Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “GAUSS 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.

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

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

ESTIMATION OF TURBULENT DIFFUSIVITY WITH DIRECT NUMERICAL SIMULATION OF STELLAR CONVECTION

We investigate the value of horizontal turbulent diffusivity {eta} by numerical calculation of thermal convection. In this study, we introduce a new method whereby the turbulent diffusivity is estimated by monitoring the time development of the passive scalar, which is initially distributed in a given Gaussian function with a spatial scale d{sub 0}. Our conclusions are as follows: (1) assuming the relation {eta} = L{sub c} v{sub rms}/3, where v{sub rms} is the root-mean-square (rms) velocity, the characteristic length L{sub c} is restricted by the shortest one among the pressure (density) scale height and the region depth. (2) The value of turbulent diffusivity becomes greater with the larger initial distribution scale d{sub 0}. (3) The approximation of turbulent diffusion holds better when the ratio of the initial distribution scale d{sub 0} to the characteristic length L{sub c} is larger.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

A direct linkage between AGN outflows in the narrow-line regions and the X-ray emission from the accretion disks

The origin of outflow in the narrow-line region (NLR) of the active galactic nucleus (AGN) is studied in this paper by focusing on the relationship between the [O iii]λ5007 line profile and the hard-X-ray (in a bandpass of 2–10 keV) emission from the central super-massive black hole (SMBH) in type-I AGNs. A sample of 47 local X-ray selected type-I AGNs at z<0.2 is extracted from the 2XMMi/SDSS-DR7 catalog, which was originally cross-matched by Pineau et al. The X-ray luminosities in an energy band from 2 to 10 keV of these luminous AGNs range from 10{sup 42} to 10{sup 44} erg s{sup −1}. A joint spectral analysis is performed on their optical and X-ray spectra, in which the [O iii] line profile is modeled by a sum of several Gaussian functions to quantify its deviation from a pure Gaussian function. The statistics allow us to identify a moderate correlation with a significance level of 2.78σ: luminous AGNs with stronger [O iii] blue asymmetry tend to have steeper hard-X-ray spectra. By identifying the role of L/L{sub Edd} on the correlation at a 2–3σ significance level in both direct and indirect ways, we argue that the photon index versus the asymmetry correlation provides evidence that the AGN’s outflow commonly observed in its NLR is related to the accretion process occurring around the central SMBH, which favors the wind/radiation model as the origin of the outflow in luminous AGNs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Multi-frequency radio profiles of PSR B1133+16: Radiation location and particle energy

The pulse profile of PSR B1133+16 is usually regarded as a conal double structure. However, its multi-frequency profiles cannot simply be fitted with two Gaussian functions, and a third component is always needed to fit the bridge region (between two peaks). This would introduce additional, redundant parameters. In this paper, through a comparison of five fitting functions (Gaussian, von Mises, hyperbolic secant, square hyperbolic secant, and Lorentz), it is found that the square hyperbolic secant function can best reproduce the profile, yielding an improved fit. Moreover, a symmetric 2D radiation beam function, instead of a simple 1D Gaussian function, is used to fit the profile. Each profile with either well-resolved or not-so-well-resolved peaks could be fitted adequately using this beam function, and the bridge emission between the two peaks does not need to be a new component. Adopting inclination and impact angles based on polarization measurements, the opening angle (θ{sub μ0}) of the radiation beam in a certain frequency band is derived from beam-function fitting. The corresponding radiation altitudes are then calculated. Based on multi-frequency profiles, we also computed the Lorentz factors of the particles and their dispersion at those locations in both the curvature-radiation and inverse-Compton-scattering models. We found that the Lorentz factors of the particles decrease rapidly as the radiation altitude increases. Besides, the radiation prefers to be generated in an annular region rather than the core region, and this needs further validation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Coupled-cluster based basis sets for valence correlation calculations

Novel basis sets are generated that target the description of valence correlation in atoms H through Ar. The new contraction coefficients are obtained according to the Atomic Natural Orbital (ANO) procedure from CCSD(T) (coupled-cluster singles and doubles with perturbative triples correction) density matrices starting from the primitive functions of Dunning et al. [J. Chem. Phys. 90, 1007 (1989); ibid. 98, 1358 (1993); ibid. 100, 2975 (1993)] (correlation consistent polarized valence X-tuple zeta, cc-pVXZ). The exponents of the primitive Gaussian functions are subject to uniform scaling in order to ensure satisfaction of the virial theorem for the corresponding atoms. These new sets, named ANO-VT-XZ (Atomic Natural Orbital Virial Theorem X-tuple Zeta), have the same number of contracted functions as their cc-pVXZ counterparts in each subshell. The performance of these basis sets is assessed by the evaluation of the contraction errors in four distinct computations: correlation energies in atoms, probing the density in different regions of space via 〈r{sup n}〉 (−3 ≤ n ≤ 3) in atoms, correlation energies in diatomic molecules, and the quality of fitting potential energy curves as measured by spectroscopic constants. All energy calculations with ANO-VT-QZ have contraction errors within “chemical accuracy” of 1 kcal/mol, which is not true for cc-pVQZ, suggesting some improvement compared to the correlation consistent series of Dunning and co-workers.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2014

Accurate potential energy curve of the LiH{sup +} molecule calculated with explicitly correlated Gaussian functions

Very accurate calculations of the ground-state potential energy curve (PEC) of the LiH{sup +} ion performed with all-electron explicitly correlated Gaussian functions with shifted centers are presented. The variational method is employed. The calculations involve optimization of nonlinear exponential parameters of the Gaussians performed with the aid of the analytical first derivatives of the energy determined with respect to the parameters. The diagonal adiabatic correction is also calculated for each PEC point. The PEC is then used to calculate the vibrational energies of the system. In that calculation, the non-adiabatic effects are accounted for by using an effective vibrational mass obtained by the minimization of the difference between the vibrational energies obtained from the calculations where the Born-Oppenheimer approximation was not assumed and the results of the present calculations.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2014

An algorithm for nonrelativistic quantum-mechanical finite-nuclear-mass variational calculations of nitrogen atom in L = 0, M = 0 states using all-electrons explicitly correlated Gaussian basis functions

An algorithm for quantum-mechanical nonrelativistic variational calculations of L = 0 and M = 0 states of atoms with an arbitrary number of s electrons and with three p electrons have been implemented and tested in the calculations of the ground {sup 4}S state of the nitrogen atom. The spatial part of the wave function is expanded in terms of all-electrons explicitly correlated Gaussian functions with the appropriate pre-exponential Cartesian angular factors for states with the L = 0 and M = 0 symmetry. The algorithm includes formulas for calculating the Hamiltonian and overlap matrix elements, as well as formulas for calculating the analytic energy gradient determined with respect to the Gaussian exponential parameters. The gradient is used in the variational optimization of these parameters. The Hamiltonian used in the approach is obtained by rigorously separating the center-of-mass motion from the laboratory-frame all-particle Hamiltonian, and thus it explicitly depends on the finite mass of the nucleus. With that, the mass effect on the total ground-state energy is determined.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Oxide-cladding aluminum nitride photonic crystal slab: Design and investigation of material dispersion and fabrication induced disorder

Photonic crystal slabs with a lower-index material surrounding the core layer are an attractive choice to circumvent the drawbacks in the fabrication of membranes suspended in air. In this work we propose a photonic crystal (PhC) slab structure composed of a triangular pattern of air holes in a multilayer thin film of aluminum nitride embedded in silicon dioxide layers designed for operating around 450 nm wavelengths. We show the design of an ideal structure and analyze the effects of material dispersion based on a first-order correction perturbation theory approach using dielectric functions obtained by experimental measurements of the thin film materials. Numerical methods were used to investigate the effects of fabrication induced disorder of typical nanofabrication processes on the bandgap size and spectral response of the proposed device. Deviation in holes radii and positions were introduced in the proposed PhC slab model with a Gaussian distribution profile. Impacts of slope in holes sidewalls that might result from the dry etching of AlN were also evaluated. The results show that for operation at the midgap frequency, slope in holes sidewalls is more critical than displacements in holes sizes and positions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Radiation dose assessment in a 320-detector-row CT scanner used in cardiac imaging

Purpose: In the present era of cone-beam CT scanners, the use of the standardized CTDI{sub 100} as a surrogate of the idealized CTDI is strongly discouraged and, consequently, so should be the use of the dose-length product (DLP) as an estimate of the total energy imparted to the patient. However, the DLP is still widely used as a reference quantity to normalize the effective dose for a given scan protocol mainly because the CTDI{sub 100} is an easy-to-measure quantity. The aim of this article is therefore to describe a method for radiation dose assessment in large cone-beam single axial scans, which leads to a straightforward estimation of the total energy imparted to the patient. The authors developed a method accessible to all medical physicists and easy to implement in clinical practice in an attempt to update the bridge between CT dosimetry and the estimation of the effective dose. Methods: The authors used commercially available material and a simple mathematical model. The method described herein is based on the dosimetry paradigm introduced by the AAPM Task Group 111. It consists of measuring the dose profiles at the center and the periphery of a long body phantom with a commercial solid-state detector. A weighted dose profile is then calculated from these measurements. To calculate the CT dosimetric quantities analytically, a Gaussian function was fitted to the dose profile data. Furthermore, the Gaussian model has the power to condense the z-axis information of the dose profile in two parameters: The single-scan central dose, f(0), and the width of the profile, {sigma}. To check the energy dependence of the solid-state detector, the authors compared the dose profiles to measurements made with a small volume ion chamber. To validate the overall method, the authors compared the CTDI{sub 100} calculated analytically to the measurement made with a 100 mm pencil ion chamber. Results: For the central and weighted dose profiles, the authors found a good agreement between the measured dose profile data and the fitted Gaussian functions. The solid-state detector had no energy dependence--within the energy range of interest--and the analytical model succeeded in reproducing the absolute dose values obtained with the pencil ion chamber. For the case of large cone-beam single axial scans, the quantity that better characterizes the total energy imparted to the patient is the weighted dose profile integral (DPI{sub w}). The DPI{sub w} can be easily determined from the two parameters that define the Gaussian functions: f(0) and {sigma}. The authors found that the DLP underestimated the total energy imparted to the patient by more than 20%. The authors also found that the calculated CT dosimetric quantities were higher than those displayed on the scanner console. Conclusions: The authors described and validated a method to assess radiation dose in large cone-beam single axial scans. This method offers a simple and more accurate estimation of the total energy imparted to the patient, thus offering the possibility to update the bridge between CT dosimetry and the estimation of the effective dose for cone-beam CT examinations in radiology, nuclear medicine, and radiation therapy.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2016

THE EVOLUTION OF POST-STARBURST GALAXIES FROM z ∼ 1 TO THE PRESENT

Post-starburst galaxies are in the transitional stage between blue, star-forming galaxies and red, quiescent galaxies and therefore hold important clues for our understanding of galaxy evolution. In this paper, we systematically searched for and identified a large sample of post-starburst galaxies from the spectroscopic data set of the Sloan Digital Sky Survey (SDSS) Data Release 9. In total, we found more than 6000 objects with redshifts between z ∼ 0.05 and z ∼ 1.3, making this the largest sample of post-starburst galaxies in the literature. We calculated the luminosity function of the post-starburst galaxies using two uniformly selected subsamples: the SDSS main galaxy sample and the Baryon Oscillation Spectroscopic Survey CMASS sample. The luminosity functions are reasonably fit by half-Gaussian functions. The peak magnitudes shift as a function of redshift from M ∼ −23.5 at z ∼ 0.8 to M ∼ −20.3 at z ∼ 0.1. This is consistent with the downsizing trend, whereby more massive galaxies form earlier than low-mass galaxies. We compared the mass of the post-starburst stellar population found in our sample to the decline of the global star formation rate and found that only a small amount (∼1%) of all star formation quenching in the redshift range z = 0.2–0.7 results in post-starburst galaxies in the luminosity range our sample is sensitive to. Therefore, luminous post-starburst galaxies are not the place where most of the decline in the star formation rate of the universe is happening.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Performance improvements of wavelength-shifting-fiber neutron detectors using high-resolution positioning algorithms

On the basis of FluoroBancroft linear-algebraic method [S.B. Andersson, Opt. Exp. 16, 18714 (2008)] three highly-resolved positioning methods were proposed for wavelength-shifting fiber (WLSF) neutron detectors. Using a Gaussian or exponential-decay light-response function (LRF), the non-linear relation of photon-number profiles vs. x-pixels was linearized and neutron positions were determined. The proposed algorithms give an average 0.03-0.08 pixel position error, much smaller than that (0.29 pixel) from a traditional maximum photon algorithm (MPA). The new algorithms result in better detector uniformity, less position misassignment (ghosting), better spatial resolution, and an equivalent or better instrument resolution in powder diffraction than the MPA. Moreover, these characters will facilitate broader applications of WLSF detectors at time-of-flight neutron powder diffraction beamlines, including single-crystal diffraction and texture analysis.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

Influence of Gaussian white noise on the frequency-dependent first nonlinear polarizability of doped quantum dot

We investigate the profiles of diagonal components of frequency-dependent first nonlinear (β{sub xxx} and β{sub yyy}) optical response of repulsive impurity doped quantum dots. We have assumed a Gaussian function to represent the dopant impurity potential. This study primarily addresses the role of noise on the polarizability components. We have invoked Gaussian white noise consisting of additive and multiplicative characteristics (in Stratonovich sense). The doped system has been subjected to an oscillating electric field of given intensity, and the frequency-dependent first nonlinear polarizabilities are computed. The noise characteristics are manifested in an interesting way in the nonlinear polarizability components. In case of additive noise, the noise strength remains practically ineffective in influencing the optical responses. The situation completely changes with the replacement of additive noise by its multiplicative analog. The replacement enhances the nonlinear optical response dramatically and also causes their maximization at some typical value of noise strength that depends on oscillation frequency.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2015

Axial acoustic radiation force on a sphere in Gaussian field

Based on the finite series method, the acoustical radiation force resulting from a Gaussian beam incident on a spherical object is investigated analytically. When the position of the particles deviating from the center of the beam, the Gaussian beam is expanded as a spherical function at the center of the particles and the expanded coefficients of the Gaussian beam is calculated. The analytical expression of the acoustic radiation force on spherical particles deviating from the Gaussian beam center is deduced. The acoustic radiation force affected by the acoustic frequency and the offset distance from the Gaussian beam center is investigated. Results have been presented for Gaussian beams with different wavelengths and it has been shown that the interaction of a Gaussian beam with a sphere can result in attractive axial force under specific operational conditions. Results indicate the capability of manipulating and separating spherical spheres based on their mechanical and acoustical properties, the results provided here may provide a theoretical basis for development of single-beam acoustical tweezers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Deconvolution of Stark broadened spectra for multi-point density measurements in a flow Z-pinch

Stark broadened emission spectra, once separated from other broadening effects, provide a convenient non-perturbing means of making plasma density measurements. A deconvolution technique has been developed to measure plasma densities in the ZaP flow Z-pinch experiment. The ZaP experiment uses sheared flow to mitigate MHD instabilities. The pinches exhibit Stark broadened emission spectra, which are captured at 20 locations using a multi-chord spectroscopic system. Spectra that are time- and chord-integrated are well approximated by a Voigt function. The proposed method simultaneously resolves plasma electron density and ion temperature by deconvolving the spectral Voigt profile into constituent functions: a Gaussian function associated with instrument effects and Doppler broadening by temperature; and a Lorentzian function associated with Stark broadening by electron density. The method uses analytic Fourier transforms of the constituent functions to fit the Voigt profile in the Fourier domain. The method is discussed and compared to a basic least-squares fit. The Fourier transform fitting routine requires fewer fitting parameters and shows promise in being less susceptible to instrumental noise and to contamination from neighboring spectral lines. The method is evaluated and tested using simulated lines and is applied to experimental data for the 229.69 nm C III line from multiple chords to determine plasma density and temperature across the diameter of the pinch. These measurements are used to gain a better understanding of Z-pinch equilibria.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Efficiency enhancement of nonlinear odd harmonics in thermal free electron laser

The effect of axial energy spread on the radiation of third harmonic is studied in the free electron laser with planar wiggler and ion-channel guiding. Spread in the longitudinal momentum and so in the initial energy of electron beam, without any spread in the transverse velocity, is assumed in the form of Gaussian distribution function. The technique that is employed is a one-dimensional and steady-state simulation. A set of self consistent nonlinear differential equations that describes the system is solved numerically by Runge-Kutta method. Due to the sensitivity of harmonics to thermal effects, gain improvement of third harmonic radiation is achieved by using ion-channel guiding technique and efficiency enhancement is applied by tapering the magnetic field of wiggler to optimize radiation. The bunching parameter of the electron beam is also studied. It is found that the growth of the magnitude of the bunching parameter that is caused by the ponderomotive wave stops before the saturation point of the radiation. This means that ponderomotive wave saturates at a shorter distance compared to the radiation.

43 PARTICLE ACCELERATORS↗
DOE OSTI2015

A novel Gaussian-Sinc mixed basis set for electronic structure calculations

A Gaussian-Sinc basis set methodology is presented for the calculation of the electronic structure of atoms and molecules at the Hartree–Fock level of theory. This methodology has several advantages over previous methods. The all-electron electronic structure in a Gaussian-Sinc mixed basis spans both the “localized” and “delocalized” regions. A basis set for each region is combined to make a new basis methodology—a lattice of orthonormal sinc functions is used to represent the “delocalized” regions and the atom-centered Gaussian functions are used to represent the “localized” regions to any desired accuracy. For this mixed basis, all the Coulomb integrals are definable and can be computed in a dimensional separated methodology. Additionally, the Sinc basis is translationally invariant, which allows for the Coulomb singularity to be placed anywhere including on lattice sites. Finally, boundary conditions are always satisfied with this basis. To demonstrate the utility of this method, we calculated the ground state Hartree–Fock energies for atoms up to neon, the diatomic systems H{sub 2}, O{sub 2}, and N{sub 2}, and the multi-atom system benzene. Together, it is shown that the Gaussian-Sinc mixed basis set is a flexible and accurate method for solving the electronic structure of atomic and molecular species.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

OBSERVATION OF TeV GAMMA RAYS FROM THE UNIDENTIFIED SOURCE HESS J1841-055 WITH THE ARGO-YBJ EXPERIMENT

We report the observation of a very high energy {gamma}-ray source whose position is coincident with HESS J1841-055. This source has been observed for 4.5 years by the ARGO-YBJ experiment from 2007 November to 2012 July. Its emission is detected with a statistical significance of 5.3 standard deviations. Parameterizing the source shape with a two-dimensional Gaussian function, we estimate an extension {sigma}=(0.40{sup +0.32}{sub -0.22}){sup o}, which is consistent with the HESS measurement. The observed energy spectrum is dN/dE = (9.0 {+-} 1.6) Multiplication-Sign 10{sup -13}(E/5 TeV){sup -2.32{+-}0.23} photons cm{sup -2} s{sup -1} TeV{sup -1}, in the energy range 0.9-50 TeV. The integral {gamma}-ray flux above 1 TeV is 1.3 {+-} 0.4 Crab, which is 3.2 {+-} 1.0 times the flux derived by HESS. The differences in the flux determination between HESS and ARGO-YBJ and possible counterparts at other wavelengths are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

SU-F-T-182: A Stochastic Approach to Daily QA Tolerances On Spot Properties for Proton Pencil Beam Scanning

Purpose: Proton pencil beam scanning is used clinically across the United States. There are no current guidelines on tolerances for daily QA specific to pencil beam scanning, specifically related to the individual spot properties (spot width). Using a stochastic method to determine tolerances has the potential to optimize tolerances on individual spots and decrease the number of false positive failures in daily QA. Individual and global spot tolerances were evaluated. Methods: As part of daily QA for proton pencil beam scanning, a field of 16 spots (corresponding to 8 energies) is measured using an array of ion chambers (Matrixx, IBA). Each individual spot is fit to two Gaussian functions (x,y). The spot width (σ) in × and y are recorded (32 parameters). Results from the daily QA were retrospectively analyzed for 100 days of data. The deviations of the spot widths were histogrammed and fit to a Gaussian function. The stochastic spot tolerance was taken to be the mean ± 3σ. Using these results, tolerances were developed and tested against known deviations in spot width. Results: The individual spot tolerances derived with the stochastic method decreased in 30/32 instances. Using the previous tolerances (± 20% width), the daily QA would have detected 0/20 days of the deviation. Using a tolerance of any 6 spots failing the stochastic tolerance, 18/20 days of the deviation would have been detected. Conclusion: Using a stochastic method we have been able to decrease daily tolerances on the spot widths for 30/32 spot widths measured. The stochastic tolerances can lead to detection of deviations that previously would have been picked up on monthly QA and missed by daily QA. This method could be easily extended for evaluation of other QA parameters in proton spot scanning.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Uniform electron gases. III. Low-density gases on three-dimensional spheres

By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGF centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids — the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) — and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗