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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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Roadmap on transformation optics

Transformation optics asks, using Maxwell's equations, what kind of electromagnetic medium recreates some smooth deformation of space? The guiding principle is Einstein's principle of covariance: that any physical theory must take the same form in any coordinate system. This requirement fixes very precisely the required electromagnetic medium. The impact of this insight cannot be overestimated. Many practitioners were used to thinking that only a few analytic solutions to Maxwell's equations existed, such as the monochromatic plane wave in a homogeneous, isotropic medium. At a stroke, transformation optics increases that landscape from 'few' to 'infinity', and to each of the infinitude of analytic solutions dreamt up by the researcher, there corresponds an electromagnetic medium capable of reproducing that solution precisely. The most striking example is the electromagnetic cloak, thought to be an unreachable dream of science fiction writers, but realised in the laboratory a few months after the papers proposing the possibility were published. But the practical challenges are considerable, requiring meta-media that are at once electrically and magnetically inhomogeneous and anisotropic. How far have we come since the first demonstrations over a decade ago? And what does the future hold? If the wizardry of perfect macroscopic optical invisibility still eludes us in practice, then what compromises still enable us to create interesting, useful, devices? While three-dimensional (3D) cloaking remains a significant technical challenge, much progress has been made in two dimensions. Carpet cloaking, wherein an object is hidden under a surface that appears optically flat, relaxes the constraints of extreme electromagnetic parameters. Surface wave cloaking guides sub-wavelength surface waves, making uneven surfaces appear flat. Two dimensions is also the setting in which conformal and complex coordinate transformations are realisable, and the possibilities in this restricted domain do not appear to have been exhausted yet. Beyond cloaking, the enhanced electromagnetic landscape provided by transformation optics has shown how fully analytic solutions can be found to a number of physical scenarios such as plasmonic systems used in electron energy loss spectroscopy and cathodoluminescence. Are there further fields to be enriched? A new twist to transformation optics was the extension to the spacetime domain. By applying transformations to spacetime, rather than just space, it was shown that events rather than objects could be hidden from view; transformation optics had provided a means of effectively redacting events from history. The hype quickly settled into serious nonlinear optical experiments that demonstrated the soundness of the idea, and it is now possible to consider the practical implications, particularly in optical signal processing, of having an 'interrupt-without-interrupt' facility that the so-called temporal cloak provides. Inevitable issues of dispersion in actual systems have only begun to be addressed. Now that time is included in the programme of transformation optics, it is natural to ask what role ideas from general relativity can play in shaping the future of transformation optics. Indeed, one of the earliest papers on transformation optics was provocatively titled 'General Relativity in Electrical Engineering'. The answer that curvature does not enter directly into transformation optics merely encourages us to speculate on the role of transformation optics in defining laboratory analogues. Quite why Maxwell's theory defines a 'perfect' transformation theory, while other areas of physics such as acoustics are not apparently quite so amenable, is a deep question whose precise, mathematical answer will help inform us of the extent to which similar ideas can be extended to other fields. Here, the contributors to this Roadmap, who are all renowned practitioners or inventors of transformation optics, will give their perspectives into the field's status and future development.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1981

Parametric study of minimum reactor mass in energy-storage dc-to-dc converters

Closed-form analytical solutions for the design equations of a minimum-mass reactor for a two-winding voltage-or-current step-up converter are derived. A quantitative relationship between the three parameters - minimum total reactor mass, maximum output power, and switching frequency - is extracted from these analytical solutions. The validity of the closed-form solution is verified by a numerical minimization procedure. A computer-aided design procedure using commercially available toroidal cores and magnet wires is also used to examine how the results from practical designs follow the predictions of the analytical solutions.

Wong, R. C.↗
DOE OSTI2018

On the Behavior of Solutions of Some Systems of Differential Equations Partially Solved with Respect to the Derivatives in the Presence of a Pole

We study the existence of analytic solutions for some systems of ordinary differential equations partially solvable with respect to the derivatives. We establish sufficient conditions for the existence of analytic solutions of the Cauchy problem in the presence of a pole. An estimate for these solutions is obtained in a certain domain and the problem of the number of solutions is investigated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Benchmark Solutions for Radiation Transport in Stochastic Media with Inhomogeneous Material Statistics

Accurately solving implicit Monte Carlo (IMC) thermal photon transport problems with mixed material cells is important in realistic applications. The production IMC package at LLNL treats mixed material cells arising from ALE remap and hydrodynamics using the same approximate model. The new Imp IMC thermal photon transport package currently under development has both a material interface reconstruction (MIR) algorithm and a Levermore-Pomraning (LP) stochastic medium algorithm for treating mixed material cells. Existing stochastic medium algorithms for treating mixed material cells in IMC lack a complete theoretical basis. The IMC LP algorithm implementation has been demonstrated to reproduce published deterministic LP solutions for the particular case of spatially homogeneous material statistics. Realistic simulations will include spatially inhomogeneous material statistics (material mean chord lengths). In a previous investigation, the LP-model for transport in binary stochastic media in rod geometry was generalized to accommodate spatially varying material chord lengths, i.e., the mixing statistics were allowed to be nonhomogeneous. Analytical solutions were obtained and used to produce a verifi cation suite for the Imp IMC Levermore-Pomraning implementation for different spatial variations of the chord lengths. However, the accuracy of the LP model when the mixing statistics are nonhomogeneous has not been assessed and leaves open the question of whether local accuracy is improved or further degraded when chord lengths are not uniform. This shortcoming is rectifi ed here by developing benchmark analytic solutions for transport in binary Markovian stochastic mixtures in rod geometry with nonhomogeneous mixing statistics, using spatially varying chord lengths considered in the previous investigation based on the LP model. Methods for sampling a nonhomogeneous Poisson process (NHPP) are first described and used to construct individual realizations of the binary mixtures in rod geometry. Analytic solutions are then obtained for the forward and backward directed fluxes on a given realization, now viewed as a deterministic medium with alternating layers of the two materials with known interface locations. Finally, material averaged scalar fluxes are obtained using these sampling schemes with spatially linear and quadratic chord lengths and used to assess the accuracy of the previously obtained LP-model results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2014

Explicit solutions of the radiative transport equation in the P{sub 3} approximation

Purpose: Explicit solutions of the monoenergetic radiative transport equation in the P{sub 3} approximation have been derived which can be evaluated with nearly the same computational effort as needed for solving the standard diffusion equation (DE). In detail, the authors considered the important case of a semi-infinite medium which is illuminated by a collimated beam of light. Methods: A combination of the classic spherical harmonics method and the recently developed method of rotated reference frames is used for solving the P{sub 3} equations in closed form. Results: The derived solutions are illustrated and compared to exact solutions of the radiative transport equation obtained via the Monte Carlo (MC) method as well as with other approximated analytical solutions. It is shown that for the considered cases which are relevant for biomedical optics applications, the P{sub 3} approximation is close to the exact solution of the radiative transport equation. Conclusions: The authors derived exact analytical solutions of the P{sub 3} equations under consideration of boundary conditions for defining a semi-infinite medium. The good agreement to Monte Carlo simulations in the investigated domains, for example, in the steady-state and time domains, as well as the short evaluation time needed suggests that the derived equations can replace the often applied solutions of the diffusion equation for the homogeneous semi-infinite medium.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2016

Long Term Evolution of Planetary Systems with a Terrestrial Planet and a Giant Planet

We study the long term orbital evolution of a terrestrial planet under the gravitational perturbations of a giant planet. In particular, we are interested in situations where the two planets are in the same plane and are relatively close. We examine both possible configurations: the giant planet orbit being either outside or inside the orbit of the smaller planet. The perturbing potential is expanded to high orders and an analytical solution of the terrestrial planetary orbit is derived. The analytical estimates are then compared against results from the numerical integration of the full equations of motion and we find that the analytical solution works reasonably well. An interesting finding is that the new analytical estimates improve greatly the predictions for the timescales of the orbital evolution of the terrestrial planet compared to an octupole order expansion. Finally, we briefly discuss possible applications of the analytical estimates in astrophysical problems.

Dynamical evolution↗
NASA NTRS1993

Analytic Theory and Control of the Motion of Spinning Rigid Bodies

Numerical simulations are often resorted to, in order to understand the attitude response and control characteristics of a rigid body. However, this approach in performing sensitivity and/or error analyses may be prohibitively expensive and time consuming, especially when a large number of problem parameters are involved. Thus, there is an important role for analytical models in obtaining an understanding of the complex dynamical behavior. In this dissertation, new analytic solutions are derived for the complete attitude motion of spinning rigid bodies, under minimal assumptions. Hence, we obtain the most general solutions reported in the literature so far. Specifically, large external torques and large asymmetries are included in the problem statement. Moreover, problems involving large angular excursions are treated in detail. A new tractable formulation of the kinematics is introduced which proves to be extremely helpful in the search for analytic solutions of the attitude history of such kinds of problems. The main utility of the new formulation becomes apparent however, when searching for feedback control laws for stabilization and/or reorientation of spinning spacecraft. This is an inherently nonlinear problem, where standard linear control techniques fail. We derive a class of control laws for spin axis stabilization of symmetric spacecraft using only two pairs of gas jet actuators. Practically, this could correspond to a spacecraft operating in failure mode, for example. Theoretically, it is also an important control problem which, because of its difficulty, has received little, if any, attention in the literature. The proposed control laws are especially simple and elegant. A feedback control law that achieves arbitrary reorientation of the spacecraft is also derived, using ideas from invariant manifold theory. The significance of this research is twofold. First, it provides a deeper understanding of the fundamental behavior of rigid bodies subject to body-fixed torques. Assessment of the analytic solutions reveals that they are very accurate; for symmetric bodies the solutions of Euler's equations of motion are, in fact, exact. Second, the results of this research have a fundamental impact on practical scientific and mechanical applications in terms of the analysis and control of all finite-sized rigid bodies ranging from nanomachines to very large bodies, both man made and natural. After all, Euler's equations of motion apply to all physical bodies, barring only the extreme limits of quantum mechanics and relativity.

Tsiotras, Panagiotis↗
DOE OSTI2014

Dynamic behaviour of thin composite plates for different boundary conditions

In the context of composite materials technology, which is increasingly present in industry, this article covers a topic of great interest and theoretical and practical importance. Given the complex design of fiber-reinforced materials and their heterogeneous nature, mathematical modeling of the mechanical response under different external stresses is very difficult to address in the absence of simplifying assumptions. In most structural applications, composite structures can be idealized as beams, plates, or shells. The analysis is reduced from a three-dimensional elasticity problem to a oneor two-dimensional problem, based on certain simplifying assumptions that can be made because the structure is thin. This paper aims to validate a mathematical model illustrating how thin rectangular orthotropic plates respond to the actual load. Thus, from the theory of thin plates, new analytical solutions are proposed corresponding to orthotropic rectangular plates having different boundary conditions. The proposed analytical solutions are considered both for solving equation orthotropic rectangular plates and for modal analysis.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Testing the Delayed Gamma Capability in MCNP6

The mission of the Domestic Nuclear Detection Office is to quickly and reliably detect unauthorized attempts to import or transport special nuclear material for use against the United States. Developing detection equipment to meet this objective requires accurate simulation of both the detectable signature and detection mechanism. A delayed particle capability was initially added to MCNPX 2.6.A in 2005 to sample the radioactive fission product parents and emit decay particles resulting from the decay chain. To meet the objectives of detection scenario modeling, the capability was designed to sample a particular time for emitting particular multiplicity of a particular energy. Because the sampling process of selecting both time and energy is interdependent, to linearize the time and emission sampling, atom densities are computed at several discrete time steps, and the time-integrated production is computed by multiplying the atom density by the decay constant and time step size to produce a cumulative distribution function for sampling the emission time, energy, and multiplicity. The delayed particle capability was initially given a time-bin structure to help reasonably reproduce, from a qualitative sense, a fission benchmark by Beddingfield, which examined the delayed gamma emission. This original benchmark was only qualitative and did not contain the magnitudes of the actual measured data but did contain relative graphical representation of the spectra. A better benchmark with measured data was later provided by Hunt, Mozin, Reedy, Selpel, and Tobin at the Idaho Accelerator Center; however, because of the complexity of the benchmark setup, sizable systematic errors were expected in the modeling, and initial results compared to MCNPX 2.7.0 showed errors outside of statistical fluctuation. Presented in this paper is a more simplified approach to benchmarking, utilizing closed form analytic solutions to the granddaughter equations for particular sets of decay systems. We examine five different decay chains (two-stage decay to stable) and show the predictability of the MCNP6 delayed gamma feature. Results do show that while the default delayed gamma calculations available in the MCNP6 1.0 release can give accurate results for some isotopes (e.g., 137 Ba), the percent differences between the closed form analytic solutions and the MCNP6 calculations were often >40% ( 28 Mg, 28 Al, 42 K, 47 Ca, 47 Sc, 60 Co). With the MCNP6 1.1 Beta release, the tenth entry on the DBCN card allows improved calculation within <5% as compared to the closed form analytic solutions for immediate parent emissions and transient equilibrium systems. While the tenth entry on the DBCN card for MCNP6 1.1 gives much better results for transient equilibrium systems and parent emissions in general, it does little to improve daughter emissions of secular equilibrium systems. Finally, hypotheses were presented as to why daughter emissions of secular equilibrium systems might be mispredicted in some cases and not in others.

42 ENGINEERING↗
DOE OSTI2017

Analytical trial functions for modelling a two-dimensional Bose condensate

Approximate analytical solutions to the time-independent two-dimensional Gross–Pitaevsky equation are obtained by a variational method. The solutions found are compared with the results of direct numerical calculations. The accuracy of analytical solutions is determined under various conditions of the problem, primarily the degree of nonlinear interaction of atoms in a Bose condensate. (paper)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

FY2021 Improvements to the New CTH Code Verification & Validation Test Suite

Over the past few years, the CTH multiphysics hydrocode has overhauled its software quality and testing processes, implementing current best practices in software quality and building a robust V&V test suite comprised of traditional hydrocode verification problems, including ASC Tri-Lab Test Suite and Enhanced Tri-Lab Test Suite problems, as well as validation problems for some of CTH’s most frequently used equations of state, materials models, and other key capabilities. Substantial progress towards building this new test suite was made in FY19 and FY20. In FY21, the test suite has been expanded to include verification and validation tests of the Steinberg-Guinan-Lund (ST) viscoplastic model and the Johnson Cook (JFRAC) fracture model. Additionally, two new verification tests were added, covering hydrodynamics and high explosive (HE) modeling capabilities: the Kidder Gaussian density problem and the Escape of HE Products (EHEP) problem from the Tri-Lab Test Suite. This report discusses each of these test problems in detail. Verification test results are compared to analytic solutions. Validation test results are compared to experimental data. Wherever possible, convergence or mesh refinement studies are included. Additionally, while implementing the Kidder verification problem, a bug was identified that affects the use of tables to initialize pressure or density in 1D or 2D calculations. A brief discussion of the bug and its fix is included. CTH demonstrates good performance overall on the new test suite problems. Simulation results showed good agreement with analytic solutions for the Kidder problem, with convergence rates ranging between 1.8 and sub-linear, and relatively good agreement for the EHEP problem, though convergence rates for pressure and density were nearly 0. The ST and JFRAC strain rate loading verification tests show good agreement with analytic solutions. Likewise, CTH simulation results show good agreement with experimental validation data, including Taylor rod impact testing, for the materials tested. Future V&V work will focus on adding 2D and 3D versions of existing verification tests as well as adding validation tests of other frequently used capabilities such as other fracture models.

42 ENGINEERING↗
DOE OSTI2011

Simulation for the assessment of wall thinning using eddy current method

A pipe with protective cladding and insulation was simplified to a four-layered structure when the diameter of a pipe is large enough, and analytical solutions for sinusoidal and pulsed wave excitation were derived. Simulation implemented by using the analytical solutions showed that sinusoidal excitation is not appropriate for the monitoring of inner thinning, while pulsed eddy current method can be used to measure wall-thickness regardless of inner or outer thinning by using the decay rate of log(Bz) as a particular parameter to evaluate wall thickness.

42 ENGINEERING↗
DOE OSTI2018

Linear fractional differential equations and eigenfunctions of fractional differential operators

Eigenfunctions associated with Riemann–Liouville and Caputo fractional differential operators are obtained by imposing a restriction on the fractional derivative parameter. Those eigenfunctions can be used to express the analytical solution of some linear sequential fractional differential equations. As a first application, we discuss analytical solutions for the so-called fractional Helmholtz equation with one variable, obtained from the standard equation in one dimension by replacing the integer order derivative by the Riemann–Liouville fractional derivative. A second application consists of an initial value problem for a fractional wave equation in two dimensions in which the integer order partial derivative with respect to the time variable is replaced by the Caputo fractional derivative. The classical Mittag-Leffler functions are important in the theory of fractional calculus because they emerge as solutions of fractional differential equations. Starting with the solution of a specific fractional differential equation in terms of these functions, we find a way to express the exponential function in terms of classical Mittag-Leffler functions. A remarkable characteristic of this relation is that it is true for any value of the parameter n appearing in the definition of the functions, i.e., we have an infinite family of different expressions for e{sup x} in terms of classical Mittag-Leffler functions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1996

Validation Tests of TASS for Application to 3-D Vortex Simulations

Direct analytical solutions can be useful in validating the Core formulation of numerical systems. In this document an exact analytical solution to the nonlinear Navier-Stokes equation is compared to the numerical results from the three-dimensional Terminal Area Simulation System (TASS). This exact solution, of which the derivation is included, is for Beltrami type flow. Direct comparison of TASS to the analytical Beltrami solution is then used in evaluating the accuracy of TASS.

Switzer, George F.↗
DOE OSTI2019

Optical-property coefficient estimation of bulky medium in experiments with a succinctly analytical calculation

Diffuse optical imaging enables to reconstruct distribution of optical properties, absorption and scattering coefficients, in tissue for breast cancer detection based on diffusion equation with the help of the initial guess obtained from measured data. To estimate the initial guess of the optical-property coefficients, an analytical solution of diffusion equation can be used and compared with the measured data. The analytical solution for a homogeneous infinite medium can be obtained in the frequency domain, expressing that the photon intensity and the phase lag relative to the distance between source and detector in a linear relationship. In this study, a succinct calculation using the trigonometric relation is proposed to estimate the optical-property coefficients. A tank-type and a cylinder Lipovenoes phantoms with two concentrations of 1.25% and 2.5% are employed and measured for verification. It is found that the method proposed here shows better results and results in estimation errors of 0–14.81% for μ{sub a} and 20–42% for μ{sub s}′.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Physical Controls on Irrigation Return Flow Contributions to Stream Flow in Irrigated Alluvial Valleys

Irrigation can be a significant source of groundwater recharge in many agricultural regions, particularly in arid and semi-arid climates. Once infiltrated, irrigation recharge can travel via subsurface flowpaths that return to the river system in a lagged manner, supplementing natural streamflow weeks, months, or even years from when the irrigation was applied. In regions that experience low flows during summer and early fall, return flows can be a significant source of supplementary streamflow. Many water planning and operations models either ignore return flows or roughly approximate them with analytical solutions. Thus, return flows represent an important but often overlooked component of the hydrological exchange and overall water balance in agricultural regions. This study uses groundwater models to explore a wide range of factors that control irrigation return flow timing in irrigated alluvial valleys. A sensitivity analysis approach is used to assess how factors such as the extent of irrigated land adjacent to a stream, irrigation recharge rate, aquifer hydraulic conductivity, aquifer thickness, water table configuration, and seasonal fluctuations in stream stage control the timing of subsurface return flows. Modeling is conducted using MODFLOW models representing an irrigated alluvial valley adjacent to a stream. While a simplification of the full complexity in real systems, the models are a significant advancement from the analytical solution and provide new insight into the timescales of return flows over a broad range of possible conditions. To contextualize our modeling results, they are compared to an analytical solution commonly used for approximating return flows to evaluate its performance. Our findings show what factors and conditions influence return flow timing and control whether they contribute to streamflow over short term (months) or longer term (seasonal) time scales.

Ferencz, Stephen B.↗
DOE OSTI2017

Cosmic-ray propagation with DRAGON2: I. numerical solver and astrophysical ingredients

We present version 2 of the DRAGON code designed for computing realistic predictions of the CR densities in the Galaxy. The code numerically solves the interstellar CR transport equation (including inhomogeneous and anisotropic diffusion, either in space and momentum, advective transport and energy losses), under realistic conditions. The new version includes an updated numerical solver and several models for the astrophysical ingredients involved in the transport equation. Improvements in the accuracy of the numerical solution are proved against analytical solutions and in reference diffusion scenarios. The novel features implemented in the code allow to simulate the diverse scenarios proposed to reproduce the most recent measurements of local and diffuse CR fluxes, going beyond the limitations of the homogeneous galactic transport paradigm. To this end, several applications using DRAGON2 are presented as well. This new version facilitates the users to include their own physical models by means of a modular C++ structure.

79 ASTRONOMY AND ASTROPHYSICS↗