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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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Studies of the Magnetocaloric and Electrical Properties of La{sub 0.7}Er{sub 0.05}Sr{sub 0.15}Ca{sub 0.1}Mn{sub 1−x}In{sub x}O{sub 3} (0 ≤ x ≤ 0.30)

We report on the study of In substitution for Mn on the magnetic and transport properties of layered manganese oxides La{sub 0.7}Er{sub 0.05}Sr{sub 0.15}Ca{sub 0.1}Mn{sub 1−x}In{sub x}O{sub 3} (0 ≤ x ≤ 0.30) synthesized via sol-gel method. For all the samples, all peaks are satisfactorily indexed in the rhombohedra structure with R 3-bar c space group. Magnetic data, under a magnetic field of 0.05 T, revealed that our compounds exhibit a continuous (second-order) transition from a ferromagnetic (FM) to a paramagnetic (PM) state upon decreasing the temperature. Also, magnetic entropy change and relative cooling power for magnetic field variation were predicted. Then, we have fitted the experimental data of resistivity using non-linear curve fitting, a typical mathematical function (Gauss function). This function can describe the carrier transport behavior of manganites as a function of temperature around the electrical phase transition. The obtained results were discussed. These predicted parameters agree with the experimental data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

A method for the characterization of intra-pixel response of infrared sensor

Due to the response variations within a pixel, response of sensor varies with the positions of the point target. The accurate measurement of intra-pixel response of the sensor is the key to high-precision centroid estimation and radiometric calibration. In this paper, we establish an intra-pixel response model based on the pixel structure and use Gauss function to describe the beam spot profile. We further calculate the full width at half maximum (FWHM) of the Gauss function and the fill factor of the infrared sensor using the grid search algorithm. Experimental results show that the Gauss function FWHM differences among different pixels using the same radius could be less than 6%. The fill factors are not constant in different pixels because of errors in the process of manufacture and assembly, and the error between model and measured values is less than 3.6%. This work could be useful for stellar calibration and centroid estimation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Localization of Carriers in Quantum Dots with Uniaxial Anisotropy of Shape and Composition

The electronic and hole states in quantum dots (QD) of cubic II–VI semiconductors with a spheroidal shape and uniaxial anisotropy have been studied theoretically. The smooth potential energy profiles simulated by the Gauss function in all three spatial directions are considered. The energy level lowering and the energy splitting of the hole state from the valence band top Γ{sub 8} by momentum 3/2 into the states with projections ±3/2, ±1/2 on the anisotropy axis are analyzed. The QD anisotropies of three types are considered: the QD size anisotropy, the QD potential barrier anisotropy, and the combined anisotropy. In the first case, flattened quantum dots, in which the characteristic size in the structure plane is larger than the size along the anisotropy axis, are considered. In the second case, QDs, in which the potential barrier height in the plane is lower than that along the anisotropy axis, are considered. In the third case, flattened quantum dots with the anisotropy of the size and the potential barrier are considered. The conditions of the charge carrier localization inside QD have been found, and the influence of the form and composition anisotropies on the energies of exciton transitions in the structures with Cd{sub x}Zn{sub 1 –} {sub x}Se quantum dots are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Size Distribution of Graphite Nodules in Hypereutectic Cast Irons of Varying Nodularity

An SGI was machined into 400 g cylindrical pieces and remelted in an electrical resistance furnace protected by Ar gas to produce materials ranging from SGI to CGI. The graphite morphology was controlled by varying the holding time at 1723 K (1450 °C) between 10 and 60 minutes. The discrete sectional size distribution of nodules by number density was measured on cross sections of the specimens and translated to volumetric distribution by volume fraction. Subpopulations of nodules were distinguished by fitting Gaussian distribution functions to the measured distribution. Primary and eutectic graphite, were found to account for most of the volume of nodular graphite in all cases. For holding times of 40 minutes and greater, corresponding to nodularity roughly below 40 pct, the primary subpopulation was very small and difficult to distinguish, leaving eutectic nodules as the dominant subpopulation. The mode and standard deviation of the two subpopulations were roughly independent of nodularity. Moreover, the nodular and vermicular graphite were segregated in the microstructure. In conclusion, the results suggest that the parallel development of the vermicular eutectic had small influence on the size distribution of eutectic graphite nodules.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Cluster truncated Wigner approximation in strongly interacting systems

We present a general method by which linear quantum Hamiltonian dynamics with exponentially many degrees of freedom is replaced by approximate classical nonlinear dynamics with the number of degrees of freedom (phase space dimensionality) scaling polynomially in the system size. This method is based on generalization of the truncated Wigner approximation (TWA) to a higher dimensional phase space, where phase space variables are associated with a complete set of quantum operators spanning finite size clusters. The method becomes asymptotically exact with increasing cluster size. The crucial feature of TWA is fluctuating initial conditions, which we approximate by a Gaussian distribution. We show that such fluctuations dramatically increase accuracy of TWA over traditional cluster mean-field approximations. In this way we can treat on equal footing quantum and thermal fluctuations as well as compute entanglement and various equal and non-equal time correlation functions. The main limitation of the method is exponential scaling of the phase space dimensionality with the cluster size, which can be significantly reduced by using the language of Schwinger bosons and can likely be further reduced by truncating the local Hilbert space variables. We demonstrate the power of this method analyzing dynamics in various spin chains with and without disorder and show that we can capture such phenomena as long time hydrodynamic relaxation, many-body localization and the ballistic spread of entanglement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2004

Plasma Dispersion Function for the Kappa Distribution

The plasma dispersion function is computed for a homogeneous isotropic plasma in which the particle velocities are distributed according to a Kappa distribution. An ordinary differential equation is derived for the plasma dispersion function and it is shown that the solution can be written in terms of Gauss' hypergeometric function. Using the extensive theory of the hypergeometric function, various mathematical properties of the plasma dispersion function are derived including symmetry relations, series expansions, integral representations, and closed form expressions for integer and half-integer values of K.

Podesta, John J.↗
DOE OSTI2018

Gaussian kernel density functions for compositional quantification in atom probe tomography

Highlights: • A methodology for compositional quantification from atom probe tomography is proposed. • A probability density function p(x) given discrete data points is constructed. • Each atom approximated by a Gaussian function with a particular smoothing parameter. • Density Kernel functions are used to find the optimum smoothing parameter. • The method is validated by using simulated data of semiconductor materials. - Abstract: Atom probe tomography (APT) has the ability to identify the nature and position of single atoms in a material with an almost 3D atomic resolution. However, the quantification of the material composition requires an appropriate treatment of the discrete APT data. When the amount of atoms selected to quantify the composition is relatively small, the spatial resolution is enhanced but the statistical error worsens. Conversely, the increase in the number of atoms considered reduces the spatial resolution, but improving the statistics. We have developed a methodology to reach an optimum equilibrium between the positional and the statistical error in an unsupervised form using Gaussian Kernel density functions. The validity of the method has been tested using APT simulated data of semiconductor materials. It has been proved that the chemical quantification in these materials requires the appropriate selection of the smoothing parameter, obtained without user intervention. In addition, the results have been compared to the usual techniques for composition measurement from APT data (voxelization and proximity histograms), showing better precision for high spatial resolution. This work supplies a data driven methodology based in Gaussian Kernel density functions for the accurate quantification of the composition from APT data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Electronic Excitation Energy Transfer in an Array of CdS Quantum Dots on a Quasi-Two-Dimensional Surface

The optical spectra of films composed of spherical silicon-dioxide particles coated with small-radius CdS quantum dots are recorded and analyzed. Large shifts of the absorption and photoluminescence bands are detected and studied in relation to the concentration of quantum dots and to the pumping density and wavelength. Analysis of the experimental data shows that the effects are due to electronic excitation energy transfer by particles through the mechanism of tunneling induced by a strong interaction between quantum dots. The results obtained at low pumping densities and different excitation wavelengths make it possible to describe the size distribution of CdS quantum dots. This distribution can be adequately approximated with a Gaussian function.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Statistical characteristics of laser interference and its effect on IR optoelectronic observation systems

We consider statistical characteristics of laser interference recorded in the focal region of an IR optoelectronic observation system under field and out-of-field illumination by laser radiation. The applicability of the analytical description of experimental histograms of the laser interference signal distribution at the photodetector array output using the probability density approximations in the form of gamma distribution and the Gaussian function is substantiated. It is shown that the specific form of these functions is determined both by the mean value (mathematical expectation) of the interference signal and by the characteristic parameter M, which depends on the statistical properties of the laser interference. (laser applications and other issues in quantum electronics)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Propagation characteristics of dark and antidark Gaussian beams in turbulent atmosphere

In this work, we investigated theoretically the propagation characteristics of dark and antidark Gaussian beams (DADGBs) in turbulent atmosphere. Based on the Huygens–Fresnel diffraction integral and by mean of the expansion form of a hard aperture function into a finite sum of Gaussian functions we derived analytically the on-axis intensity distribution of an apertured DADGB propagating in turbulent atmosphere. The dependence of the axial intensity distribution on the turbulent strength and on the parameters of the beam is illustrated with numerical examples. The results show that the axial intensity decreases rapidly when the turbulent strength parameter is large, and the propagation distance is shorter for large wavelengths and for small beam waist width.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

On the Five-Moment Hamburger Maximum Entropy Reconstruction

We consider the Maximum Entropy Reconstruction (MER) as a solution to the five-moment truncated Hamburger moment problem in one dimension. In the case of five monomial moment constraints, the probability density function (PDF) of the MER takes the form of the exponential of a quartic polynomial. This implies a possible bimodal structure in regions of moment space. An analytical model is developed for the MER PDF applicable near a known singular line in a centered, two-component, third- and fourth-order moment (μ{sub 3}, μ{sub 4}) space, consistent with the general problem of five moments. The model consists of the superposition of a perturbed, centered Gaussian PDF and a small-amplitude packet of PDF-density, called the outlying moment packet (OMP), sitting far from the mean. Asymptotic solutions are obtained which predict the shape of the perturbed Gaussian and both the amplitude and position on the real line of the OMP. The asymptotic solutions show that the presence of the OMP gives rise to an MER solution that is singular along a line in (μ{sub 3}, μ{sub 4}) space emanating from, but not including, the point representing a standard normal distribution, or thermodynamic equilibrium. We use this analysis of the OMP to develop a numerical regularization of the MER, creating a procedure we call the Hybrid MER (HMER). Compared with the MER, the HMER is a significant improvement in terms of robustness and efficiency while preserving accuracy in its prediction of other important distribution features, such as higher order moments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Universal upper bounds for Gaussian information capacity

The most natural way to describe an information-carrying system containing a specific noise is an additive white Gaussian-noise (AWGN) channel. In bosonic quantum systems (especially the Gaussian case), although the classical information capacity for a phase-insensitive and thermal-noise channel is additive based on a proof of the minimum output entropy conjecture, several open questions remain. By generalizing the Gaussian noise model from thermal noise to general Gaussian noise, we rigorously revisit and calculate these strong upper bounds on the information capacity for single-mode with general Gaussian-noise channels. In this study, we use the quantum entropy power inequality (QEPI) approach. This framework gives a new formula for finding upper bounds on the information capacity of bosonic Gaussian channels.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Application of the locally self-consistent embedding approach to the Anderson model with non-uniform random distributions

Highlights: • Typical Medium Theory (TMT) for the Anderson Localization. • Locally Self-Consistent Multiple Scattering Method (LSMS) for Random Disordered Systems. • Linear Scaling Computational Method for Random Disordered Systems. We apply the recently developed embedding scheme for the locally self-consistent method to random disorder electrons systems. The method is based on the locally self-consistent multiple scattering theory and the typical medium theory. The locally self-consistent multiple scattering theory divides a system into many small designated local interaction zones. The subsystem within each local interaction zone is embedded in a self-consistent field from the typical medium theory. This approximation allows the study of random systems with large numbers of sites. We present results for the three dimensional Anderson model with different random disorder potential distributions. Using the typical density of states as an indicator of Anderson localization, we find that the method can capture the localization for commonly studied disorder potentials. These include the uniform distribution, the Gaussian distribution, and even the unbounded Cauchy distribution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A Characteristics Approach to the Finite Element Method

Herein, we present a new method for solving the linear Boltzmann transport equation. Two commonly used and well-understood methods for solving partial differential equations are the method of characteristics (MOC) and the finite element method (FEM). We propose a new method that combines the fundamental concept of the FEM with the analytic solution from the MOC to obtain coefficients for the FEM basis function expansion. Traditionally, coefficients for the FEM basis function expansion are obtained via matrix inversion. Instead, we solve for the coefficients with the MOC and represent the underlying fields with the basis function expansion using these coefficients. We provide a convergence study for our method with results from two sets of FEM basis functions: Gauss-Legendre and Gauss-Lobatto sets. We also compare two different variations of our method categorized as short characteristics and intermediate characteristics.

42 ENGINEERING↗