Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “function approximation”

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 1,567 records · Page 87
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Ponderomotive and weakly relativistic self-focusing of Gaussian laser beam in plasma: Effect of light absorption

This paper presents an influence of light absorption on self-focusing of laser beam propagation in plasma. The differential equation for beam-width parameter is obtained using the Wentzel-Kramers-Brillouin and paraxial approximations through parabolic equation approach. The nonlinearity in dielectric function is assumed to be aroused due to the combined effect of weakly relativistic and ponderomotive regime. To highlight the nature of propagation, behavior of beam-width parameter with dimensionless distance of propagation is presented graphically and discussed. The present work is helpful to understand issues related to the beam propagation in laser plasma interaction experiments where light absorption plays a vital role.

43 PARTICLE ACCELERATORS↗
DOE OSTI2016

Characterizing Fluence as a Function of Areal Density for 1 and 14 MeV Neutrons Transported Through Air

Computing neutron dosimetry involves transporting neutrons [n] from a source to a sink, determining the neutron heating within the sink and multiplying the neutron heating by a quality factor to compute the dose equivalent. The space and energy dependent neutron fluence is a measure of the amount of neutrons crossing a particular surface area, about a particular energy and is given in units of [n/cm{sup 2}]. Microscopic cross sections are given in units of area and vary by isotope and reaction type as a function of energy. The product of the atom density of a particular atom in a specie and the microscopic cross section of a particular reaction results in the macroscopic cross section of a particular reaction, given in units of per length [1/cm] as a function of energy. Summing the macroscopic cross sections of all isotopes, and all collisions resulting in heating, within a volume, results in a total collision heating macroscopic cross section for that volume. The product of the energy and spatial dependent collision heating macroscopic cross section and the energy and spatial dependent fluence, within an energy group, results in a collision heating reaction density for that particular reaction in that energy group. Weighting each energy group's collision heating reactions, with the corresponding energy dependent particle damage per collision heating event (usually biological damage), and then integrating over energy and volume results in the delivered dose. Therefore understanding dose delivery involves examining the spatial and energy (and time) dependent fluence behavior. Because of the coupled energy and space dependence of the heating weighting and macroscopic cross sections, the fluence is not so easily separable in energy and space; however, the energy integrated fluence can be used as a first order approximation of the relative magnitude of reactions as a function of space. Here we examine the first part in the dosimetry calculation process, transporting neutrons from source to sink, as applied to neutron transport in air, examining characteristics of the fluence. Presented here is analysis regarding the nature of the fluence peak between 10 g/cm{sup 2} and 100 g/cm{sup 2} for a typical air transport calculation. Due to the high concentration of nitrogen and oxygen isotopes of these elements, these isotopes tend to dominate the transport. From the analysis presented here, the fluence peak is the result of scatter back and forth across the peak regime, and (n,2n) has a minimal (<4%) contribution. Further evidence of minimal (n,2n) impact in the 10-100 g/cm{sup 2} span includes the 1 MeV fluence peak being so much larger than the 14 MeV peak; where 1 MeV is not above the (n,2n) threshold. Also presented here is the usefulness of using tally tagging with cell flagging to further dissect the nature of the fluence. These technologies allow us to understand the originating volume that makes a contribution to a scoring regime. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2018

Energy release rate approximation for edge cracks using higher-order topological derivatives

Topological derivatives provide the variation of a functional when an infinitesimal hole is introduced into the domain. In Silva et al. (J Mech Phys Solids 59(5):925–939, 2011), the authors developed a first-order approximation of the energy release rate associated with a small crack at any boundary location and at any orientation using a first-order topological derivative. This approach offers significant computational advantages over other methods because (i) it requires only a single analysis while other methods require an analysis for each crack size-location-direction combination, and (ii) it is performed on the non-cracked domain, removing the need to create very fine meshes in the vicinity of the crack. In the present study, higher-precision approximations of the energy release rate are developed using higher-order topological derivatives which allow the analyst to accurately treat longer cracks and determine the crack lengths for which the first-order approximation is accurate.

42 ENGINEERING↗
DOE OSTI2016

Coupled cluster evaluation of the frequency dispersion of the first and second hyperpolarizabilities of water, methanol, and dimethyl ether

The static and dynamic first (β{sub ‖}) and second (γ{sub ‖}) hyperpolarizabilities of water, methanol, and dimethyl ether have been evaluated within the response function approach using a hierarchy of coupled cluster levels of approximation and doubly augmented correlation consistent atomic basis sets. For the three compounds, the electronic β{sub ‖} and γ{sub ‖} values calculated at the CCSD and CC3 levels are in good agreement with gas phase electric field-induced second harmonic generation (EFISHG) measurements. In addition, for dimethyl ether, the frequency dispersion of both properties follows closely recent experimental values [V. W. Couling and D. P. Shelton, J. Chem. Phys. 143, 224307 (2015)] demonstrating the reliability of these methods and levels of approximation. This also suggests that the vibrational contributions to the EFISHG responses of these molecules are small.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Accelerated Testing and Modeling of Potential-Induced Degradation as a Function of Temperature and Relative Humidity

An acceleration model based on the Peck equation was applied to power performance of crystalline silicon cell modules as a function of time and of temperature and humidity, the two main environmental stress factors that promote potential-induced degradation. This model was derived from module power degradation data obtained semi-continuously and statistically by in-situ dark current-voltage measurements in an environmental chamber. The modeling enables prediction of degradation rates and times as functions of temperature and humidity. Power degradation could be modeled linearly as a function of time to the second power; additionally, we found that coulombs transferred from the active cell circuit to ground during the stress test is approximately linear with time. Therefore, the power loss could be linearized as a function of coulombs squared. With this result, we observed that when the module face was completely grounded with a condensed phase conductor, leakage current exceeded the anticipated corresponding degradation rate relative to the other tests performed in damp heat.

14 SOLAR ENERGY↗
DOE OSTI2025

Overset-Grid Method with Smooth Orbital Partitioning for Molecular Scattering Calculations

To solve molecular photoionization and electron scattering problems, we use an overset-grid representation of electronic continuum functions, which has an extended central spherical grid that overlaps small spherical grids (subgrids) centered on each atom of a polyatomic molecule. Here, in this work, we present an improved algorithm that smoothly partitions the total wave function between the central grid and the atomic subgrids. The smooth partitioning allows one to use approximately one-fourth the number of partial waves on the central grid compared to our previous implementation with switching functions. The resulting numerical method for treating electron scattering and photoionization of polyatomic molecules combines the accuracy and flexibility of pure numerical grid representations with the rapid convergence of hybrid combinations of atom-centered basis-set expansions and grid methods. The overset-grid representation is implemented using the complex Kohn variational principle for scattering and photoionization amplitudes. The faster convergence with respect to the number of central grid partial waves is demonstrated and accuracy is verified by comparisons with the previous implementation and with far more computationally demanding single-center numerical expansions in electron-molecule scattering and photoionization calculations on the neon dimer (Ne 2 ) system, carbon tetrafluoride (CF 4 ) molecule, and the pyridine (C 5 H 5 N) molecule in the static-exchange approximation.

Molecules↗
DOE OSTI2020

A least-squares finite element method based on the Helmholtz decomposition for hyperbolic balance laws

In this paper, a least-squares finite element method for scalar nonlinear hyperbolic balance laws is proposed and studied. The approach is based on a formulation that utilizes an appropriate Helmholtz decomposition of the flux vector and is related to the standard notion of a weak solution. This relationship, together with a corresponding connection to negative-norm least-squares, is described in detail. As a consequence, an important numerical conservation theorem is obtained, similar to the famous Lax–Wendroff theorem. The numerical conservation properties of the method in this paper do not fall precisely in the framework introduced by Lax and Wendroff, but they are similar in spirit as they guarantee that when L 2 convergence holds, the resulting approximations approach a weak solution to the hyperbolic problem. The least-squares functional is continuous and coercive in an H -1 -type norm, but not L 2 -coercive. Nevertheless, the L 2 convergence properties of the method are discussed. Convergence can be obtained either by an explicit regularization of the functional, that provides control of the L 2 norm, or by properly choosing the finite element spaces, providing implicit control of the L 2 norm. Numerical results for the inviscid Burgers equation with discontinuous source terms are shown, demonstrating the L 2 convergence of the obtained approximations to the physically admissible solution. The numerical method utilizes a least-squares functional, minimized on finite element spaces, and a Gauss–Newton technique with nested iteration. Finally, we believe that the linear systems encountered with this formulation are amenable to multigrid techniques and combining the method with adaptive mesh refinement would make this approach an efficient tool for solving balance laws (this is the focus of a future study).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Interparticle Interactions in Dilute Solutions of Polyelectrolyte Complex Micelles.

The application of dilute solutions of poly electrolyte complex (PEC) micelles for delivering therapeutic nucleic acids into disease sites has gained momentum. This Letter reports a detailed characterization of PEC micelles in dilute solutions including their internal structures and the determination of the interparticle interactions. The polymer concentration ranges from 0.1 to 0.5 wt %, a regime where micelle-micelle interactions are infrequent. We employ synchrotron small-angle X-ray scattering (SAXS) to simultaneously probe the morphology, internal structure, and radius of gyration (R-g) of the self-assemblies formed by charged diblock polyelectrolytes and homopolyelectrolytes. The emerging appearance of the structure factor in SAXS profiles with the increasing polymer concentration demonstrates the presence of the repulsive intermicellar correlations, which is further confirmed by the differences between the "reciprocal R-g" estimated by Guinier approximation and the "real space R-g" determined by pair distribution functions. We find that the soft corona chains tethered on the surface of phase-separated complex domains are compressed when micelles come close to the point where a hard-sphere interaction takes over. These findings contribute to the fundamental understanding of the structure and space-filling constraints in the complexation-driven self-assemblies and advance the rational design of cationic polymer-based nonviral gene delivery vectors.

Wu, Hao↗
DOE OSTI2024

Exploring interlayer coupling in the twisted bilayer PtTe 2

We have investigated interlayer interactions in the bilayer PtTe 2 system, which influence the electronic energy bands near the Fermi level. Our diffusion Monte Carlo (DMC) calculations for the high-symmetry bilayer stackings (AA, AB, AC) manifest distinct interlayer binding characteristics among the stacking modes by revealing significantly different interlayer separations depending on the stacking, which is critical to understanding the interlayer coupling of the twisted bilayers consisting of various local stacking arrangements. Furthermore, a comparison between the interlayer separations obtained from DMC and density functional theory (DFT) shows that meta-generalized gradient approximation (GGA)-based van der Waals–DFT results agree with DMC for different layer stackings, including twisted bilayers, but only the ground-state AA stacking matches well with GGA-based DFT predictions. This underscores the importance of accurate exchange-correlation potentials even for capturing the stacking-dependent interlayer binding properties. We further show that the variability in DFT-predicted interlayer separations is responsible for the large discrepancy of band structures in the 21 . 79 ∘ twisted bilayer PtTe 2 , affecting its classification as metallic or insulating. These results demonstrate the importance of obtaining a correct description of stacking-dependent interlayer coupling in modeling delicate bilayer systems at finite twists. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗
DOE OSTI2021

Progress towards understanding ultranonlocality through the wave-vector and frequency dependence of approximate exchange-correlation kernels

In the framework of time-dependent density functional theory (TDDFT), the exact exchange-correlation (xc) kernel f xc (n, q, ω) determines the ground-state energy, excited-state energies, lifetimes, and the time-dependent linear density response of any many-electron system. The recently developed MCP07 xc kernel f xc (n, q, ω) of A. Ruzsinszky et al. [Phys. Rev. B 101, 245135 (2020)] yields excellent uniform electron gas (UEG) ground-state energies and plausible plasmon lifetimes. As MCP07 is constructed to describe f xc of the UEG, it cannot capture optical properties of real materials. To verify this claim, we follow Nazarov et al. [Phys. Rev. Lett. 102, 113001 (2009)] to construct the long-range, dynamic xc kernel, lim q→0 f xc (n, q, ω) = -α(ω)e 2 /q 2 , of a weakly inhomogeneous electron gas, using MCP07 and other common xc kernels. The strong wavevector and frequency dependence of the “ultranonlocality” coefficient α(ω) is demonstrated for a variety of simple metals and semiconductors. We examine how imposing exact constraints on an approximate kernel shapes α(ω). Comparisons to kernels derived from correlated-wavefunction calculations are drawn.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Soil Moisture Stress as a Major Driver of Carbon Cycle Uncertainty

Future projections suggest an increase in drought globally with climate change. Current vegetation models typically regulate the plant photosynthetic response to soil moisture stress through an empirical function, rather than a mechanistic response where plant water potentials respond to changes in soil water. This representation of soil moisture stress may introduce significant uncertainty into projections for the terrestrial carbon cycle. We examined the use of the soil moisture limitation function in historical and future emissions scenarios in nine Earth system models. We found that soil moisture-limited productivity across models represented a large and uncertain component of the simulated carbon cycle, comparable to 3–286% of current global productivity. Approximately 40–80% of the intermodel variability was due to the functional form of the limitation equation alone. Our results highlight the importance of implementing mechanistic water limitation schemes in models and illuminate several avenues for improving projections of the land carbon sink.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

From Bethe–Salpeter Wave functions to Generalised Parton Distributions

We review recent works on the modelling of Generalised Parton Distributions within the Dyson-Schwinger formalism. We highlight how covariant computations, using the impulse approximation, allows one to fulfil most of the theoretical constraints of the GPDs. A specific attention is brought to chiral properties and especially the so-called soft pion theorem, and its link with the Axial-Vector Ward-Takahashi identity. The limitation of the impulse approximation are also explained. Beyond impulse approximation computations are reviewed in the forward case. Finally, we stress the advantages of the overlap of lightcone wave functions, and possible ways to construct covariant GPD models within this framework, in a two-body approximation

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

ANALYTICAL MODELING OF ELECTRON BACK-BOMBARDMENT INDUCED CURRENT INCREASE IN UN-GATED THERMIONIC CATHODE RF GUNS

In this paper we derive analytical expressions for the output current of an un-gated thermionic cathode RF gun in the presence of back-bombardment heating. We provide a brief overview of back-bombardment theory and discuss comparisons between the analytical back-bombardment predictions and simulation models. We then derive an expression for the output current as a function of the RF repetition rate and discuss relationships between back-bombardment, fieldenhancement, and output current. We discuss in detail the relevant approximations and then provide predictions about how the output current should vary as a function of repetition rate for some given system configurations.

Edelen, J. P.↗
DOE OSTI2021

Analytic insights into nonlocal energy transport. III. steady state Fokker Planck theory in spherical and planar geometry

This paper develops an approximate steady state Fokker Planck theory for energetic electron transport in a spherical laser fusion target. First, we apply the theory to only a small population of electrons, which is specified at the outset. Then, one determines the nonlocal electron energy flux of these electrons at a particular position. These energetic electrons may either come from the tail of the thermal distribution function or be generated by an instability. This paper develops two approximate methods of solution, which we call the “characteristic method” and “sparse eigenfunction.” The former works only in planar geometry and the latter in both planar and spherical geometry. Comparison of the two methods in planar geometry shows that even though the approximations are very different, they give about the same result, increasing their credibility. For the example we have chosen, spherical effects are not important for electrons from the tail of the distribution function but may well be for instability generated electrons, which have much higher energy. Comparing planar to spherical, one finds an additional spherical barrier protecting the fuel. It turns out that the associated fuel preheat a Fokker Planck model predicts is considerably less than that predicted by the Krook models as developed at both NRL and other places.

Manheimer, Wallace (ORCID:0000000163342591)↗
DOE OSTI2015

Investigating the domain of validity of the Gubser solution to the Boltzmann equation

Here, we study the evolution of the one particle distribution function that solves exactly the relativistic Boltzmann equation within the relaxation time approximation for a conformal system undergoing simultaneously azimuthally symmetric transverse and boost-invariant longitudinal expansion. We show, for arbitrary values of the shear viscosity to entropy density ratio, that the distribution function can become negative in certain kinematic regions of the available phase space depending on the boundary conditions. For thermal equilibrium initial conditions, we determine numerically the physical boundary in phase space where the distribution function is always positive definite. The requirement of positivity of this particular exact solution restricts its domain of validity, and it imposes physical constraints on its applicability.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Modeling surface roughness scattering in metallic nanowires

Ando's model provides a rigorous quantum-mechanical framework for electron-surface roughness scattering, based on the detailed roughness structure. We apply this method to metallic nanowires and improve the model introducing surface roughness distribution functions on a finite domain with analytical expressions for the average surface roughness matrix elements. This approach is valid for any roughness size and extends beyond the commonly used Prange-Nee approximation. The resistivity scaling is obtained from the self-consistent relaxation time solution of the Boltzmann transport equation and is compared to Prange-Nee's approach and other known methods. The results show that a substantial drop in resistivity can be obtained for certain diameters by achieving a large momentum gap between Fermi level states with positive and negative momentum in the transport direction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Beam Signal Recovery Using Wiener Deconvolution

This project explores the use of Wiener deconvolution to recover an original signal that has been distorted by a known transfer function and by noise. A simulated Gaussian pulse was used as the test signal, and a transfer function was applied in the frequency domain to model system distortion. Controlled noise was then introduced to approximate real-world signal degradation. A Wiener filter was implemented to reverse the effects of the transfer function while minimizing the influence of noise. The recovered signal was compared to the original pulse to evaluate the effectiveness of the filter. Results demonstrate that Wiener deconvolution offers a stable and effective approach to signal recovery, balancing complete transfer function inversion and noise suppression.

Campbell, Savanna [El Camino Coll.]↗
DOE OSTI2018

Effect of Pressure on the Electronic, Magnetic, and Optical Properties of the In{sub 0.75}Cr{sub 0.25}P Compound

Using the density functional theory (DFT) approach and full-potential linearized augmented plane waves (FP-LAPW) method, some of the electronic (density of states, band structure, and Fermi surfaces), magnetic (total and local magnetic moments, spin polarization, exchange constants), and optical properties (dielectric function, energy loss function, and refractive index) were investigated. The GGA + U approximation was used for the exchange-correlation term. The effect of hydrostatic pressure up to 20 GP has been studied on these properties. The results show that the In{sub 0.75}Cr{sub 0.25}P compound is a half metal with 100% spin polarization at the Fermi level and the increment of pressure does not change its half-metallic behavior. The half-metal gap achieved for this compound is variable between 1.38 and 1.5 eV. The interaction between Cr and P atoms in this compound is an anti-ferromagnetic type. It was observed that the total magnetic moment for this compound is about 3 μ{sub B}. Local magnetic moments change with increasing pressure, but the total magnetic moment remains unaffected by increasing the pressure. Calculations of the optical properties of the In{sub 0.75}Cr{sub 0.25}P compound showed that the dominant mechanism for the low-energy photons is due to the induced free carriers of the Cr atom, and the optical properties of this compound, in particular the refractive index in the visible region, change with increasing pressure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗