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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 379 records · Page 21

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NASA NTRS1996

Interface Morphology During Crystal Growth: Effects of Anisotropy and Fluid Flow

The effect of a parallel shear flow and anisotropic interface kinetics on the onset of instability during growth from a supersaturated solution is analyzed. The model used for anisotropy is based on the microscopic picture of step motion. A shear flow (linear Couette flow or asymptotic suction profile) parallel to the crystal solution interface in the same direction as the step motion decreases interface stability. A shear flow counter to the step motion enhances stability and for sufficiently large shear rates the interface is absolutely morphologically stable. For large wave numbers, the perturbed flow field can be neglected and a simple analytic approximation for the stability-instability demarcation is found.

Coriell, S. R.↗

NASA NTRS1974

Gravity tectonics and seismic gaps in the mantle

The concept of gravity tectonics is applied to reveal the major clue as to the conditions which result in the correspondence of seismic and tectonic gaps in the mantle. An asymptotic theory is developed for the calculation of the thrust and moment when a descending lithospheric plate encounters resistance to its downward motion in the mesosphere. Dynamic analysis falls into two parts: (1) deriving equations for forces in the descending lithosphere, (2) deducing moment distribution which causes the detachment of lithosphere. For the analysis of forces a mathematical theory of shells is given. In order to determine the detachment mechanism, solutions of equations are obtained by asymptotic integration. It is found that a thrust N sub phi coupled with a moment M sub phi due to gravitational forces generated by density contrast may play a key role in the initial detachment of a piece of descending lithosphere. The results are in agreement with the observed seismic gaps beneath South America, Toga-Fiji, New Zealand and New Hebrides regions.

Liu, H. S.↗

NASA NTRS1983

Asymptotic analysis of numerical wave propagation in finite difference equations

An asymptotic technique is developed for analyzing the propagation and dissipation of wave-like solutions to finite difference equations. It is shown that for each fixed complex frequency there are usually several wave solutions with different wavenumbers and the slowly varying amplitude of each satisfies an asymptotic amplitude equation which includes the effects of smoothly varying coefficients in the finite difference equations. The local group velocity appears in this equation as the velocity of convection of the amplitude. Asymptotic boundary conditions coupling the amplitudes of the different wave solutions are also derived. A wavepacket theory is developed which predicts the motion, and interaction at boundaries, of wavepackets, wave-like disturbances of finite length. Comparison with numerical experiments demonstrates the success and limitations of the theory. Finally an asymptotic global stability analysis is developed.

Giles, M.↗

DOE OSTI2021

Efficient quadrature rules for finite element discretizations of nonlocal equations

Here, in this paper, we design efficient quadrature rules for finite element (FE) discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work, we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first show that the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient FE assembly.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Efficient quadrature rules for finite element discretizations of nonlocal equations

In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first showthat the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient finite element assembly.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1986

Time-dependent solution for axisymmetric flow over a blunt body with ideal gas, CF4, or equilibrium air chemistry

A time-asymptotic method has been used to obtain steady-flow solutions for axisymmetric inviscid flow over several blunt bodies including spheres, paraboloids, ellipsoids, and spherically blunted cones. Comparisons with experimental data and results of other computational methods have demonstrated that accurate solutions can be obtained using this approach. The method should prove useful as an analysis tool for comparing with experimental data and for making engineering calculations for blunt reentry vehicles.

Hamilton, H. H., II↗

NASA NTRS1992

Finite-difference scheme for the numerical solution of the Schroedinger equation

A finite-difference scheme for numerical integration of the Schroedinger equation is constructed. Asymptotically (r goes to infinity), the method gives the exact solution correct to terms of order r exp -2.

Mickens, Ronald E.↗

DOE OSTI2020

Modeling of resistive plasma response in toroidal geometry using an asymptotic matching approach

The method of solving linear resistive plasma response, based on the asymptotic matching approach, is developed for full toroidal tokamaks by upgrading the Resistive DCON code [A.H. Glasser, Z.R. Wang and J.-K. Park, Physics of Plasmas, \textbf{23}, 112506 (2016)]. The derived matching matrix, asymptotically matching the outer and inner regions, indicates that the applied three dimension (3-D) magnetic perturbations contribute additional small solutions at each resonant surface due to the toroidal coupling of poloidal modes. In contrast, the resonant harmonic only affects the corresponding resonant surface in the cylindrical plasma. Since the solution of ideal outer region is critical to the asymptotic matching and is challenging to be solved in the toroidal geometry due to the singular power series solution at the resonant surfaces, systematic verification of the outer region $\Delta^\prime$ matrix is made by reproducing the well known analytical $\Delta^{\prime}$ result in [H.P. Furth, P.H. Rutherford and H. Selberg, The Physics of Fluids, \textbf{16}, 1054-1063 (1073)] as well as by making a quantitative benchmark with the PEST3 code [A. Pletzer and R.L. Dewar, J. Plasma Physics, \textbf{45}, 427-451 (1991)]. Finally, the reconstructed numerical solution of resistive plasma response from the toroidal matching matrix is presented. Comparing with the ideal plasma response, the global structure of the response can be affected by the small finite island at the resonant surfaces.

MHD simulation↗

NASA NTRS1971

Some three-body numerical solutions for low-thrust orbiter missions.

A ?velocity at the sphere of influence' method and an asymptotic matching method of patching together two-body low thrust solutions are compared to a number of three-body numerical results for outer planet orbiter missions. The two patching methods compare well with the numerical three-body results and do not depend on any particular choice for the size of the sphere of influence. The results apply, in a strict sense, only to the operational mode used-high-thrust terminal retro into orbit. Low-thrust spirals are not considered in the three-body analysis. The terminal low-thrust phase of thrusting is almost entirely reverse to the velocity vector during the planet centered phase of the trajectory. This may lead to important simplifications for low-thrust guidance and navigation procedures.

Mackay, J. S.↗

NASA NTRS1973

A study of selected radiation and propagation problems related to antennas and probes in magneto-ionic media

Research consisted of computations toward the solution of the problem of the current distribution on a cylindrical antenna in a magnetoplasma. The case of an antenna parallel to the applied magnetic field was investigated. A systematic method of asymptotic expansion was found which simplifies the solution in the general case by giving the field of a dipole even at relatively short range. Some useful properties of the dispersion surfaces in a lossy medium have also been found. A laboratory experiment was directed toward evaluating nonlinear effects, such as those due to power level, bias voltage and electron heating. The problem of reflection and transmission of waves in an electron heated plasma was treated theoretically. The profile inversion problem has been pursued. Some results are very encouraging, however, the general question of stability of the solution remains unsolved.

Source record↗

DOE OSTI2021

Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: $\phi$ 3 QFT in 6 Dimensions

We analyze the asymptotically free massless scalar $\phi$ 3 quantum field theory in 6 dimensions, using resurgent asymptotic analysis to find the trans-series solutions which yield the non-perturbative completion of the divergent perturbative solutions to the Kreimer–Connes Hopf-algebraic Dyson–Schwinger equations for the anomalous dimension. This scalar conformal field theory is asymptotically free and has a real Lipatov instanton. In the Hopf-algebraic approach we find a trans-series having an intricate Borel singularity structure, with three distinct but resonant non-perturbative terms, each repeated in an infinite series. These expansions are in terms of the renormalized coupling. The resonant structure leads to powers of logarithmic terms at higher levels of the trans-series, analogous to logarithmic terms arising from interactions between instantons and anti-instantons, but arising from a purely perturbative formalism rather than from a semi-classical analysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1986

Transonic flow solutions using a composite velocity procedure for potential, Euler and RNS equations

Solutions for transonic viscous and inviscid flows using a composite velocity procedure are presented. The velocity components of the compressible flow equations are written in terms of a multiplicative composite consisting of a viscous or rotational velocity and an inviscid, irrotational, potential-like function. This provides for an efficient solution procedure that is locally representative of both asymptotic inviscid and boundary layer theories. A modified conservative form of the axial momentum equation that is required to obtain rotational solutions in the inviscid region is presented and a combined conservation/nonconservation form is applied for evaluation of the reduced Navier-Stokes (RNS), Euler and potential equations. A variety of results is presented and the effects of the approximations on entropy production, shock capturing, and viscous interaction are discussed.

Gordnier, R. E.↗

NASA NTRS1989

Transonic flow solutions using a composite velocity procedure for potential, Euler and RNS equations

Gordnier, R. E.↗

NASA NTRS1994

An analysis code for the Rapid Engineering Estimation of Momentum and Energy Losses (REMEL)

Nonideal behavior has traditionally been modeled by defining efficiency (a comparison between actual and isentropic processes), and subsequent specification by empirical or heuristic methods. With the increasing complexity of aeropropulsion system designs, the reliability of these more traditional methods is uncertain. Computational fluid dynamics (CFD) and experimental methods can provide this information but are expensive in terms of human resources, cost, and time. This report discusses an alternative to empirical and CFD methods by applying classical analytical techniques and a simplified flow model to provide rapid engineering estimates of these losses based on steady, quasi-one-dimensional governing equations including viscous and heat transfer terms (estimated by Reynold's analogy). A preliminary verification of REMEL has been compared with full Navier-Stokes (FNS) and CFD boundary layer computations for several high-speed inlet and forebody designs. Current methods compare quite well with more complex method results and solutions compare very well with simple degenerate and asymptotic results such as Fanno flow, isentropic variable area flow, and a newly developed, combined variable area duct with friction flow solution. These solution comparisons may offer an alternative to transitional and CFD-intense methods for the rapid estimation of viscous and heat transfer losses in aeropropulsion systems.

Dechant, Lawrence J.↗

NASA NTRS1977

Analytic theory of orbit contraction

The motion of a satellite in orbit, subject to atmospheric force and the motion of a reentry vehicle are governed by gravitational and aerodynamic forces. This suggests the derivation of a uniform set of equations applicable to both cases. For the case of satellite motion, by a proper transformation and by the method of averaging, a technique appropriate for long duration flight, the classical nonlinear differential equation describing the contraction of the major axis is derived. A rigorous analytic solution is used to integrate this equation with a high degree of accuracy, using Poincare's method of small parameters and Lagrange's expansion to explicitly express the major axis as a function of the eccentricity. The solution is uniformly valid for moderate and small eccentricities. For highly eccentric orbits, the asymptotic equation is derived directly from the general equation. Numerical solutions were generated to display the accuracy of the analytic theory.

Vinh, N. X.↗

DOE OSTI2024

Parity solution to the strong CP problem and a unified framework for inflation, baryogenesis, and dark matter

It has been known for some time that asymptotic parity invariance of weak interactions can provide a solution to the strong CP problem without the need for the axion. Left-right symmetric theories which employ a minimal Higgs sector consisting of a left-handed and a right-handed doublet is an example of such a theory wherein all fermion masses arise through a generalized seesaw mechanism. In this paper we present a way to understand the origin of matter-antimatter asymmetry as well as the dark matter content of the universe in these theories using the Affleck-Dine (AD) leptogenesis mechanism and inflaton decay, respectively. Three gauge singlet fermions are needed for this purpose, two of which help to implement the Dirac seesaw for neutrino masses while the third one becomes the non-thermal dark matter candidate. A soft lepton number breaking term involving the AD scalar field is used to generate lepton asymmetry which suffers no wash-out effects and maintains the Dirac nature of neutrinos. This framework thus provides a unified description of many of the unresolved puzzles of the standard model that require new physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Modeling of resistive plasma response in toroidal geometry using an asymptotic matching approach

The method of solving the linear resistive plasma response, based on the asymptotic matching approach, is developed for full toroidal tokamaks by upgrading the resistive DCON code [A. H. Glasser, Z. R. Wang, and J.-K. Park, Phys. Plasmas 23, 112506 (2016)]. The derived matching matrix, asymptotically matching the outer and inner regions, indicates that the applied three dimension (3-D) magnetic perturbations contribute additional small solutions at each resonant surface due to the toroidal coupling of poloidal modes. In contrast, the resonant harmonic only affects the corresponding resonant surface in the cylindrical plasma. Additionally, the solution of the ideal outer region is critical to the asymptotic matching and is challenging in toroidal geometry due to the singular power series solution at the resonant surfaces. Thus, a systematic verification of the outer region Δ' matrix is made by reproducing the well-known analytical Δ' result in Furth et al. [Phys. Fluids 16, 1054–1063 (1073)] and by making a quantitative benchmark with the PEST3 code [A. Pletzer and R. L. Dewar, J. Plasma Phys. 45, 427–451 (1991)]. Finally, the reconstructed numerical solution of the resistive plasma response from the toroidal matching matrix is presented. Compared with the ideal plasma response, the global structure of the response can be affected by the small finite island at the resonant surfaces.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1971

Asymptotic stability properties of linear Volterra integrodifferential equations.

The Liapunov stability properties of solution to a certain system of Volterra integrodifferential equations is studied. Various types of Liapunov stability are defined; the definitions are natural extensions of the corresponding notions for ordinary differential equations. Necessary and sufficient conditions, in general, for uniform stability and uniform asymptotic stability are obtained in the form of a theorem. Connections between the stability of the system studied and the stability properties of a related Volterra integrodifferential equation with infinite memory are examined. Sufficient conditions in order that the trivial solution to the system studied be stable, uniformly stable, asymptotically stable, or uniformly asymptotically stable are derived.

Miller, R. K.↗