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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

Particle acceleration by circularly and elliptically polarised dispersive Alfven waves in a transversely inhomogeneous plasma in the inertial and kinetic regimes

Dispersive Alfven waves (DAWs) offer, an alternative to magnetic reconnection, opportunity to accelerate solar flare particles in order to alleviate the problem of delivering flare energy to denser parts of the solar atmosphere to match x-ray observations. Here, we focus on the effect of DAW polarisation, left, right, circular and elliptical, in the different regimes inertial and kinetic, aiming to study these effects on the efficiency of particle acceleration. We use 2.5D particle-in-cell simulations to study how the particles are accelerated when DAW, triggered by a solar flare, propagates in the transversely inhomogeneous plasma that mimics solar coronal loop. (1) In the inertial regime, fraction of accelerated electrons (along the magnetic field) in the density gradient regions is {approx_equal}20% by the time when DAW develops three wavelengths and is increasing to {approx_equal}30% by the time when DAW develops thirteen wavelengths. In all considered cases, ions are heated in the transverse to the magnetic field direction and fraction of heated particles is {approx_equal}35%. (2) The case of right circular, left and right elliptical polarisation DAWs, with the electric field in the non-ignorable transverse direction exceeding several times that of in the ignorable direction, produce more pronounced parallel electron beams (with larger maximal electron velocities) and transverse ion beams in the ignorable direction. In the inertial regime, such polarisations yield the fraction of accelerated electrons 20%. In the kinetic regime, this increases to 35%. (3) The parallel electric field that is generated in the density inhomogeneity regions is independent of the electron-ion mass ratio and stays of the order 0.03 {omega}{sub pe}cm{sub e}/e which for solar flaring plasma parameters exceeds Dreicer electric field by eight orders of magnitude. (4) Electron beam velocity has the phase velocity of the DAW. Thus, electron acceleration is via Landau damping of DAWs. For the Alfven speeds of V{sub A} = 0.3c, the considered mechanism can accelerate electrons to energies circa 20 keV. (5) The increase of mass ratio from m{sub i}/m{sub e} = 16 to 73.44 increases fraction of accelerated electrons from 20% to 30-35% (depending on DAW polarisation). For the mass ratio m{sub i}/m{sub e} = 1836, the fraction of accelerated electrons would be >35%. (6) DAWs generate significant density and temperature perturbations that are located in the density gradient regions. DAWs propagating in the transversely inhomogeneous plasma can effectively accelerate electrons along the magnetic field and heat ions across it.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Asymptotic quasisymmetric high-beta three-dimensional magnetohydrodynamic equilibria near axisymmetry

Quasisymmetry (QS), a hidden symmetry of the magnetic field strength, is known to support nested flux surfaces and provide superior particle confinement in stellarators. In this work, we study the ideal magnetohydrodynamic (MHD) equilibrium and stability of high-beta plasma in a large-aspect-ratio stellarator. In particular, we show that the lowest-order description of a near-axisymmetric equilibrium vastly simplifies the problem of three-dimensional quasisymmetric MHD equilibria, which can be reduced to a standard elliptic Grad–Shafranov equation for the flux function. We show that any large-aspect-ratio tokamak, deformed periodically in the vertical direction, is a stellarator with approximate volumetric QS. We discuss exact analytical solutions and numerical benchmarks. Finally, we discuss the ideal ballooning and interchange stability of some of our equilibrium configurations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Modeling Simulation and Optimization of a Pressure Relief Feature in a Hermetically Sealed Volume Exposed to Abnormal Thermal Environments

This project investigates the behavior of a venting feature on a hermetically sealed volume under abnormal thermal environments. A pressure profile is used to simulate internal pressure build up due to thermal decomposition of foam caused by temperatures approaching 800K. For the purposes of his scoping study a small can composed of 304L stainless steel is used to emulate the problem at hand and simplify the model. The venting feature can be described as an elliptical thinned area with X-like scoring marks on the circumferential surface of the can where the highest stresses are located without the feature. The feature variables include elliptical size, depth, and quantity to optimize the venting feature geometry to vent at a desired pressure range. Cubit, SIERRA: Solid Mechanics, and Ensight modeling programs are used to simulate and analyze several iterations of this feature to determine the most optimal geometry. The model indicates through the simulations that the feature does in fact vent in a predictable manner and can be used in a variety of pressure vessel applications where uncontrolled over pressurizations are undesirable. Future work includes model validation tests, looking at different geometries, and using a more accurate failure criterion.

42 ENGINEERING↗
DOE OSTI2016

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility of the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Spectrally Stabilized Interface Capturing Formulation and Implementation in Nek5000/NekRS

This report documents the formulation of a novel level-set method for incompressible two-phase flows in the continuous Galerkin (CG) high order spectral element framework. The overall method hinges on a novel implementation of the spectral vanishing viscosity (SVV) operator for the stabilization of linear/non-linear hyperbolic problems. The multidimensional SVV convolution kernels, which in essence, have a similar effect as a high pass filter applied to the derivatives, are formulated by exploiting the tensor product form, analogous to the construction of the usual stiffness matrix system. The resulting kernels are directionally decoupled and ensure a linear, symmetric positive definite, elliptic matrix operator. The SVV formulation is demonstrated to provide a robust stabilizing mechanism through challenging linear and non-linear hyperbolic problems, including problems pertinent to the level-set formulation. The two-phase framework conceptualized herein is based on the conservative level-set (CLS) method which represents the interface between the fluids by the 0.5 iso-contour of the smoothed Heaviside function. The CLS method is augmented with a preconditioning procedure for interface normals using the signed distance function which precludes the manifestation of spurious oscillations in the vicinty of the interface. Further, the existing mixed explicit-implicit approach for the solution of Navier-Stokes equations in Nek5000, as described in Tomboulides et al, is augmented with a pressure coefficient splitting approach for the Poisson equation, which greatly accelerated the convergence of pressure solver for two-phase systems with large density ratio. The robustness and accuracy of the overall two-phase method is demonstrated through canonical challenging problems involving high density and viscosity ratios, with and without surface tension. The two-phase formulation is wholly implemented in Nek5000 and the SVV stabilization method is implemented in NekRS, which is the essential precursor to the two-phase framework, undergoing active development.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Discrete restricted four-body problem: Existence of proof of equilibria and reproducibility of periodic orbits

We propose the discrete-time restricted four-body problem (d-R4BP), which approximates the orbits of the restricted four-body problem (R4BP). The d-R4BP is given as a special case of the discrete-time chain regularization of the general N-body problem published in Minesaki. Moreover, we analytically prove that the d-R4BP yields the correct orbits corresponding to the elliptic relative equilibrium solutions of the R4BP when the three primaries form an equilateral triangle at any time. Such orbits include the orbit of a relative equilibrium solution already discovered by Baltagiannis and Papadakis. Until the proof in this work, there has been no discrete analog that preserves the orbits of elliptic relative equilibrium solutions in the R4BP. For a long time interval, the d-R4BP can precisely compute some stable periodic orbits in the Sun–Jupiter–Trojan asteroid–spacecraft system that cannot necessarily be reproduced by other generic integrators.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Applying Physics-Informed Neural Networks to Solve Navier–Stokes Equations for Laminar Flow around a Particle

In recent years, Physics-Informed Neural Networks (PINNs) have drawn great interest among researchers as a tool to solve computational physics problems. Unlike conventional neural networks, which are black-box models that “blindly” establish a correlation between input and output variables using a large quantity of labeled data, PINNs directly embed physical laws (primarily partial differential equations) within the loss function of neural networks. By minimizing the loss function, this approach allows the output variables to automatically satisfy physical equations without the need for labeled data. The Navier–Stokes equation is one of the most classic governing equations in thermal fluid engineering. This study constructs a PINN to solve the Navier–Stokes equations for a 2D incompressible laminar flow problem. Flows passing around a 2D circular particle are chosen as the benchmark case, and an elliptical particle is also examined to enrich the research. The velocity and pressure fields are predicted by the PINNs, and the results are compared with those derived from Computational Fluid Dynamics (CFD). Additionally, the particle drag force coefficient is calculated to quantify the discrepancy in the results of the PINNs as compared to CFD outcomes. The drag coefficient maintained an error within 10% across all test scenarios.

Hu, Beichao (ORCID:0009000163215151)↗
DOE OSTI2014

TIDALLY DRIVEN DYNAMOS IN A ROTATING SPHERE

Large-scale planetary or stellar magnetic fields generated by a dynamo effect are mostly attributed to flows forced by buoyancy forces in electrically conducting fluid layers. However, these large-scale fields may also be controlled by tides, as previously suggested for the star τ-boo, Mars, or the early Moon. By simulating a small local patch of a rotating fluid, Barker and Lithwick have recently shown that tides can drive small-scale dynamos by exciting a hydrodynamic instability, the so-called elliptical (or tidal) instability. By performing global magnetohydrodynamic simulations of a rotating spherical fluid body, we investigate if this instability can also drive the observed large-scale magnetic fields. We are thus interested in the dynamo threshold and the generated magnetic field in order to test if such a mechanism is relevant for planets and stars. Rather than solving the problem in a geometry deformed by tides, we consider a spherical fluid body and add a body force to mimic the tidal deformation in the bulk of the fluid. This allows us to use an efficient spectral code to solve the magnetohydrodynamic problem. We first compare the hydrodynamic results with theoretical asymptotic results and numerical results obtained in a truly deformed ellipsoid, which confirms the presence of elliptical instability. We then perform magnetohydrodynamic simulations and investigate the dynamo capability of the flow. Kinematic and self-consistent dynamos are finally simulated, showing that the elliptical instability is capable of generating a dipole-dominated large-scale magnetic field in global simulations of a fluid rotating sphere.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Semi-Supervised Domain Adaptation for Cross-Survey Galaxy Morphology Classification and Anomaly Detection

In the era of big astronomical surveys, our ability to leverage artificial intelligence algorithms simultaneously for multiple datasets will open new avenues for scientific discovery. Unfortunately, simply training a deep neural network on images from one data domain often leads to very poor performance on any other dataset. Here we develop a Universal Domain Adaptation method DeepAstroUDA, capable of performing semi-supervised domain alignment that can be applied to datasets with different types of class overlap. Extra classes can be present in any of the two datasets, and the method can even be used in the presence of unknown classes. For the first time, we demonstrate the successful use of domain adaptation on two very different observational datasets (from SDSS and DECaLS). We show that our method is capable of bridging the gap between two astronomical surveys, and also performs well for anomaly detection and clustering of unknown data in the unlabeled dataset. We apply our model to two examples of galaxy morphology classification tasks with anomaly detection: 1) classifying spiral and elliptical galaxies with detection of merging galaxies (three classes including one unknown anomaly class); 2) a more granular problem where the classes describe more detailed morphological properties of galaxies, with the detection of gravitational lenses (ten classes including one unknown anomaly class).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism

We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalization of multiple polylogarithms, we construct our set of integration kernels ensuring that they have at most simple poles, implying that the iterated integrals have at most logarithmic singularities. We study the properties of our iterated integrals and their relationship to the multiple elliptic polylogarithms from the mathematics literature. On the one hand, we find that our iterated integrals span essentially the same space of functions as the multiple elliptic polylogarithms. On the other, our formulation allows for a more direct use to solve a large variety of problems in high-energy physics. As a result, we demonstrate the use of our functions in the evaluation of the Laurent expansion of some hypergeometric functions for values of the indices close to half integers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

High-beta analytic equilibria in circular, elliptical, and D-shaped large aspect ratio axisymmetric configurations with poloidal and toroidal flows

The Grad-Shafranov-Bernoulli system of equations is a single fluid magnetohydrodynamical description of axisymmetric equilibria with mass flows. Using a variational perturbative approach [E. Hameiri, Phys. Plasmas 20, 024504 (2013)], analytic approximations for high-beta equilibria in circular, elliptical, and D-shaped cross sections in the high aspect ratio approximation are found, which include finite toroidal and poloidal flows. Assuming a polynomial dependence of the free functions on the poloidal flux, the equilibrium problem is reduced to an inhomogeneous Helmholtz partial differential equation (PDE) subject to homogeneous Dirichlet conditions. An application of the Green's function method leads to a closed form for the circular solution and to a series solution in terms of Mathieu functions for the elliptical case, which is valid for arbitrary elongations. In order to extend the elliptical solution to a D-shaped domain, a boundary perturbation in terms of the triangularity is used. A comparison with the code FLOW [L. Guazzotto et al., Phys. Plasmas 11(2), 604-614 (2004)] is presented for relevant scenarios.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2012

On estimations of maximum and average interfacial temperature rise in sliding elliptical contacts

his study considers the approaches of Blok and Jaeger for the estimation of maximum and average temperatures in sliding elliptical contacts with both uniform and semi-ellipsoidal (Hertzian) heat distributions. The accuracy of each of these methods, which are based on single-point temperature matching between contacting bodies, is assessed relative to a numerical solution of the heat partition problem developed in a previous work, which imposed temperature matching at all nodal points. Comparisons are made for a wide range of Peclet numbers, as well as for moderate ranges of thermal conductivity ratio and elliptical ratio. It is found that the application of Blok's hypothesis yields remarkably accurate predictions of the maximum interfacial temperature, with typical errors less than 3%, whereas the hypothesis of Jaeger leads to predictions of the average interfacial temperature that have typical errors of around 6%. The authors also assess the accuracy of approximate formula developed by Tian and Kennedy to predict the maximum temperature at the interface for the case of sliding circular contacts and find the error to be no more than 2.6% for the full range of Peclet number. Further, the authors of the current study use fundamental heat source solutions developed by Tian and Kennedy to arrive at formulae for average temperature rise for circular contacts that are analogous to the Tian and Kennedy maximum temperature rise formulae. It is found that the formulae for computing the average interfacial temperature rise are also quite accurate, but have slightly more error than the maximum temperature rise formulae. Finally, in the present work, extensions are suggested to the maximum and average temperature rise formulae of Tian and Kennedy to include the effects of elliptical contact geometry. It is found that these formulae are at least 91% accurate for elliptical ratios between 0.4 and 5.0.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2011

Homogenization of a thin plate reinforced with periodic families of rigid rods

The asymptotics of the solution to the elastic bending problem for a thin plate reinforced with several periodic families of closely spaced but disjoint rods are constructed and justified, the result of homogenization being substantially different from the case when the rods are welded together into a single periodic mesh. The material in the rods is assumed to be appreciably more rigid than that in the plate. An averaged fourth-order differential operator is obtained from summing the nonelliptic operators generated by each of the families of the rods. This operator is shown to be elliptic if and only if the rods from at least two families are nonparallel. As a simplified example, the paper examines a similar stationary heat conduction problem. Bibliography: 24 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Integral Kernel Methods for Nonlinear Parabolic-Elliptic Systems

Nonlinear parabolic-elliptic systems arise in many physical, biological, and chemical phenomena such as chemotaxis, ion transport, self-gravitating particles, and Brownian vortices. Existing methods struggle with the strong coupling and high nonlinearity and nonlocality of some of these systems, especially the ill-conditioned, convection-dominated problems. To overcome numerical difficulties, current approaches rely on initial guesses, preconditioning, or iterative techniques with no convergence guarantees. They might suffer from poor scalability, large memory usage, and difficulty to parallelize. Inspired by the connection of parabolic-elliptic systems to stochastic processes, we introduce a novel meshless, monolithic, and fully explicit method that naturally encapsulates the elliptic and parabolic operators into a single step which updates each node deterministically with global information. By being fully quadrature-based, it avoids solving systems of discretized equations and does not utilize initial guesses or preconditioning, while requiring little memory and being easy to parallelize. We first derive the method in an integral kernel formulation with quadratic complexity in the number of integration nodes and then leverage kernel-independent fast multipole methods (FMM) to present a scalable algorithm with linear complexity. We provide numerical examples for the Poisson-Nernst-Planck equations in one, two, and three dimensions, together with the derivation of the integral kernel for each case. Furthermore, the examples demonstrate the fast convergence and scalability of the FMM-accelerated algorithm, as well as its suitability for convection-dominated problems, making it competitive against traditional PDE solvers.

PDE systems↗
DOE OSTI2013

Risk-Sensitive Control of Pure Jump Process on Countable Space with Near Monotone Cost

In this article, we study risk-sensitive control problem with controlled continuous time pure jump process on a countable space as state dynamics. We prove multiplicative dynamic programming principle, elliptic and parabolic Harnack’s inequalities. Using the multiplicative dynamic programing principle and the Harnack’s inequalities, we prove the existence and a characterization of optimal risk-sensitive control under the near monotone condition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

On the Theory of Anisotropic Flat Elasticity

For the Lamé system from the flat anisotropic theory of elasticity, we introduce generalized double-layer potentials in connection with the function-theory approach. These potentials are built both for the translation vector (the solution of the Lamé system) and for the adjoint vector functions describing the stress tensor. The integral representation of these solutions is obtained using the potentials. As a corollary, the first and the second boundary-value problems in various spaces (Hölder, Hardy, and the class of functions just continuous in a closed domain) are reduced to the equivalent system of the Fredholm boundary equations in corresponding spaces. Note that such an approach was developed in [19, 20] for common second-order elliptic systems with constant (higher-order only) coefficients. However, due to important applications, it makes sense to consider this approach in detail directly for the Lamé system. To illustrate these results, in the last two sections we consider the Dirichlet problem with piecewise-constant Lamé coefficients when contact conditions are given on the boundary between two media. This problem is reduced to the equivalent system of the Fredholm boundary equations. The smoothness of kernels of the obtained integral operators is investigated in detail depending on the smoothness of the boundary contours.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Motions of Kepler circumbinary planets in restricted three-body problem under radiating primaries

By observing continuously a single field of view in the sky, Kepler mission reveals outstanding results on discoveries of exoplanets. One of its recent progress is the discoveries of circumbinary planets. A circumbinary planet is an exoplanet that moves around a binary system. In this study we investigate motions of Kepler circumbinary planets belong to six binary systems, namely Kepler-16, -34, -35, -38, -47, and -413. The motions are considered to follow the Restricted Three-Body Problem (RTBP). Because the primaries (central massive objects) are stars, they are both radiatives, while the planet is an infinitesimal object. The primaries move in nearly circular and elliptic orbits with respect to their center of masses. We describe, in general, motions of the circumbinary planets in RTBP under radiating primaries. With respect to the averaged zero velocity curves, we show that motions of the exoplanets are stable, in accordance with their Hill stabilities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗