Search NASA⌕ Search

SEARCH · Search NASA

Results for “Gaussian Processes”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 451 records · Page 25

Emittance preservation for the electron arm in a single PWFA-LC stage using quasi-adiabatic plasma density ramp matching sections

Plasma-based acceleration (PBA) is being considered for a next generation linear collider (LC). In some PBA-LC designs for the electron arm, the extreme beam parameters are expected to trigger background ion motion within the witness beam, which can lead to longitudinally varying nonlinear focusing forces and result in an unacceptable emittance growth of the beam. To mitigate this, we propose to use quasi-adiabatic plasma density ramps as matching sections at the entrance and exit of each stage. We match the witness electron beam to the low density plasma entrance, where the beam initially has a large matched spot size so the ion motion effects are relatively small. As the beam propagates in the plasma density upramp, it is quasi-adiabatically focused, and its distribution maintains a non-Gaussian equilibrium distribution in each longitudinal slice throughout the process, even when severe ion collapse has occurred. This only causes small amounts of slice emittance growth. The phase mixing between slices with different betatron frequencies leads to additional projected emittance growth within the acceleration stage. A density downramp at the exit of an acceleration section can eliminate much of the slice and projected emittance growth as the beam and ion motion adiabatically defocuses and decreases, respectively. Simulation results from QuickPIC with Azimuthal Decomposition show that within a single acceleration stage with a 25 GeV energy gain, this concept can limit the projected emittance growth to only ∼2% for a 25 GeV, 100 nm emittance witness beam and ∼20% for a 100 GeV, 100 nm normalized emittance witness beam. The trade-off between the adiabaticity of the plasma density ramp and the initial ion motion at the entrance for a given length of the plasma density ramp is also discussed.

Physics↗

Damping of surface pressure fluctuations in hypersonic turbulent flow past expansion corners

Surface pressure fluctuations of Mach 8 turbulent flow past a 2.5- and a 4.25-deg expansion corner maintained a Gaussian distribution but were severely attenuated by the expansion process. The pressure fluctuations did not recover to those of an equilibrium turbulent flow even though the mean pressures reached downstream inviscid values in four to six boundary-layer thicknesses. The fluctuations were convected with a velocity comparable to that on a flat plate, and they maintained their identities longer for the stronger expansion. The damping of pressure fluctuations at hypersonic Mach numbers, even by small corner angles, may be exploited in fatigue design.

Chung, Kung-Ming↗

Parallel Gaussian elimination of a block tridiagonal matrix using multiple microcomputers

The solution of a block tridiagonal matrix using parallel processing is demonstrated. The multiprocessor system on which results were obtained and the software environment used to program that system are described. Theoretical partitioning and resource allocation for the Gaussian elimination method used to solve the matrix are discussed. The results obtained from running 1, 2 and 3 processor versions of the block tridiagonal solver are presented. The PASCAL source code for these solvers is given in the appendix, and may be transportable to other shared memory parallel processors provided that the synchronization outlines are reproduced on the target system.

Blech, Richard A.↗

Hardware Implementation of a Bilateral Subtraction Filter

A bilateral subtraction filter has been implemented as a hardware module in the form of a field-programmable gate array (FPGA). In general, a bilateral subtraction filter is a key subsystem of a high-quality stereoscopic machine vision system that utilizes images that are large and/or dense. Bilateral subtraction filters have been implemented in software on general-purpose computers, but the processing speeds attainable in this way even on computers containing the fastest processors are insufficient for real-time applications. The present FPGA bilateral subtraction filter is intended to accelerate processing to real-time speed and to be a prototype of a link in a stereoscopic-machine- vision processing chain, now under development, that would process large and/or dense images in real time and would be implemented in an FPGA. In terms that are necessarily oversimplified for the sake of brevity, a bilateral subtraction filter is a smoothing, edge-preserving filter for suppressing low-frequency noise. The filter operation amounts to replacing the value for each pixel with a weighted average of the values of that pixel and the neighboring pixels in a predefined neighborhood or window (e.g., a 9 9 window). The filter weights depend partly on pixel values and partly on the window size. The present FPGA implementation of a bilateral subtraction filter utilizes a 9 9 window. This implementation was designed to take advantage of the ability to do many of the component computations in parallel pipelines to enable processing of image data at the rate at which they are generated. The filter can be considered to be divided into the following parts (see figure): a) An image pixel pipeline with a 9 9- pixel window generator, b) An array of processing elements; c) An adder tree; d) A smoothing-and-delaying unit; and e) A subtraction unit. After each 9 9 window is created, the affected pixel data are fed to the processing elements. Each processing element is fed the pixel value for its position in the window as well as the pixel value for the central pixel of the window. The absolute difference between these two pixel values is calculated and used as an address in a lookup table. Each processing element has a lookup table, unique for its position in the window, containing the weight coefficients for the Gaussian function for that position. The pixel value is multiplied by the weight, and the outputs of the processing element are the weight and pixel-value weight product. The products and weights are fed to the adder tree. The sum of the products and the sum of the weights are fed to the divider, which computes the sum of products the sum of weights. The output of the divider is denoted the bilateral smoothed image. The smoothing function is a simple weighted average computed over a 3 3 subwindow centered in the 9 9 window. After smoothing, the image is delayed by an additional amount of time needed to match the processing time for computing the bilateral smoothed image. The bilateral smoothed image is then subtracted from the 3 3 smoothed image to produce the final output. The prototype filter as implemented in a commercially available FPGA processes one pixel per clock cycle. Operation at a clock speed of 66 MHz has been demonstrated, and results of a static timing analysis have been interpreted as suggesting that the clock speed could be increased to as much as 100 MHz.

Huertas, Andres↗

Study of photon correlation techniques for processing of laser velocimeter signals

The objective was to provide the theory and a system design for a new type of photon counting processor for low level dual scatter laser velocimeter (LV) signals which would be capable of both the first order measurements of mean flow and turbulence intensity and also the second order time statistics: cross correlation auto correlation, and related spectra. A general Poisson process model for low level LV signals and noise which is valid from the photon-resolved regime all the way to the limiting case of nonstationary Gaussian noise was used. Computer simulation algorithms and higher order statistical moment analysis of Poisson processes were derived and applied to the analysis of photon correlation techniques. A system design using a unique dual correlate and subtract frequency discriminator technique is postulated and analyzed. Expectation analysis indicates that the objective measurements are feasible.

Mayo, W. T., Jr.↗

Statistical properties of two sine waves in Gaussian noise.

A detailed study is presented of some statistical properties of a stochastic process that consists of the sum of two sine waves of unknown relative phase and a normal process. Since none of the statistics investigated seem to yield a closed-form expression, all the derivations are cast in a form that is particularly suitable for machine computation. Specifically, results are presented for the probability density function (pdf) of the envelope and the instantaneous value, the moments of these distributions, and the relative cumulative density function (cdf).

Esposito, R.↗

Ion and electron temperatures in the SUMMA mirror device by emission spectroscopy

Ion temperatures were obtained in the SUMMA mirror device by observing the Doppler-broadened charge-exchange component of the 667.8and 587.6-nm He lines in He plasma and the H alpha and H beta lines in H2 plasma. The second moment of the line profiles was used as the parameter to determine ion temperature. Corrections for magnetic splitting, fine structure, monochromator slit function, and variation in charge-exchange cross section with energy are derived and included. Even for constant cross section, no magnetic splitting or fine structure, and infinitely narrow slit function, the line profile is not Gaussian, because the excitation results from a change-exchange process. Comparison is made with temperatures from a neutral particle analyzer.-

Patch, R. W.↗

MEM application to IRAS CPC images

A method for applying the Maximum Entropy Method (MEM) to Chopped Photometric Channel (CPC) IRAS additional observations is illustrated. The original CPC data suffered from problems with repeatability which MEM is able to cope with by use of a noise image, produced from the results of separate data scans of objects. The process produces images of small areas of sky with circular Gaussian beams of approximately 30 in. full width half maximum resolution at 50 and 100 microns. Comparison is made to previous reconstructions made in the far-infrared as well as morphologies of objects at other wavelengths. Some projects with this dataset are discussed.

Marston, A. P.↗

A non-gaussian model of continuous atmospheric turbulence for use in aircraft design

A non-Gaussian model of atmospheric turbulence is presented and analyzed. The model is restricted to the regions of the atmosphere where the turbulence is steady or continuous, and the assumptions of homogeneity and stationarity are justified. Also spatial distribution of turbulence is neglected, so the model consists of three independent, stationary stochastic processes which represent the vertical, lateral, and longitudinal gust components. The non-Gaussian and Gaussian models are compared with experimental data, and it is shown that the Gaussian model underestimates the number of high velocity gusts which occur in the atmosphere, while the non-Gaussian model can be adjusted to match the observed high velocity gusts more satisfactorily. Application of the proposed model to aircraft response is investigated, with particular attention to the response power spectral density, the probability distribution, and the level crossing frequency. A numerical example is presented which illustrates the application of the non-Gaussian model to the study of an aircraft autopilot system. Listings and sample results of a number of computer programs used in working with the model are included.

Reeves, P. M.↗

Report on 3 and 4-point correlation statistics in the COBE DMR anisotrophy maps

As part of the work performed under NASA contract # NAS5-32648, we have computed the 3-point and 4-point correlation functions of the COBE-DNIR 2-year and 4-year anisotropy maps. The motivation for this study was to search for evidence of non-Gaussian statistical fluctuations in the temperature maps: skewness or asymmetry in the case of the 3-point function, kurtosis in the case of the 4-point function. Such behavior would have very significant implications for our understanding of the processes of galaxy formation, because our current models of galaxy formation predict that non-Gaussian features should not be present in the DMR maps. The results of our work showed that the 3-point correlation function is consistent with zero and that the 4-point function is not a very sensitive probe of non-Gaussian behavior in the COBE-DMR data. Our computation and analysis of 3-point correlations in the 2-year DMR maps was published in the Astrophysical Journal Letters, volume 446, page L67, 1995. Our computation and analysis of 3-point correlations in the 4-year DMR maps will be published, together with some additional tests, in the June 10, 1996 issue of the Astrophysical Journal Letters. Copies of both of these papers are attached as an appendix to this report.

Hinshaw, Gary↗

Extraction of Qualitative Features from Sensor Data Using Windowed Fourier Transform

In this paper, we use Matlab to model the health monitoring of a system through the information gathered from sensors. This implies assessment of the condition of the system components. Once a normal mode of operation is established any deviation from the normal behavior indicates a change. This change may be due to a malfunction of an element, a qualitative change, or a change due to a problem with another element in the network. For example, if one sensor indicates that the temperature in the tank has experienced a step change then a pressure sensor associated with the process in the tank should also experience a step change. The step up and step down as well as sensor disturbances are assumed to be exponential. An RC network is used to model the main process, which is step-up (charging), drift, and step-down (discharging). The sensor disturbances and spike are added while the system is in drift. The system is allowed to run for a period equal to three time constant of the main process before changes occur. Then each point of the signal is selected with a trailing data collected previously. Two trailing lengths of data are selected, one equal to two time constants of the main process and the other equal to two time constants of the sensor disturbance. Next, the DC is removed from each set of data and then the data are passed through a window followed by calculation of spectra for each set. In order to extract features the signal power, peak, and spectrum are plotted vs time. The results indicate distinct shapes corresponding to each process. The study is also carried out for a number of Gaussian distributed noisy cases.

Amini, Abolfazl M.↗

Hybrid Basis and Multi-Center Grid Method for Strong-Field Processes

We present a time-dependent framework that combines a hybrid basis, consisting of Gaussian-type orbitals (GTOs) and finite-element discrete-variable representation (FEDVR) functions, with a multicenter grid to simulate strong-field and attosecond dynamics in atoms and molecules. The method incorporates the construction of the orthonormal hybrid basis, the evaluation of electronic integrals, a unitary time-propagation scheme, and the extraction of optical and photoelectron observables. Its accuracy and robustness are benchmarked on one-electron systems such as atomic hydrogen and the dihydrogen cation (H$^+_2$) through comparisons with essentially-exact reference results for bound-state energies, high-harmonic generation spectra, photoionization cross sections, and photoelectron momentum distributions. This work establishes the groundwork for its integration with quantum-chemistry methods, which is already operational but will be detailed in future work, thereby enabling ab initio simulations of correlated polyatomic systems in intense ultrafast laser fields.

74 ATOMIC AND MOLECULAR PHYSICS↗

3-center and 4-center 2-particle Gaussian AO integrals on modern accelerated processors

We report an implementation of the McMurchie–Davidson (MD) algorithm for 3-center and 4-center 2-particle integrals over Gaussian atomic orbitals (AOs) with low and high angular momenta l and varying degrees of contraction for graphical processing units (GPUs). This work builds upon our recent implementation of a matrix form of the MD algorithm that is efficient for GPU evaluation of 4-center 2-particle integrals over Gaussian AOs of high angular momenta (l ≥ 4) [A. Asadchev and E. F. Valeev, J. Phys. Chem. A 127, 10889–10895 (2023)]. The use of unconventional data layouts and three variants of the MD algorithm allow for the evaluation of integrals with double precision and sustained performance between 25% and 70% of the theoretical hardware peak. Performance assessment includes integrals over AOs with l ≤ 6 (a higher l is supported). Preliminary implementation of the Hartree–Fock exchange operator is presented and assessed for computations with up to a quadruple-zeta basis and more than 20 000 AOs. The corresponding C++ code is part of the experimental open-source LibintX library available at https://github.com/ValeevGroup/libintx.

Chemistry↗

Image-gathering system design for information and fidelity

Image gathering and processing are assessed in terms of information and fidelity, and the relationship between these two figures of merit is examined. It is assumed that the system is linear and isoplanatic and that the signal and noise amplitudes are Gaussian, wide-sense stationary, and statistically independent. Within these constraints, it is found that the combined process of image gathering and reconstruction (which is intended to reproduce the output of the image-gathering system) behaves as optical, or photographic, image formation in that the informationally optimized design of the image-gathering system ordinarily does not maximize the fidelity of the reconstructed image. The combined process of image gathering and restoration (which is intended to reproduce the input of the image-gathering system) behaves more as a communication channel in that the informationally optimized design of the image-gathering system tends to maximize the fidelity of optimally restored representations of the input.

Huck, Friedrich O.↗