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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 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Hybrid time dependent/independent solution for the He I line ratio temperature and density diagnostic for a thermal helium beam with applications in the scrape-off layer-edge regions in tokamaks

Spectroscopic studies of line emission intensities and ratios offer an attractive option in the development of non-invasive plasma diagnostics. Evaluating ratios of selected He I line emission profiles from the singlet and triplet neutral helium spin systems allows for simultaneous measurement of electron density (n{sub e}) and temperature (T{sub e}) profiles. Typically, this powerful diagnostic tool is limited by the relatively long relaxation times of the {sup 3}S metastable term of helium that populates the triplet spin system, and on which electron temperature sensitive lines are based. By developing a time dependent analytical solution, we model the time evolution of the two spin systems. We present a hybrid time dependent/independent line ratio solution that improves the range of application of this diagnostic technique in the scrape-off layer (SOL) and edge plasma regions when comparing it against the current equilibrium line ratio helium model used at TEXTOR.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

Solid–Liquid Phase Change Driven by Internal Heat Generation

This article presents results of solid-liquid phase change, the Stefan Problem, where melting is driven internal heat generation, in a cylindrical geometry. The comparison between a quasi-static analytical solution for Stefan numbers less than one and numerical solutions shows good agreement. The computational results of phase change with internal heat generation show how convection cells form in the liquid region. A scale analysis of the same problem shows four distinct regions of the melting process.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2011

Diffuse interface field approach to modeling arbitrarily-shaped particles at fluid-fluid interfaces

We present a novel mesoscale simulation approach to modeling the evolution of solid particles segregated at fluid-fluid interfaces. The approach involves a diffuse- interface field description of each fluid phase in addition to the set of solid particles. The unique strength of the model is its generality to include particles of arbitrary shapes and orientations, as well as the ability to incorporate electrostatic particle interactions and external forces via a previous work [Millett PC, Wang YU, Acta Mater 2009;57:3101]. In this work, we verify that the model produces the correct capillary forces and contact angles by comparing with a well-defined analytical solution. In addition, simulation results of rotations of various-shaped particles at fluid-fluid interfaces, external force- induced capillary attraction/repulsion between particles, and spinodal decomposition arrest due to colloidal particle jamming at the interfaces are presented.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Displacement and localisation of a transparent nanosphere by light-pressure forces in the field of a focused laser beam

We report the results of a numerical simulation of the Langevin equation describing the motion of a transparent nanosphere under the action of a resulting light-pressure force in the field of a continuous focused Gaussian laser beam. The conditions for the localisation of the nanosphere near the focal waist of the beam focused by the lens are determined. An analytical solution of the approximate (truncated) equation of motion is found, which almost exactly coincides with the results of the numerical simulation of the initial equation. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Specific features of propagation of femtosecond laser pulses through a molecular gaseous medium under conditions of efficient alignment of molecules

The propagation of femtosecond laser pulses in a molecular gaseous medium is studied with the rotational dynamics of molecules under the action of these pulses taken into account. Based on the simultaneous numerical solution of the wave equation describing the laser pulse evolution and the Schroedinger equation that determines the quantum state evolution of the medium molecules, the rotational dynamics of molecules in the laser field and the laser pulse evolution are analysed with their mutual influence taken into account. Efficient dynamic alignment of molecules along the direction of laser radiation polarisation is observed, which causes variation in the spatiotemporal pulse profile, as well as significant broadening and deformation of its spectrum in the course of propagation through the medium. The physical mechanisms of the observed phenomena are analysed by using the approximate analytical solution of the problem, derived for the case of preliminary excitation of the medium by a pump pulse (the pump-probe scheme). (nonlinear optical phenomena)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Nonlinear evolution of an arbitrary density perturbation in a cold homogeneous unmagnetized plasma

An exact and general analytical solution describing the nonlinear evolution of a large amplitude plasma oscillation initiated by an arbitrary density perturbation which can be expressed as a Fourier series in x is found. This general solution is first used to reproduce the earlier results of R. C. Davidson and P. P. Schram [Nucl. Fusion 8, 183 (1968)] and J. M. Dawson [Phys. Rev. 113, 383 (1959)] using appropriate initial conditions and later applied to derive the space time evolution for a square wave and a triangular wave. It is found that the addition of a second harmonic increases the wave breaking limit of the fundamental mode. Analytical results pertaining to this two mode case have been verified using one-dimensional particle-in-cell simulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Bending of an Isotropic Plate with Two Identical Coaxial Through Cracks Depending on the Width of the Contact Zone of Their Faces and in the Presence of Plastic Zones Near Their Tips

We formulate and solve the problem of biaxial bending of an isotropic plate with two coaxial through cracks of identical lengths by distributed bending moments applied at infinity under the action of external load symmetric about the cracks with regard for the contact zone of their faces and in the presence of plastic zones near the crack tips, where the Tresca plasticity conditions are satisfied in the form of a surface layer or a plastic hinge. By using complex potentials of the plane problem and the classical theory of bending of the plates, we obtain an analytic solution of the problem in the class of functions bounded in the vicinity of the vertices of the plastic zones. The length of the plastic zones and the crack-tip opening displacements are found numerically.

42 ENGINEERING↗
DOE OSTI2011

Displacement operator for quantum systems with position-dependent mass

A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique commutation relation for x and p{sub {gamma}}. Such a formalism naturally leads to a Schroedinger-like equation that is reminiscent of wave equations typically used to model electrons with position-dependent (effective) masses propagating through abrupt interfaces in semiconductor heterostructures. The distinctive features of our approach are demonstrated through analytical solutions calculated for particles under null and constant potentials like infinite wells in one and two dimensions and potential barriers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Numerical simulation of the hydrodynamical combustion to strange quark matter

We present results from a numerical solution to the burning of neutron matter inside a cold neutron star into stable u,d,s quark matter. Our method solves hydrodynamical flow equations in one dimension with neutrino emission from weak equilibrating reactions, and strange quark diffusion across the burning front. We also include entropy change from heat released in forming the stable quark phase. Our numerical results suggest burning front laminar speeds of 0.002-0.04 times the speed of light, much faster than previous estimates derived using only a reactive-diffusive description. Analytic solutions to hydrodynamical jump conditions with a temperature-dependent equation of state agree very well with our numerical findings for fluid velocities. The most important effect of neutrino cooling is that the conversion front stalls at lower density (below {approx_equal}2 times saturation density). In a two-dimensional setting, such rapid speeds and neutrino cooling may allow for a flame wrinkle instability to develop, possibly leading to detonation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Solitons in yttrium iron garnet thin films with localized gain

We present the exact analytical solutions of cubic-quintic nonlinear Schrödinger equation with localized gain. We have demonstrated that the bright and dark solitons exist for the repulsive cubic and attractive quintic nonlinearity. These solutions have been obtained for those values of parameters which support the formation of solitons in Yttrium iron garnet thin films. Our results may be useful to understand the nonlinear pulse excitations in thin films.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2010

Early stage of superradiance from Bose-Einstein condensates

We investigate the dynamics of matter and optical waves at the early stage of superradiant Rayleigh scattering from Bose-Einstein condensates. Our analysis is within a spatially dependent quantum model which is capable of providing analytic solutions for the operators of interest. The predictions of the present model are compared to the predictions of a closely related mean-field model, and we provide a procedure that allows one to calculate quantum expectation values by averaging over semiclassical solutions. The coherence properties of the outgoing scattered light are also analyzed, and it is shown that the corresponding correlation functions may provide detailed information about the internal dynamics of the system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Flow of immiscible ferrofluids in a planar gap in a rotating magnetic field

Analytical solutions are obtained for the steady, fully developed flow of two layers of immiscible ferrofluids of different thicknesses between two parallel plates. Interfacial linear and internal angular momentum balance relations are derived for the case when there is a ferrofluid-ferrofluid interface to obtain the translational and spin velocity profiles in the gap. As expected for the limit of low applied field amplitude, the magnitude of the translational velocity is directly proportional to the frequency of the applied magnetic field and to the square of the magnetic field amplitude. Expressions for the velocity profiles are obtained for the zero spin viscosity and non-zero spin viscosity cases and the effect of applied pressure gradient on the flows is studied. The spin velocity in both ferrofluid phases is in the direction of the rotating magnetic field, except for cases of extreme applied pressure gradients for which the fluid vorticity opposes the spin. We find that for the case of non-zero spin viscosity, flow reversals are predicted using representative ferrofluid property values and field conditions. The unique predictions of the solution with non-zero spin viscosity could be used to experimentally test the existence of couple stresses in ferrofluids and the validity of previously reported values of the so-called spin viscosity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Second-harmonic generation in shear wave beams with different polarizations

A coupled pair of nonlinear parabolic equations was derived by Zabolotskaya [1] that model the transverse components of the particle motion in a collimated shear wave beam propagating in an isotropic elastic solid. Like the KZK equation, the parabolic equation for shear wave beams accounts consistently for the leading order effects of diffraction, viscosity and nonlinearity. The nonlinearity includes a cubic nonlinear term that is equivalent to that present in plane shear waves, as well as a quadratic nonlinear term that is unique to diffracting beams. The work by Wochner et al. [2] considered shear wave beams with translational polarizations (linear, circular and elliptical), wherein second-order nonlinear effects vanish and the leading order nonlinear effect is third-harmonic generation by the cubic nonlinearity. The purpose of the current work is to investigate the quadratic nonlinear term present in the parabolic equation for shear wave beams by considering second-harmonic generation in Gaussian beams as a second-order nonlinear effect using standard perturbation theory. In order for second-order nonlinear effects to be present, a broader class of source polarizations must be considered that includes not only the familiar translational polarizations, but also polarizations accounting for stretching, shearing and rotation of the source plane. It is found that the polarization of the second harmonic generated by the quadratic nonlinearity is not necessarily the same as the polarization of the source-frequency beam, and we are able to derive a general analytic solution for second-harmonic generation from a Gaussian source condition that gives explicitly the relationship between the polarization of the source-frequency beam and the polarization of the second harmonic.

42 ENGINEERING↗
DOE OSTI2013

Cosmological perturbations in theories with non-minimal coupling between curvature and matter

In this work, we examine how the presence of a non-minimal coupling between spacetime curvature and matter affects the evolution of cosmological perturbations on a homogeneous and isotropic Universe, and hence the formation of large-scale structure. This framework places constraints on the terms which arise due to the coupling with matter and, in particular, on the modified growth of matter density perturbations. We derive approximate analytical solutions for the evolution of matter overdensities during the matter dominated era and discuss the compatibility of the obtained results with the hypothesis that the late time acceleration of the Universe is driven by a non-minimal coupling.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2010

Inflation and reheating in spontaneously generated gravity

Inflation is studied in the context of induced gravity (IG) {gamma}{sigma}{sup 2}R, where R is the Ricci scalar, {sigma} a scalar field and {gamma} a dimensionless constant, and diverse symmetry-breaking potentials V({sigma}) are considered. In particular we compared the predictions for Landau-Ginzburg and Coleman-Weinberg type potentials and their possible generalizations with the most recent data. We find that large field inflation generally leads to fewer constraints on the parameters and the shape of the potential whereas small field inflation is more problematic and, if viable, implies more constraints, in particular, on the parameter {gamma}. We also examined the reheating phase and obtained an accurate analytical solution for the dynamics of the inflaton and the Hubble parameter by using a multiple scale analysis. The solutions were then used to study the average expansion of the Universe, the average equation of state for the scalar field and both the perturbative and resonant decays of the inflaton field.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

A stochastic Galerkin method for the Boltzmann equation with uncertainty

We develop a stochastic Galerkin method for the Boltzmann equation with uncertainty. The method is based on the generalized polynomial chaos (gPC) approximation in the stochastic Galerkin framework, and can handle random inputs from collision kernel, initial data or boundary data. We show that a simple singular value decomposition of gPC related coefficients combined with the fast Fourier-spectral method (in velocity space) allows one to compute the high-dimensional collision operator very efficiently. In the spatially homogeneous case, we first prove that the analytical solution preserves the regularity of the initial data in the random space, and then use it to establish the spectral accuracy of the proposed stochastic Galerkin method. Several numerical examples are presented to illustrate the validity of the proposed scheme.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Incidence of an electron layer on an electrically insulated body with an unsteady self-consistent positive charge

Dynamics of an electron layer incident on the surface of an electrically insulated conducting body with an unsteady self-consistent positive charge is investigated. At the initial instant, the electron velocity is directed toward the body and the electron layer is not adjacent to the body surface. One-dimensional plane, cylindrical, and spherical electron motions in vacuum and against the background of motionless ions and neutral particles are considered. Exact analytical solutions to the set of nonlinear plasma hydrodynamics equations with absorbing boundary conditions for electrons are obtained. The spatial and time dependences of the electric field, electron density, and electron velocity are found. The time evolution of the surface charge density is determined.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗