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All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Theories of multiple equilibria and weather regimes : A critical reexamination. II - Baroclinic two-layer models

Previous results based on low- and intermediate-order truncations of the two-layer model suggest the existence of multiple equilibria and/or multiple weather regimes for the extratropical large-scale flow. The importance of the transient waves in the synoptic scales in organizing the large-scale flow and in the maintenance of weather regimes was emphasized. The result shows that multiple equilibria/weather regimes that are present in lower-order models examined disappear when a sufficient number of modes are kept in the spectral expansion of the solution to the governing partial differential equations. Much of the chaotic behavior of the large-scale flow that is present in intermediate-order models is now found to be spurious. Physical reasons for the drastic modification are offered. A peculiarity in the formulation of most existing two-layer models is noted that also tends to exaggerate the importance of baroclinic processes and increase the degree of unpredictability of the large-scale flow.

Cehelsky, Priscilla↗
NASA NTRS1989

Seismic analysis of the solar interior. I - Can opacity changes improve the theoretical frequencies?

The paper describes the application of seismic inverse theory to the deduction of properties of the solar interior using presently available measured frequencies of the solar oscillations. Only the solar opacity is included in this application. This study has used the spectral expansion method of Lanczos and Jackson to derive changes to the opacity which improve agreement between the theoretical and observed frequencies of oscillation. It is found that a family of opacity changes exists which yields models that improve the frequency agreement by amounts that are indistinguishable among the family members.

Korzennik, Sylvain G.↗
NASA NTRS1989

Dynamics of baroclinic wave systems

The research carried out in the past year dealt with nonlinear baroclinic wave dynamics. The model consisted of an Eady baroclinic basic state and uneven Elkman dissipation at the top and bottom boundaries with/without slopes. The method of solution used a truncated spectral expansion with three zonal waves and one or two meridional modes. Numerical experiments were performed on synoptic scale waves or planetary scale waves with/without wave-wave interaction.

Barcilon, Albert↗
NASA NTRS1989

Parallel pseudospectral domain decomposition techniques

The influence of interface boundary conditions on the ability to parallelize pseudospectral multidomain algorithms is investigated. Using the properties of spectral expansions, a novel parallel two domain procedure is generalized to an arbitrary number of domains each of which can be solved on a separate processor. This interface boundary condition considerably simplifies influence matrix techniques.

Gottlieb, David↗
NASA NTRS1984

A spectral element method for fluid dynamics - Laminar flow in a channel expansion

A spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible Navier-Stokes equations. In the spectral element discretization, the computational domain is broken into a series of elements, and the velocity in each element is represented as a high-order Lagrangian interpolant through Chebyshev collocation points. The hyperbolic piece of the governing equations is then treated with an explicit collocation scheme, while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle. The implementation of the technique is demonstrated on a one-dimensional inflow-outflow advection-diffusion equation, and the method is then applied to laminar two-dimensional (separated) flow in a channel expansion. Comparisons are made with experiment and previous numerical work.

Patera, A. T.↗
NASA NTRS1983

Viscous, resistive MHD stability computed by spectral techniques

Expansions in Chebyshev polynomials are used to study the linear stability of one dimensional magnetohydrodynamic (MHD) quasi-equilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds like numbers involving Alfven speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds like numbers. Marginal stability curves, growth rates versus Reynolds like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result which appears general is that instability was found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.

Dahlburg, R. B.↗
NASA NTRS1983

Viscous, resistive magnetohydrodynamic stability computed by spectral techniques

Expansions in Chebyshev polynomials are used to study the linear stability of one-dimensional magnetohydrodynamic quasi-equilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds-like numbers involving Alfven speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds-like numbers. Marginal stability curves, growth rates versus Reynolds-like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result that appears general is that instability has been found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three-dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.

Dahlburg, R. B.↗
NASA NTRS1977

The expansion velocities of laser-produced plasmas determined from extreme ultraviolet spectral line profiles

The expansion of laser-produced plasma is determined from the shapes of spectral lines of highly ionized iron emitted in the extreme ultraviolet. The plasmas were produced by focusing the pulse from a Nd:glass laser onto solid planar targets, and spectra were recorded with a high-resolution grazing-incidence spectrograph. From the Doppler broadening of lines of Fe XX and Fe XXI, expansion velocities of about 830 km/s were determined. The relative time-averaged ion abundances of Fe XVIII, Fe XIX, Fe XX, and Fe XXI are estimated for three different spectra. The abundances do not differ by more than a factor of 4 for any of the spectra.

Feldman, U.↗
NASA NTRS2019

NICER Discovers Spectral Lines During Photospheric Radius Expansion Bursts from 4U 1820-30: Evidence for Burst-Driven Winds

We report the discovery with the Neutron Star Interior Composition Explorer (NICER) of narrow emission and absorption lines during photospheric radius expansion (PRE) X-ray bursts from the ultracompact binary 4U 1820 −30. NICER observed 4U 1820−30 in 2017 August during a low-flux, hard spectral state, accumulating about 60 ks of exposure. Five thermonuclear X-ray bursts were detected, of which four showed clear signs of PRE. We extracted spectra during the PRE phases and fit each to a model that includes a Comptonized component to describe the accretion-driven emission, and a blackbody for the burst thermal radiation. The temperature and spherical emitting radius of the fitted blackbody are used to assess the strength of PRE in each burst. The two strongest PRE bursts (burst pair 1) had blackbody temperatures of ≈0.6 keV and emitting radii of ≈100 km (at a distance of 8.4 kpc). The other two bursts (burst pair 2) had higher temperatures (≈0.67 keV) and smaller radii (≈75 km). All of the PRE bursts show evidence of narrow line emission near 1 keV. By coadding the PRE phase spectra of burst pairs 1 and, separately, 2, we find, in both coadded spectra, significant, narrow, spectral features near 1.0 (emission), 1.7, and 3.0 keV (both in absorption). Remarkably, all the fitted line centroids in the coadded spectrum of burst pair 1 appear systematically blueshifted by a factor of 1.046±0.006 compared to the centroids of pair 2, strongly indicative of a gravitational shift, a wind-induced blueshift, or more likely some combination of both effects. The observed shifts are consistent with this scenario in that the stronger PRE bursts in pair 1 reach larger photospheric radii, and thus have weaker gravitational redshifts, and they generate faster outflows, yielding higher blueshifts. We discuss possible elemental identifications for the observed features in the context of recent burst-driven wind models.

Strohmayer, T. E.↗
NASA NTRS1991

Continuum opacity produced by spectral lines in supernovae and similar expansions

Within rapidly expanding objects such as supernovae, the large velocity gradient Doppler spreads the spectral lines to such an extent that even relatively weak transitions affect the propagation of radiation. It is shown that under appropriate conditions (involving the separation between lines and the velocity gradient), the effects of many lines within a small frequency interval produce a contribution to the transfer equation which acts like an ordinary continuum opacity. This expansion opacity is a surprisingly simple function of the Sobolev optical depth of the lines. The dependence of this opacity on frequency, temperature, density, velocity gradient (1/time), and heavy element abundance is evaluated.

Wagoner, Robert V.↗
DOE OSTI2022

Spectral function for 4 He using the Chebyshev expansion in coupled-cluster theory

Here, we compute spectral function for 4 He by combining coupled-cluster theory with an expansion of integral transforms into Chebyshev polynomials. Our method allows us to estimate the uncertainty of spectral reconstruction. The properties of the Chebyshev polynomials make the procedure numerically stable and considerably lower in memory usage than the typically employed Lanczos algorithm. We benchmark our predictions with other calculations in the literature and with electron-scattering data in the quasi-elastic peak. The spectral function formalism allows one to extend ab initio lepton-nucleus cross sections into the relativistic regime. This makes it a promising tool for modeling this process at higher-energy transfers. The results we present open the door for studies of heavier nuclei, important for the neutrino oscillation programs.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Physics-based adaptivity of a spectral method for the Vlasov–Poisson equations based on the asymmetrically-weighted Hermite expansion in velocity space

We propose a spectral method for the 1D-1V Vlasov–Poisson system where the discretization in velocity space is based on asymmetrically-weighted Hermite functions, dynamically adapted via a scaling α and shifting u of the velocity variable. Specifically, at each time instant an adaptivity criterion selects new values of α and u based on the numerical solution of the discrete Vlasov–Poisson system obtained at that time step. Once the new values of the Hermite parameters α and u are fixed, the Hermite expansion is updated and the discrete system is further evolved for the next time step. The procedure is applied iteratively over the desired temporal interval. The key aspects of the adaptive algorithm are: the map between approximation spaces associated with different values of the Hermite parameters that preserves total mass, momentum and energy; and the adaptivity criterion to update α and u based on physics considerations relating the Hermite parameters to the average velocity and temperature of each plasma species. For the discretization of the spatial coordinate, we rely on Fourier functions and use the implicit midpoint rule for time stepping. The resulting numerical method possesses intrinsically the property of fluid-kinetic coupling, where the low-order terms of the expansion are akin to the fluid moments of a macroscopic description of the plasma, while kinetic physics is retained by adding more spectral terms. Moreover, the scheme features conservation of total mass, momentum and energy associated in the discrete, for periodic boundary conditions. A set of numerical experiments confirms that the adaptive method outperforms the non-adaptive one in terms of accuracy and stability of the numerical solution.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2006

Anisotropic Developments for Homogeneous Shear Flows

The general decomposition of the spectral correlation tensor R(sub ij)(k) by Cambon et al. (J. Fluid Mech., 202, 295; J. Fluid Mech., 337, 303) into directional and polarization components is applied to the representation of R(sub ij)(k) by spherically averaged quantities. The decomposition splits the deviatoric part H(sub ij)(k) of the spherical average of R(sub ij)(k) into directional and polarization components H(sub ij)(sup e)(k) and H(sub ij)(sup z)(k). A self-consistent representation of the spectral tensor in the limit of weak anisotropy is constructed in terms of these spherically averaged quantities. The directional polarization components must be treated independently: models that attempt the same representation of the spectral tensor using the spherical average H(sub ij)(k) alone prove to be inconsistent with Navier-Stokes dynamics. In particular, a spectral tensor consistent with a prescribed Reynolds stress is not unique. The degree of anisotropy permitted by this theory is restricted by realizability requirements. Since these requirements will be less severe in a more accurate theory, a preliminary account is given of how to generalize the formalism of spherical averages to higher expansion of the spectral tensor. Directionality is described by a conventional expansion in spherical harmonics, but polarization requires an expansion in tensorial spherical harmonics generated by irreducible representations of the spatial rotation group SO(exp 3). These expansions are considered in more detail in the special case of axial symmetry.

Cambon, Claude↗
DOE OSTI2024

Absorptive effects and classical black hole scattering

Abstract We describe an approach to incorporating the physical effects of the absorption of energy by the event horizon of black holes in the scattering amplitudes based post-Minkowskian, point-particle effective description. Absorptive dynamics are incorporated in a model-independent way by coupling the usual point-particle description to an invisible sector of gapless internal degrees-of-freedom. The leading order dynamics of this sector are encoded in the low-energy expansion of a spectral density function obtained by matching an absorption cross section in the ultraviolet description. This information is then recycled using the scattering amplitudes based Kosower-Maybee-O’Connell in-in formalism to calculate the leading absorptive contribution to the impulse and change in rest mass of a Schwarzschild black hole scattering with a second compact body sourcing a massless scalar, electromagnetic or gravitational field. The results obtained are in complete agreement with previous worldline Schwinger-Keldysh calculations and provide an alternative on-shell scattering amplitudes approach to incorporating horizon absorption effects in the gravitational two-body problem.

Physics↗
NASA NTRS1978

Calculation of optical depths from an integral of the Voigt function

The optical depth along a vertical path in an atmosphere in hydrostatic equilibrium can be calculated from an integral of the Voigt function for the case where the absorption is due to spectral lines. Series expansions are presented that allow rapid evaluation of this integral over all values of the independent variables, frequency and pressure.

Milman, A. S.↗
DOE OSTI2025

Neural chaos: A spectral stochastic neural operator

Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.

Polynomial chaos expansion↗
NASA NTRS1985

The synthesis and analysis of color images

A method is described for performing the synthesis and analysis of digital color images. The method is based on two principles. First, image data are represented with respect to the separate physical factors, surface reflectance and the spectral power distribution of the ambient light, that give rise to the perceived color of an object. Second, the encoding is made efficient by using a basis expansion for the surface spectral reflectance and spectral power distribution of the ambient light that takes advantage of the high degree of correlation across the visible wavelengths normally found in such functions. Within this framework, the same basic methods can be used to synthesize image data for color display monitors and printed materials, and to analyze image data into estimates of the spectral power distribution and surface spectral reflectances. The method can be applied to a variety of tasks. Examples of applications include the color balancing of color images, and the identification of material surface spectral reflectance when the lighting cannot be completely controlled.

Wandell, B. A.↗