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Results for “Analytic linearization”

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 1,369 records · Page 76
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Estimating unsteady aerodynamic forces on a cascade in a three-dimensional turbulence field

An analytical method has been developed to estimate the unsteady aerodynamic forces caused by flow field turbulence on a wind tunnel turning vane cascade system (vane set). This method approximates dynamic lift and drag by linearly perturbing the appropriate steady state force equations, assuming that the dynamic loads are due only to free stream turbulence and that this turbulence is homogeneous, isotropic, and Gaussian. Correlation and unsteady aerodynamic effects are also incorporated into the analytical model. Using these assumptions, equations relating dynamic lift and drag to flow turbulence, mean velocity, and vane set geometry are derived. From these equations, estimates for the power spectra and rms (root mean squared value, delta) loading of both lift and drag can be determined.

Norman, T.↗
NASA NTRS1986

Estimating unsteady aerodynamic forces on a cascade in a three-dimensional turbulence field

An analytical method has been developed to estimate tne unsteady aerodynamic forces caused by flow field turbulence on a wind tunnel turning vane cascade system (vane set). This method approximates dynamic lift and drag by linearly perturbing the appropriate steady state force equations, assuming that the dynamic loads are due only to free stream turbulence and that this turbulence is homogeneous, isotropic, and Gaussian. Correlation and unsteady aerodynamic effects are also incorporated into the analytical model. Using these assumptions, equations relating dynamic lift and drag to flow turbulence, mean velocity, and vane set geometry are derived. From these equations, estimates for the power spectra and rms (root mean squared value, delta) loading of both lift and drag can be determined.

Norman, T. R.↗
DOE OSTI2022

An analytical approach to evaluating magnetic-field closure and topological changes in FRC devices

Here, we describe mathematical methods based on optimizing a modified non-linear flux function (MFF) to evaluate whether odd-parity perturbations affect the local closure of magnetic field lines in field-reversed configurations. Using the MFF methodology, quantitative formulas are derived that provide the shift of the field minimum and the threshold for field-line opening, a discontinuous change in field topology.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1988

Properties of finite difference models of non-linear conservative oscillators

Finite-difference (FD) approaches to the numerical solution of the differential equations describing the motion of a nonlinear conservative oscillator are investigated analytically. A generalized formulation of the Duffing and modified Duffing equations is derived and analyzed using several FD techniques, and it is concluded that, although it is always possible to contstruct FD models of conservative oscillators which are themselves conservative, caution is required to avoid numerical solutions which do not accurately reflect the properties of the original equation.

Mickens, R. E.↗
DOE OSTI2015

Machine Learning for Quantum Mechanical Properties of Atoms in Molecules

Here we introduce machine learning models of quantum mechanical observables of atoms in molecules. Instant out-of-sample predictions for proton and carbon nuclear chemical shifts, atomic core level excitations, and forces on atoms reach accuracies on par with density functional theory reference. Locality is exploited within nonlinear regression via local atom-centered coordinate systems. The approach is validated on a diverse set of 9 k small organic molecules. Linear scaling of computational cost in system size is demonstrated for saturated polymers with up to submesoscale lengths.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Analytical and numerical studies of dark current in radiofrequency structures for short-pulse high-gradient acceleration

High-gradient acceleration is a key research area that could enable compact linear accelerators for future colliders, light sources, and other applications. In the pursuit of high-gradient operation, rf breakdown limits the attainable accelerating gradient in normal-conducting rf structures. Recent experiments at the Argonne Wakefield Accelerator suggest a promising approach: using short rf pulses with durations of a few nanoseconds. Experimental studies show that these 𝒪⁡(1⁢ ⁢ns) rf pulses can mitigate breakdown limitations, resulting in higher gradients. For example, an electric field of nearly 400 MV/m was achieved in an 𝑋-band photoemission gun driven by 6-ns-long rf pulses, with rapid rf conditioning and low dark current observed. Despite these promising results, the short-pulse regime remains an underexplored parameter space, and rf breakdown physics under nanosecond-long pulses requires further investigation. In this paper, we present analytical and numerical simulations of dark current dynamics in accelerating cavities operating in the short-pulse regime. We study breakdown-associated processes spanning different time scales, including field emission, multipacting, and plasma formation, using simulations of the 𝑋-band photogun cavities. The results reveal the advantages of using short rf pulses to reduce dark current and mitigate rf breakdown, offering a path toward a new class of compact accelerators with enhanced performance and reduced susceptibility to breakdown.

Linear accelerators↗
NASA NTRS2000

A polymer, random walk model for the size-distribution of large DNA fragments after high linear energy transfer radiation

DNA double-strand breaks (DSBs) produced by densely ionizing radiation are not located randomly in the genome: recent data indicate DSB clustering along chromosomes. Stochastic DSB clustering at large scales, from > 100 Mbp down to < 0.01 Mbp, is modeled using computer simulations and analytic equations. A random-walk, coarse-grained polymer model for chromatin is combined with a simple track structure model in Monte Carlo software called DNAbreak and is applied to data on alpha-particle irradiation of V-79 cells. The chromatin model neglects molecular details but systematically incorporates an increase in average spatial separation between two DNA loci as the number of base-pairs between the loci increases. Fragment-size distributions obtained using DNAbreak match data on large fragments about as well as distributions previously obtained with a less mechanistic approach. Dose-response relations, linear at small doses of high linear energy transfer (LET) radiation, are obtained. They are found to be non-linear when the dose becomes so large that there is a significant probability of overlapping or close juxtaposition, along one chromosome, for different DSB clusters from different tracks. The non-linearity is more evident for large fragments than for small. The DNAbreak results furnish an example of the RLC (randomly located clusters) analytic formalism, which generalizes the broken-stick fragment-size distribution of the random-breakage model that is often applied to low-LET data.

DNA/radiation effects↗
DOE OSTI2020

Average nonlinear dynamics of particles in gravitational pulses: Effective Hamiltonian, secular acceleration, and gravitational susceptibility

Particles interacting with a prescribed quasimonochromatic gravitational wave (GW) exhibit secular (average) nonlinear dynamics that can be described by Hamilton’s equations. We derive the Hamiltonian of this “ponderomotive” dynamics to the second order in the GW amplitude for a general background metric. For the special case of vacuum GWs, we show that our Hamiltonian is equivalent to that of a free particle in an effective metric, which we calculate explicitly. We also show that already a linear GW pulse displaces a particle from its unperturbed trajectory by a finite distance that is independent of the GW phase and proportional to the integral of the pulse intensity.This effect is independent from the nonlinear memory effects that has been known. We calculate the particle displacement analytically and show that our result is in agreement with numerical simulations. We also show how the Hamiltonian of the nonlinear averaged dynamics naturally leads to the concept of the linear gravitational susceptibility of a particle gas with an arbitrary phase-space distribution. We calculate this susceptibility explicitly to apply it, in a follow-up paper, toward studying self-consistent GWs in inhomogeneous media within the geometrical-optics approximation

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Quantitative analysis of Cu XANES spectra using linear combination fitting of binary mixtures simulated by FEFF9

We report x-ray absorption near edge structure (XANES) is a powerful tool to probe the fingerprint of local structures, and when coupled with X-ray microscopy, the small spot size enables one to probe very specific regions of interest in a device or material, e.g. interfaces/bulk, different grains, good/bad electrical areas. In this work, we investigate the use of linear combination fitting (LCF) of XANES spectra for the particular case of Cu doping in CdTe. We show that the experimental data seem to be accurately represented by standards of Cu 2 Te and its substoichiometric counterpart, Cu 1.43 Te. We use Cu in CdTe as a case study to evaluate the accuracy of linear combination fitting using simulated standards, given that experimental standards for certain phases (e.g. Cu 1.43 Te) or defect structures (e.g. vacancies) cannot be readily obtained. We discuss how spectral features of the FEFF9-simulated standards, fitting ranges, and noise levels all dictate the accuracy of this type of analysis. We show that the greater the spectral difference between the two standards, the better the LCF is able to differentiate between the two structures and to tolerate experimental noise. Finally, we estimate the error of the fitted weights for different spectral features and noise levels and propose a framework to study local structures semi-quantitatively by using binary mixtures of FEFF9-simulated standards.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

SU-E-J-110: TG 51 Dosimetry : With Or Without Lead

TG-51 Dosimetry: With or Without Lead. Purpose: In this project, an analytical method has been introduced for adjustment of the TG-51 recommended KQ in order to produce accurate dosimetric data for high energy photons without the lead foil. Methods: These investigations were performed using a 30 cm × 30 cm × 30 cm CIVCO water tank, A12 EXRADIN Water proof Farmer Chamber, a Standard Imaging MAX 4000 electrometer, and 1 mm thick lead foil from Standard Imaging. Complete TG-51 was performed every month with and without lead. The results were analyzed and an analytical model has been developed for comparing the values of KQ. TG-51 Table I was used to obtain KQ values. Results: The dosimetric evaluations were obtained for Varian Linear accelerators Model 21ix and 21ex. These results indicates that the measured data with lead foil in place as recommended by TG-51 is in excellent agreement (within 0.1%) with the calculated data obtained by the new model, from our dosimetry data without-lead. If equation 15 of the TG-51 report is used without any adjustments, it will lead to differences of about 1.6 % (on the average) in relative data which will Resultin differences of about 0.3 % (on the average) in the KQ Values. The KQ value for 18 MV obtained consistently with the equation of TG-51 “with lead” and “without lead” were 0.971 and 0.974, respectively. The 0.3 % higher results for KQ without lead eventually will lead to 0.3% larger output. However, by considering this model the KQ value was found to be 0.971 for dosimetry without lead. Conclusion: The analytical model that was introduced in this project was able to reproduce the dosimetric data of the high energy linear accelerators to within 0.1% without the use of the lead foil.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2015

On the theory of current passage via an ideal insulator

An analytic solution to the problem of current passage via an ideal insulator in the case of monopolar hole injection has been found. The current-voltage (J-V) characteristics have been obtained for the first time in a broad range of parameters (insulator length, hole concentrations at boundaries, temperature, etc.) and applied voltages. It is shown that the Mott-Gurney quadratic J-V relation is valid only in a certain interval of currents between J{sub 1} and J{sub 2}. For J < J{sub 1}, the current linearly depends on voltage V to within V{sup 3} terms. A new mode has been found for J > J{sub 2}, where the J-V characteristic also becomes linear because the insulator is completely filled with injected holes. The integration constants are determined in the entire range of parameters and currents. Analytic expressions for the spatial electric-field and hole-concentration distributions are derived.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Self-consistent initial conditions for primordial black hole formation

For an arbitrarily strong, spherically symmetric super-horizon curvature perturbation, we present analytic solutions of the Einstein equations in terms of the asymptotic expansion over the ratio of the Hubble radius to the length-scale of the curvature perturbation to set initial conditions for numerical computations of primordial black hole formation. To obtain this solution we develop a recursive method of quasi-linearization which reduces the problem to a system of coupled ordinary differential equations for the Nth order terms in the asymptotic expansion with sources consisting of a non-linear combination of the lower order terms.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1987

A theory for the Langmuir waves in the electron foreshock

A comprehensive theory for the Langmuir waves in the earth's foreshock involving saturation of the kinetic version of the beam instability by quasi-linear relaxation is proposed in this paper. Reactive and kinetic beam instabilities are shown to be the two limiting versions of a single instability whose analytically and numerically derived descriptions are shown to form a consistent picture. It is pointed out that the reactive instability gives rise only to narrow-band growth while the kinetic instability gives rise to wide-band growth. Arguments for describing the Langmuir wave growth in terms of the kinetic instability are given, and four suppression mechanisms for the kinetic instability are discussed. It is suggested that quasi-linear relaxation limits the Langmuir growth and gives rise to distributions qualitatively similar to the observed distribution functions, and arguments in favor of this hypothesis are presented.

Cairns, Iver H.↗
DOE OSTI2016

Breathers in a locally resonant granular chain with precompression

Here we study a locally resonant granular material in the form of a precompressed Hertzian chain with linear internal resonators. Using an asymptotic reduction, we derive an effective nonlinear Schrödinger (NLS) modulation equation. In turn, this leads us to provide analytical evidence, subsequently corroborated numerically, for the existence of two distinct types of discrete breathers related to acoustic or optical modes: (a) traveling bright breathers with a strain profile exponentially vanishing at infinity and (b) stationary and traveling dark breathers, exponentially localized, time-periodic states mounted on top of a non-vanishing background. Moreover, the stability and bifurcation structure of numerically computed exact stationary dark breathers is also examined. Stationary bright breathers cannot be identified using the NLS equation, which is defocusing at the upper edges of the phonon bands and becomes linear at the lower edge of the optical band.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Hydrodynamic description of an unmagnetized plasma with multiple ion species. II. Two and three ion species plasmas

Paper I [A. N. Simakov and K. Molvig, Phys. Plasmas23, 032115 (2016)] obtained a fluid description for an unmagnetized collisional plasma with multiple ion species. To evaluate collisional plasmatransport fluxes, required for such a description, two linear systems of equations need to be solved to obtain corresponding transport coefficients. In general, this should be done numerically. Herein, the general formalism is used to obtain analytical expressions for such fluxes for several specific cases of interest: a deuterium-tritium plasma; a plasma containing two ion species with strongly disparate masses, which agrees with previously obtained results; and a three ion species plasma made of deuterium, tritium, and gold. We find that these results can be used for understanding the behavior of the aforementioned plasmas, or for verifying a code implementation of the general multi-ion formalism.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Excitation correlation photoluminescence in the presence of Shockley-Read-Hall recombination

Excitation correlation photoluminescence (ECPL) measurements are often analyzed in the approximation of a cross correlation of charge carrier populations generated by the two delayed pulses. In semiconductors, this approach is valid for a linear non-radiative recombination path, but not for a non-linear recombination rate as in the general Shockley-Read-Hall recombination scenario. Here, the evolution of the ECPL signal was studied for deep trap recombination following Shockley-Read-Hall statistics. Analytic solutions can be obtained for a fast minority trapping regime and steady state recombination. For the steady state case, our results show that the quadratic radiative term plays only a minor role, and that the shape of the measured signal is mostly determined by the non-linearity of the recombination itself. We find that measurements with unbalanced intense pump and probe pulses can directly provide information about the dominant non-radiative recombination mechanism. The signal traces follow the charge carrier concentrations, despite the complex origins of the signal, thus showing that ECPL can be applied to study charge carrier dynamics in semiconductors without requiring elaborate calculations. The model is compared with measurements on a reference sample with alternating layers of InGaAs/InAlAs that were additionally cross-checked with time resolved optical pump terahertz probe measurements and found to be in excellent agreement.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

An In-Depth Exploration of the Electrochemical Oxygen Reduction Reaction (ORR) Phenomenon on Carbon-Based Catalysts in Alkaline and Acidic Mediums

Detailed studies of the electrochemical oxygen reduction reaction (ORR) on catalyst materials are crucial to improving the performance of different electrochemical energy conversion and storage systems (e.g., fuel cells and batteries), as well as numerous chemical synthesis processes. In the effort to reduce the loading of expensive platinum group metal (PGM)-based catalysts for ORR in the electrochemical systems, many carbon-based catalysts have already shown promising results and numerous investigations on those catalysts are in progress. Most of these studies show the catalyst materials’ ORR performance as current density data obtained through the rotating disk electrode (RDE), rotating ring-disk electrode (RRDE) experiments taking cyclic voltammograms (CV) or linear sweep voltammograms (LSV) approaches. However, the provided descriptions or interpretations of those data curves are often ambiguous and recondite which can lead to an erroneous understanding of the ORR phenomenon in those specific systems and inaccurate characterization of the catalyst materials. In this paper, we presented a study of ORR on a newly developed carbon-based catalyst, the nitrogen-doped graphene/metal-organic framework (N-G/MOF), through RDE and RRDE experiments in both alkaline and acidic mediums, taking the LSV approach. The functions and crucial considerations for the different parts of the RDE/RRDE experiment such as the working electrode, reference electrode, counter electrode, electrolyte, and overall RDE/RRDE process are delineated which can serve as guidelines for the new researchers in this field. Experimentally obtained LSV curves’ shapes and their correlations with the possible ORR reaction pathways within the applied potential range are discussed in depth. We also demonstrated how the presence of hydrogen peroxide (H2O2), a possible intermediate of ORR, in the alkaline electrolyte and the concentration of acid in the acidic electrolyte can maneuver the ORR current density output in compliance with the possible ORR pathways.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗