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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 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Analysis of thermo-elastic problems using the improved element-free Galerkin method

The improved element-free Galerkin method (IEFG) is presented to deal with thermo-elastic problems. This mesh-free method is a combination between the element-free Galerkin method and the improved moving least-square approximation. It has not the Kronecker delta property, and the penalty method is used to impose the essential boundary conditions. In this paper, linear and stationary thermo-elasticity is treated. To solve the thermo-elastic problem, this latter is decoupled into two separate parts: first, the heat transfer problem is analyzed to reach the temperature field, which is used as input in the mechanical problem to calculate the displacement field and then the stress fields. Numerical examples with different boundary conditions are illustrated. The performance and the accuracy of the IEFG method are approved when obtained results are compared to finite-element results and analytical solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2010

Effective cubic nonlinearity and cnoidal waves in the degenerate parametric frequency conversion

It is shown that under the degenerate conditions (SHG and type-I degenerate parametric generation), the increase in the order of a system of truncated wave equations reduces the initial problem to the solution of two independent nonlinear Schroedinger equations, which allows one to write down the analytic solutions of the corresponding problems by using the standard methods for constructing the searched-for solutions in the form of cnoidal waves. It is established that in realising of cascade processes (quasi-synchronism), one of which is degenerate, this approach based on the introduction of the concept of the effective cascade cubic nonlinearity is not very convenient because the latter in the general case is no longer the Kerr one.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

A Method for Understanding the Behaviour of Radioactive Decay Chains in Radiological Assessments - 19382

In many radiological groundwater pathway assessments, especially those where the assessment timescales of interest are relatively short (say a few thousand years or less), contributions to effective dose or radiological risk are dominated by radionuclides such as C-14, Cl-36 or I-129. Over longer timescales, additional radionuclides can also become key contributors to risk. In particular, members of the U-238 decay chain, notably Ra-226 and Pb-210, are likely to be key radionuclides. Other decay chains that can contribute significantly to dose or risk at times far into the future include Np-237 → U-233 → Th-229 and U-235 → Pa-231 → Ac-227. In this paper, a method is described for understanding decay chain behaviour in radiological assessments. The method uses a graphical approach in which the various modes of transport and decay in a system of connected compartments are represented as pathways between two nodes in a two-dimensional grid. Each pathway corresponds to a distinct transport and decay process. By so doing, the different transport and decay processes can be identified in a systematic way. The result is an algorithm for generating the contributions to effective dose or radiological risk without explicit solution of the transport equations. The method has been tested against numerical models and analytic solutions and found to give excellent agreement, while at the same time providing information about decay chain behaviour that would be difficult to obtain from a numerical assessment model. The power of the method is illustrated by applying it to some examples based on real repository concepts. (authors)

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2016

Solution of D dimensional Dirac equation for hyperbolic tangent potential using NU method and its application in material properties

The analytical solution of D-dimensional Dirac equation for hyperbolic tangent potential is investigated using Nikiforov-Uvarov method. In the case of spin symmetry the D dimensional Dirac equation reduces to the D dimensional Schrodinger equation. The D dimensional relativistic energy spectra are obtained from D dimensional relativistic energy eigen value equation by using Mat Lab software. The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi polynomials. The thermodynamically properties of materials are generated from the non-relativistic energy eigen-values in the classical limit. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy. The thermal quantities of the system, partition function and specific heat, are expressed in terms of error function and imaginary error function which are numerically calculated using Mat Lab software.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Neutral skyrmion configurations in the low-energy effective theory of spinor-condensate ferromagnets

We study the low-energy effective theory of spinor condensate ferromagnets for the superfluid velocity and magnetization degrees of freedom. This effective theory describes the competition between spin stiffness and a long-range interaction between skyrmions, topological objects familiar from the theory of ordinary ferromagnets. We find exact solutions to the nonlinear equations of motion describing neutral configurations of skyrmions and antiskyrmions. These analytical solutions provide a simple physical picture for the origin of crystalline magnetic order in spinor condensate ferromagnets with dipolar interactions. We also point out the connections to effective theories for quantum Hall ferromagnets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Testing the Delayed Gamma Capability in MCNP6 - Paper 86

The mission of the Domestic Nuclear Detection Office (DNDO) is to quickly and reliably detect unauthorized attempts to import or transport special nuclear material (SNM) for use against the United States. Developing detection equipment to meet this objective requires accurate simulation of both the detectable signature and detection mechanism. MCNP6 is capable of transporting the various types of radiation encountered in these scenarios; however, the accuracy of MCNP6 must be quantified such that we can be confident in the results of the simulations. Delayed gamma transport is one important component of these detection scenarios. Delayed gamma transport is defined as the combination of gamma emission from radioactive and subsequent transport through matter. MCNP always possessed the ability to emit delayed neutrons from fission; however, these delayed neutron spectra and intensity were functional fits and not directly sampled from the created fission products. Furthermore, there existed no method to emit the decay photons from radioactive fission products (or any radioactive nucleus) 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. At the point of capture, a residual nucleus is created and decayed using the CINDER90 depletion code. MCNP only sends CINDER90 a residual radioactive nucleus and not a flux (i.e. capture rate). As a result, the Bateman equations for the solution are coupled first order differential equations with constant coefficients. Theoretically, these equations could be solved analytically; however, CINDER90 employs a numerical Markov linear chain scheme to solve these equations. This paper addresses a more simplified approach to benchmarking in order to best assess: (1) whether or not deficiencies exist in the current methodology for certain types of decay chains; and (2) paths forward for improving the delayed particle emission capability. We utilize closed form analytic solutions to the granddaughter equations for particular sets of isotope systems to compare the accuracy of the delayed gamma capability in MCNP6. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2010

Analytical and semianalytical solutions to the kinetic equation with Coulomb collision term and a monoenergetic source function

Analytical and semianalytical solutions have been obtained using a practical dimensionless form of Boltzmann kinetic equation assuming spatial homogeneity, azimuthal symmetry, and Maxwellian distributions of target plasma species. In contrast with formerly considered simplified equations with truncated collision terms, the exact Landau-Boltzmann collision operator is used, which conserves the number of particles, nullifies the collision term at statistical equilibrium, and describes the Maxwellization process naturally observed in correct solutions. A comparison with previous stationary and time-dependent analytical solutions is given. The new semianalytical results can be used in numerical modeling, for verification of solutions in more complex models, and in experimental data analysis, especially concerning nuclear processes and advanced localized, angle-resolved suprathermal particle diagnostics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Mixed convective heat transfer to Sisko fluid over a radially stretching sheet in the presence of convective boundary conditions

In this article, the mixed convective heat transfer to Sisko fluid over a radially stretching surface in the presence of convective boundary conditions is investigated. The viscous dissipation and thermal radiation effects are also taken into account. The suitable transformations are applied to convert the governing partial differential equations into a set of nonlinear coupled ordinary differential equations. The analytical solution of the governing problem is obtained by using the homotopy analysis method (HAM). Additionally, these analytical results are compared with the numerical results obtained by the shooting technique. The obtained results for the velocity and temperature are analyzed graphically for several physical parameters for the assisting and opposing flows. It is found that the effect of buoyancy parameter is more prominent in case of the assisting flow as compared to the opposing flow. Further, in tabular form the numerical values are given for the local skin friction coefficient and local Nusselt number. A remarkable agreement is noticed by comparing the present results with the results reported in the literature as a special case.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Group velocity and pulse lengthening of mismatched laser pulses in plasma channels

Analytic solutions are presented to the non-paraxial wave equation describing an ultra-short, low-power, laser pulse propagating in a plasma channel. Expressions for the laser pulse centroid motion and laser group velocity are derived, valid for matched and mismatched propagation in a parabolic plasma channel, as well as in vacuum, for an arbitrary Laguerre-Gaussian laser mode. The group velocity of a mismatched laser pulse, for which the laser spot size is strongly oscillating, is found to be independent of propagation distance and significantly less than that of a matched pulse. Laser pulse lengthening of a mismatched pulse owing to laser mode slippage is examined and found to dominate over that due to dispersive pulse spreading for sufficiently long pulses. Analytic results are shown to be in excellent agreement with numerical solutions of the full Maxwell equations coupled to the plasma response. Implications for plasma channel diagnostics are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

Cosmological solutions in bimetric gravity and their observational tests

We obtain the general cosmological evolution equations for a classically consistent theory of bimetric gravity. Their analytic solutions are demonstrated to generically allow for a cosmic evolution starting out from a matter dominated FLRW universe and relaxing towards a de Sitter (anti-de Sitter) phase at late cosmic time. In particular, we examine a subclass of models which contain solutions that are able to reproduce the expansion history of the cosmic concordance model inspite of the nonlinear couplings of the two metrics. This is demonstrated explicitly by fitting these models to observational data from Type Ia supernovae, Cosmic Microwave Background and Baryon Acoustic Oscillations. In the appendix we comment on the relation to massive gravity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Diaboloidal mirrors: algebraic solution and surface shape approximations

A new type of optical element that can focus a cylindrical wave to a point focus (or vice versa) is analytically described. Such waves are, for example, produced in a beamline where light is collimated in one direction and then doubly focused by a single optic. A classical example in X-ray optics is the collimated two-crystal monochromator, with toroidal mirror refocusing. The element here replaces the toroid, and in such a system provides completely aberration free, point-to-point imaging of rays from the on-axis source point. We present an analytic solution for the mirror shape in its laboratory coordinate system with zero slope at the centre, and approximate solutions, based on bending an oblique circular cone and a bent right circular cylinder, that may facilitate fabrication and metrology.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2017

Development of a point-kinetic verification scheme for nuclear reactor applications

In this paper, a new method that can be used for checking the proper implementation of time- or frequency-dependent neutron transport models and for verifying their ability to recover some basic reactor physics properties is proposed. This method makes use of the application of a stationary perturbation to the system at a given frequency and extraction of the point-kinetic component of the system response. Even for strongly heterogeneous systems for which an analytical solution does not exist, the point-kinetic component follows, as a function of frequency, a simple analytical form. The comparison between the extracted point-kinetic component and its expected analytical form provides an opportunity to verify and validate neutron transport solvers. The proposed method is tested on two diffusion-based codes, one working in the time domain and the other working in the frequency domain. As long as the applied perturbation has a non-zero reactivity effect, it is demonstrated that the method can be successfully applied to verify and validate time- or frequency-dependent neutron transport solvers. Although the method is demonstrated in the present paper in a diffusion theory framework, higher order neutron transport methods could be verified based on the same principles.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

The liquid-conduction, vapor-flow heat pipe model in Sockeye

A single-phase heat pipe flow model implemented in the heat pipe application Sockeye is described. This model solves one-dimensional, compressible flow equations for the vapor phase in the center of a heat pipe, which are coupled to the two-dimensional heat conduction equation for the wick, liquid, and cladding, as well as to an ordinary differential equation tracking the working fluid inventory in the evaporator section of the heat pipe. This model is demonstrated with several test problems, including comparisons to analytic solutions for the vapor flow fields, analytic curves for sonic and capillary limitations of heat pipe operation, and some experimental data. The numerical solution gives excellent agreement for verification problems and good agreement with experimental results. Also, demonstrations show that the model is very robust, allowing for full simulations of heat pipe transients, including frozen startup, sonic-limited (supersonic) flow, and heat pipe shutdown.

42 ENGINEERING↗
DOE OSTI2010

Mixing Cell Model: A One-Dimensional Numerical Model for Assessment of Water Flow and Contaminant Transport in the Unsaturated Zone

This report describes the Mixing Cell Model code, a one-dimensional model for water flow and solute transport in the unsaturated zone under steady-state or transient flow conditions. The model is based on the principles and assumptions underlying mixing cell model formulations. The unsaturated zone is discretized into a series of independent mixing cells. Each cell may have unique hydrologic, lithologic, and sorptive properties. Ordinary differential equations describe the material (water and solute) balance within each cell. Water flow equations are derived from the continuity equation assuming that unit-gradient conditions exist at all times in each cell. Pressure gradients are considered implicitly through model discretization. Unsaturated hydraulic conductivity and moisture contents are determined by the material-specific moisture characteristic curves. Solute transport processes include explicit treatment of advective processes, first-order chain decay, and linear sorption reactions. Dispersion is addressed through implicit and explicit dispersion. Implicit dispersion is an inherent feature of all mixing cell models and originates from the formulation of the problem in terms of mass balance around fully mixed volume elements. Expressions are provided that relate implicit dispersion to the physical dispersion of the system. Two FORTRAN codes were developed to solve the water flow and solute transport equations: (1) the Mixing-Cell Model for Flow (MCMF) solves transient water flow problems and (2) the Mixing Cell Model for Transport (MCMT) solves the solute transport problem. The transient water flow problem is typically solved first by estimating the water flux through each cell in the model domain as a function of time using the MCMF code. These data are stored in either ASCII or binary files that are later read by the solute transport code (MCMT). Code output includes solute pore water concentrations, water and solute inventories in each cell and at each specified output time, and water and solute fluxes through each cell and specified output time. Computer run times for coupled transient water flow and solute transport were typically several seconds on a 2 GHz Intel Pentium IV desktop computer. The model was benchmarked against analytical solutions and finite-element approximations to the partial differential equations (PDE) describing unsaturated flow and transport. Differences between the maximum solute flux estimated by the mixing-cell model and the PDE models were typically less than two percent.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS1973

Interior radiances in optically deep absorbing media. I - Exact solutions for one-dimensional model.

An exact analytic solution to the one-dimensional scattering problem with arbitrary single scattering albedo and arbitrary surface albedo is presented. Expressions are given for the emergent flux from a homogeneous layer, the internal flux within the layer, and the radiative heating. A comparison of these results with the values calculated from the matrix operator theory indicates an exceedingly high accuracy. A detailed study is made of the error in the matrix operator results and its dependence on the accuracy of the starting value.

Kattawar, G. W.↗
DOE OSTI2015

On the motion of a quantum particle in the spinning cosmic string space–time

We analyze the energy spectrum and the wave function of a particle subjected to magnetic field in the spinning cosmic string space–time and investigate the influence of the spinning reference frame and topological defect on the system. To do this we solve Schrödinger equation in the spinning cosmic string background. In our work, instead of using an approximation in the calculations, we use the quasi-exact ansatz approach which gives the exact solutions for some primary levels. - Highlights: • Solving the Schrödinger equation in the spinning cosmic string space time. • Proposing a quasi-exact analytical solution to the general form of the corresponding equation. • Generalizing the previous works.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Distinctive aspects of the evolution of galactic magnetic fields

We perform an in-depth analysis of the evolution of galactic magnetic fields within a semi-analytic galaxy formation and evolution framework, determine various distinctive aspects of the evolution process, and obtain analytic solutions for a wide range of possible evolution scenarios.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Approximate solutions for diffusive fracture-matrix transfer: Application to storage of dissolved CO 2 in fractured rocks

Analytical solutions with infinite exponential series are available to calculate the rate of diffusive transfer between low-permeability blocks and high-permeability zones in the subsurface. Truncation of these series is often employed by neglecting the early-time regime. Here in this paper, we present unified-form approximate solutions in which the early-time and the late-time solutions are continuous at a switchover time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the first coefficient dependent only on the dimensionless area-to-volume ratio. The last two coefficients are either determined analytically for isotropic blocks (e.g., spheres and slabs) or obtained by fitting the exact solutions, and they solely depend on the aspect ratios for rectangular columns and parallelepipeds. For the late-time solutions, only the leading exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic rectangular blocks. The optimal switchover time is between 0.157 and 0.229, with highest relative approximation error less than 0.2%. The solutions are used to demonstrate the storage of dissolved CO 2 in fractured reservoirs with low-permeability matrix blocks of single and multiple shapes and sizes. These approximate solutions are building blocks for development of analytical and numerical tools for hydraulic, solute, and thermal diffusion processes in low-permeability matrix blocks.

54 ENVIRONMENTAL SCIENCES↗