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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

A 3-D CFD Analysis of the Space Shuttle RSRM With Propellant Fins @ 1 sec. Burn-Back

In this study 3-D Computational Fluid Dynamic (CFD) runs have been made for the Space Shuttle RSRM using 2 different grids and 4 different turbulent models, which were the Standard KE, the RNG KE, the Realizable KE, and the Reynolds stress model. The RSRM forward segment consists of 11 fins. By taking advantage of the forward fin symmetry only half of one fin along the axis had to be used in making the grid. This meant that the 3-D model consisted of a pie slice that encompassed 1/22nd of the motor circumference and went along the axis of the entire motor. The 3-D flow patterns in the forward fin region are of particular interest. Close inspection of these flow patterns indicate that 2 counter-rotating axial vortices emerge from each submerged solid propellant fin. Thus, the 3-D CFD analysis allows insight into complicated internal motor flow patterns that are not available from the simpler 2-D axi-symmetric studies. In addition, a comparison is made between the 3-D bore pressure drop and the 2-D axi-symmetric pressure drop.

Morstadt, Robert A.↗
NASA NTRS1997

Estimating the Uncertainty in Passive-Microwave Rain-Retrievals

Current passive-microwave rain-retrieval methods are largely based on databases built off-line using cloud models. The vertical distribution of hydrometeors within the cloud has a large impact on upwelling brightness temperatures ([31,[5]). Thus, a forward radiative transfer model can predict off-line the radiance associated with different rain scenarios. To estimate the rain from measured brightness temperatures, one simply looks for the rain scenario whose associated radiances are closest to the measurements. To understand the uncertainties in this process, we first study the dependence of the simulated brightness temperatures on different hydrometeor size distribution (DSD) models. We then analyze the marginal and joint distributions of the radiances observed by the Tropical Rainfall Measuring Mission satellite and of those in the databases used in the TRMM rain retrievals. We finally calculate the covariances of the rain profiles and brightness temperatures in the TRMM passive-microwave database and derive a simple parametric model for the conditional uncertainty, given measured radiances. These results are used to characterize the uncertainty inherent in the passive-microwave retrieval.

Coppens, Dorothee↗
NASA NTRS2000

An Assessment of the Ozone Loss During the 1999-2000 SOLVE Campaign

Ozone observations from ozonesondes, the DIAL and AROTEL lidars aboard the DC-8, in situ ozone measurements from the ER-2 and satellite ozone measurements from POAM were used to assess ozone loss during the SOLVE 1999-2000 campaign. We compare three different methods of computing the ozone loss. The first method simply compares the time sequence of ozonesondes taken at the same station inside the vortex from December through the end of March. In the second method, ozonesondes from a variety of stations are compared using a variant on the Match technique. This method uses short (approx. 5-10 day) forward diabatic trajectories to connect various sonde launches. In the third method, the measurements are simply injected into a diabatic trajectory model and carried forward in time from December 1 to March 16. Over 60,000 individual measurements were used in the last calculation. Again, ozone loss is estimated by comparing vortex interior measurements made early in the campaign with those made later in the campaign. The diabatic nature of the second and third methods calculation presumably corrects for the normal increase in ozone within the vortex due to downward advection. The three methods agree that the largest ozone loss occurs between 400 and 460 K potential temperatures (approx. 16-20 km) with slightly over 1.5 ppmv lost over the winter period. Between 460 K and 500 K (approx. 22 km) net ozone loss is less than 0.8 ppmv. From 500K to 600K (26 km) net loss is less than 0.5 ppmv.

Schoeberl, M. R.↗
NASA NTRS2000

Controlling Microbial Byproducts using Model-Based Substrate Monitoring and Control Strategies

We have developed a computer-controlled bioreactor system to study various aspects of microbially-mediated nitrogen cycling. The system has been used to investigate methods for controlling microbial denitrification (the dissimilatory reduction of nitrate to N2O and N2) in hydroponic plant growth chambers. Such chambers are key elements of advanced life support systems being designed for use on long duration space missions, but nitrogen use efficiency in them is reduced by denitrification. Control software architecture was designed which permits the heterogeneous control of system hardware using traditional feedback control, and quantitative and qualitative models of various system features. Model-based feed forward control entails prediction of future systems in states and automated regulation of system parameters to achieve desired and avoid undesirable system states. A bacterial growth rate model based on the classic Monod model of saturation kinetics was used to evaluate the response of several individual denitrifying species to varying environmental conditions. The system and models are now being applied to mixed microbial communities harvested from the root zone of a hydroponic growth chamber. The use of a modified Monod organism interaction model was evaluated as a means of achieving more accurate description of the dynamic behavior of the communities. A minimum variance parameter estimation routine was also' used to calibrate the constant parameters in the model by iterative evaluation of substrate (nitrate) uptake and growth kinetics. This representation of processes and interactions aids in the formulation of control laws. The feed forward control strategy being developed will increase system autonomy, reduce crew intervention and limit the accumulation of undesirable waste products (NOx).

Smernoff, David T.↗
NASA NTRS1997

Radio Occultation Investigation of the Rings of Saturn and Uranus

The proposed work addresses two main objectives: (1) to pursue the development of the random diffraction screen model for analytical/computational characterization of the extinction and near-forward scattering by ring models that include particle crowding, uniform clustering, and clustering along preferred orientations (anisotropy). The characterization is crucial for proper interpretation of past (Voyager) and future (Cassini) ring, occultation observations in terms of physical ring properties, and is needed to address outstanding puzzles in the interpretation of the Voyager radio occultation data sets; (2) to continue the development of spectral analysis techniques to identify and characterize the power scattered by all features of Saturn's rings that can be resolved in the Voyager radio occultation observations, and to use the results to constrain the maximum particle size and its abundance. Characterization of the variability of surface mass density among the main ring, features and within individual features is important for constraining the ring mass and is relevant to investigations of ring dynamics and origin. We completed the developed of the stochastic geometry (random screen) model for the interaction of electromagnetic waves with of planetary ring models; used the model to relate the oblique optical depth and the angular spectrum of the near forward scattered signal to statistical averages of the stochastic geometry of the randomly blocked area. WE developed analytical results based on the assumption of Poisson statistics for particle positions, and investigated the dependence of the oblique optical depth and angular spectrum on the fractional area blocked, vertical ring profile, and incidence angle when the volume fraction is small. Demonstrated agreement with the classical radiative transfer predictions for oblique incidence. Also developed simulation procedures to generate statistical realizations of random screens corresponding to uniformly packed ring models, and used the results to characterize dependence of the extinction and near-forward scattering on ring thickness, packing fraction, and the ring opening angle.

Marouf, Essam A.↗
NASA NTRS1989

Numerical simulation and comparison of symmetrical/supercritical airfoils for the near tip region of a helicopter in forward flight

Aerodynamic loads on a multi-bladed helicopter rotor in forward flight at transonic tip conditions are calculated. The unsteady, three-dimensional, time-accurate compressible Reynolds-averaged thin layer Navier-Stokes equations are solved in a rotating coordinate system on a body-conformed, curvilinear grid of C-H topology. Detailed boundary layer and global numerical comparisons of NACA-0012 symmetrical and CAST7-158 supercritical airfoils are made under identical forward flight conditions. The rotor wake effects are modeled by applying a correction to the geometric angle of attack of the blade. This correction is obtained by computing the local induced downwash velocity with a free wake analysis program. The calculations are performed on the Numerical Aerodynamic Simulation Cray 2 and the VPS32 (a derivative of a Cyber 205 at the Langley Research Center) for a model helicopter rotor in forward flight.

Badavi, F. F.↗
NASA NTRS2020

Assessing the Impact of Soil Layer Depth Specification on the Observability of Modeled Soil Moisture and Brightness Temperature

The utility of hydrologic land surface models (LSMs) can be enhanced by using information from observational platforms, but mismatches between the two are common.This study assesses the degree to which model agreement with observations (observability) is affected by two mechanisms in particular: 1) physical incongruities between the support volumes being characterized and 2) inadequateor inconsistent parameterizations of physical processes. The Noah and Noah-MP LSMs by default characterize surface soil moisture (SSM) in the top 10 cm of the soil column. This depth may be reasonable when comparing against soil moisture from in situ probes centered at 5 cm,but it is notably different from the 5 cm (or less) sensing depth of NASA’s Soil Moisture Active Passive (SMAP) satellite mission. These depth inconsistencies are examined by using thinner model layers in the Noah and Noah-MP LSMs and comparing resultant simulations to in situ and SMAP soil moisture. In addition, a forward radiative transfer model to simulate microwave brightness temperatures (Tbs) is used to facilitate direct comparisons of LSM-based and SMAP-based L-band Tb retrievals. Observability is quantified using Kolmogorov-Smirnov distance values, calculated from empirical cumulative distribution functions of SSM and Tb time series. Experiment results depend on the particular subspace being analyzed (SSM or Tb). This study concludes that therole of increasedsoil layer discretizationon LSM observability is secondary to the influence of component parameterizations, the effects of which dominate systematic differences with observations

SMAP↗
NASA NTRS1986

Pressure distributions obtained on a 0.10-scale model of the space shuttle Orbiter's forebody in the AEDC 16T propulsion wind tunnel

Pressure distribution test data obtained on a 0.10-scale model of the forward fuselage of the Space Shuttle Orbiter are presented without analysis. The tests were completed in the AEDC 16T Propulsion Wind Tunnel. The 0.10-scale model was tested at angles of attack from -2 deg to 18 deg and angles of side slip from -6 to 6 deg at Mach numbers from 0.25 to 1/5 deg. The tests were conducted in support of the development of the Shuttle Entry Air Data System (SEADS). In addition to modeling the 20 SEADS orifices, the wind-tunnel model was also instrumented with orifices to match Development Flight Instrumentation (DFI) port locations that existed on the Space Shuttle Orbiter Columbia (OV-102) during the Orbiter Flight Test program. This DFI simulation has provided a means of comparisons between reentry flight pressure data and wind-tunnel and computational data.

Siemers, P. M., III↗
NASA NTRS1987

Noise reduction for model counterrotation propeller at cruise by reducing aft-propeller diameter

The forward propeller of a model counterrotation propeller was tested with its original aft propeller and with a reduced diameter aft propeller. Noise reductions with the reduced diameter aft propeller were measured at simulated cruise conditions. Reductions were as large as 7.5 dB for the aft-propeller passing tone and 15 dB in the harmonics at specific angles. The interaction tones, mostly the first, were reduced probably because the reduced-diameter aft-propeller blades no longer interacted with the forward propeller tip vortex. The total noise (sum of primary and interaction noise) at each harmonic was significantly reduced. The chief noise reduction at each harmonic came from reduced aft-propeller-alone noise, with the interaction tones contributing little to the totals at cruise. Total cruise noise reductions were as much as 3 dB at given angles for the blade passing tone and 10 dB for some of the harmonics. These reductions would measurably improve the fuselage interior noise levels and represent a definite cruise noise benefit from using a reduced diameter aft propeller.

Dittmar, James H.↗
NASA NTRS1960

Photographic Evidence of Streamwise Arrays of Vortices in Boundary-Layer Flow

Photographs are presented of various models coated with fluorescent oil to show evidence of surface vortices at a Mach number of 3.03. Vortex formation was evidently present on models with forward-facing steps, rearward-facing steps, wires, discrete surface particles, or unswept flat surfaces with sharp leading edges. Some photographs are also presented for the models coated with a sublimation material which clearly indicates the location of boundary-layer transition; however, it does not show the vortices as clearly as the fluorescent oil. The study was made on the models at an angle of attack of 0 deg at unit Reynolds numbers of 7.7 and 10.7 million per foot. The spacing of the vortices as indicated by the flow studies on the unswept model was smaller at the higher Reynolds number in accordance with Gortler's theory. The flow studies also indicated that stable surface vortices produced by either steps or surface roughness persisted over model areas known to have turbulent boundary layers.

Hopkins, Edward J.↗
NASA NTRS1976

Analysis of neutrally stable atmospheric flow over a two-dimensional forward facing step

A mathematical model describing ground-wind induced flow fields around surface obstructions such as buildings, bridges or other man-made structures is presented. The Navier-Stokes equations with a two-equation turbulence model are used to analyze the flow over a two-dimensional forward facing step. A study of the assumed logarithmic approach velocity profile shows that an increase of surface roughness produces a rise to higher turbulence levels in the shear layer originating from the step corner. This rise leads to higher Reynolds stress and to faster reattachment of the separated flow.

Bitte, J.↗
NASA NTRS1958

Hovering and Transition Flight Tests of a 1/5-Scale Model of a Jet-Powered Vertical-Attitude VTOL Research Airplane

An experimental investigation has been made to determine the dynamic stability and control characteristics of a 1/5-scale flying model of a jet-powered vertical-attitude VTOL research airplane in hovering and transition flight. The model was powered with either a hydrogen peroxide rocket motor or a compressed-air jet exhausting through an ejector tube to simulate the turbojet engine of the airplane. The gyroscopic effects of the engine were simulated by a flywheel driven by compressed-air jets. In hovering flight the model was controlled by jet-reaction controls which consisted of a swiveling nozzle on the main jet and a movable nozzle on each wing tip; and in forward flight the model was controlled by elevons and a rudder. If the gyroscopic effects of the jet engine were not represented, the model could be flown satisfactorily in hovering flight without any automatic stabilization devices. When the gyroscopic effects of the jet engine were represented, however, the model could not be controlled without the aid of artificial stabilizing devices because of the gyroscopic coupling of the yawing and pitching motions. The use of pitch and yaw dampers made these motions completely stable and the model could then be controlled very easily. In the transition flight tests, which were performed only with the automatic pitch and yaw dampers operating, it was found that the transition was very easy to perform either with or without the engine gyroscopic effects simulated, although the model had a tendency to fly in a rolled and sideslipped attitude at angles of attack between approximately 25 and 45 deg because of static directional instability in this range.

Smith, Charles C., Jr.↗
NASA NTRS1961

Hovering and Transition Flight Tests of a 1/5-Scale Model of a Jet-Powered Vertical-Attitude VTOL Research Airplane

An experimental investigation has been made to determine the dynamic stability and control characteristics of a 1/5-scale flying model of a jet-powered vertical-attitude VTOL research airplane in hovering and transition flight. The model was powered with either a hydrogen peroxide rocket motor or a compressed-air jet exhausting through an ejector tube to simulate the turbojet engine of the airplane. The gyroscopic effects of the engine were simulated by a flywheel driven by compressed-air jets. In hovering flight the model was controlled by jet-reaction controls which consisted of a swiveling nozzle on the main jet and a movable nozzle on each wing tip; and in forward flight the model was controlled by elevons and a rudder. If the gyroscopic effects of the jet engine were not represented, the model could be flown satisfactorily in hovering flight without any automatic stabilization devices. When the gyroscopic effects of the jet engine were represented, however, the model could not be controlled without the aid of artificial stabilizing devices because of the gyroscopic coupling of the yawing and pitching motions. The use of pitch and yaw dampers made these motions completely stable and the model could then be controlled very easily. In the transition flight tests, which were performed only with the automatic pitch and yaw dampers operating, it was found that the transition was very easy to perform either with or without the engine gyroscopic effects simulated, although the model had a tendency to fly in a rolled and sideslipped attitude at angles of attack between approximately 25 deg and 45 deg because of static directional instability in this range.

Smith, Charles C., Jr.↗
NASA NTRS1998

A Conceptual Approach to Assimilating Remote Sensing Data to Improve Soil Moisture Profile Estimates in a Surface Flux/Hydrology Model: Overview - Part 1

Knowledge of the amount of water in the soil is of great importance to many earth science disciplines. Soil moisture is a key variable in controlling the exchange of water and energy between the land surface and the atmosphere. Thus, soil moisture information is valuable in a wide range of applications including weather and climate, runoff potential and flood control, early warning of droughts, irrigation, crop yield forecasting, soil erosion, reservoir management, geotechnical engineering, and water quality. Despite the importance of soil moisture information, widespread and continuous measurements of soil moisture are not possible today. Although many earth surface conditions can be measured from satellites, we still cannot adequately measure soil moisture from space. Research in soil moisture remote sensing began in the mid 1970s shortly after the surge in satellite development. Recent advances in remote sensing have shown that soil moisture can be measured, at least qualitatively, by several methods. Quantitative measurements of moisture in the soil surface layer have been most successful using both passive and active microwave remote sensing, although complications arise from surface roughness and vegetation type and density. Early attempts to measure soil moisture from space-borne microwave instruments were hindered by what is now considered sub-optimal wavelengths (shorter than 5 cm) and the coarse spatial resolution of the measurements. L-band frequencies between 1 and 3 GHz (10-30 cm) have been deemed optimal for detection of soil moisture in the upper few centimeters of soil. The Electronically Steered Thinned Array Radiometer (ESTAR), an aircraft-based instrument operating a 1,4 GHz, has shown great promise for soil moisture determination. Initiatives are underway to develop a similar instrument for space. Existing space-borne synthetic aperture radars (SARS) operating at C- and L-band have also shown some potential to detect surface wetness. The advantage of radar is its much higher resolution than passive microwave systems, but it is currently hampered by surface roughness effects and the lack of a good algorithm based on a single frequency and single polarization. In addition, its repeat frequency is generally low (about 40 days). In the meantime, two new radiometers offer some hope for remote sensing of soil moisture from space. The Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), launched in November 1997, possesses a 10.65 GHz channel and the Advanced Microwave Scanning Radiometer (AMSR) on both the ADEOS-11 and Earth Observing System AM-1 platforms to be launched in 1999 possesses a 6.9 GHz channel. Aside from issues about interference from vegetation, the coarse resolution of these data will provide considerable challenges pertaining to their application. The resolution of TMI is about 45 km and that of AMSR is about 70 km. These resolutions are grossly inconsistent with the scale of soil moisture processes and the spatial variability of factors that control soil moisture. Scale disparities such as these are forcing us to rethink how we assimilate data of various scales in hydrologic models. Of particular interest is how to assimilate soil moisture data by reconciling the scale disparity between what we can expect from present and future remote sensing measurements of soil moisture and modeling soil moisture processes. It is because of this disparity between the resolution of space-based sensors and the scale of data needed for capturing the spatial variability of soil moisture and related properties that remote sensing of soil moisture has not met with more widespread success. Within a single footprint of current sensors at the wavelengths optimal for this application, in most cases there is enormous heterogeneity in soil moisture created by differences in landcover, soils and topography, as well as variability in antecedent precipitation. It is difficult to interpret the meaning of 'mean' soil moisture under such conditions and even more difficult to apply such a value. Because of the non-linear relationships between near-surface soil moisture and other variables of interest, such as surface energy fluxes and runoff, mean soil moisture has little applicability at such large scales. It is for these reasons that the use of remote sensing in conjunction with a hydrologic model appears to be of benefit in capturing the complete spatial and temporal structure of soil moisture. This paper is Part I of a four-part series describing a method for intermittently assimilating remotely-sensed soil moisture information to improve performance of a distributed land surface hydrology model. The method, summarized in section II, involves the following components, each of which is detailed in the indicated section of the paper or subsequent papers in this series: Forward radiative transfer model methods (section II and Part IV); Use of a Kalman filter to assimilate remotely-sensed soil moisture estimates with the model profile (section II and Part IV); Application of a soil hydrology model to capture the continuous evolution of the soil moisture profile within and below the root zone (section III); Statistical aggregation techniques (section IV and Part II); Disaggregation techniques using a neural network approach (section IV and Part III); and Maximum likelihood and Bayesian algorithms for inversely solving for the soil moisture profile in the upper few cm (Part IV).

Crosson, William L.↗
NASA NTRS2010

Analysis of Snow Bidirectional Reflectance from ARCTAS Spring-2008 Campaign

The spring 2008 Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS) experiment was one of major intensive field campaigns of the International Polar Year aimed at detailed characterization of atmospheric physical and chemical processes in the Arctic region. A part of this campaign was a unique snow bidirectional reflectance experiment on the NASA P-3B aircraft conducted on 7 and 15 April by the Cloud Absorption Radiometer (CAR) jointly with airborne Ames Airborne Tracking Sunphotometer (AATS) and ground-based Aerosol Robotic Network (AERONET) sunphotometers. The CAR data were atmospherically corrected to derive snow bidirectional reflectance at high 1 degree angular resolution in view zenith and azimuthal angles along with surface albedo. The derived albedo was generally in good agreement with ground albedo measurements collected on 15 April. The CAR snow bidirectional reflectance factor (BRF) was used to study the accuracy of analytical Ross-Thick Li-Sparse (RTLS), Modified Rahman-Pinty-Verstraete (MRPV) and Asymptotic Analytical Radiative Transfer (AART) BRF models. Except for the glint region (azimuthal angles phi less than 40 degrees), the best fit MRPV and RTLS models fit snow BRF to within 0.05. The plane-parallel radiative transfer (PPRT) solution was also analyzed with the models of spheres, spheroids, randomly oriented fractal crystals, and with a synthetic phase function. The latter merged the model of spheroids for the forward scattering angles with the fractal model in the backscattering direction. The PPRT solution with synthetic phase function provided the best fit to measured BRF in the full range of angles. Regardless of the snow grain shape, the PPRT model significantly over-/underestimated snow BRF in the glint/backscattering regions, respectively, which agrees with other studies. To improve agreement with experiment, we introduced a model of macroscopic snow surface roughness by averaging the PPRT solution over the slope distribution function and by adding a simple model of shadows. With macroscopic roughness described by two parameters, the AART model achieved an accuracy of about plus or minus 0.05 with a possible bias of plus or minus 0.03 in the spectral range 0.4-2.2 micrometers. This high accuracy holds at view zenith angles below 55-60 degrees covering the practically important range for remote sensing applications, and includes both glint and backscattering directions.

Lyapustin, A.↗
NASA NTRS2010

Improving a Spectral Bin Microphysical Scheme Using TRMM Satellite Observations

Comparisons between cloud model simulations and observations are crucial in validating model performance and improving physical processes represented in the mod Tel.hese modeled physical processes are idealized representations and almost always have large rooms for improvements. In this study, we use data from two different sensors onboard TRMM (Tropical Rainfall Measurement Mission) satellite to improve the microphysical scheme in the Goddard Cumulus Ensemble (GCE) model. TRMM observed mature-stage squall lines during late spring, early summer in central US over a 9-year period are compiled and compared with a case simulation by GCE model. A unique aspect of the GCE model is that it has a state-of-the-art spectral bin microphysical scheme, which uses 33 different bins to represent particle size distribution of each of the seven hydrometeor species. A forward radiative transfer model calculates TRMM Precipitation Radar (PR) reflectivity and TRMM Microwave Imager (TMI) 85 GHz brightness temperatures from simulated particle size distributions. Comparisons between model outputs and observations reveal that the model overestimates sizes of snow/aggregates in the stratiform region of the squall line. After adjusting temperature-dependent collection coefficients among ice-phase particles, PR comparisons become good while TMI comparisons worsen. Further investigations show that the partitioning between graupel (a high-density form of aggregate), and snow (a low-density form of aggregate) needs to be adjusted in order to have good comparisons in both PR reflectivity and TMI brightness temperature. This study shows that long-term satellite observations, especially those with multiple sensors, can be very useful in constraining model microphysics. It is also the first study in validating and improving a sophisticated spectral bin microphysical scheme according to long-term satellite observations.

Li, Xiaowen↗
NASA NTRS2008

If We Can't Predict Solar Cycle 24, What About Solar Cycle 34?

Predictions of solar activity in Solar Cycle 24 range from 50% larger than SC 23 to the onset of a Grand Minimum. Because low levels of solar activity are associated with global cooling in paleoclimate and isotopic records, anticipating these extremes is required in any longterm extrapolation of climate variability. Climate models often look forward 100 or more years, which would mean 10 solar cycles into the future. Predictions of solar activity are derived from a number of methods, most of which, such as climatology and physics-based models, will be familiar to atmospheric scientists. More than 50 predictions of the maximum amplitude of SC 24 published before solar minimum will be discussed. Descriptions of several methods that result in the extreme predictions and some anticipation of even longer term predictions will be presented.

Pesnell. William Dean↗
NASA NTRS1982

Simple phenomenological modeling of transition-region capacitance of forward-biased p-n junction diodes and transistor diodes

The derivation of a simple expression for the capacitance C(V) associated with the transition region of a p-n junction under a forward bias is derived by phenomenological reasoning. The treatment of C(V) is based on the conventional Shockley equations, and simpler expressions for C(V) result that are in general accord with the previous analytical and numerical results. C(V) consists of two components resulting from changes in majority carrier concentration and from free hole and electron accumulation in the space-charge region. The space-charge region is conceived as the intrinsic region of an n-i-p structure for a space-charge region markedly wider than the extrinsic Debye lengths at its edges. This region is excited in the sense that the forward bias creates hole and electron densities orders of magnitude larger than those in equilibrium. The recent Shirts-Gordon (1979) modeling of the space-charge region using a dielectric response function is contrasted with the more conventional Schottky-Shockley modeling.

Lindholm, F. A.↗