy for more complicated models. This allows us to execute a sufficient number of training scenarios to fully evaluate the feasibility of using PIML to support pressure management activities. We quantify the number of physics-model parameters required for automatic differentiation to become more efficient than finite-difference gradient calculations. We use a simple scenario with a single injector, extractor, and critical location for our feasibility analysis. We evaluate the effect of the size of the training dataset (i.e., the number of reservoir condition samples) on the accuracy and efficiency of the PIML framework. For an equivalent number of model evaluations, the larger training dataset took less time to train and produced a neural network that was able to more accurately manage reservoir pressures. We also evaluate the effect of the training dataset batch size (i.e., number of reservoir condition samples used to update the neural network coefficients during training; i.e., how the training dataset is partitioned). While training ran faster with larger batch sizes, they produced neural networks that managed pressures less accurately. We demonstrate the approach on a more complex scenario involving 10 injectors, 10 extractors, and 4 critical locations (a relatively high well density of 20 wells/km2). We provide the number of forward and adjoint model evaluations required in each case as an indication of the feasibility of using PIML for pressure management when more complicated physics models with longer execution times are used.

54 ENVIRONMENTAL SCIENCES↗

Facile and quantitative estimation of strain in nanobubbles with arbitrary symmetry in 2D semiconductors verified using hyperspectral nano-optical imaging

When layers of van der Waals materials are deposited via exfoliation or viscoelastic stamping, nanobubbles are sometimes created from aggregated trapped fluids. Though they can be considered a nuisance, nanobubbles have attracted scientific interest in their own right owing to their ability to generate large in-plane strain gradients that lead to rich optoelectronic phenomena, especially in the semiconducting transition metal dichalcogenides. Determination of the strain within the nanobubbles, which is crucial to understanding these effects, can be approximated using elasticity theory. However, the Föppl–von Kármán equations that describe strain in a distorted thin plate are highly nonlinear and often necessitate assuming circular symmetry to achieve an analytical solution. Here, we present an easily implemented numerical method to solve for strain tensors of nanobubbles with arbitrary symmetry in 2D crystals. The method only requires topographic information from atomic force microscopy and the Poisson ratio of the 2D material. We verify that this method reproduces the strain for circularly symmetric nanobubbles that have known analytical solutions. Finally, we use the method to reproduce the Grüneisen parameter of the E' mode for 1L-WS2 nanobubbles on template-stripped Au by comparing the derived strain with measured Raman shifts from tip-enhanced Raman spectroscopy, demonstrating the utility of our method for estimating localized strain in 2D crystals.

2D materials↗

Deep learning assisted jet tomography for the study of Mach cones in QGP

Abstract Mach cones are expected to form in the expanding quark-gluon plasma (QGP) when energetic quarks and gluons traverse the hot medium at a velocity faster than the speed of sound in high-energy heavy-ion collisions. The shape of the Mach cone and the associated diffusion wake are sensitive to the initial jet production location and the propagation direction of the parton shower relative to the radial flow because of the distortion caused by the collective expansion of the QGP and the large density gradient. The shape of jet-induced Mach cones and their distortions in heavy-ion collisions provide a unique and direct probe of the dynamical evolution and the equation of state of QGP. However, it is difficult to identify the Mach cone and the diffusion wake in current experimental measurements of final hadron distributions because they are averaged over all possible initial jet production locations and parton-shower propagation directions. To overcome this difficulty, we develop a deep learning assisted jet tomography which uses the full information of the final hadrons from jets to localize the initial jet production positions. This method can help to constrain the initial regions of jet production in heavy-ion collisions and enable a differential study of Mach-cones with different path lengths and orientations relative to the radial flow of the QGP in heavy-ion collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Design principles for high efficiency small-grain polysilicon solar cells, with supporting experimental studies

Design principles suggested here aim toward high conversion efficiency (greater than 15 percent) in polysilicon cells. The principles seek to decrease the liabilities of both intragranular and grain-boundary-surface defects. The advantages of a phosphorus atom concentration gradient in a thin (less than 50 microns) base of a p(+)/n(x)/n(+) drift-field solar cell, which produces favorable gradients in chemical potential, minority-carrier mobility and diffusivity, and recombination lifetime (via phosphorus gettering) are suggested. The degrading effects of grain boundaries are reduced by these three gradients and by substituting atoms (P, H, F or Li) for vacancies on the grain-boundary surface. From recent experiments comes support for the benefits of P diffusion down grain boundaries and, for quasi-grain-boundary-free and related structures. New analytic solutions for the n(x)-base include the effect of a power-law dependence between P concentration and lifetime. These provide an upper-bound estimate on the open circuit voltage. Finite-difference numerical solutions of the six Shockley equations furnish complete information about all solar-cell parameters and add insight concerning design.

Lindholm, F. A.↗