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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Near-axis expansion of stellarator equilibrium at arbitrary order in the distance to the axis

A direct construction of equilibrium magnetic fields with toroidal topology at arbitrary order in the distance from the magnetic axis is carried out, yielding an analytical framework able to explore the landscape of possible magnetic flux surfaces in the vicinity of the axis. This framework can provide meaningful analytical insight into the character of high-aspect-ratio stellarator shapes, such as the dependence of the rotational transform and the plasma beta limit on geometrical properties of the resulting flux surfaces. The approach developed here is based on an asymptotic expansion on the inverse aspect ratio of the ideal magnetohydrodynamics equation. The analysis is simplified by using an orthogonal coordinate system relative to the Frenet–Serret frame at the magnetic axis. The magnetic field vector, the toroidal magnetic flux, the current density, the field line label and the rotational transform are derived at arbitrary order in the expansion parameter. Moreover, a comparison with a near-axis expansion formalism employing an inverse coordinate method based on Boozer coordinates (the so-called Garren–Boozer construction) is made, where both methods are shown to agree at lowest order. Finally, as a practical example, a numerical solution using a W7-X equilibrium is presented, and a comparison between the lowest-order solution and the W7-X magnetic field is performed.

Physics↗
NASA NTRS1992

The three-dimensional turbulent boundary layer near a plane of symmetry

The asymptotic structure of the three-dimensional turbulent boundary layer near a plane of symmetry is considered in the limit of large Reynolds number. A self-consistent two-layer structure is shown to exist wherein the streamwise velocity is brought to rest through an outer defect layer and an inner wall layer in a manner similar to that in two-dimensional boundary layers. The cross-stream velocity distribution is more complex and two terms in the asymptotic expansion are required to yield a complete profile which is shown to exhibit a logarithmic region. The flow in the inner wall layer is demonstrated to be collateral to leading order; pressure-gradient effects are formally of higher order but can cause the velocity profile to skew substantially near the wall at the large but finite Reynolds numbers encountered in practice. The governing set of ordinary differential equations describing a self-similar flow is derived. The calculated numerical solutions of these equations are matched asymptotically to an inner wall-layer solution and the results show trends that are consistent with experimental observations.

Degani, A. T.↗
NASA NTRS1991

Techniques for developing approximate optimal advanced launch system guidance

An extension to the authors' previous technique used to develop a real-time guidance scheme for the Advanced Launch System is presented. The approach is to construct an optimal guidance law based upon an asymptotic expansion associated with small physical parameters, epsilon. The trajectory of a rocket modeled as a point mass is considered with the flight restricted to an equatorial plane while reaching an orbital altitude at orbital injection speeds. The dynamics of this problem can be separated into primary effects due to thrust and gravitational forces, and perturbation effects which include the aerodynamic forces and the remaining inertial forces. An analytic solution to the reduced-order problem represented by the primary dynamics is possible. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in an asymptotic series where the zeroth-order term (epsilon = 0) can be obtained in closed form.

Feeley, Timothy S.↗
NASA NTRS1993

The structure of a three-dimensional turbulent boundary layer

The three-dimensional turbulent boundary layer is shown to have a self-consistent two-layer asymptotic structure in the limit of large Reynolds number. In a streamline coordinate system, the streamwise velocity distribution is similar to that in two-dimensional flows, having a defect-function form in the outer layer which is adjusted to zero at the wall through an inner wall layer. An asymptotic expansion accurate to two orders is required for the cross-stream velocity which is shown to exhibit a logarithmic form in the overlap region. The inner wall-layer flow is collateral to leading order but the influence of the pressure gradient, at large but finite Reynolds numbers, is not negligible and can cause substantial skewing of the velocity profile near the wall. Conditions under which the boundary layer achieves self-similarity and the governing set of ordinary differential equations for the outer layer are derived. The calculated solution of these equations is matched asymptotically to an inner wall-layer solution and the composite profiles so formed describe the flow throughout the entire boundary layer. The effects of Reynolds number and cross-stream pressure gradient on the crossstream velocity profile are discussed and it is shown that the location of the maximum cross-stream velocity is within the overlap region.

Degani, A. T.↗
DOE OSTI2022

Interpolating between small- and large-$\mathscr{g}$ expansions using Bayesian model mixing

Bayesian model mixing (BMM) is a statistical technique that can be used to combine models that are predictive in different input domains into a composite distribution that has improved predictive power over the entire input space. We explore the application of BMM to the mixing of two expansions of a function of a coupling constant $\mathscr{g}$ that are valid at small and large values of $\mathscr{g}$ respectively. This type of problem is quite common in nuclear physics, where physical properties are straightforwardly calculable in strong and weak interaction limits or at low and high densities or momentum transfers, but difficult to calculate in between. Interpolation between these limits is often accomplished by a suitable interpolating function, e.g., Padé approximants, but it is then unclear how to quantify the uncertainty of the interpolant. We address this problem in the simple context of the partition function of zero-dimensional Φ 4 theory, for which the (asymptotic) expansion at small $\mathscr{g}$ and the (convergent) expansion at large $\mathscr{g}$ are both known. We consider three mixing methods: linear mixture BMM, localized bivariate BMM, and localized multivariate BMM with Gaussian processes. Here, we find that employing a Gaussian process in the intermediate region between the two predictive models leads to the best results of the three methods. The methods and validation strategies we present here should be generalizable to other nuclear physics settings.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1973

Dynamics of Flexible Spinning Satellites with Radial Wire Antennas

A dynamic analysis is presented for a spin stabilized spacecraft employing four radial wire antennas with tip masses, a configuration first employed in the IMP-J spacecraft. The use of wires in place of the usual booms represents the ultimate in weight reduction at the expanse of flexibility. The satellite is modelled as a 14 degree of freedom system, and the linearized equations of motion are found. The lowest order vibrational modes and natural frequencies of the gyroscopically coupled system are then determined. Because the satellite spin rate is decreased by antenna deployment, a spin-up maneuver is needed. The response of the time varying mode equations during spin-up is found, for the planar modes, in terms of Bessel functions and a Struve function of order -1/4. Because tables of the latter are not readily available, the particular solution is expressed in various forms including an infinite series of Bessel functions and a particularly useful asymptotic expansion.

Longman, R. W.↗
DOE OSTI2022

Likelihood Maximization and Moment Matching in Low SNR Gaussian Mixture Models

We derive an asymptotic expansion for the log-likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in the low signal-to-noise regime. The expansion reveals an intimate connection between two types of algorithms for parameter estimation: the method of moments and likelihood optimizing algorithms such as Expectation-Maximization (EM). We show that likelihood optimization in the low SNR regime reduces to a sequence of least squares optimization problems that match the moments of the estimate to the ground truth moments one by one. This connection is a stepping stone towards the analysis of EM and maximum likelihood estimation in a wide range of models. A motivating application for the study of low SNR mixture models is cryo-electron microscopy data, which can be modeled as a GMM with algebraic constraints imposed on the mixture centers. We discuss the application of our expansion to algebraically constrained GMMs, among other example models of interest. © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Renormalon cancellation and linear power correction to threshold-like asymptotics of space-like parton correlators

Abstract In this paper, we show that the common hard kernel of double-log-type or threshold-type factorization for certain space-like parton correlators that arise in the context of lattice parton distributions, theheavy-light Sudakov hard kernel, has linear infrared (IR) renormalon. We explicitly demonstrate how this IR renormalon correlates with ultraviolet (UV) renormalons of next-to-leading power operators in two explicit examples: threshold asymptotics of space-like quark-bilinear coefficient functions and transverse momentum dependent (TMD) factorization of quasi wave function amplitude. Theoretically, the pattern of renormalon cancellation complies with general expectations to marginal asymptotics in the UV limit. Practically, this linear renormalon explains the slow convergence of imaginary parts observed in lattice extraction of the Collins-Soper kernel and signals the relevance of next-to-leading power contributions. Fully factorized, fully controlled threshold asymptotic expansion for space-like quark-bilinear coefficient functions in coordinate and moment space has also been proposed.

Physics↗
DOE OSTI2022

Exact WKB and the quantum Seiberg-Witten curve for 4d $N$ = 2 pure SU(3) Yang-Mills. Abelianization

We investigate the exact WKB method for the quantum Seiberg-Witten curve of 4d N = 2 pure SU(3) Yang-Mills in the language of abelianization. The relevant differential equation is a third-order equation on $\mathbb{CP}^1$ with two irregular singularities. We employ the exact WKB method to study the solutions to such a third-order equation and the associated Stokes phenomena. We also investigate the exact quantization condition for a certain spectral problem. Moreover, exact WKB analysis leads us to consider new Darboux coordinates on a moduli space of flat SL(3,$\mathbb{C}$)-connections. In particular, in the weak coupling region we encounter coordinates of the higher length-twist type generalizing Fenchel-Nielsen coordinates. The Darboux coordinates are conjectured to admit asymptotic expansions given by the formal quantum periods series and we perform numerical analysis supporting this conjecture.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Universality aspects of quantum corrections to transverse momentum broadening in QCD media

We study non-linear quantum corrections to transverse momentum broadening (TMB) of a fast parton propagating in dense QCD matter in the leading logarithmic approximation. These non-local corrections yield an anomalous super-diffusive behavior characterized by a heavy tailed distribution which is associated with Lévy random walks. Using a formal analogy with the physics of traveling waves, we show that at late times the transverse momentum distribution tends to a universal scaling regime. We derive analytic solutions in terms of an asymptotic expansion around the scaling limit for both fixed and running coupling. We note that our analytic approach yields a good agreement with the exact numerical solutions down to realistic values of medium length. Finally, we discuss the interplay between system size and energy dependence of the diffusion coefficient $\hat{q}$ and its connection with the gluon distribution function that is manifest at large transverse momentum transfer.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Multiscale simulations for multi-continuum Richards equations

In this paper, we study a multiscale method for simulating a dual-continuum unsaturated flow problem within complex heterogeneous fractured porous media. Mathematically, each of the dual continua is modeled by a multiscale Richards equation (for pressure head), and these equations are coupled to one another by transfer terms. On its own, Richards equation is already a nonlinear partial differential equation, and it is exceedingly difficult to solve numerically due to the extra nonlinear dependencies involving the soil water. To deal with multiple scales, our strategy is that starting from a microscopic scale, we upscale the coupled system of dual-continuum Richards equations via homogenization by the two-scale asymptotic expansion, to obtain a homogenized system, at an intermediate scale (level). Based on a hierarchical approach, the homogenization’s effective coefficients are computed through solving the arising cell problems. Furthermore, to tackle the nonlinearity, after time discretization, we use Picard iteration procedure for linearization of the homogenized Richards equations. At each Picard iteration, some degree of multiscale still remains from the intermediate level, so we utilize the generalized multiscale finite element method (GMsFEM) combining with a multi-continuum approach, to upscale the homogenized system to a macroscopic (coarse-grid) level. This scheme involves building uncoupled and coupled multiscale basis functions, which are used not only to construct coarse-grid solution approximation with high accuracy but also (with the coupled multiscale basis) to capture the interactions among continua. These prospects and convergence are demonstrated by several numerical results for the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

The role of moisture in MgCl 2 salt: A multiscale approach to TES performance

This study presents a comprehensive multiscale analysis to evaluate the influence of moisture on the thermal performance of thermal energy storage systems using magnesium chloride (MgCl 2 ) as the phase-changing material. The system uses graphite foam with 90% relative density to enhance thermal conductivity. The analysis includes thermal conductivity calculations and specific heat capacity for different hydrate phases of MgCl 2 : Anhydrous, Mono, Di, Tetra, and Hexa. These properties were evaluated for the first time using the phonon density of states from Density Functional Theory simulations. Results showed that thermal conductivity decreased, while specific heat capacity increased by a factor of two as the phase changed from anhydrous to hexahydrate. Meso-scale models were created to account for the anisotropy of graphite foam and property variations of the MgCl 2 hydrate phases. Asymptotic Expansion homogenization simulations determined the anisotropic thermal conductivity for all phases. This unique methodology improved simulation accuracy, which matched experimental data for anhydrous MgCl 2 . A parametric study examined various operating conditions and their effect on TES performance. It revealed that higher charging temperatures did not enhance exergy efficiency, but increased discharge mass flow rates improved it due to better heat transfer. Thermal performance evaluated by the exergy efficiency remained consistent across hydrate systems under the tested conditions. Furthermore, the study suggests that this uniformity is linked to missing key data, particularly latent heat and melting point for different hydrates. Overall, it highlights the importance of multiscale effects and accurate material properties in designing and optimizing TES systems.

Molten salt degradation↗
DOE OSTI2023

Interface models for three-dimensional Rayleigh–Taylor instability

We derive interface models for three-dimensional Rayleigh–Taylor instability (RTI), making use of a novel asymptotic expansion in the non-locality of the fluid flow. These interface models are derived for the purpose of studying universal features associated with RTI such as the Froude number in single-mode RTI, the predicted quadratic growth of the interface amplitude under multi-mode random perturbations, the optimal (viscous) mixing rates induced by the RTI and the self-similarity of horizontally averaged density profiles and the remarkable stabilization of the mixing layer growth rate which arises for the three-fluid two-interface heavy–light–heavy configuration, in which the addition of a third fluid bulk slows the growth of the mixing layer to a linear rate. Our interface models can capture the formation of small-scale structures induced by severe interface roll-up, reproduce experimental data in a number of different regimes and study the effects of multiple interface interactions even as the interface separation distance becomes exceedingly small. Compared with traditional numerical schemes used to study such phenomena, our models provide a computational speed-up of at least two orders of magnitude.

Mechanics↗
DOE OSTI2021

Exploring and enhancing the accuracy of interior-scaled Perdew–Zunger self-interaction correction

The Perdew–Zunger self-interaction correction (PZ-SIC) improves the performance of density functional approximations for the properties that involve significant self-interaction error (SIE), as in stretched bond situations, but overcorrects for equilibrium properties where SIE is insignificant. This overcorrection is often reduced by local scaling self-interaction correction (LSIC) of the PZ-SIC to the local spin density approximation (LSDA). Here, we propose a new scaling factor to use in an LSIC-like approach that satisfies an additional important constraint: the correct coefficient of the atomic number Z in the asymptotic expansion of the exchange–correlation (xc) energy for atoms. LSIC and LSIC+ are scaled by functions of the iso-orbital indicator z σ , which distinguishes one-electron regions from many-electron regions. LSIC+ applied to the LSDA works better for many equilibrium properties than LSDA-LSIC and the Perdew, Burke, and Ernzerhof generalized gradient approximation (GGA), and almost close to the strongly constrained and appropriately normed (SCAN) meta-GGA. LSDA-LSIC and LSDA-LSIC+, however, fail to predict interaction energies involving weaker bonds, in sharp contrast to their earlier successes. It is found that more than one set of localized SIC orbitals can yield a nearly degenerate energetic description of the same multiple covalent bond, suggesting that a consistent chemical interpretation of the localized orbitals requires a new way to choose their Fermi orbital descriptors. To make a locally scaled down SIC to functionals beyond the LSDA requires a gauge transformation of the functional’s energy density. Here, the resulting SCAN-sdSIC, evaluated on SCAN-SIC total and localized orbital densities, leads to an acceptable description of many equilibrium properties including the dissociation energies of weak bonds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Finite-difference multiple fluid solution for source-driven rotation in highly magnetized linear plasma device

The rotation profile of a magnetized plasma cylinder composed of multiple fluids is investigated analytically, expanding on previous results. The analytic steady-state solution is used as a benchmark for a time-dependent multiple-fluid finite-difference code, MITNS: Multiple-Ion Transport Numerical Solver. Magnetic field evolution is taken into account, both analytically and numerically. Its details are shown to be of importance when particles are allowed out of the domain. MITNS reproduces the asymptotic expansion results for a small parameter $δ<<<1$. For $\sqrt{m_elm_i} ~ δ << 1$ , a slightly different regime, dominated by viscosity-induced transport of ions, is found numerically and analytically. Finally, this verification supports the use of this code for more complex time-dependent calculations in the future. Additionally, we derive the angular velocity profile of each species due to radial particle and charge fluxes of various strengths.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

A Grad-Shafranov model for compact quasisymmetric stellarators

A Grad-Shafranov equation (GSE) valid for compact quasisymmetric stellarators is derived by an asymptotic expansion around a vacuum field carried to first order. We obtain an equation for the existence of flux surfaces leading up to the GSE. The flux surface label must simultaneously satisfy the existence equation and the GSE, which generally leads to an overdetermined problem. We show how the overdetermined problem can be resolved within our model for a class of hybrid devices similar to that studied by Henneberg and Plunk [Phys. Rev. Res. 6, L022052 (2024)]. We are also able to solve the existence equation for flux surfaces analytically in the most general case by introducing a special coordinate system. This will enable us to carry out an optimization seeking to minimize the error in our GSE while obeying the flux surface existence equation, which will allow us to find solutions outside the class of hybrid devices. This will allow for a coarse-grained approximate search in the space of quasisymmetric equilibria that should be faster than a conventional stellarator optimization. Nevertheless, it would still be necessary to fine-tune the approximate solutions using conventional tools to obtain a more precise optimized equilibrium.

Nikulsin, N. (ORCID:0000000318611777)↗
DOE OSTI2021

Gluon distributions and their applications to Ioffe-time distributions

We investigate unpolarized and polarized gluon distributions and their applications to the Ioffe-time distributions, which are related to lattice QCD calculations of parton distribution functions. Guided by the counting rules based on the perturbative QCD at large momentum fraction x and the color coherence of gluon couplings at small x, we parametrize gluon distributions in the helicity basis. By fitting the unpolarized gluon distribution, the inferred polarized gluon distribution from our parametrization agrees with the one from global analysis. A simultaneous fit to both unpolarized and polarized gluon distributions is also performed to explore the model uncertainty. The agreement with the global analysis supports the (1 - x) power suppression of the helicity-antialigned distribution relative to the helicity-aligned distribution. The corresponding Ioffe-time distributions and their asymptotic expansions are calculated from the gluon distributions. Our results of the Ioffe-time distributions can provide guidance to the extrapolation of lattice QCD data to the region lacking precise gluonic matrix elements. Therefore, they can help regulate the ill-posed inverse problem associated with extracting the gluon distributions from discrete data from first-principle calculations, which are available in a limited range of the nucleon momentum and the spatial separation between the gluonic currents. Given various limitations in obtaining lattice QCD data at large Ioffe time, phenomenological approaches can provide important complementary information to extract the gluon distributions in the entire momentum fraction region, especially at small x. The possibility of investigating higher-twist effects and other systematic uncertainties in the contemporary first-principle calculations of parton distributions from phenomenologically well-determined Ioffe-time distributions in the large Ioffe-time region is also discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗