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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 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

NON-RELATIVISTIC RADIATION-MEDIATED SHOCK BREAKOUTS. I. EXACT BOLOMETRIC PLANAR BREAKOUT SOLUTIONS

The problem of a non-steady planar radiation-mediated shock (RMS) breaking out from a surface with a power-law density profile, {rho}{proportional_to}x{sup n} , is numerically solved in the approximation of diffusion with constant opacity. For an appropriate choice of time, length, and energy scales, determined by the breakout opacity, velocity, and density, the solution is universal, i.e., depends only on the density power-law index n. The resulting luminosity depends weakly on the value of n. An approximate analytic solution, based on the self-similar hydrodynamic solutions and on the steady RMS solutions, is constructed and shown to agree with the numerical solutions as long as the shock is far from the surface, {tau} >> c/v{sub sh}. Approximate analytic expressions, calibrated based on the exact solutions, are provided, which describe the escaping luminosity as a function of time. These results can be used to calculate the bolometric properties of the bursts of radiation produced during supernova shock breakouts. For completeness, we also use the exact breakout solutions to provide an analytic approximation for the maximum surface temperature for fast (v{sub sh} {approx}> 0.1) non-thermal breakouts and show that it is a few times smaller than inferred based on steady state RMS solutions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

On the possible gain of the application of the SP{sub 3} solution in nodal codes

The simplified P{sub N} method has attracted much attention in reactor physics. The implementation of an increased order expansion has the potential to improve the results. It is investigated if this potential can be released under the specific features of nodal codes with fuel assembly sized calculation cells. One dimensional analytical solutions for the one and two energy-group diffusion, SP{sub 3} and P{sub 3} equations are derived. The results are compared to reference solutions calculated with ONEDANT and HELIOS. Tests are performed on the Brantley/Larsen one-group test case and on a pin cell with real reactor materials. For the evaluation of the differences between the diffusion and the SP{sub 3} solutions in the nodal code configuration, benchmark configurations are investigated. A comparison of the diffusion and the SP{sub 3} results show improvements for the test case using fuel element size nodes, where the reference solution uses the identical cross section basis. Comparing with a multi-group reference solution shows that the diffusion solution sometimes behaves better due to error cancellation. To achieve the full gain of the SP{sub 3} method in nodal calculations, a new standard for light water reactor calculations has to be defined with a refined energy-group structure. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Boundary node Petrov–Galerkin method in solid structures

Based on the interpolation of the Lagrange series and the Finite Block Method (FBM), the formulations of the Boundary Node Petrov–Galerkin Method (BNPGM) are presented in the weak form in this paper and their applications are demonstrated to the elasticity of functionally graded materials, subjected to static and dynamic loads. By introducing the mapping technique, a block of quadratic type is transformed from the Cartesian coordinate to the normalized coordinate with 8 seeds for two-dimensional problems. The first-order partial differential matrices of boundary nodes are obtained in terms of the nodal values of the boundary node, which can be utilized to determine the tractions on the boundary. Time-dependent partial differential equations are analyzed in the Laplace transformed domain and the Durbin’s inversion method is applied to determine the physical values in the time domain. Illustrative numerical examples are given and comparison has been made with the analytical solutions, the Boundary Element Method (BEM) and the Finite Element Method (FEM).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2010

Nonlinear lower-hybrid oscillations in cold plasma

In a fluid description nonlinear lower-hybrid oscillation have been studied in a cold quasineutral magnetized plasma using Lagrangian variables. An exact analytical solution with nontrivial space and time dependence is obtained. The solution demonstrates that under well defined initial and boundary conditions the amplitude of the oscillations increases due to nonlinearity and then comes back to its initial condition again. These solutions indicate a class of nonlinear transient structures in magnetized plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Donut wakefields generated by intense laser pulses with orbital angular momentum

We study the wakefields produced in a plasma by intense laser pulses carrying a finite amount of orbital angular momentum. We show that these wakefields have new donut-like shapes, different from those usually considered in the literature, and could be used to accelerate hollow electron beams. Wakefields with a more general angular structure were also considered. The analytical solutions are corroborated by relativistic particle-in-cell simulations using OSIRIS.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

A method for evaluating the expectation value of a power spectrum using the probability density function of phases

Here, we present a new method to evaluate the expectation value of the power spectrum of a time series. A statistical approach is adopted to define the method. After its demonstration, it is validated showing that it leads to the known properties of the power spectrum when the time series contains a periodic signal. The approach is also validated in general with numerical simulations. The method puts into evidence the importance that is played by the probability density function of the phases associated to each time stamp for a given frequency, and how this distribution can be perturbed by the uncertainties of the parameters in the pulsar ephemeris. We applied this method to solve the power spectrum in the case the first derivative of the pulsar frequency is unknown and not negligible. We also undertook the study of the most general case of a blind search, in which both the frequency and its first derivative are uncertain. We found the analytical solutions of the above cases invoking the sum of Fresnel's integrals squared.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

The Thermal Phase Curve Offset on Tidally and Nontidally Locked Exoplanets: A Shallow Water Model

Using a shallow water model with time-dependent forcing, we show that the peak of an exoplanet thermal phase curve is, in general, offset from the secondary eclipse when the planet is rotating. That is, the planetary hot spot is offset from the point of maximal heating (the substellar point) and may lead or lag the forcing; the extent and sign of the offset are functions of both the rotation rate and orbital period of the planet. We also find that the system reaches a steady state in the reference frame of the moving forcing. The model is an extension of the well-studied Matsuno–Gill model into a full spherical geometry and with a planetary-scale translating forcing representing the insolation received on an exoplanet from a host star. The speed of the gravity waves in the model is shown to be a key metric in evaluating the phase curve offset. If the velocity of the substellar point (relative to the planet’s surface) exceeds that of the gravity waves, then the hot spot will lag the substellar point, as might be expected by consideration of forced gravity wave dynamics. However, when the substellar point is moving slower than the internal wave speed of the system, the hottest point may lead the passage of the forcing. We provide an interpretation of this result by consideration of the Rossby and Kelvin wave dynamics, as well as, in the very slowly rotating case, a one-dimensional model that yields an analytic solution. Finally, we consider the inverse problem of constraining planetary rotation rate from an observed phase curve.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Design of and data reduction from compact Thomson parabola spectrometers

Thomson parabola spectrometers are used to characterize MeV ion beams produced in high intensity laser interactions. These spectrometers disperse multiple ion species according to their charge to mass ratio through the use of parallel electric and magnetic fields. Analytical solutions for ion deflection in electric and magnetic fields have been used to extract ion spectra with the assumption that fringing effects are negligible. Experimental space restrictions and dynamic range requirements necessitate designs that stress the analytical assumptions. Depending on design parameters, the error in the analytical assumption can be comparable to the energy resolution. Estimates are provided to approximate the error on the total ion deflection. A method for modeling ion trajectories including fringing effects is presented using software freely available or in common use. The magnetostatic fields are modeled in 3D, including material properties of nearby magnetic materials using RADIA. Electrostatic fields are modeled in 2D for a spectrometer implementing angled plates using the partial differential equation toolbox in MATLAB. Using these models to calculate the ion trajectory allows for analysis of a Thomson parabola spectrometer with an arbitrary field configuration.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

Intrinsic toroidal rotation in the scrape-off layer of tokamaks

The origin and nature of intrinsic toroidal plasma rotation in the scrape-off-layer (SOL) of tokamaks is investigated both analytically and through numerical simulations. It is shown that the equilibrium poloidal E × B flow, the sheath physics, and the presence of poloidal asymmetries in the pressure profile act as sources of momentum, while turbulence provides the mechanism for the radial momentum transport. An equation for the radial and poloidal dependence of the equilibrium parallel ion flow is derived, and a simple analytical solution is presented. This solution reproduces and explains the main experimental trends for the Mach number found in the SOL of tokamaks. Global, three-dimensional fluid simulations of SOL turbulence in different limiter configurations confirm the validity of the analytical theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Hydrodynamic growth and decay of planar shock waves

A model for the hydrodynamic attenuation (growth and decay) of planar shocks is presented. The model is based on the approximate integration of the fluid conservation equations, and it does not require the heuristic assumptions used in some previous works. A key issue of the model is that the boundary condition on the piston surface is given by the retarded pressure, which takes into account the transit time of the sound waves between the piston and any position at the bulk of the shocked fluid. The model yields the shock pressure evolution for any given pressure pulse on the piston, as well as the evolution of the trajectories, velocities, and accelerations on the shock and piston surfaces. An asymptotic analytical solution is also found for the decay of the shock wave.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Solving fractional Schrödinger-type spectral problems: Cauchy oscillator and Cauchy well

This paper is a direct offspring of the work of Garbaczewski and Stephanovich [“Lévy flights and nonlocal quantum dynamics,” J. Math. Phys. 54, 072103 (2013)] where basic tenets of the nonlocally induced random and quantum dynamics were analyzed. A number of mentions were made with respect to various inconsistencies and faulty statements omnipresent in the literature devoted to so-called fractional quantum mechanics spectral problems. Presently, we give a decisive computer-assisted proof, for an exemplary finite and ultimately infinite Cauchy well problem, that spectral solutions proposed so far were plainly wrong. As a constructive input, we provide an explicit spectral solution of the finite Cauchy well. The infinite well emerges as a limiting case in a sequence of deepening finite wells. The employed numerical methodology (algorithm based on the Strang splitting method) has been tested for an exemplary Cauchy oscillator problem, whose analytic solution is available. An impact of the inherent spatial nonlocality of motion generators upon computer-assisted outcomes (potentially defective, in view of various cutoffs), i.e., detailed eigenvalues and shapes of eigenfunctions, has been analyzed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Quantum tomography meets dynamical systems and bifurcations theory

A powerful tool for studying geometrical problems in Hilbert spaces is developed. We demonstrate the convergence and robustness of our method in every dimension by considering dynamical systems theory. This method provides numerical solutions to hard problems involving many coupled nonlinear equations in low and high dimensions (e.g., quantum tomography problem, existence and classification of Pauli partners, mutually unbiased bases, complex Hadamard matrices, equiangular tight frames, etc.). Additionally, this tool can be used to find analytical solutions and also to implicitly prove the existence of solutions. Here, we develop the theory for the quantum pure state tomography problem in finite dimensions but this approach is straightforwardly extended to the rest of the problems. We prove that solutions are always attractive fixed points of a nonlinear operator explicitly given. As an application, we show that the statistics collected from three random orthonormal bases is enough to reconstruct pure states from experimental (noisy) data in every dimension d ⩽ 32.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Analysis and approximations for crossing two nearby spin resonances

Solutions to the T-BMT spin equation have to date been confined to the single resonance crossing. However, in reality most cases of interest concern the overlapping of several resonances. To date there has been several serious studies of this problem; however, a good analytical solution or even approximation has eluded the community. We show that the T-BMT equation can be transformed into a Hill’s like equation. In this representation it can be shown that, while the single resonance crossing represents the solution to the Parabolic Cylinder equation, the overlapping case becomes a parametric type of resonance. We present possible approximations for both the non-accelerating case and accelerating case.

43 PARTICLE ACCELERATORS↗
DOE OSTI2011

Efficient spectral and pseudospectral algorithms for 3D simulations of whistler-mode waves in a plasma

Efficient spectral and pseudospectral algorithms for simulation of linear and nonlinear 3D whistler waves in a cold electron plasma are developed. These algorithms are applied to the simulation of whistler waves generated by loop antennas and spheromak-like stationary waves of considerable amplitude. The algorithms are linearly stable and show good stability properties for computations of nonlinear waves over tens of thousands of time steps. Additional speedups by factors of 10-20 (comparing single core CPU and one GPU) are achieved by using graphics processors (GPUs), which enable efficient numerical simulation of the wave propagation on relatively high resolution meshes (tens of millions nodes) in personal computing environment. Comparisons of the numerical results with analytical solutions and experiments show good agreement. The limitations of the codes and the performance of the GPU computing are discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2010

Effective contact pairing forces from realistic calculations in infinite homogeneous nuclear matter

Nonempirical effective contact pairing forces to be used in self-consistent mean-field calculations are presented. These pairing forces, constructed so as to reproduce exactly any given microscopic pairing gaps in infinite homogeneous nuclear matter for any isospin asymmetry, are given in analytical form. As a by-product, this work provides an analytical solution of the BCS gap equations which could be applied to describe various many-body systems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Verification of the Two-Fluid Model in the Spectral Element Code Nek-2P for Adiabatic Flow Conditions

The simulation of multiphase flow is a difficult physical, computational, and numerical problem. Sophisticated tools are necessary to provide results encompassing a wide range of physical phenomena. The development of these tools must be supported by rigorous analysis and ongoing efforts of verification and validation to ensure the accuracy of simulations. The Nek-2P multiphase code is being developed at Argonne with the general goal of simulating a wide range of multiphase flows and the primary goal of simulating boiling flows in LWR fuel assemblies. As part of this, there is an ongoing effort to verify the code and validate the underlying physical models. The objective of this work is to present recent results in the verification of Nek-2P. As a starting point, this work is focused on adiabatic flows for the sake of simplicity with the immediate next planned step to expand the effort to include heat and mass transfer. Details of the verification of the implemented mass fraction transport, momentum conservation, and pressure equations in Nek-2P are presented. Results of simulations are compared to analytic solutions when possible, however due to the complexity of multiphase flows, these are seldom available. To overcome this difficulty, an independent model is used to provide solutions for comparison.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2010

The physics of FEL in an infinite electron beam

We solve linearized Vlasov-Maxwell FEL equations for a 3-D perturbation in the infinite electron beam with Lorentzian energy distributions using paraxial approximation. We present analytical solutions for various initial perturbations and discuss the effect of optical guiding in such system.

43 PARTICLE ACCELERATORS↗