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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

An analytic solution for the response of the neutral atmosphere to the high-latitude convection pattern

The analytic solutions to a two-dimensional, shallow-water model of the high-latitude thermosphere are developed. The equations are a linearized representation of the response of the neutral atmosphere to the momentum source due to the plasma convection pattern. The obtained results show how the neutral winds depend on the Pedersen and Hall ion drag coefficients and the horizontal wave number. The response depends on the dimensionless scale as it appears in the product of the Rossby radius of deformation and the wave number. The flow pattern is shifted in local time from the plasma flow pattern by an amount that depends on the average electron density. At the largest scales there is a 180 deg phase shift between the rotational flow components in the E and F regions. The model applies to quiet magnetic conditions and below 200 km of altitude.

Mikkelsen, I. S.↗
DOE OSTI2012

Neutron noise calculations in a hexagonal geometry and comparison with analytical solutions

This paper presents the development of a neutronic and kinetic solver for hexagonal geometries. The tool is developed based on the diffusion theory with multi-energy groups and multi-groups of delayed neutron precursors allowing the solutions of forward and adjoint problems of static and dynamic states, and is applicable to both thermal and fast systems with hexagonal geometries. In the dynamic problems, the small stationary fluctuations of macroscopic cross sections are considered as noise sources, and then the induced first order noise is calculated fully in the frequency domain. Numerical algorithms for solving the static and noise equations are implemented with a spatial discretization based on finite differences and a power iterative solution. A coarse mesh finite difference method has been adopted for speeding up the convergence. Since no other numerical tool could calculate frequency-dependent noise in hexagonal geometry, validation calculations have been performed and benchmarked to analytical solutions based on a 2-D homogeneous system with two-energy groups and one-group of delayed neutron precursor, in which point-like perturbations of thermal absorption cross section at central and non-central positions are considered as noise sources. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1994

An analytic solution of the radiative transfer equation for a gray scattering atmosphere in motion

We provide a formal analytic solution of the radiative transfer equation for a gray moving atmosphere in a plane parallel geometry. A formal solution in the diffusion and the free-streaming limit is also provided in the case of a spherically extended atmosphere. The formal solutions are written explicitly for scattering atmospheres in which the density and the velocity fields are given by a power law. A self-consistent temperature profile accurate to O(Beta = v/c) is provided for the case in which the absorption or the scattering are temperature independent. The gray extinction temperature profile is considerably simplified in the case of a scattering atmosphere. Steady state flow and homologous expansion are special cases that are considered in detail.

Pistinner, Shlomi↗
DOE OSTI2014

ANALYTICAL SOLUTION FOR WAVES IN PLANETS WITH ATMOSPHERIC SUPERROTATION. II. LAMB, SURFACE, AND CENTRIFUGAL WAVES

This paper is the second in a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases where the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the background wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this second part, we study the waves' solutions when several atmospheric approximations are applied: Lamb, surface, and centrifugal waves. Lamb and surface waves are found to be quite similar to those in a geostrophic regime. By contrast, centrifugal waves turn out to be a special case of Rossby waves that arise in atmospheres in cyclostrophic balance. Finally, we use our results to identify the nature of the waves behind atmospheric periodicities found in polar and lower latitudes of Venus's atmosphere.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Technical Note: Analytical Solution for Transient Partitioning and Reaction of a Condensing Vapor Species in a Droplet

We present the exact analytical solution of the transient equation of gas-phase diffusion of a condensing vapor to, and diffusion and reaction in, an aqueous droplet. Droplet-phase reaction is represented by first-order chemistry. The solution facilitates study of the dynamic nature of the vapor uptake process as a function of droplet size, Henry’s law coefficient, and first-order reaction rate constant for conversion in the droplet phase.

Liu, Albert T.↗
NASA NTRS1989

An approximate analytic solution of a set of nonlinear model alpha-omega-dynamo equations for marginally unstable systems

An approximate analytic solution of a set of nonlinear model alpha-omega-dynamo equations is obtained. The reaction of the Lorentz force on the velocity shear which stretches and, hence, amplifies the magnetic field is incorporated into the model. To single out the effect of the Lorentz force on the omega-effect, the effect of the Lorentz force on the alpha-effect is neglected in this study. The solution represents a nonlinear oscillation with the amplitude and period determined by the dynamo number N. The amplitude is proportional to N - 1, while the period is almost exactly the same as the dissipation time of the unstable mode (proportional to N).

Hinata, S.↗
DOE OSTI2013

DYNAMICS OF ASTROPHYSICAL BUBBLES AND BUBBLE-DRIVEN SHOCKS: BASIC THEORY, ANALYTICAL SOLUTIONS, AND OBSERVATIONAL SIGNATURES

Bubbles in the interstellar medium are produced by astrophysical sources, which continuously or explosively deposit large amounts of energy into the ambient medium. These expanding bubbles can drive shocks in front of them, the dynamics of which is markedly different from the widely used Sedov-von Neumann-Taylor blast wave solution. Here, we present the theory of a bubble-driven shock and show how its properties and evolution are determined by the temporal history of the source energy output, generally referred to as the source luminosity law, L(t). In particular, we find the analytical solutions for a driven shock in two cases: the self-similar scaling law, L{proportional_to}(t/t{sub s} ) {sup p} (with p and t{sub s} being constants) and the finite activity time case, L{proportional_to}(1 - t/t{sub s} ){sup -p}. The latter with p > 0 describes a finite-time-singular behavior, which is relevant to a wide variety of systems with explosive-type energy release. For both luminosity laws, we derived the conditions needed for the driven shock to exist and predict the shock observational signatures. Our results can be relevant to stellar systems with strong winds, merging neutron star/magnetar/black hole systems, and massive stars evolving to supernovae explosions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2010

Analytical solution of thermal magnetization on memory stabilizer structures

We return to the question of how the choice of stabilizer generators affects the preservation of information on structures whose degenerate ground state encodes a classical redundancy code. Controlled-not gates are used to transform the stabilizer Hamiltonian into a Hamiltonian consisting of uncoupled single spins and/or pairs of spins. This transformation allows us to obtain an analytical partition function and derive closed-form equations for the relative magnetization and susceptibility. These equations are in agreement with the numerical results presented in Viteri et al. [Phys. Rev. A 80, 042313 (2009)] for finite size systems. Analytical solutions show that there is no finite critical temperature, T{sub c}=0, for all of the memory structures in the thermodynamic limit. This is in contrast to the previously predicted finite critical temperatures based on extrapolation. The mismatch is a result of the infinite system being a poor approximation even for astronomically large finite-size systems, where spontaneous magnetization still arises below an apparent finite critical temperature. We extend our analysis to the canonical stabilizer Hamiltonian. Interestingly, Hamiltonians with two-body interactions have a higher apparent critical temperature than the many-body Hamiltonian.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Examination of Semi-Analytical Solution Methods in the Coarse Operator of Parareal Algorithm for Power System Simulation

With continuing advances in high-performance parallel computing platforms, parallel algorithms have become powerful tools for development of faster than real-time power system dynamic simulations. In particular, it has been demonstrated in recent years that parallel-in-time (Parareal) algorithms have the potential to achieve such an ambitious goal. Here, the selection of a fast and reasonably accurate coarse operator of the Parareal algorithm is crucial for its effective utilization and performance. This paper examines semi-analytical solution (SAS) methods as the coarse operators of the Parareal algorithm and explores performance of the SAS methods to the standard numerical time integration methods. Two promising time-power series-based SAS methods were considered; Adomian decomposition method and Homotopy analysis method with a windowing approach for improving the convergence. Numerical performance case studies on 10-generator 39-bus system and 327-generator 2383-bus system were performed for these coarse operators over different disturbances, evaluating the number of Parareal iterations, computational time, and stability of convergence. All the coarse operators tested with different scenarios have converged to the same corresponding true solution (if they are convergent) and the SAS methods provide comparable computational speed, while having more stable convergence to the true solution in many cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

MAGNETO-FRICTIONAL MODELING OF CORONAL NONLINEAR FORCE-FREE FIELDS. I. TESTING WITH ANALYTIC SOLUTIONS

We report our implementation of the magneto-frictional method in the Message Passing Interface Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC). The method aims at applications where local adaptive mesh refinement (AMR) is essential to make follow-up dynamical modeling affordable. We quantify its performance in both domain-decomposed uniform grids and block-adaptive AMR computations, using all frequently employed force-free, divergence-free, and other vector comparison metrics. As test cases, we revisit the semi-analytic solution of Low and Lou in both Cartesian and spherical geometries, along with the topologically challenging Titov–Démoulin model. We compare different combinations of spatial and temporal discretizations, and find that the fourth-order central difference with a local Lax–Friedrichs dissipation term in a single-step marching scheme is an optimal combination. The initial condition is provided by the potential field, which is the potential field source surface model in spherical geometry. Various boundary conditions are adopted, ranging from fully prescribed cases where all boundaries are assigned with the semi-analytic models, to solar-like cases where only the magnetic field at the bottom is known. Our results demonstrate that all the metrics compare favorably to previous works in both Cartesian and spherical coordinates. Cases with several AMR levels perform in accordance with their effective resolutions. The magneto-frictional method in MPI-AMRVAC allows us to model a region of interest with high spatial resolution and large field of view simultaneously, as required by observation-constrained extrapolations using vector data provided with modern instruments. The applications of the magneto-frictional method to observations are shown in an accompanying paper.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

NUMERICAL AND ANALYTICAL SOLUTIONS OF NEUTRINO-DOMINATED ACCRETION FLOWS WITH A NON-ZERO TORQUE BOUNDARY CONDITION AND ITS APPLICATIONS IN GAMMA-RAY BURSTS

A stellar-mass black hole (BH) surrounded by a neutrino-dominated accretion flow (NDAF) has been discussed in a number of works as the central engine of gamma-ray bursts (GRBs). It is widely believed that NDAF cannot liberate enough energy for bright GRBs. However, these works have been based on the assumption of a “no torque” boundary condition, which is invalid when the disk is magnetized. In this paper, we present both numerical and analytical solutions for NDAFs with non-zero boundary stresses and reexamine their properties. We find that an NDAF with such a boundary torque can be powerful enough to account for those bright short GRBs, energetic long GRBs, and ultra-long GRBs. The disk becomes viscously unstable, which makes it possible to interpret the variability of GRB prompt emission and the steep decay phase in the early X-ray afterglow. Finally, we study the gravitational waves radiated from a processing BH-NDAF. We find that the effects of the boundary torque on the strength of the gravitational waves can be ignored.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

ANALYTIC SOLUTIONS FOR CURRENT SHEET STRUCTURE DETERMINED BY SELF-CONSISTENT, ANISOTROPIC TRANSPORT PROCESSES IN A GRAVITATIONAL FIELD

A Harris sheet magnetic field with maximum magnitude B{sub 0} and length scale L is combined with the anisotropic electrical conductivity, viscosity, and thermoelectric tensors for an electron-proton plasma to define a magnetohydrodynamic model that determines the steady state of the plasma. The transport tensors are functions of temperature, density, and magnetic field strength, and are computed self-consistently as functions of position x normal to the current sheet. The flow velocity, magnetic field, and gravitational force lie along the z-axis. The plasma is supported against gravity by the viscous force. Analytic solutions are obtained for temperature, density, and velocity. They are valid over a broad range of temperature, density, and magnetic field strength, and so may be generally useful in astrophysical applications. Numerical examples of solutions in the parameter range of the solar atmosphere are presented. The objective is to compare Joule and viscous heating rates, determine the velocity shear that generates viscous forces that support the plasma and are self-consistent with a mean outward mass flux comparable to the solar wind mass flux, and compare the thermoelectric and conduction current contributions to the Joule heating rate. The ratio of the viscous to Joule heating rates per unit mass can exceed unity by orders of magnitude, and increases rapidly with L. The viscous heating rate can be concentrated outside the region where the current density is localized, corresponding to a resistively heated layer of plasma bounded by viscously heated plasma. The temperature gradient drives a thermoelectric current density that can have a magnitude greater than that of the electric-field-driven conduction current density, so thermoelectric effects are important in determining the Joule heating rate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Analytical solutions of Landau (1+1)-dimensional hydrodynamics

To help guide our intuition, summarize important features, and point out essential elements, we review the analytical solutions of Landau (1+1)-dimensional hydrodynamics and exhibit the full evolution of the dynamics from the very beginning to subsequent times. Special emphasis is placed on the matching and the interplay between the Khalatnikov solution and the Riemann simple wave solution at the earliest times and in the edge regions at later times.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2006

An Analytical Solution of Radiative Transfer in the Coupled Atmosphere-Ocean System with Rough Surface

Using the efficient discrete-ordinate method, we present an analytical solution for radiative transfer in the coupled atmosphere-ocean system with rough air-water interface. The theoretical formulations of the radiative transfer equation and solution are described. The effects of surface roughness on radiation field in the atmosphere and ocean are studied and compared with measurements. The results show that ocean surface roughness has significant effects on the upwelling radiation in the atmosphere and the downwelling radiation in the ocean. As wind speed increases, the angular domain of sunglint broadens, the surface albedo decreases, and the transmission to ocean increases. The downward radiance field in the upper ocean is highly anisotropic, but this anisotropy decreases rapidly as surface wind increases and as depth in ocean increases. The effects of surface roughness on radiation also depend greatly on both wavelength and angle of incidence (i.e., solar elevation); these effects are significantly smaller throughout the spectrum at high sun. The model-observation discrepancies may indicate that the Cox-Munk surface roughness model is not sufficient for high wind conditions.

Jin, Zhonghai↗
NASA NTRS1987

Analytical solutions for static elastic deformations of wire ropes

This paper develops closed-form solutions for extension of twisted wire ropes subjected to axial forces for two different end conditions. The analytical results are compared with the corresponding numerical results obtained by Costello and Phillips. A close agreement between the two establishes validity of the analytical solutions. Finally, an expression for the effective rigidity modulus of the wire ropes is obtained in terms of the helix angle and the number of helical wires in the rope for each of the two end conditions.

Kumar, K.↗