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All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

A new VLSI complex integer multiplier which uses a quadratic-polynomial residue system with Fermat numbers

A quadratic-polynomial Fermat residue number system (QFNS) has been used to compute complex integer multiplications. The advantage of such a QFNS is that a complex integer multiplication requires only two integer multiplications. In this article, a new type Fermat number multiplier is developed which eliminates the initialization condition of the previous method. It is shown that the new complex multiplier can be implemented on a single VLSI chip. Such a chip is designed and fabricated in CMOS-Pw technology.

Shyu, H. C.↗
NASA NTRS1973

A compilation of studies from Atmospheric Variability Experiment (AVE)

Five methods for obtaining the sign of vertical motion at various levels in the atmosphere were investigated to determine which gave the best explanation for areas of rain and no-rain in the southeastern United States during the period February 19-22, 1964. The methods used were the terrain-induced vertical motion, the kinematic method including the terrain effect, the adiabatic method, the omega equation, and the vorticity equation combined with Dines' Compensation Principle. Stability and moisture availability were considered but not as extensively as vertical motion. Values of vertical motion obtained by the kinetic method, including orographic lifting produced the best agreement with the observed areas. When terms in the omega equation were added through use of constant multipliers, results comparable to the adiabatic method were obtained. Without this addition large uncertainties occurred. Maps showing areas where terms of the omega equation would indicate positive vertical motion did not correlate well with the observed rainfall patterns.

Scoggins, J. R.↗
NASA NTRS1988

Tracing structural optima as a function of available resources by a homotopy method

Optimization problems are typically solved by starting with an initial estimate and proceeding iteratively to improve it until the optimum is found. The design points along the path from the initial estimate to the optimum are usually of no value. The present work proposes a strategy for tracing a path of optimum solutions parameterized by the amount of available resources. The paper specifically treats the optimum design of a structure to maximize its buckling load. Equations for the optimum path are obtained using Lagrange multipliers, and solved by a homotopy method. The solution path has several transitions from unimodal to bimodal solutions. The Lagrange multipliers and second-order optimality conditions are used to detect branching points and to switch to the optimum solution path. The procedure is applied to the design of a foundation which supports a column for maximum buckling load. Using the total available foundation stiffness as a homotopy parameter, a set of optimum foundation designs is obtained.

Haftka, Raphael T.↗
NASA NTRS1977

Circuit regulates voltage of dc-dc converter

Method of regulating voltage-multiplier dc-dc converter utilizes regulating circuit that directly controls only fraction of input voltage, resulting in lightweight, efficient regulator.

Harrigill, W. T., Jr.↗
NASA NTRS1984

A means for stationing additional geosynchronous satellites and space ladder

A practical method is analytically shown for multiplying the number of orbital slots for synchronous satellites. This is by radially tethering satellites above the synchronous orbit (forces outwards) balanced to satellites below this orbit (forces inwards). The term practical applies because the tether tension force is of second order smallness. Thus, several thousand miles of synchronous satellites can be radiated along a small tether line sized for tension of about one percent of a satellite weight. A vertical tether line also provides a track for transport, that is, a ladder or elevator. Analysis for an optimized diameter tether line is developed which is particularly effective when the tether, line is extended to the ground, thus, making a space ladder. Mars is the best candidate for a space ladder. With the optimized tether the total system mass is minimum when the outer satellite is far out. Tethered satellites have G-forces.

Deyoung, J.↗
NASA NTRS1993

Laplace's equation and the Dirichlet-Neumann map in multiply connected domains

A variety of problems in material science and fluid dynamics require the solution of Laplace's equation in multiply connected domains. Integral equation methods are natural candidates for such problems, since they discretize the boundary alone, require no special effort for free boundaries, and achieve superalgebraic convergence rates on sufficiently smooth domains in two space dimensions, regardless of shape. Current integral equation methods for the Dirichlet problem, however, require the solution of M independent problems of dimension N, where M is the number of boundary components and N is the total number of points in the discretization. In this paper, we present a new boundary integral equation approach, valid for both interior and exterior problems, which requires the solution of a single linear system of dimension N + M. We solve this system by making use of an iterative method (GMRES) combined with the last multipole method for the rapid calculation of the necessary matrix vector products. For a two-dimensional system with 200 components and 100 points on each boundary, we gain a speedup of a factor of 100 from the new analytic formulation and a factor of 50 from the fast multipole method. The resulting scheme brings large scale calculations in extremely complex domains within practical reach.

Greenbaum, A.↗
NASA NTRS2005

Retrieving Storm Electric Fields From Aircraft Field Mill Data: Applications - Part 2

The Lagrange multiplier theory and "pitch down method" developed in Part I of this study are applied to complete the calibration of a Citation aircraft that is instrumented with six field mill sensors. When side constraints related to average fields are used, the method performs well in computer simulations. For mill measurement errors of 1 V/m and a 5 V/m error in the mean fair weather field function, the 3-D storm electric field is retrieved to within an error of about 12%. A side constraint that involves estimating the detailed structure of the fair weather field was also tested using computer simulations. For mill measurement errors of 1 V/m, the method retrieves the 3-D storm field to within an error of about 8% if the fair weather field estimate is typically within 1 V/m of the true fair weather field. Using this side constraint and data from fair weather field maneuvers taken on 29 June 2001, the Citation aircraft was calibrated. The resulting calibration matrix was then used to retrieve storm electric fields during a Citation flight on 2 June 2001. The storm field results are encouraging and agree favorably with the results obtained from earlier calibration analyses that were based on iterative techniques.

Koshak, W. J.↗
NASA NTRS2018

Low Excess Noise, High Gain Avalanche Photodiodes

A system, method, and apparatus for an avalanche photodiode with an enhanced multiplier layer are disclosed herein. In particular, the present disclosure teaches an avalanche photodiode having a multiplier with alternating layers of one or more quantum wells and one or more spacers. A method of making the avalanche photodiode includes growing the multiplier on a substrate.

Bai, Xiaogang↗
NASA NTRS1989

A hybrid-perturbation-Galerkin technique which combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗
NASA NTRS1990

A hybrid perturbation-Galerkin technique that combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be used to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗
NASA NTRS1996

The Newton Modified Barrier Method for QP Problems

The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a "hot start". Starting at such a "hot start", at most Omicron(1n 1n epsilon(exp -1)) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, epsilon > 0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that only Omicron(1n epsilon(exp -1))omicron(ln 1n epsilon(exp-1)) Newton steps are required to reach an epsilon-approximation to the solution from any "hot start". In order to reach the "hot start", one has to perform Omicron(square root(m) 1n C) Newton steps, where m characterizes the size of the problem and C > 0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.

Melman, A.↗
NASA NTRS1947

Method for calculating wing characteristics by lifting-line theory using nonlinear section lift data

A method is presented for calculating wing characteristics by lifting-line theory using nonlinear section lift data. Material from various sources is combined with some original work into the single complete method described. Multhopp's systems of multipliers are employed to obtain the induced angle of attack directly from the spanwise lift distribution. Equations are developed for obtaining these multipliers for any even number of spanwise stations, and values are tabulated for 10 stations along the semispan for asymmetrical, symmetrical, and antisymmetrical lift distributions. In order to minimize the computing time and to illustrate the procedures involved, simplified computing forms containing detailed examples are given for symmetrical lift distributions. Similar forms for asymmetrical and antisymmetrical lift distributions, although not shown, can be readily constructed in the same manner as those given. The adaptation of the method for use with linear section lift data is also illustrated. The adaptation has been found to require less computing time than most existing methods.

Sivells, James C↗
NASA NTRS2011

Evaluation of Pulse Counting for the Mars Organic Mass Analyzer (MOMA) Ion Trap Detection Scheme

The Mars Organic Mass Analyzer is being developed at Goddard Space Flight Center to identify organics and possible biological compounds on Mars. In the process of characterizing mass spectrometer size, weight, and power consumption, the use of pulse counting was considered for ion detection. Pulse counting has advantages over analog-mode amplification of the electron multiplier signal. Some advantages are reduced size of electronic components, low power consumption, ability to remotely characterize detector performance, and avoidance of analog circuit noise. The use of pulse counting as a detection method with ion trap instruments is relatively rare. However, with the recent development of high performance electrical components, this detection method is quite suitable and can demonstrate significant advantages over analog methods. Methods A prototype quadrupole ion trap mass spectrometer with an internal electron ionization source was used as a test setup to develop and evaluate the pulse-counting method. The anode signal from the electron multiplier was preamplified. The an1plified signal was fed into a fast comparator for pulse-level discrimination. The output of the comparator was fed directly into a Xilinx FPGA development board. Verilog HDL software was written to bin the counts at user-selectable intervals. This system was able to count pulses at rates in the GHz range. The stored ion count nun1ber per bin was transferred to custom ion trap control software. Pulse-counting mass spectra were compared with mass spectra obtained using the standard analog-mode ion detection. Prelin1inary Data Preliminary mass spectra have been obtained for both analog mode and pulse-counting mode under several sets of instrument operating conditions. Comparison of the spectra revealed better peak shapes for pulse-counting mode. Noise levels are as good as, or better than, analog-mode detection noise levels. To artificially force ion pile-up conditions, the ion trap was overfilled and ions were ejected at very high scan rates. Pile-up of ions was not significant for the ion trap under investigation even though the ions are ejected in so-called 'ion-micro packets'. It was found that pulse counting mode had higher dynamic range than analog mode, and that the first amplification stage in analog mode can distort mass peaks. The inherent speed of the pulse counting method also proved to be beneficial to ion trap operation and ion ejection characterization. Very high scan rates were possible with pulse counting since the digital circuitry response time is so much smaller than with the analog method. Careful investigation of the pulse-counting data also allowed observation of the applied resonant ejection frequency during mass analysis. Ejection of ion micro packets could be clearly observed in the binned data. A second oscillation frequency, much lower than the secular frequency, was also observed. Such an effect was earlier attributed to the oscillation of the total plasma cloud in the ion trap. While the components used to implement pulse counting are quite advanced, due to their prevalence in consumer electronics, the cost of this detection system is no more than that of an analog mode system. Total pulse-counting detection system electronics cost is under $250

Van Amerom, Friso H.↗
NASA NTRS1992

Structural optimization of large structural systems by optimality criteria methods

The fundamental concepts of the optimality criteria method of structural optimization are presented. The effect of the separability properties of the objective and constraint functions on the optimality criteria expressions is emphasized. The single constraint case is treated first, followed by the multiple constraint case with a more complex evaluation of the Lagrange multipliers. Examples illustrate the efficiency of the method.

Berke, Laszlo↗
NASA NTRS1985

Development and application of a unified balancing approach with multiple constraints

The development of a general analytic approach to constrained balancing that is consistent with past influence coefficient methods is described. The approach uses Lagrange multipliers to impose orbit and/or weight constraints; these constraints are combined with the least squares minimization process to provide a set of coupled equations that result in a single solution form for determining correction weights. Proper selection of constraints results in the capability to: (1) balance higher speeds without disturbing previously balanced modes, thru the use of modal trial weight sets; (2) balance off-critical speeds; and (3) balance decoupled modes by use of a single balance plane. If no constraints are imposed, this solution form reduces to the general weighted least squares influence coefficient method. A test facility used to examine the use of the general constrained balancing procedure and application of modal trial weight ratios is also described.

Zorzi, E. S.↗
NASA NTRS1991

A Lagrange multiplier based divide and conquer finite element algorithm

A novel domain decomposition method based on a hybrid variational principle is presented. Prior to any computation, a given finite element mesh is torn into a set of totally disconnected submeshes. First, an incomplete solution is computed in each subdomain. Next, the compatibility of the displacement field at the interface nodes is enforced via discrete, polynomial and/or piecewise polynomial Lagrange multipliers. In the static case, each floating subdomain induces a local singularity that is resolved very efficiently. The interface problem associated with this domain decomposition method is, in general, indefinite and of variable size. A dedicated conjugate projected gradient algorithm is developed for solving the latter problem when it is not feasible to explicitly assemble the interface operator. When implemented on local memory multiprocessors, the proposed methodology requires less interprocessor communication than the classical method of substructuring. It is also suitable for parallel/vector computers with shared memory and compares favorably with factorization based parallel direct methods.

Farhat, C.↗
NASA NTRS1976

Investigations with satellite data temperature retrievals

A method is presented for using satellite measurements to interpolate vertical temperature soundings between radiosonde stations. The method finds a set of coefficients, which when multiplied by corresponding measured radiance quantities, yield zero temperature error at a radiosonde station. This derived set of coefficients is then applied to satellite radiance measurements at places between radiosonde stations. The computations show, for example, that the average absolute error in the layer 1000-800 mbs is only 0.3K when the corresponding 'minimum-information' method error was 2.9K. The method may be most applicable to measurements from geostationary satellites, but should also be applicable to measurements from polar orbiting satellites under certain conditions.

Fritz, S.↗
NASA NTRS1977

Temperature retrievals from satellite radiance measurements - An empirical method

This paper presents a method for using satellite measurements to interpolate vertical temperature soundings between radiosonde stations. The calculations presented show that especially in the 1000-800 mb layer, where linear methods of temperature retrieval usually contain large errors, the proposed method reduces the errors substantially. The method finds a set of coefficients, which when multiplied by corresponding measured radiance quantities, yield zero temperature error at a radiosonde station. This derived set of coefficients is then applied to satellite radiance measurements at places between the radiosonde stations. The computations show, for example, that the average absolute error in the layer 1000-800 mb is only 0.3 K when the corresponding 'minimum-information' method error was 2.9 K. The method may be most applicable to measurements from geostationary satellites, but should also be applicable to measurements from polar orbiting satellites under certain conditions.

Fritz, S.↗