Results for “discretization error” — Page 49

NASA NTRS1995

Equalization and detection for digital communication over nonlinear bandlimited satellite communication channels

This dissertation evaluates receiver-based methods for mitigating the effects due to nonlinear bandlimited signal distortion present in high data rate satellite channels. The effects of the nonlinear bandlimited distortion is illustrated for digitally modulated signals. A lucid development of the low-pass Volterra discrete time model for a nonlinear communication channel is presented. In addition, finite-state machine models are explicitly developed for a nonlinear bandlimited satellite channel. A nonlinear fixed equalizer based on Volterra series has previously been studied for compensation of noiseless signal distortion due to a nonlinear satellite channel. This dissertation studies adaptive Volterra equalizers on a downlink-limited nonlinear bandlimited satellite channel. We employ as figure of merits performance in the mean-square error and probability of error senses. In addition, a receiver consisting of a fractionally-spaced equalizer (FSE) followed by a Volterra equalizer (FSE-Volterra) is found to give improvement beyond that gained by the Volterra equalizer. Significant probability of error performance improvement is found for multilevel modulation schemes. Also, it is found that probability of error improvement is more significant for modulation schemes, constant amplitude and multilevel, which require higher signal to noise ratios (i.e., higher modulation orders) for reliable operation. The maximum likelihood sequence detection (MLSD) receiver for a nonlinear satellite channel, a bank of matched filters followed by a Viterbi detector, serves as a probability of error lower bound for the Volterra and FSE-Volterra equalizers. However, this receiver has not been evaluated for a specific satellite channel. In this work, an MLSD receiver is evaluated for a specific downlink-limited satellite channel. Because of the bank of matched filters, the MLSD receiver may be high in complexity. Consequently, the probability of error performance of a more practical suboptimal MLSD receiver, requiring only a single receive filter, is evaluated.

Gutierrez, Alberto, Jr.↗

NASA NTRS2012

Highlights of TOMS Version 9 Total Ozone Algorithm

The fundamental basis of TOMS total ozone algorithm was developed some 45 years ago by Dave and Mateer. It was designed to estimate total ozone from satellite measurements of the backscattered UV radiances at few discrete wavelengths in the Huggins ozone absorption band (310-340 nm). Over the years, as the need for higher accuracy in measuring total ozone from space has increased, several improvements to the basic algorithms have been made. They include: better correction for the effects of aerosols and clouds, an improved method to account for the variation in shape of ozone profiles with season, latitude, and total ozone, and a multi-wavelength correction for remaining profile shape errors. These improvements have made it possible to retrieve total ozone with just 3 spectral channels of moderate spectral resolution (approx. 1 nm) with accuracy comparable to state-of-the-art spectral fitting algorithms like DOAS that require high spectral resolution measurements at large number of wavelengths. One of the deficiencies of the TOMS algorithm has been that it doesn't provide an error estimate. This is a particular problem in high latitudes when the profile shape errors become significant and vary with latitude, season, total ozone, and instrument viewing geometry. The primary objective of the TOMS V9 algorithm is to account for these effects in estimating the error bars. This is done by a straightforward implementation of the Rodgers optimum estimation method using a priori ozone profiles and their error covariances matrices constructed using Aura MLS and ozonesonde data. The algorithm produces a vertical ozone profile that contains 1-2.5 pieces of information (degrees of freedom of signal) depending upon solar zenith angle (SZA). The profile is integrated to obtain the total column. We provide information that shows the altitude range in which the profile is best determined by the measurements. One can use this information in data assimilation and analysis. A side benefit of this algorithm is that it is considerably simpler than the present algorithm that uses a database of 1512 profiles to retrieve total ozone. These profiles are tedious to construct and modify. Though conceptually similar to the SBUV V8 algorithm that was developed about a decade ago, the SBUV and TOMS V9 algorithms differ in detail. The TOMS algorithm uses 3 wavelengths to retrieve the profile while the SBUV algorithm uses 6-9 wavelengths, so TOMS provides less profile information. However both algorithms have comparable total ozone information and TOMS V9 can be easily adapted to use additional wavelengths from instruments like GOME, OMI and OMPS to provide better profile information at smaller SZAs. The other significant difference between the two algorithms is that while the SBUV algorithm has been optimized for deriving monthly zonal means by making an appropriate choice of the a priori error covariance matrix, the TOMS algorithm has been optimized for tracking short-term variability using month and latitude dependent covariance matrices.

Bhartia, Pawan↗

NASA NTRS2013

An Application of UAV Attitude Estimation Using a Low-Cost Inertial Navigation System

Unmanned Aerial Vehicles (UAV) are playing an increasing role in aviation. Various methods exist for the computation of UAV attitude based on low cost microelectromechanical systems (MEMS) and Global Positioning System (GPS) receivers. There has been a recent increase in UAV autonomy as sensors are becoming more compact and onboard processing power has increased significantly. Correct UAV attitude estimation will play a critical role in navigation and separation assurance as UAVs share airspace with civil air traffic. This paper describes attitude estimation derived by post-processing data from a small low cost Inertial Navigation System (INS) recorded during the flight of a subscale commercial off the shelf (COTS) UAV. Two discrete time attitude estimation schemes are presented here in detail. The first is an adaptation of the Kalman Filter to accommodate nonlinear systems, the Extended Kalman Filter (EKF). The EKF returns quaternion estimates of the UAV attitude based on MEMS gyro, magnetometer, accelerometer, and pitot tube inputs. The second scheme is the complementary filter which is a simpler algorithm that splits the sensor frequency spectrum based on noise characteristics. The necessity to correct both filters for gravity measurement errors during turning maneuvers is demonstrated. It is shown that the proposed algorithms may be used to estimate UAV attitude. The effects of vibration on sensor measurements are discussed. Heuristic tuning comments pertaining to sensor filtering and gain selection to achieve acceptable performance during flight are given. Comparisons of attitude estimation performance are made between the EKF and the complementary filter.

Eure, Kenneth W.↗

DOE OSTI2024

Quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian

We provide an explicit recursive divide-and-conquer approach for simulating quantum dynamics and derive a discrete first-quantized nonrelativistic QED Hamiltonian based on the many-particle Pauli-Fierz Hamiltonian. We apply this recursive divide-and-conquer algorithm to this Hamiltonian and compare it to a concrete simulation algorithm that uses qubitization. Our divide-and-conquer algorithm, using lowest-order Trotterization, scales for fixed grid spacing as O ~ ( Λ N 2 η 2 t 2 / ϵ ) for grid size N , η particles, simulation time t , field cutoff Λ , and error ϵ . Our qubitization algorithm scales as O ~ ( N ( η + N ) ( η + Λ 2 ) t log ( 1 / ϵ ) ) . This shows that even a naive partitioning and low-order splitting formula can yield, through our divide-and-conquer formalism, superior scaling to qubitization for large Λ . We compare the relative costs of these two algorithms on systems that are relevant for applications such as the spontaneous emission of photons and the photoionization of electrons. We observe that for different parameter regimes, one method can be favored over the other. Finally, we give new algorithmic and circuit-level techniques for gate optimization, including a new way of implementing a group of multicontrolled- X gates that can be used for better analysis of circuit cost. Published by the American Physical Society 2024

Mukhopadhyay, Priyanka (ORCID:0000000164639100)↗

DOE OSTI2026

Profusion of symmetry-protected qubits from stable ergodicity breaking

We show how combining a discrete symmetry with topological Hilbert space fragmentation can give rise to exponentially many topologically stable qubits protected by a single discrete symmetry. We illustrate this explicitly with the example of the CZ𝑝 model, where the encoded qubits are prethermally stable to arbitrary symmetry-respecting perturbations for parametrically long times, substantially enhancing the robustness of a recently proposed construction based on nontopological fragmentation. In this model, the encoded qubits naturally come in pairs for which a universal set of transversal logical gates can be performed, ruling out (by the Eastin-Knill theorem) the possibility of using them for quantum error correction. We also comment on the combination of symmetry enrichment and topological fragmentation more generally, and the implications for use of systems exhibiting Hilbert space fragmentation as quantum memories.

kinetically constrained models↗

NASA NTRS1992

Indirect decentralized learning control

The new field of learning control develops controllers that learn to improve their performance at executing a given task, based on experience performing this specific task. In a previous work, the authors presented a theory of indirect learning control based on use of indirect adaptive control concepts employing simultaneous identification and control. This paper develops improved indirect learning control algorithms, and studies the use of such controllers in decentralized systems. The original motivation of the learning control field was learning in robots doing repetitive tasks such as on an assembly line. This paper starts with decentralized discrete time systems, and progresses to the robot application, modeling the robot as a time varying linear system in the neighborhood of the nominal trajectory, and using the usual robot controllers that are decentralized, treating each link as if it is independent of any coupling with other links. The basic result of the paper is to show that stability of the indirect learning controllers for all subsystems when the coupling between subsystems is turned off, assures convergence to zero tracking error of the decentralized indirect learning control of the coupled system, provided that the sample time in the digital learning controller is sufficiently short.

Longman, Richard W.↗

NASA NTRSDate not supplied

Recent Developments in the Assimilation of Microwave and Radar Observations Into NWP Models

Microwave observations play a very important role in improving the weather forecasts. Although these observations are routinely assimilated into NWP models in clear-sky conditions, assimilation of all-sky microwave observations is very limited. Two main factors contributing to this limitation are inaccuracy in the input cloud and hydrometeor profiles used as input to the radiative transfer model and also error in scattering calculations performed by the radiative transfer model itself. The Mie theory is used by many fast RT models to estimate the optical properties of single particles. The Mie theory assumes spherical shapes for ice or snow particles with mixture of air and ice. However, hydrometeors scattering radiation at microwave frequencies have different shapes, sizes, and orientations. Therefore, using Mie theory to determine their optical properties leads to large uncertainties in all-sky radiative transfer calculations. The discrete dipole approximation (DDA) which approximates the optical properties of large objects in terms of discrete dipoles has shown promise in calculating the scattering properties of particles with different shapes in the microwave frequencies. This presentation focuses on recent advancements in the CRTM scattering calculations for frozen hydrometeors in the microwave frequencies using the DDA technique. In addition to using stand-alone CRTM calculations using collocated ATMS and reanalysis profiles, the data assimilation experiments conducted using the NOAA FV3GFS forecast system are used to evaluate the scattering improvements. Additionally, the backscattering information from the DDA database was used to implement a radar simulator into CRTM. The radar operator takes advantage of CRTM different modules to calculate clouds absorption and scattering properties. In addition to the forward model both adjoint and tangent linear of the radar simulator are implemented and evaluated as well. The radar simulator is currently being tested within the JEDI/GEOS data assimilation framework to facilitate the assimilation of radar measurements such as CloudSat CPR and GPM DPR into the NASA GEOS model.

Isaac Moradi↗

NASA NTRSDate not supplied

Enhancing CRTM All-Sky Simulations and Implementation of A New Active Sensor Module

Microwave observations play a very important role in improving the weather forecasts. Although these observations are routinely assimilated into NWP models in clear-sky conditions, assimilation of all-sky microwave observations is very limited. Two main factors contributing to this limitation are inaccuracy in the input cloud and hydrometeor profiles used as input to the radiative transfer model and also error in scattering calculations performed by the radiative transfer model itself. The Mie theory is used by many fast RT models to estimate the optical properties of single particles. The Mie theory assumes spherical shapes for ice or snow particles with mixture of air and ice. However, hydrometeors scattering radiation at microwave frequencies have different shapes, sizes, and orientations. Therefore, using Mie theory to determine their optical properties leads to large uncertainties in all-sky radiative transfer calculations. The discrete dipole approximation (DDA) which approximates the optical properties of large objects in terms of discrete dipoles has shown promise in calculating the scattering properties of particles with different shapes in the microwave frequencies. This presentation focuses on recent advancements in the CRTM scattering calculations for frozen hydrometeors in the microwave frequencies using the DDA technique. In addition to using stand-alone CRTM calculations using collocated ATMS and reanalysis profiles, the data assimilation experiments conducted using the NOAA FV3GFS forecast system are used to evaluate the scattering improvements. Additionally, the backscattering information from the DDA database was used to implement a radar simulator into CRTM. The radar operator takes advantage of CRTM different modules to calculate clouds absorption and scattering properties. In addition to the forward model both adjoint and tangent linear of the radar simulator are implemented and evaluated as well. The radar simulator is currently being tested within the JEDI/GEOS data assimilation framework to facilitate the assimilation of radar measurements such as CloudSat CPR and GPM DPR into the NASA GEOS model.

Isaac Moradi↗

NASA NTRSDate not supplied

CRTM Microwave Cloud Scattering Lookup Tables and Radar Simulator

Microwave observations play a very important role in improving the weather forecasts. Although these observations are routinely assimilated into NWP models in clear-sky conditions, assimilation of all-sky microwave observations is very limited. Two main factors contributing to this limitation are inaccuracy in the input cloud and hydrometeor profiles used as input to the radiative transfer model and also error in scattering calculations performed by the radiative transfer model itself. The Mie theory is used by many fast RT models to estimate the optical properties of single particles. The Mie theory assumes spherical shapes for ice or snow particles with mixture of air and ice. However, hydrometeors scattering radiation at microwave frequencies have different shapes, sizes, and orientations. Therefore, using Mie theory to determine their optical properties leads to large uncertainties in all-sky radiative transfer calculations. The discrete dipole approximation (DDA) which approximates the optical properties of large objects in terms of discrete dipoles has shown promise in calculating the scattering properties of particles with different shapes in the microwave frequencies. This presentation focuses on recent advancements in the CRTM scattering calculations for frozen hydrometeors in the microwave frequencies using the DDA technique. In addition to using stand-alone CRTM calculations using collocated ATMS and reanalysis profiles, the data assimilation experiments conducted using the NOAA FV3GFS forecast system are used to evaluate the scattering improvements. Additionally, the backscattering information from the DDA database was used to implement a radar simulator into CRTM. The radar operator takes advantage of CRTM different modules to calculate clouds absorption and scattering properties. In addition to the forward model both adjoint and tangent linear of the radar simulator are implemented and evaluated as well. The radar simulator is currently being tested within the JEDI/GEOS data assimilation framework to facilitate the assimilation of radar measurements such as CloudSat CPR and GPM DPR into the NASA GEOS model.

Isaac Moradi↗

DOE OSTI2020

Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad–Shafranov equation by extension from polygonal subdomains

In this work, we propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modeling magnetic plasma equilibrium in axisymmetric confinement devices. In the fixed boundary case, the equation is posed on curved domains with piecewise smooth curved boundaries that may present corners. The solution method we present is based on the hybridizable discontinuous Galerkin method and sidesteps the need for geometry-conforming triangulations thanks to a transfer technique that allows to approximate the solution using only a polygonal subset as computational domain. Moreover, the solver features automatic mesh refinement driven by a residual-based a posteriori error estimator. As the mesh is locally refined, the computational domain is automatically updated in order to always maintain the distance between the actual boundary and the computational boundary of the order of the local mesh diameter. Numerical evidence is presented of the suitability of the estimator as an approximate error measure for physically relevant equilibria with pressure pedestals, internal transport barriers, and current holes on realistic geometries.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Control optimization for parametric Hamiltonians by pulse reconstruction

Optimal control techniques provide a means to tailor the control pulses required to generate customized quantum gates, which helps to improve the resilience of quantum simulations to gate errors and device noise. However, the significant amount of (classical) computation required to generate customized gates can quickly undermine the effectiveness of this approach, especially when pulse optimization needs to be iterated. We propose a method to reduce the computational time required to generate the control pulse for a Hamiltonian that is parametrically dependent on a time-varying quantity. We use simple interpolation schemes to accurately reconstruct the control pulses from a set of pulses obtained in advance for a discrete set of predetermined parameter values. We obtain a reconstruction with very high fidelity and a significant reduction in computational effort. We report the results of the application of the proposed method to device-level quantum simulations of the unitary (real) time evolution of two interacting neutrons based on superconducting qubits.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1981

Improved methods for fan sound field determination

Several methods for determining acoustic mode structure in aircraft turbofan engines using wall microphone data were studied. A method for reducing data was devised and implemented which makes the definition of discrete coherent sound fields measured in the presence of engine speed fluctuation more accurate. For the analytical methods, algorithms were developed to define the dominant circumferential modes from full and partial circumferential arrays of microphones. Axial arrays were explored to define mode structure as a function of cutoff ratio, and the use of data taken at several constant speeds was also evaluated in an attempt to reduce instrumentation requirements. Sensitivities of the various methods to microphone density, array size and measurement error were evaluated and results of these studies showed these new methods to be impractical. The data reduction method used to reduce the effects of engine speed variation consisted of an electronic circuit which windowed the data so that signal enhancement could occur only when the speed was within a narrow range.

Cicon, D. E.↗

NASA NTRS1983

Network simulation using the simulation language for alternate modeling (SLAM 2)

The simulation language for alternate modeling (SLAM 2) is a general purpose language that combines network, discrete event, and continuous modeling capabilities in a single language system. The efficacy of the system's network modeling is examined and discussed. Examples are given of the symbolism that is used, and an example problem and model are derived. The results are discussed in terms of the ease of programming, special features, and system limitations. The system offers many features which allow rapid model development and provides an informative standardized output. The system also has limitations which may cause undetected errors and misleading reports unless the user is aware of these programming characteristics.

Shen, S.↗

DOE OSTI2026

Parametric reduced order models for graded lattice structures

Graded lattice structures, characterized by smoothly varying mechanical properties, hold significant promise for optimizing material distribution in advanced engineering applications. However, accurately modeling these structures poses substantial computational challenges due to the continuous geometric variations within their unit cells. Here, to address these challenges, this paper introduces a novel Efficient Reduced Order Model (EROM) that integrates the Matrix Discrete Empirical Interpolation Method (MDEIM) and Discrete Empirical Interpolation Method (DEIM) with polynomial regression to efficiently manage geometric parametrization in lattice structures. Unlike traditional reduced order models (ROMs) that require extensive precomputed libraries for each geometric configuration, our approach enables continuous geometric variations through a flexible algebraic formulation, significantly reducing computational costs while preserving high accuracy. The method constructs projection matrices for individual unit cells that can be efficiently assembled into global systems, leveraging the repetitive nature of lattice structures. Numerical studies demonstrate that our EROM achieves displacement errors below 1% and von Mises stress prediction errors below 4%, coupled with computational speedups exceeding two orders of magnitude compared to full-order simulations. The proposed method's modularity and scalability make it particularly suitable for design optimization and real-time simulation of functionally graded lattice structures, with applications spanning aerospace to biomedical engineering.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

A Statistical Interpolation Code for Ocean Analysis and Forecasting

Abstract We present a data assimilation package for use with ocean circulation models in analysis, forecasting, and system evaluation applications. The basic functionality of the package is centered on a multivariate linear statistical estimation for a given predicted/background ocean state, observations, and error statistics. Novel features of the package include support for multiple covariance models, and the solution of the least squares normal equations either using the covariance matrix or its inverse—the information matrix. The main focus of this paper, however, is on the solution of the analysis equations using the information matrix, which offers several advantages for solving large problems efficiently. Details of the parameterization of the inverse covariance using Markov random fields are provided and its relationship to finite-difference discretizations of diffusion equations are pointed out. The package can assimilate a variety of observation types from both remote sensing and in situ platforms. The performance of the data assimilation methodology implemented in the package is demonstrated with a yearlong global ocean hindcast with a 1/4° ocean model. The code is implemented in modern Fortran, supports distributed memory, shared memory, multicore architectures, and uses climate and forecasts compliant Network Common Data Form for input/output. The package is freely available with an open source license from www.tendral.com/tsis/ .

Srinivasan, Ashwanth↗

NASA NTRS2010

SEU/SET Tolerant Phase-Locked Loops

The phase-locked loop (PLL) is an old and widely used circuit for frequency and phase demodulation, carrier and clock recovery, and frequency synthesis [1]. Its implementations range from discrete components to fully integrated circuits and even to firmware or software. Often the PLL is a highly critical component of a system, as for example when it is used to derive the on-chip clock, but as of this writing no definitive single-event upset (SET)/single-event transient (SET) tolerant PLL circuit has been described. This chapter hopes to rectify that situation, at least in regard to PLLs that are used to generate clocks. Older literature on fault-tolerant PLLs deals with detection of a hard failure, which is recovered by replacement, repair, or manual restart of discrete component systems. Several patents exist along these lines (6349391, 6272647, and 7089442). A newer approach is to harden the parts of a PLL system, to one degree or another, such as by using a voltage-based charge pump or a triple modular redundant (TMR) voted voltage-controlled oscillator (VCO). A more comprehensive approach is to harden by triplication and voting (TMR) all the digital pieces (primarily the divider) of a frequency synthesis PLL, but this still leaves room for errors in the VCO and the loop filter. Instead of hardening or voting pieces of a system, such as a frequency synthesis system (i.e., clock multiplier), we will show how the entire system can be voted. There are two main ways of doing this, each with advantages and drawbacks. We will show how each has advantages in certain areas, depending on the lock acquisition and tracking characteristics of the PLL. Because of this dependency on PLL characteristics, we will briefly revisit the theory of PLLs. But first we will describe the characteristics of voters and their correct application, as some literature does not follow the voting procedure that guarantees elimination of errors. Additionally, we will find that voting clocks is a bit trickier than voting data where an infallible clock is assumed. It is our job here to produce (or recover) that assumed infallible clock!

Shuler, Robert L., Jr.↗

DOE OSTI2020

NEON AOP foliar trait maps, maps of model uncertainty estimates, and conifer map, East River, CO 2018

This data package contains mapped trait estimates and their uncertainties, and conifer map, for the National Ecological Observatory Network's Airborne Observation Platform survey data acquired over the Upper East River, Colorado in 2018. For full details, please see associated reference. in brief, trait models were developed independently for needle and non-needle leaf species using partial least squares regression (PLSR) using ground data from additional datasets: doi:10.15485/1618130, doi:10.15485/1618132, and doi:10.15485/1631278, merged with extracted spectral data from doi:10.15485/1618131. We separated vegetated pixels into needle and non-needle classes in order to generate a classification map based on the spectral differences between these leaf types (conifer.tif). We trained a deep learning model with custom architecture, detailed in Chadwick et al. In Press. The model performed with 0.998 true positive rate and 0.982 true negative rate, with ‘positives’ being non-needle identification. We then utilized PLSR to generate models of foliar traits for each leaf type. So that we could also map uncertainty in these predictions, we generated ten different models for needle and non-needle leaf species using different testing holdout sets of discrete sites. Each of these models was developed with a 100-fold cross validation procedure that utilized a 70% training set and 30% validation set with each fold, and then assessed based on the 10% of testing sites that were not included in that model’s development. The mean predicted value across the 10 models is used for the trait estimate in each pixel across the study area. The models are applied according to the leaf type designation in the conifer.tif map. The errors are the standard deviation across the 10 different models developed, with high error suggesting instability in model prediction and areas where values may not be reliable for ecological inference. These maps are only applied to areas with a NDVI > 0.5 to exclude non-vegetated areas. Shade masks could be applied to these data (doi:10.15485/1618131), but have not been for this data package. These data are also available on Google Earth Engine: https://code.earthengine.google.com/?asset=users/kdc/ER_NEON

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1989

Gallium arsenide processing for gate array logic

The development of a reliable and reproducible GaAs process was initiated for applications in gate array logic. Gallium Arsenide is an extremely important material for high speed electronic applications in both digital and analog circuits since its electron mobility is 3 to 5 times that of silicon, this allows for faster switching times for devices fabricated with it. Unfortunately GaAs is an extremely difficult material to process with respect to silicon and since it includes the arsenic component GaAs can be quite dangerous (toxic) especially during some heating steps. The first stage of the research was directed at developing a simple process to produce GaAs MESFETs. The MESFET (MEtal Semiconductor Field Effect Transistor) is the most useful, practical and simple active device which can be fabricated in GaAs. It utilizes an ohmic source and drain contact separated by a Schottky gate. The gate width is typically a few microns. Several process steps were required to produce a good working device including ion implantation, photolithography, thermal annealing, and metal deposition. A process was designed to reduce the total number of steps to a minimum so as to reduce possible errors. The first run produced no good devices. The problem occurred during an aluminum etch step while defining the gate contacts. It was found that the chemical etchant attacked the GaAs causing trenching and subsequent severing of the active gate region from the rest of the device. Thus all devices appeared as open circuits. This problem is being corrected and since it was the last step in the process correction should be successful. The second planned stage involves the circuit assembly of the discrete MESFETs into logic gates for test and analysis. Finally the third stage is to incorporate the designed process with the tested circuit in a layout that would produce the gate array as a GaAs integrated circuit.

Cole, Eric D.↗