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Results for “EXPONENTIAL FUNCTION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Compression of transmission bandwidth requirements for a certain class of band-limited functions.

A study of source-encoding techniques that afford a reduction of data-transmission rates is made with particular emphasis on the compression of transmission bandwidth requirements of band-limited functions. The feasibility of bandwidth compression through analog signal rooting is investigated. It is found that the N-th roots of elements of a certain class of entire functions of exponential type possess contour integrals resembling Fourier transforms, the Cauchy principal values of which are compactly supported on an interval one N-th the size of that of the original function. Exploring this theoretical result, it is found that synthetic roots can be generated, which closely approximate the N-th roots of a certain class of band-limited signals and possess spectra that are essentially confined to a bandwidth one N-th that of the signal subjected to the rooting operation. A source-encoding algorithm based on this principle is developed that allows the compression of data-transmission requirements for a certain class of band-limited signals.

Smith, I. R.↗
NASA NTRS1978

The velocity distribution of interstellar gas observed in strong UV absorption lines

Observations of three strong interstellar UV absorption lines of N I (1199 A), N II (1083 A), and Si III (1206 A) in 47 stars of widely varying distance and a variety of spectral types are analyzed to obtain a velocity distribution function for the interstellar gas. A technique based on the maximum and minimum velocities observed along a line of sight is adopted because of heavy line blending, and results are discussed for both power-law and exponential distribution functions. The expected distribution of radiative-phase supernova remnants (SNRs) in the interstellar medium is calculated as a function of SNR birthrate and of the interstellar density in which they evolve. The results are combined with observed distance estimates, and it is shown that an interstellar density in excess of 0.1 per cu cm would be required to keep the SNRs sufficiently confined so that their cross sections are consistent with the observed number of components. The alternative possibility is considered that SNRs do not enter the radiative phase before escaping from the Galaxy or colliding with neighboring remnants.

Cowie, L. L.↗
NASA NTRS1992

Scattering properties of Venus' surface

Radar backscatter functions Sigma-(carat)(sub 0)(phi) for incidence angles between 0 less than or equal to phi less than or equal to 4-10 deg were derived from Magellan altimetry radar echoes. The procedure includes constrained solution of a system of simultaneous equations for which the echo-spectrum and echo time profile are inputs. A practical and workable set of constraints was applied; optimization and improved results are expected as the analysis matures. The scattering functions yield information on small-scale surface structures (tens of centimeters to tens of meters) but averaged over hundreds of sq km. RMS surface slopes derived from fits of analytic functions to the Sigma-(carat)(sub 0)(phi) results were converted to map form and show patterns similar to those reported using other techniques. While all three forms are found on Venus, fit residuals imply that an exponential scattering function matches data better than either the Hagfors or Gaussian form in most areas, although the Hagfors function may be a better descriptor at some sites. Limited study of image data indicates that average backscatter cross section, and possibly its slope, can be derived at oblique angles (17 deg less than or equal to phi less than or equal to 45 deg). Offsets of the echo peak in altimetry spectra are surprisingly common and are loosely correlated with Venus topography, but no cause for this phenomenon was identified.

Tyler, G. L.↗
NASA NTRSDate not supplied

A Methodology for Actuating RCS Jets in a Continuous, Time-Accurate CFD Simulation

Computational fluid dynamics simulations of Mars entry vehicle reaction control systems have been used to gain a better understanding of the wide range of flow phenomena encountered during various phases of flight. One aspect of this is simulating the system during controlled flight. Current practices model the system in a continuously actuated state, but this methodology is unable to accurately model the dynamic behavior of the system during EDL. One method to improve this is to create a coupled CFD-RBD-Control simulation. The first step to this is establishing a method of accurately actuating an RCS jet during a time accurate CFD simulation. This paper presents a method to achieve this actuation. There are three phases to the methodology: establishing the off state, creating a ramping function that will initialize the jet flow, and establishing the on state. A test case of a jet in a supersonic crossflow is implemented to establish the success of the methodology in being able to actuate a jet in the midst of an ongoing CFD simulation. It shows significant improvement in boundary condition responsiveness for linear and exponential ramping functions in comparison to the step function. A preliminary demonstration of the methodology is presented for the MSL vehicle which shows significant advantages for the implementation of a linear ramping function over a step function.

Alexandra Hickey↗
NASA NTRSDate not supplied

A Methodology for Actuating RCS Jets in a Continuous, Time-Accurate CFD Simulation

Computational fluid dynamics simulations of Mars entry vehicle reaction control systems have been used to gain a better understanding of the wide range of flow phenomena encountered during various phases of flight. One aspect of this is simulating the system during controlled flight. Current practices model the system in a continuously actuated state, but this methodology is unable to accurately model the dynamic behavior of the system during EDL. One method to improve this is to create a coupled CFD-RBD-Control simulation. The first step to this is establishing a method of accurately actuating an RCS jet during a time accurate CFD simulation. This paper presents a method to achieve this actuation. There are three phases to the methodology: establishing the off state, creating a ramping function that will initialize the jet flow, and establishing the on state. A test case of a jet in a supersonic crossflow is implemented to establish the success of the methodology in being able to actuate a jet in the midst of an ongoing CFD simulation. It shows significant improvement in boundary condition responsiveness for linear and exponential ramping functions in comparison to the step function. A preliminary demonstration of the methodology is presented for the MSL vehicle which shows significant advantages for the implementation of a linear ramping function over a step function.

Alexandra Hickey↗
NASA NTRS1974

Design data for radars based on 13.9 GHz Skylab scattering coefficient measurements

The author has identified the following significant results. Measurements made at 13.9 GHz with the radar scatterometer on Skylab have been combined to produce median curves of the variation of scattering coefficient with angle of incidence out to 45 deg. Because of the large number of observations, and the large area averaged for each measured data point, these curves may be used as a new design base for radars. A reasonably good fit at larger angles is obtained using the theoretical expression based on an exponential height correlation function and also using Lambert's law. For angles under 10 deg, a different fit based on the exponential correlation function, and a fit based on geometric optics expressions are both reasonably valid.

Moore, R. K.↗
NASA NTRS1988

Correlation function study for sea ice

For active and passive microwave remote sensing of sea ice, a correlation function of exponential form is extracted from the photograph of a horizontal thin section taken from a sample of artificially grown saline ice that closely resembled Arctic congelation sea ice. It is found that the extracted correlation lengths are consistent with the published average size of brine pockets. With the application of strong fluctuation theory and the bilocal approximation, the effective permittivity tensor is derived in the low-frequency limit for an unbounded uniaxial random medium with two-phase mixtures. Using the extracted correlation lengths, the effective permittivity tensor is computed as a function of fractional volume of brine inclusions and compared with in situ measurements at 4.8 and 9.5 GHz.

Lin, F. C.↗
NASA NTRS2008

Spiking Neurons for Analysis of Patterns

Artificial neural networks comprising spiking neurons of a novel type have been conceived as improved pattern-analysis and pattern-recognition computational systems. These neurons are represented by a mathematical model denoted the state-variable model (SVM), which among other things, exploits a computational parallelism inherent in spiking-neuron geometry. Networks of SVM neurons offer advantages of speed and computational efficiency, relative to traditional artificial neural networks. The SVM also overcomes some of the limitations of prior spiking-neuron models. There are numerous potential pattern-recognition, tracking, and data-reduction (data preprocessing) applications for these SVM neural networks on Earth and in exploration of remote planets. Spiking neurons imitate biological neurons more closely than do the neurons of traditional artificial neural networks. A spiking neuron includes a central cell body (soma) surrounded by a tree-like interconnection network (dendrites). Spiking neurons are so named because they generate trains of output pulses (spikes) in response to inputs received from sensors or from other neurons. They gain their speed advantage over traditional neural networks by using the timing of individual spikes for computation, whereas traditional artificial neurons use averages of activity levels over time. Moreover, spiking neurons use the delays inherent in dendritic processing in order to efficiently encode the information content of incoming signals. Because traditional artificial neurons fail to capture this encoding, they have less processing capability, and so it is necessary to use more gates when implementing traditional artificial neurons in electronic circuitry. Such higher-order functions as dynamic tasking are effected by use of pools (collections) of spiking neurons interconnected by spike-transmitting fibers. The SVM includes adaptive thresholds and submodels of transport of ions (in imitation of such transport in biological neurons). These features enable the neurons to adapt their responses to high-rate inputs from sensors, and to adapt their firing thresholds to mitigate noise or effects of potential sensor failure. The mathematical derivation of the SVM starts from a prior model, known in the art as the point soma model, which captures all of the salient properties of neuronal response while keeping the computational cost low. The point-soma latency time is modified to be an exponentially decaying function of the strength of the applied potential. Choosing computational efficiency over biological fidelity, the dendrites surrounding a neuron are represented by simplified compartmental submodels and there are no dendritic spines. Updates to the dendritic potential, calcium-ion concentrations and conductances, and potassium-ion conductances are done by use of equations similar to those of the point soma. Diffusion processes in dendrites are modeled by averaging among nearest-neighbor compartments. Inputs to each of the dendritic compartments come from sensors. Alternatively or in addition, when an affected neuron is part of a pool, inputs can come from other spiking neurons. At present, SVM neural networks are implemented by computational simulation, using algorithms that encode the SVM and its submodels. However, it should be possible to implement these neural networks in hardware: The differential equations for the dendritic and cellular processes in the SVM model of spiking neurons map to equivalent circuits that can be implemented directly in analog very-large-scale integrated (VLSI) circuits.

Huntsberger, Terrance↗
NASA NTRS1994

The Area Coverage of Geophysical Fields as a Function of Sensor Field-of View

In many remote sensing studies of geophysical fields such as clouds, land cover, or sea ice characteristics, the fractional area coverage of the field in an image is estimated as the proportion of pixels that have the characteristic of interest (i.e., are part of the field) as determined by some thresholding operation. The effect of sensor field-of-view on this estimate is examined by modeling the unknown distribution of subpixel area fraction with the beta distribution, whose two parameters depend upon the true fractional area coverage, the pixel size, and the spatial structure of the geophysical field. Since it is often not possible to relate digital number, reflectance, or temperature to subpixel area fraction, the statistical models described are used to determine the effect of pixel size and thresholding operations on the estimate of area fraction for hypothetical geophysical fields. Examples are given for simulated cumuliform clouds and linear openings in sea ice, whose spatial structures are described by an exponential autocovariance function. It is shown that the rate and direction of change in total area fraction with changing pixel size depends on the true area fraction, the spatial structure, and the thresholding operation used.

Key, Jeffrey R.↗
DOE OSTI2025

Topology-Aware Reinforcement Learning for Voltage Control: Centralized and Decentralized Strategies

Volt-VAR control (VVC) methods based on deep reinforcement learning (DRL) can effectively control distribution grid voltage and minimize power loss by implementing corrective and preventive control measures on the reactive power output of inverter-based distributed energy resources (DERs). However, model-free DRL-based VVC approaches usually cannot capture the important topological feature of the power system since they use a fully-connected network (FCN) to deliver the action. Therefore, this paper proposes a graph convolutional network (GCN)-based DRL approach that can employ the topological information of the network to take better control action for regulating the voltage. Our implementation allows for both centralized and decentralized configurations, utilizing a single agent and multiple agents respectively. Although the centralized GCN-based DRL approach has its advantages of minimizing voltage fluctuation and power loss, it is not suitable for large scale power systems due to its challenges in terms of scalability, computation speed and potential single points of failure. Therefore, these problems can be resolved using the decentralized GCN-based DRL approach. Moreover, to ensure the safe operation of the model, our proposed approach incorporates an exponential barrier function while formulating the reward function for each agent. To validate performance of the proposed approaches, the proposed model is tested on modified IEEE test systems and the performances are measured in terms on voltage fluctuation reduction, minimization of power loss and computational speed. Finally, the results show that the proposed topology-aware approach outperforms the FCN-based DRL approach in terms of reducing voltage fluctuation and minimizing power loss of the network. Moreover, it is shown that the decentralized GCN-based DRL has faster computational speed than other approaches.

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