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At least 1,477 records · Page 82
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Caustic-induced features in microlensing magnification probability distributions

Numerical simulations have uncovered a previously unrecognized 'bump' in the macroimage magnification probabilities produced by a planar distribution of point masses. The result could be relevant to cases of microlensing by star fields in single galaxies, for which this lensing geometry is an excellent approximation. The bump is produced by bright pairs of microimages formed by sources lying near the caustics of the lens. The numerically calculated probabilities for the magnifications in the range between 3 and 30 are significantly higher than those given by the asymptotic relation derived by Schneider. The bump present in the two-dimensional lenses appears not to exist in the magnification probability distribution produced by a fully three-dimensional lens.

Rauch, Kevin P.↗
DOE OSTI2024

Dark black holes in the mass gap

Abstract In the standard picture of stellar evolution, pair-instability — the energy loss in stellar cores due to electron-positron pair production — is predicted to prevent the collapse of massive stars into black holes with mass in the range between approximately 50 and 130 solar masses — a range known as the “black hole mass gap”. LIGO and Virgo detection of black hole binary mergers containing one or both black holes with masses in thismass gapthus challenges the standard picture, possibly pointing to an unexpected merger history, unanticipated or poorly understood astrophysical mechanisms, or new physics. Here, we entertain the possibility that a “dark sector” exists, consisting of dark electrons, dark protons, and electromagnetic-like interactions, but no nuclear forces. Dark stars would inevitably form given such dark sector constituents, possibly collapsing into black holes with masses within the mass gap. We study in detail the cooling processes necessary for successful stellar collapse in the dark sector and show that for suitable choices of the particle masses, we indeed predict populating the mass gap with dark sector black holes. In particular, we numerically find that the heavier of the two dark sector massive particles cannot be lighter than, approximately, the visible sector proton for the resulting dark sector black holes to have masses within the mass gap. We discuss constraints on this scenario and how to test it with future, larger black hole merger statistics.

Astronomy & Astrophysics↗
NASA NTRS1998

A Modified Through-Flow Wave Rotor Cycle with Combustor Bypass Ducts

A wave rotor cycle is described which avoids the inherent problem of combustor exhaust gas recirculation (EGR) found in four-port, through-flow wave rotor cycles currently under consideration for topping gas turbine engines. The recirculated hot gas is eliminated by the judicious placement of a bypass duct which transfers gas from one end of the rotor to the other. The resulting cycle, when analyzed numerically, yields an absolute mean rotor temperature 18% below the already impressive value of the conventional four-port cycle (approximately the turbine inlet temperature). The absolute temperature of the gas leading to the combustor is also reduced from the conventional four-port design by 22%. The overall design point pressure ratio of this new bypass cycle is approximately the same as the conventional four-port cycle. This paper will describe the EGR problem and the bypass cycle solution including relevant wave diagrams. Performance estimates of design and off-design operation of a specific wave rotor will be presented. The results were obtained using a one-dimensional numerical simulation and design code.

Paxson Daniel E.↗
NASA NTRS1988

Hybrid transfinite element modeling/analysis of nonlinear heat conduction problems involving phase change

The present paper describes the applicability of hybrid transfinite element modeling/analysis formulations for nonlinear heat conduction problems involving phase change. The methodology is based on application of transform approaches and classical Galerkin schemes with finite element formulations to maintain the modeling versatility and numerical features for computational analysis. In addition, in conjunction with the above, the effects due to latent heat are modeled using enthalpy formulations to enable a physically realistic approximation to be dealt computationally for materials exhibiting phase change within a narrow band of temperatures. Pertinent details of the approach and computational scheme adapted are described in technical detail. Numerical test cases of comparative nature are presented to demonstrate the applicability of the proposed formulations for numerical modeling/analysis of nonlinear heat conduction problems involving phase change.

Tamma, Kumar K.↗
NASA NTRS1977

Numerical simulation of spacecraft charging phenomena

A numerical simulation program is being constructed having the following features: (1) infinite circular cylindrical geometry with angle-dependence, (2) inclusion of incident particles, photoelectrons, secondary electrons, backscattered electrons, any gun emissions, and any internal current pathways including surface conductive layers, (3) quasistatic time-dependent iteration, in which sheath potential changes during particle transit times are ignored, (4) use of approximate, locally-dependent space charge density expressions in solving Poisson's equation for sheath potentials, with use of numerical orbit-following to determine surface currents, and (5) incident particle velocity distributions isotropic or beam-like, or some superposition of these. Rationales for each of these features are discussed.

Laframboise, J. G.↗
NASA NTRS1980

Two-stream approximations to radiative transfer in planetary atmospheres - A unified description of existing methods and a new improvement

Existing two-stream approximations to radiative transfer theory for particulate media are shown to be represented by identical forms of coupled differential equations if the intensity is replaced by integrals of the intensity over hemispheres. One set of solutions thus suffices for all methods and provides convenient analytical comparisons. The equations also suggest modifications of the standard techniques so as to duplicate exact solutions for thin atmospheres and thus permit accurate determinations of the effects of typical aerosol layers. Numerical results for the plane albedos of plane-parallel atmospheres are given for conventional and modified Eddington approximations, conventional and modified two-point quadrature schemes, the hemispheric-constant method and the delta-function method, all for comparison with accurate discrete-ordinate solutions. A new two-stream approximation is introduced that reduces to the modified Eddington approximation in the limit of isotropic phase functions and to the exact solution in the limit of extreme anisotropic scattering. Comparisons of plane albedos and transmittances show the new method to be generally superior over a wide range of atmospheric conditions (including cloud and aerosol layers), especially in the case of nonconservative scattering.

Meador, W. E.↗
NASA NTRS2000

A Posteriori Error Estimation for Finite Volume and Finite Element Approximations Using Broken Space Approximation

We consider a posteriori error estimates for finite volume and finite element methods on arbitrary meshes subject to prescribed error functionals. Error estimates of this type are useful in a number of computational settings: (1) quantitative prediction of the numerical solution error, (2) adaptive meshing, and (3) load balancing of work on parallel computing architectures. Our analysis recasts the class of Godunov finite volumes schemes as a particular form of discontinuous Galerkin method utilizing broken space approximation obtained via reconstruction of cell-averaged data. In this general framework, weighted residual error bounds are readily obtained using duality arguments and Galerkin orthogonality. Additional consideration is given to issues such as nonlinearity, efficiency, and the relationship to other existing methods. Numerical examples are given throughout the talk to demonstrate the sharpness of the estimates and efficiency of the techniques. Additional information is contained in the original.

Barth, Timothy J.↗
DOE OSTI2020

A Method for Dimensionally Adaptive Sparse Trigonometric Interpolation of Periodic Functions

We present a method for dimensionally adaptive sparse trigonometric interpolation of multidimensional periodic functions belonging to a smoothness class of finite order. This method targets applications where periodicity must be preserved and the precise anisotropy is not known a priori. To the authors' knowledge, this is the first instance of a dimensionally adaptive sparse interpolation algorithm that uses a trigonometric interpolation basis. The motivating application behind this work is the adaptive approximation of a multi-input model for a molecular potential energy surface (PES) where each input represents an angle of rotation. Our method is based on an anisotropic quasi-optimal estimate for the decay rate of the Fourier coefficients of the model; a least-squares fit to the coefficients of the interpolant is used to estimate the anisotropy. Thus, our adaptive approximation strategy begins with a coarse isotropic interpolant, which is gradually refined using the estimated anisotropic rates. The procedure takes several iterations where ever-more accurate interpolants are used to generate ever-improving anisotropy rates. We present several numerical examples of our algorithm where the adaptive procedure successfully recovers the theoretical “best” convergence rate, including an application to a periodic PES approximation. An open-source implementation of our algorithm resides in the Tasmanian UQ library developed at Oak Ridge National Laboratory.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

Explicit and implicit compact high-resolution shock-capturing methods for multidimensional Euler equations 1: Formulation

Two classes of explicit compact high-resolution shock-capturing methods for the multidimensional compressible Euler equations for fluid dynamics are constructed. Some of these schemes can be fourth-order accurate away from discontinuities. For the semi-discrete case their shock-capturing properties are of the total variation diminishing (TVD), total variation bounded (TVB), total variation diminishing in the mean (TVDM), essentially nonoscillatory (ENO), or positive type of scheme for 1-D scalar hyperbolic conservation laws and are positive schemes in more than one dimension. These fourth-order schemes require the same grid stencil as their second-order non-compact cousins. One class does not require the standard matrix inversion or a special numerical boundary condition treatment associated with typical compact schemes. Due to the construction, these schemes can be viewed as approximations to genuinely multidimensional schemes in the sense that they might produce less distortion in spherical type shocks and are more accurate in vortex type flows than schemes based purely on one-dimensional extensions. However, one class has a more desirable high-resolution shock-capturing property and a smaller operation count in 3-D than the other class. The extension of these schemes to coupled nonlinear systems can be accomplished using the Roe approximate Riemann solver, the generalized Steger and Warming flux-vector splitting or the van Leer type flux-vector splitting. Modification to existing high-resolution second- or third-order non-compact shock-capturing computer codes is minimal. High-resolution shock-capturing properties can also be achieved via a variant of the second-order Lax-Friedrichs numerical flux without the use of Riemann solvers for coupled nonlinear systems with comparable operations count to their classical shock-capturing counterparts. The simplest extension to viscous flows can be achieved by using the standard fourth-order compact or non-compact formula for the viscous terms.

Yee, H. C.↗
NASA NTRS1985

Numerical solution of the unsteady Navier-Stokes equation

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws are discussed. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most first-order accuracy, in the sense of truncation error, at extrema of the solution. In this paper a uniformly second-order approximation is constructed, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Osher, Stanley J.↗
DOE OSTI2022

Droplet formation simulation using mixed finite elements

Droplet formation happens in finite time due to the surface tension force. The linear stability analysis is useful to estimate the size of a droplet but fails to approximate the shape of the droplet. This is due to a highly nonlinear flow description near the point where the first pinch-off happens. A one-dimensional axisymmetric mathematical model was first developed by Eggers and Dupont [“Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] using asymptotic analysis. This asymptotic approach to the Navier–Stokes equations leads to a universal scaling explaining the self-similar nature of the solution. Numerical models for the one-dimensional model were developed using the finite difference [Eggers and Dupont, “Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] and finite element method [Ambravaneswaran et al., “Drop formation from a capillary tube: Comparison of one-dimensional and two-dimensional analyses and occurrence of satellite drops,” Phys. Fluids 14, 2606–2621 (2002)]. The focus of this study is to provide a robust computational model for one-dimensional axisymmetric droplet formation using the Portable, Extensible Toolkit for Scientific Computation. The code is verified using the Method of Manufactured Solutions and validated using previous experimental studies done by Zhang and Basaran [“An experimental study of dynamics of drop formation,” Phys. Fluids 7, 1184–1203 (1995)]. The present model is used for simulating pendant drops of water, glycerol, and paraffin wax, with an aspiration of extending the application to simulate more complex pinch-off phenomena.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1987

Effective propagation constants in dense random media under effective medium approximation

The effective medium approximation is applied to study the effective propagation constants in a dense random medium. The dyadic Green's function is introduced to establish the effective medium approximation formalism for electromagnetic waves. The multiple scattering equations and the Lippmann-Schwinger equations for the transition operator are obtained in the configuration average form. The dispersion equations of multiple scattering is derived by using a standard method in quantum mechanics. To obtain an expression for the effective propagation constants the matrix elements of the configuration average dyadic transiton operator are calculated in momentum representation. Numerical illustations are carried out to demonstrate the difference in the effective propagation constants between the use of this approximation and the well-known quasi-crystalline approximation. A comparison is made with measured loss tangent in dry snow.

Zhu, P. Y.↗
NASA NTRS1978

A model for close encounters in the planetary problem

A model is proposed for single close encounters between two small masses, m1 and m2, which orbit a much larger mass, M. The main new feature of the model is the assumption of conic motion of the center of mass of m1 and m2 in the gravitational field of M. Comparisons of the model with the three-body equations of motion indicate that the model is a useful approximation for m1, m2 not exceeding 0.00001 M. The model is therefore applicable for encounters between bodies of the order of an earth mass or smaller in the presence of the sun. Comparisons are also made of outcomes obtained by the model with outcomes of numerical integration for a large variety of close encounters. The above comparisons reveal that for many purposes the model is an adequate approximation for encounters with an eccentricity of the hyperbolic orbit of m1 about m2 not less than 4.

Cox, L. P.↗
NASA NTRS2001

Computation of Nonlinear Backscattering Using a High-Order Numerical Method

The nonlinear Schrodinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way artificial boundary conditions (ABCs) to solve the NLH as a boundary value problem. Our numerical methodology allows for a direct comparison of the NLH and NLS models and for an accurate quantitative assessment of the backscattered signal.

Fibich, G.↗
NASA NTRS1979

A simplified model for the viscous crossflow in a slotted test section

A simplified physical model was constructed which simulates the viscous crossflow in a fluid layer near the slots at a fixed streamwise location in a slotted wind tunnel. For low to moderate Reynolds numbers, numerical solutions of the two dimensional, incompressible Navier-Stokes equations in stream function and vorticity, which govern the model flow, were obtained. Fairly general slot geometry was incorporated by means of the Thompson-Thames-Mastin transformation. An approximate factorization scheme with cyclic acceleration parameters was employed to solve a finite difference analog of the stream function equation. The vorticity equation was numerically solved with a modified version of the classical alternating direction implicit scheme. Although no quantitative assessment of solution accuracy can be made, numerical results for variations in incremental wall pressure around the slat are at least qualitatively similar to some experimental results.

Cooke, C. H.↗
DOE OSTI2024

A Provably Accurate Randomized Sampling Algorithm for Logistic Regression

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we present a simple, randomized sampling-based algorithm for logistic regression problem that guarantees high-quality approximations to both the estimated probabilities and the overall discrepancy of the model. Our analysis builds upon two simple structural conditions that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized numerical linear algebra. We analyze the properties of estimated probabilities of logistic regression when leverage scores are used to sample observations, and prove that accurate approximations can be achieved with a sample whose size is much smaller than the total number of observations. To further validate our theoretical findings, we conduct comprehensive empirical evaluations. Overall, our work sheds light on the potential of using randomized sampling approaches to efficiently approximate the estimated probabilities in logistic regression, offering a practical and computationally efficient solution for large-scale datasets.

Chowdhury, Agniva↗
DOE OSTI2020

A holey cavity for single-transducer 3D ultrasound imaging with physical optimization

Within the compressive sensing (CS) framework, one effective way to increase the likelihood of successful signal reconstruction is to employ random processes in the construction of the sensing matrix. This work presents a 3D holey cavity, with diverse frequency modes, to spectrally code, that is, randomize, the ultrasound wave fields. The simulated results show that the use of such a cavity enables imaging simple or complex targets, such as spheres or the letter E, by only a single transceiver—something that is not possible without the use of a coding structure like the cavity. The effect of noise on imaging results and the size of the targets on the first-order Born approximation (BA) are also investigated. Moreover, this study attempts to optimize the cavity, based on a single numerical metric, such as the sum of singular values (SSV) or mutual coherence (MC). Yet, it will be shown that neither of these metrics can consistently compare the norm-one imaging performance between two cavities of different materials or hole sizes. This leaves finding a quantitative metric for these kinds of optimizations an open problem.

42 ENGINEERING↗
NASA NTRS2011

Observational and Numerical Diagnostics of Galaxy Cluster Outer Regions

Aims. We present the analysis of a local (z = 0.04 - 0.2) sample of 31 galaxy clusters with the aim of measuring the density of the X-ray emitting gas in cluster outskirts. We compare our results with numerical simulations to set constraints on the azimuthal symmetry and gas clumping in the outer regions of galaxy clusters. Methods. We exploit the large field-of-view and low instrumental background of ROSAT/PSPC to trace the density of the intracluster gas out to the virial radius. We perform a stacking of the density profiles to detect a signal beyond r(sub 200) and measure the typical density and scatter in cluster outskirts. We also compute the azimuthal scatter of the profiles with respect to the mean value to look for deviations from spherical symmetry. Finally, we compare our average density and scatter profiles with the results of numerical simulations. Results. As opposed to several recent results, we observe a steepening of the density profiles beyond approximately 0.3r(sub 500). Comparing our density profiles with simulations, we find that non-radiative runs predict too steep density profiles, whereas runs including additional physics and/or gas clumping are in better agreement with the observed gas distribution. We note a systematic difference between cool-core and non-cool core clusters beyond approximately 0.3r(sub 200), which we explain by a different distribution of the gas in the two classes. Beyond approximately r(sub 500), galaxy clusters deviate significantly from spherical symmetry, with only little differences between relaxed and disturbed systems. We find good agreement between the observed and predicted scatter profiles, but only when the 1% densest clumps are filtered out in the simulations. Conclusions. The general trend of steepening density around the virial radius indicates that the shallow density profiles found in several recent works were probably obtained along particular directions (e.g., filaments) and are not representative of the typical behavior of clusters. Comparing our results with numerical simulations, we find that non-radiative simulations fail to reproduce the gas distribution, even well outside cluster cores. Therefore, a detailed treatment of gas cooling, star formation, clumping, and AGN feedback is required to construct realistic models of cluster outer regions.

Eckert, D.↗