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Articles 11041 - 11070 of 12167
Full-Text Articles in Entire DC Network
Dual Function Euv Multilayer Mirrors For The Image Mission, David D. Allred, R. Steven Turley, Matthew B. Squires
Dual Function Euv Multilayer Mirrors For The Image Mission, David D. Allred, R. Steven Turley, Matthew B. Squires
Faculty Publications
We have developed a new family of EUV multilayer mirror coatings using uranium. Using this approach we have coated a set of six mirrors for the EUV Imager, a component of the IMAGE mission. This mission is a Medium Explorer (MIDEX) program, which is scheduled for launch early in 2000. The EUV Imager will study the distribution of He+ in the Earth's plasmasphere by detecting its resonantly scattered emission at 30.4 nm (41 eV) and will produce images of the structure and dynamics of the cold plasma on a global scale. There is, however, a bright at 58.4 nm (21 …
Simulation And Density Functional Study Of A Simple Membrane Separating Two Restricted Primitive Model Electrolytes, Richard L. Rowley, Dezso Boda, Douglas Henderson, Stefan Sokolowski
Simulation And Density Functional Study Of A Simple Membrane Separating Two Restricted Primitive Model Electrolytes, Richard L. Rowley, Dezso Boda, Douglas Henderson, Stefan Sokolowski
Faculty Publications
A simple membrane, supporting charge densities on its inner and outer surfaces, is considered. In addition to the electrostatic potential, the membrane interacts with the surrounding fluid by a short range van der Waals-like potential. The fluid beyond the outer surface is a three-component restricted primitive electrolyte consisting of two cations and one anion. The membrane is impermeable to one of the cations so that the fluid in the membrane and beyond the inner surface is a two-component restricted primitive electrolyte. We use Monte Carlo simulations and density functional theory to study the density profiles of the electrolyte and the …
Selective Excitation And Thermal Quenching Of The Yellow Luminescence Of Gan, John S. Colton, P. Y. Yu, K. L. Teo, E. R. Weber, P. Perlin, I. Grzegory, K. Uchida
Selective Excitation And Thermal Quenching Of The Yellow Luminescence Of Gan, John S. Colton, P. Y. Yu, K. L. Teo, E. R. Weber, P. Perlin, I. Grzegory, K. Uchida
Faculty Publications
We report the observation of narrower structures in the yellow luminescence of bulk and thin-film n-type GaN, using the technique of selective excitation. These fine structures exhibit thermal quenching associated with an activated behavior. We attribute these fine structures to phonons and electronic excitations of a shallow donor-deep acceptor complex, and determine its activation energy for delocalization. Our results suggest that in addition to distant donor-acceptor pairs, the yellow luminescence can also involve emission complexes of shallow donors and deep acceptors.
Accuracy Of Scatterometer-Derived Winds Using The Cramer-Rao Bound, David G. Long, Travis E. Oliphant
Accuracy Of Scatterometer-Derived Winds Using The Cramer-Rao Bound, David G. Long, Travis E. Oliphant
Faculty Publications
A wind scatterometer makes measurements of the normalized radar-backscatter coefficient O of the ocean surface. To retrieve the wind, a geophysical model function (GMF), which relates O to the near-surface wind, is used. The wind vector can be estimated using maximum-likelihood techniques from several O measurements made at different azimuth angles. The probability density of the measured O is assumed to be Gaussian with a variance that depends on the true O and therefore, depends on the wind through the GMF. With this model for wind estimation, the Cramer-Rao (C-R) bound is derived for wind estimation, and its implications for …
Annotated Bibliography Of Research In The Teaching Of English, Deborah Brown, Wayne Martino, Gert Rijlaarsdam, Anne D'Antonio Stinson, Melissa E. Whiting
Annotated Bibliography Of Research In The Teaching Of English, Deborah Brown, Wayne Martino, Gert Rijlaarsdam, Anne D'Antonio Stinson, Melissa E. Whiting
Faculty Publications
Twice a year in die May and November issues, RTE publishes a selected bibliography of recent research in the teaching of English. Most of the studies appeared during the six-month period preceding the compilation of the bibliography (January through June, 1999, for the present bibliography), but some studies that appeared earlier are occasionally included. The listing is selective; we make no attempt to include all research and research-related articles that appeared in the period tinder review Comments on the bibliography and suggestions about items for inclusion may be directed to the bibliography editors. We encourage you to send your suggestions …
Piezoelectric Doping In Alingan/Gan Heterostructures, M. Asif Khan, J. W. Yang, Grigory Simin, R. Gaska, M. S. Shur, A. D. Bykovski
Piezoelectric Doping In Alingan/Gan Heterostructures, M. Asif Khan, J. W. Yang, Grigory Simin, R. Gaska, M. S. Shur, A. D. Bykovski
Faculty Publications
We report on the piezoelectricdoping and two-dimensional (2D) electron mobility in AlInGaN/GaN heterostructures grown on 6H–SiC substrates. The contribution of piezoelectricdoping to the sheet electron density was determined using an In-controlled built-in strain-modulation technique. Our results demonstrate that in strained AlGaN/GaN heterostructures, the piezoelectric field generates at least 50% of the 2D electrons. The strain modulation changes the potential distribution at the heterointerface, which, in turn, strongly affects the 2D electron mobility, especially at cryogenic temperatures. The obtained results demonstrate the potential of strain engineering and piezoelectricdoping for GaN-based electronics.
Low-Frequency Noise In N-Gan With High Electron Mobility, M. E. Levinshtein, S. L. Rumyantsev, D. C. Look, R. J. Molnar, M. Asif Khan, Grigory Simin, V. Adivarahan, M. S. Shur
Low-Frequency Noise In N-Gan With High Electron Mobility, M. E. Levinshtein, S. L. Rumyantsev, D. C. Look, R. J. Molnar, M. Asif Khan, Grigory Simin, V. Adivarahan, M. S. Shur
Faculty Publications
We report on the results of measurements of low frequency noise in n-type gallium nitride (GaN) grown on sapphire with 300 K electron mobility of 790 cm2/V s. The noise spectra have the form of 1/f noise with a Hooge parameter α of approximately 5×10−2. This value of α is two orders of magnitude smaller than that observed before in n-GaN. The obtained results show that the level of flicker noise in GaN, just like that in GaAs and Si, strongly depends on the structural perfection of the material (the amplitude of the 1/f …
Optical And Radio Observations Of The Afterglow From Grb 990510: Evidence For A Jet, F. A. Harrison, J. S. Bloom, D. A. Frail, R. Sari, S. R. Kulkarni, S. G. Djorgovski, T. Axelrod, J. Mould, B. P. Schmidt, M. H. Wieringa, R. M. Wark, R. Subrahmanyan, D. Mcconnell, P. J. Mccarthy, B. E. Schaefer, R. G. Mcmahon, R. O. Markze, E. Firth, P. Soffitta, L. Amati
Optical And Radio Observations Of The Afterglow From Grb 990510: Evidence For A Jet, F. A. Harrison, J. S. Bloom, D. A. Frail, R. Sari, S. R. Kulkarni, S. G. Djorgovski, T. Axelrod, J. Mould, B. P. Schmidt, M. H. Wieringa, R. M. Wark, R. Subrahmanyan, D. Mcconnell, P. J. Mccarthy, B. E. Schaefer, R. G. Mcmahon, R. O. Markze, E. Firth, P. Soffitta, L. Amati
Faculty Publications
We present multicolor optical and two-frequency radio observations of the bright BeppoSAX event GRB 990510. Neither the well-sampled optical decay nor the radio observations are consistent with simple spherical afterglow models. The achromatic steepening in the optical band and the early decay of the radio afterglow, which both occur at t ∼ 1 day, are evidence for hydrodynamical evolution of the source and can be most easily interpreted by models in which the gamma-ray burst ejecta are collimated in a jet. Employing a simple jet model to explain the observations, we derive a jet opening angle of θ0 = 0.08(n/l …
Pretransitional Behavior Above The Nematic-Isotropic Phase Transition Of An Auxetic Trimer Liquid Crystal, Daeseung Kang, Milind P. Mahajan, Shiyong Zhang, Rolfe G. Petschek, Charles Rosenblatt, Chaobin He, Puwei Lu, A.C. Griffin
Pretransitional Behavior Above The Nematic-Isotropic Phase Transition Of An Auxetic Trimer Liquid Crystal, Daeseung Kang, Milind P. Mahajan, Shiyong Zhang, Rolfe G. Petschek, Charles Rosenblatt, Chaobin He, Puwei Lu, A.C. Griffin
Faculty Publications
Static Light scattering and electric field-induced Kerr measurements were performed above the nematic-isotropic phase transition of a terminal-lateral-lateral-terminal negative Poisson ratio trimer. Far both measurements the inverse susceptibility was observed to be nearly linear with temperature, a result inconsistent with our previously reported Kerr data [Phys. Rev. E 58, 2041 (1998)]. [S1063-651X(99)11010-9].
Manufacturing Ideology: Scientific Management In Twentieth-Century Japan, By William M. Tsutsui, William Dean Kinzley
Manufacturing Ideology: Scientific Management In Twentieth-Century Japan, By William M. Tsutsui, William Dean Kinzley
Faculty Publications
A review of Manufacturing Ideology: Scientific Management in Twentieth-Century Japan, by William M. Tsutsui
Collisional Dynamics Of Bi2 A(0U+). I. Quantum-Resolved Vibrational Energy Transfer For V′=0–4, Robert E. Franklin, Glen P. Perram
Collisional Dynamics Of Bi2 A(0U+). I. Quantum-Resolved Vibrational Energy Transfer For V′=0–4, Robert E. Franklin, Glen P. Perram
Faculty Publications
Vibrational-to-translational energy transfer between the lowest vibrational levels (v′=0–4) of the A(0+u) state of Bi2 has been investigated using spectrally resolved, laser-induced fluorescence techniques. The small vibrational spacing (ω′e≃132 cm−1) leads to highly nonadiabatic conditions, particularly for the Bi2(A)–He collision pair. However, the Δv=−1 transition probabilities for collisions with the rare gases range from 0.75% to 1.75% per collision, considerably lower than would be anticipated from standard vibrational energy transfer theory. Multiquantum (Δv′=±2) transfer rates are low, consistent with the low anharmonicity of the A(0+u) state. The rates for …
Evaluation Of The Use Of Optical Fiber Thermometers For Thermal Control Of The Quench Module Insert, Matthew R. Jones, Jeffery T. Farmer, Shawn P. Breeding
Evaluation Of The Use Of Optical Fiber Thermometers For Thermal Control Of The Quench Module Insert, Matthew R. Jones, Jeffery T. Farmer, Shawn P. Breeding
Faculty Publications
Issues regarding the use of optical fiber thermometers to control heater settings in a microgravity vacuum furnace are addressed. It is desirable to use these probes in environments such as the International Space Station, because they can be operated without re-calibration for extended periods. However, the analysis presented in this paper shows that temperature readings obtained using optical fiber thermometers can be corrupted by emissions from the fiber when extended portions of the probe are exposed to elevated temperatures.
Demons, Spirits, And Elephants: Reflections On The Failure Of Public Administration Theory, Melvin J. Dubnick
Demons, Spirits, And Elephants: Reflections On The Failure Of Public Administration Theory, Melvin J. Dubnick
Faculty Publications
For the past half-century, those defining the field of Public Administration in their role as its leading “theorists” have been preoccupied with defending the enterprise against the evils of value-neutral logical positivism. This polemical review of that period focuses on the Simon-Waldo debate that ultimately leads the field to adopt a “professional” identity rather than seek disciplinary status among the social sciences. A survey of recent works by the field’s intellectual leaders and “gatekeepers” demonstrates that the anti-positivist obsession continues, oblivious to significant developments in the social sciences. The paper ends with a call for Public Administrationists to engage in …
Theoretical And Practical Requirements For A System Of Pre-Design Analysis, Andrew S. Gibbons, Jon S. Nelson, Robert E. Richards
Theoretical And Practical Requirements For A System Of Pre-Design Analysis, Andrew S. Gibbons, Jon S. Nelson, Robert E. Richards
Faculty Publications
This research is aimed at bridging the worlds of simulation design as practiced by computer scientists and systems engineers and instructional design as practiced by a multitude of corporate, government, and military instructional designers, most of whom lack formal schooling in the techniques of either area.
Nonlinear Robust Missile Autopilot Design Using Successive Galerkin Approximation, Timothy Mclain, Randal W. Beard
Nonlinear Robust Missile Autopilot Design Using Successive Galerkin Approximation, Timothy Mclain, Randal W. Beard
Faculty Publications
The application of a new nonlinear robust control strategy to the design of missile autopilots is presented. The control approach described and demonstrated here is based upon the numerical solution of the Hamilton-Jacobi-Isaacs equation by Successive Galerkin Approximation. Using this approach, feedback controllers are computed by an iterative application of a numerical Galerkin-type PDE solver. Application of this approach to the design of a pitch-axis autopilot for a missile having uncertain pitch moment and lift force is described.
A Neural Model Of Centered Tri-Gram Speech Recognition, Tony R. Martinez, Dan A. Ventura, D. Randall Wilson, Brian Moncur
A Neural Model Of Centered Tri-Gram Speech Recognition, Tony R. Martinez, Dan A. Ventura, D. Randall Wilson, Brian Moncur
Faculty Publications
A relaxation network model that includes higher order weight connections is introduced. To demonstrate its utility, the model is applied to the speech recognition domain. Traditional speech recognition systems typically consider only that context preceding the word to be recognized. However, intuition suggests that considering both preceding context as well as following context should improve recognition accuracy. The work described here tests this hypothesis by applying the higher order relaxation network to consider both precedes and follows context in speech recognition. The results demonstrate both the general utility of the higher order relaxation network as well as its improvement over …
Combining Cross-Validation And Confidence To Measure Fitness, Tony R. Martinez, D. Randall Wilson
Combining Cross-Validation And Confidence To Measure Fitness, Tony R. Martinez, D. Randall Wilson
Faculty Publications
Neural network and machine learning algorithms often have parameters that must be tuned for good performance on a particular task. Leave-one-out cross-validation (LCV) accuracy is often used to measure the fitness of a set of parameter values. However, small changes in parameters often have no effect on LCV accuracy. Many learning algorithms can measure the confidence of a classification decision, but often confidence alone is an inappropriate measure of fitness. This paper proposes a combined measure of Cross- Validation and Confidence (CVC) for obtaining a continuous measure of fitness for sets of parameters in learning algorithms. This paper also proposes …
Successive Galerkin Approximation Of The Isaacs Equation, Timothy Mclain, Randal W. Beard, John T. Wen
Successive Galerkin Approximation Of The Isaacs Equation, Timothy Mclain, Randal W. Beard, John T. Wen
Faculty Publications
The successive Galerkin approximation (SGA) algorithm has recently been developed for approximating solutions to the Hamilton-Jacobi-Isaacs equation. The algorithm produces feedback control laws that are stabilizing on a well-defined region of state space. The objective of this paper is to demonstrate the application of the SGA algorithm to two simple examples. The examples serve several purposes: first they illustrate how the algorithm is applied in a setting that is simple enough to write out in detail, second they demonstrate the convergence of the algorithm in a setting where the actual solution can be derived analytically.
Blue Crab Larval Dispersion And Retention In The Mississippi Bight, Donald R. Johnson, Harriet M. Perry
Blue Crab Larval Dispersion And Retention In The Mississippi Bight, Donald R. Johnson, Harriet M. Perry
Faculty Publications
A conceptual hypothesis relating physical forcing to dispersion and retention was developed for blue crab larvae within the Mississippi Eight. The spawning period for blue crabs in the northern Gulf of Mexico is protracted. Hatching of eggs occurs near the barrier islands and mouths of coastal bays from March through October. Larvae are released on ebbing tides and spend the next 30 to 50 d offshore where they develop through seven zoeal stages before undergoing metamorphosis to megalopae. Duration of the megalopal stage is variable but generally persists from 6 to 20 d. Blue crabs recruit to Gulf estuaries as …
Local Data Assimilation In The Estimation Of Barotropic And Baroclinic Open Boundary Conditions, Igor Shulman, James K. Lewis, John G. Mayer
Local Data Assimilation In The Estimation Of Barotropic And Baroclinic Open Boundary Conditions, Igor Shulman, James K. Lewis, John G. Mayer
Faculty Publications
The problem of data assimilation in the specification of open boundary conditions for limited area models is addressed in this paper. Optimization approaches are detailed, which are based on combining available data on an open boundary with the physics of the hydrodynamical model. In our case the physics is in terms of the flux of energy through the open boundary. These optimized boundary conditions, for both barotropic and baroclinic situations, interpreted physically as special Linearizations of the Bernoulli equation for each normal mode. Because of the complexity of decomposing variables into normal modes for open boundaries with varying bathymetry, we …
Functional Characterization Of The Hvea Homolog Specified By African Green Monkey Kidney Cells With A Herpes Simplex Virus Expressing The Green Fluorescence Protein, Timothy P. Foster, Vladimir N. Chouljenko, Konstantin G. Kousoulas
Functional Characterization Of The Hvea Homolog Specified By African Green Monkey Kidney Cells With A Herpes Simplex Virus Expressing The Green Fluorescence Protein, Timothy P. Foster, Vladimir N. Chouljenko, Konstantin G. Kousoulas
Faculty Publications
We cloned the gene specified by African monkey kidney cells (Vero) that codes for the homolog of the herpes virus entry mediator (HveA) specified by HeLa cells. The primary sequence of the monkey HveA (HveAs) differed significantly from HveA. Single amino acid differences were distributed throughout the amino and carboxyl terminal portions of the HveAs in comparison with the HveA, whereas certain regions were highly conserved. The predicted membrane spanning domains of the two receptors differed substantially due to insertions and deletions of short amino acid sequences. The ability of HveAs to mediate HSV virus entry was tested in a …
Successive Galerkin Approximation Of A Nonlinear Optimal Attitude Control, Timothy Mclain, Randal W. Beard, Johnathan Lawton
Successive Galerkin Approximation Of A Nonlinear Optimal Attitude Control, Timothy Mclain, Randal W. Beard, Johnathan Lawton
Faculty Publications
This paper presents the application of the successive Galerkin approximation (SGA) to the Hamilton-Jacobi-Bellman equation to obtain solutions of the optimal attitude control problem. Galerkin's method approximates the value function by a truncated Galerkin series expansion. To do so, a truncated Galerkin basis set is formed. A sufficient number of functions must be included in this Galerkin basis set in order to guarantee that the solution will be a stabilizing control. By increasing the size of the Galerkin basis the quality of the approximation is improved at the cost of rapid growth in the computation load of the SGA. A …
A Five-Year Development Plan For The California Aviation Database, H.-S. Jacob Tsao
A Five-Year Development Plan For The California Aviation Database, H.-S. Jacob Tsao
Faculty Publications
The California Aviation Database (CAvD) project was suggested by Caltrans Aeronautics Program to fulfill a need of the planners involved in aviation system planning and programming activities to locate and access aviation data and information in an efficient and comprehensive way. CAvD is being implemented in the form of an Internet website and is currently intended as a five-year project. However, the development can be accelerated, and the duration will depend on the available resources. CAvD is a joint project between the National Center of Excellence for Aviation Operations Research (NEXTOR) and the California Department of Transportation (Caltrans). Its primary …
Overview: Nonlinear Dynamics Related To Polymeric Systems, Irving R. Epstein, John A. Pojman
Overview: Nonlinear Dynamics Related To Polymeric Systems, Irving R. Epstein, John A. Pojman
Faculty Publications
No abstract provided.
Synthesis And Experimental Testing Of A Nonlinear Optimal Tracking Controller, Timothy Mclain, Randal W. Beard, Christopher A. Bailey
Synthesis And Experimental Testing Of A Nonlinear Optimal Tracking Controller, Timothy Mclain, Randal W. Beard, Christopher A. Bailey
Faculty Publications
This paper presents a novel approach for developing tracking controllers for nonlinear systems. The approach involves the numerical solution, by Galerkin approximation, of the time-varying Hamilton-Jacobi-Bellman (HJB) equation and results in a nonlinear controller approximating the optimal tracking control law for a specified desired trajectory and cost function. Experimental results are presented for a nonlinear pendulum system.
Model Predictive Satisficing Fuzzy Logic Control, Richard L. Frost, Michael A. Goodrich, Wynn C. Stirling
Model Predictive Satisficing Fuzzy Logic Control, Richard L. Frost, Michael A. Goodrich, Wynn C. Stirling
Faculty Publications
Model-predictive control, which is an alternative to conventional optimal control, provides controller solutions to many constrained and nonlinear control problems. However, even when a good model is available, it may be necessary for an expert to specify the relationship between local model predictions and global system performance. We present a satisficing fuzzy logic controller that is based on a receding control horizon, but which employs a fuzzy description of system consequences via model predictions. This controller considers the gains and losses associated with each control action, is compatible with robust design objectives, and permits flexible defuzzifier design. We demonstrate the …
Oxygen Permeation Through Composite Oxide-Ion And Electronic Conductors, Kevin Huang, Michael Schroeder, John B. Goodenough
Oxygen Permeation Through Composite Oxide-Ion And Electronic Conductors, Kevin Huang, Michael Schroeder, John B. Goodenough
Faculty Publications
Oxygen permeation through composites consisting of four well-known oxide-ion conductors and a noble metal, Pd or Ag, is reported. The oxides were Zr0.9Y0.1O1.95 (YSZ), (Bi1.75Y0.25O3)0.95(CeO2)0.05 (BYC5), Ce0.8Sm0.2O1.9 (SSC), and La0.8Sr0.2Ga0.83Mg0.17O2.815 (LSGM). The results show that (BYC5 + Ag) yields the highest oxygen permeation flux, but the composite deteriorates with time. The composites (SSC + Pd), (LSGM + Pd), and (YSZ + Pd) give stable, but relatively lower oxygen permeation flux …
The Probability Density Of Spectral Estimates Based On Modified Periodogram Averages, David G. Long, Paul E. Johnson
The Probability Density Of Spectral Estimates Based On Modified Periodogram Averages, David G. Long, Paul E. Johnson
Faculty Publications
Welch's (1967) method for spectral estimation of averaging modified periodograms has been widely used for decades. Because such an estimate relies on random data, the estimate is also a random variable with some probability density function. Here, the PDF of a power estimate is derived for an estimate based on an arbitrary number of frequency bins, overlapping data segments, amount of overlap, and type of data window, given a correlated Gaussian input sequence. The PDFs of several cases are plotted and found to be distinctly non-Gaussian (the asymptotic result of averaging frequency bins and/or data segments), using the Kullback-Leibler distance …
Ultrasonic Enhancement Of Antibiotic Action On Escherichia Coli Biofilms: An In Vivo Model, Andrea M. Rediske, Beverly L. Roeder, Maren K. Brown, Jared L. Nelson, Rachel L. Robison, David O. Draper, G. Bruce Schaalje, Richard A. Robison, William G. Pitt
Ultrasonic Enhancement Of Antibiotic Action On Escherichia Coli Biofilms: An In Vivo Model, Andrea M. Rediske, Beverly L. Roeder, Maren K. Brown, Jared L. Nelson, Rachel L. Robison, David O. Draper, G. Bruce Schaalje, Richard A. Robison, William G. Pitt
Faculty Publications
Biofilm infections are a common complication of prosthetic devices in humans. Previous in vitro research has determined that low-frequency ultrasound combined with aminoglycoside antibiotics is an effective method of killing biofilms. We report the development of an in vivo model to determine if ultrasound enhances antibiotic action. Two 24-h-old Escherichia coli (ATCC 10798) biofilms grown on polyethylene disks were implanted subcutaneously on the backs of New Zealand White female rabbits, one on each side of the spine. Low-frequency (28.48-kHz) and low-power-density (100- and 300-mW/cm2) continuous ultrasound treatment was applied for 24 h with and without systemic administration of gentamicin. The …
Postlaunch Sensor Verification And Calibration Of The Nasa Scatterometer, David G. Long, Wu-Yang Tsai, James E. Graf, Carroll Winn, James N. Huddleston, R. Scott Dunbar, Michael H. Freilich, Frank J. Wentz, W. Linwood Jones
Postlaunch Sensor Verification And Calibration Of The Nasa Scatterometer, David G. Long, Wu-Yang Tsai, James E. Graf, Carroll Winn, James N. Huddleston, R. Scott Dunbar, Michael H. Freilich, Frank J. Wentz, W. Linwood Jones
Faculty Publications
Scatterometer instruments are active microwave sensors that transmit a series of microwave pulses and measure the returned echo power to determine the normalized radar backscattering cross section (sigma-0) of the ocean surface from which the speed and direction of near-surface ocean winds are derived. The NASA Scatterometer (NSCAT) was launched on board the ADEOS spacecraft in August 1996 and returned ten months of high-quality data before the failure of the ADEOS spacecraft terminated the data stream in June 1997. The purpose of this paper is to provide an overview of the NSCAT instrument and sigma-0 computation and to describe the …