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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 847 records · Page 47
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DOE OSTI2010

Flat-top oscillons in an expanding universe

Oscillons are extremely long lived, oscillatory, spatially localized field configurations that arise from generic initial conditions in a large number of nonlinear field theories. With an eye towards their cosmological implications, we investigate their properties in an expanding universe. We (1) provide an analytic solution for one-dimensional oscillons (for the models under consideration) and discuss their generalization to three dimensions, (2) discuss their stability against long wavelength perturbations, and (3) estimate the effects of expansion on their shapes and lifetimes. In particular, we discuss a new, extended class of oscillons with surprisingly flat tops. We show that these flat-topped oscillons are more robust against collapse instabilities in (3+1) dimensions than their usual counterparts. Unlike the solutions found in the small amplitude analysis, the width of these configurations is a nonmonotonic function of their amplitudes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Sub-horizon evolution of cold dark matter perturbations through dark matter-dark energy equivalence epoch

We consider a cosmological model of the late universe constituted by standard cold dark matter plus a dark energy component with constant equation of state w and constant effective speed of sound. By neglecting fluctuations in the dark energy component, we obtain an equation describing the evolution of sub-horizon cold dark matter perturbations through the epoch of dark matter-dark energy equality. We explore its analytic solutions and calculate an exact w-dependent correction for the dark matter growth function, logarithmic growth function and growth index parameter through the epoch considered. We test our analytic approximation with the numerical solution and find that the discrepancy is less than 1% for 0k = during the cosmic evolution up to a = 100.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

General solution to gradient-induced transverse and longitudinal relaxation of spins undergoing restricted diffusion

We develop an approach, by calculating the autocorrelation function of spins, to derive the magnetic field gradient-induced transverse (T{sub 2}) relaxation of spins undergoing restricted diffusion. This approach is an extension to the method adopted by McGregor. McGregor's approach solves the problem only in the fast diffusion limit; however, our approach yields a single analytical solution suitable in all diffusion regimes, including the intermediate regime. This establishes a direct connection between the well-known slow diffusion result of Torrey and the fast diffusion result. We also perform free induction decay measurements on spin-exchange optically polarized {sup 3}He gas with different diffusion constants. The measured transverse relaxation profiles are compared with the theory and satisfactory agreement has been found throughout all diffusion regimes. In addition to the transverse relaxation, this approach is also applicable to solving the longitudinal relaxation (T{sub 1}) regardless of the diffusion limits. It turns out that the longitudinal relaxation in the slow diffusion limit differs by a factor of 2 from that in the fast diffusion limit.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2010

Diffraction in time in tunneling phenomena

This paper reviews exact analytical results on diffraction in time for tunneling of a particle through an arbitrary potential of finite range. It emphasizes the essential role played by the formalism of resonant states to derive the analytical solution to the time-dependent Schroedinger equation as an initial value problem and in the analysis of the corresponding transient behavior.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Hydro-chemo-mechanical phase field formulation for corrosion induced cracking in reinforced concrete

Steel corrosion induced cracking in reinforced concrete structures is often caused by volumetric straining at the steel-concrete interface. This volumetric strain is mainly controlled by the rate of generation of corrosion product, which depends on the diffusion of Cl{sup −} and dissolved O{sub 2} as well as the chemical reaction at the steel-concrete interface. While many numerical modeling techniques have been proposed to tackle this complex phenomenon, most have been limited to using staggered solution schemes, where the diffusion, chemical reaction, mechanical strain, and crack fields are solved for separately. Unfortunately, such approaches introduce numerical errors that can lead to unrealistic predictions. Therefore, a coupled solution, is needed to remove the formulation induced errors and understand this complex phenomenon. To provide a unifying solution framework for corrosion induced cracking in reinforced concrete, a phase field formulation is presented and implemented with FEM algorithms. The governing equations are derived from the system's free energy and Fick's law of diffusion. The proposed formulation was first validated in 1D by comparing the modeling results with the semi-analytical solution approximated via Laurent series to avoid singularities in the complex domain. 2D plane strain solutions to the embedded rebar undergoing corrosion induced cracking with pre-cracks are also presented and compared with the approximated solutions from linear elastic fracture mechanics theory (LEFM). The modeling of crack propagation enabled by the proposed formulation is also presented along with parametric studies to reveal the roles of the fracture toughness and permeability of the concrete on the corrosion induced cracking. A case study was also conducted on H-pile steel with concrete jackets to demonstrate the feasibility of modeling corrosion induced fracture in reinforced concrete structures with complex steel-concrete interfaces.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Solution of second order quasi-linear boundary value problems by a wavelet method

A wavelet Galerkin method based on expansions of Coiflet-like scaling function bases is applied to solve second order quasi-linear boundary value problems which represent a class of typical nonlinear differential equations. Two types of typical engineering problems are selected as test examples: one is about nonlinear heat conduction and the other is on bending of elastic beams. Numerical results are obtained by the proposed wavelet method. Through comparing to relevant analytical solutions as well as solutions obtained by other methods, we find that the method shows better efficiency and accuracy than several others, and the rate of convergence can even reach orders of 5.8.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Dynamics of Majorana fermions in two-dimensions

A Majorana fermion is the single fermionic particle that is its own antiparticle. Its dynamics is determined by the Majorana equation where the spinor field (ψ) is by definition equal to its charge-conjugate field (ψ{sub c}). Here, we study the dynamics of Majorana fermions in the presence of the most general static external field in 1+1 dimensions, which is just a scalar potential, by implementing for the first time the methods of supersymmetric quantum mechanics. In particular, for potentials for which shape invariance holds, we show how to obtain analytical solutions. We find that although this equation does have bound states, it does not have stationary states. The approach is illustrated with a linear potential.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Quantum Fisher information flow and non-Markovian processes of open systems

We establish an information-theoretic approach for quantitatively characterizing the non-Markovianity of open quantum processes. Here, the quantum Fisher information (QFI) flow provides a measure to statistically distinguish Markovian and non-Markovian processes. A basic relation between the QFI flow and non-Markovianity is unveiled for quantum dynamics of open systems. For a class of time-local master equations, the exactly analytic solution shows that for each fixed time the QFI flow is decomposed into additive subflows according to different dissipative channels.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Application of GOTHIC to Groundwater Transport Analysis - 20152

Migration of pollutants and hazardous wastes, potentially containing radioactive isotopes, via groundwater transport is a concern at most waste cleanup sites. Predictive analysis can be used to evaluate mitigating actions intended to minimize impact on the environment and public exposure. GOTHIC is a multipurpose thermal hydraulics code that is used extensively in the nuclear industry for design, licensing and operation evaluations. It combines the capabilities of typical one-dimensional system codes and the essential features of Computational Fluid Dynamics (CFD) codes for three-dimensional analysis. There are other codes that are specifically developed for groundwater transport analysis and the results presented here are consistent with prior analyses. However, GOTHIC has some unique features that offer advantages for applications related to nuclear waste. Most importantly, it has been developed and maintained under a Quality Assurance program in compliance with the requirements of 10CFR50 Appendix B [2] and applicable portions of ASME NQA-1 [3] since 1995. Available GOTHIC capabilities that make the code especially useful for groundwater transport of nuclear materials include: - Tracking of any number of tracer elements for contaminants and other species of interest; - Radioactive decay and progeny of tracer elements; - Adsorption/desorption of tracer elements; - Tracking of any number of dissolved gases; - Release and absorption for dissolved gases; - Vapor phase tracking; - Non-Newtonian fluid modeling. The general porous body modeling approach makes GOTHIC well suited to groundwater transport analysis. The multi-region modeling approach used by GOTHIC simplifies model construction for regions of varying hydrologic characteristics and focuses the computational effort on regions of particular interest while simultaneously capturing the macroscopic response and any feedback effects across the larger domain. The applicability of GOTHIC to groundwater transport applications is demonstrated by comparing code results with available analytic or semi-analytic solutions for groundwater behavior. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2019

Recent Regulatory Challenges Associated with Managing NORM and TENORM Waste Streams in the United States - 19609

Recent regulatory changes in several states in the United States (U.S.) have introduced new challenges to industries impacted with naturally occurring radioactive materials (NORM) and/or technologically enhanced NORM (TENORM) requiring innovative solutions. Because NORM and TENORM are specifically exempt from U.S. Nuclear Regulatory Commission (NRC) regulations, the onus falls on the 50 states to regulate their use and disposal. Over the past 10 years, regulations applying to NORM and TENORM have been drafted, passed, or updated in multiple states, including North Dakota, Pennsylvania, Illinois, and West Virginia to name a few. Solutions and lessons learned before and during the recent regulatory changes for a variety of clients, including specialty metals, mining, and oil and gas (O and G), are presented. In addition, the design and implementation of the comprehensive study of NORM/TENORM associated with conventional and unconventional O and G production activities in Pennsylvania on behalf of the Pennsylvania Department of Environmental Protection (PADEP) is presented, and the development of analytical solutions and waste processes designed to minimize the impact of the new regulations while maintaining compliance is discussed. (author)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2016

New Tools to Prepare ACE Cross-section Files for MCNP Analytic Test Problems

Monte Carlo calculations using one-group cross sections, multigroup cross sections, or simple continuous energy cross sections are often used to: (1) verify production codes against known analytical solutions, (2) verify new methods and algorithms that do not involve detailed collision physics, (3) compare Monte Carlo calculation methods with deterministic methods, and (4) teach fundamentals to students. In this work we describe 2 new tools for preparing the ACE cross-section files to be used by MCNP ® for these analytic test problems, simple_ace.pl and simple_ace_mg.pl.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2010

A Three Level Analytic Model for Alkali Vapor Lasers

A three level analytic model for optically pumped alkali metal vapor lasers is developed considering the steady-state rate equations for the longitudinally averaged number densities of the ground {sup 2}S{sub 1/2} and first excited {sup 2}P{sub 1/2} and {sup 2}P{sub 3/2} states. The threshold pump intensity includes both the requirements to fully bleach the pump transition and exceed optical losses, typically about 200 W/cm{sup 2}. Slope efficiency depends critically on the fraction of incident photons absorbed and the overlap of pump and resonator modes, approaching the quantum efficiency of 0.95-0.98, depending on alkali atom. For efficient operation, the collisional relaxation between the two upper levels should be fast relative to stimulated emission. By assuming a statistical distribution between the upper levels, the limiting analytic solution for the quasi-two level system is achieved. Application of the model and comparisons to recent laser demonstrations is presented.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2014

Quantum harmonic oscillator with superoscillating initial datum

In this paper, we study the evolution of superoscillating initial data for the quantum driven harmonic oscillator. Our main result shows that superoscillations are amplified by the harmonic potential and that the analytic solution develops a singularity in finite time. We also show that for a large class of solutions of the Schrödinger equation, superoscillating behavior at any given time implies superoscillating behavior at any other time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge–Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid–solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

A model and numerical method for compressible flows with capillary effects

A new model for interface problems with capillary effects in compressible fluids is presented together with a specific numerical method to treat capillary flows and pressure waves propagation. This new multiphase model is in agreement with physical principles of conservation and respects the second law of thermodynamics. A new numerical method is also proposed where the global system of equations is split into several submodels. Each submodel is hyperbolic or weakly hyperbolic and can be solved with an adequate numerical method. This method is tested and validated thanks to comparisons with analytical solutions (Laplace law) and with experimental results on droplet breakup induced by a shock wave.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2011

On Certain Reductions of Integrable Equations on Symmetric Spaces

We derive a Z{sub 2}xZ{sub 2} reduced integrable system which is deeply connected with the famous Heisenberg ferromagnet equation. Its Lax pair is associated with the symmetric space SO(5)/SO(2)xSO(3). We study the spectral properties of the scattering operator, introduce the basic notions of its direct scattering problem and construct fundamental analytic solutions in terms of Volterra integral equations. We obtain recursion operator to describe the hierarchy of higher order equations associated with the same Lax operator L.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Plasmas generated by ultra-violet light rather than electron impact

We analyze, in both plane and cylindrical geometries, a collisionless plasma consisting of an inner region where generation occurs by UV illumination, and an un-illuminated outer region with no generation. Ions generated in the inner region flow outwards through the outer region and into a wall. We solve for this system's steady state, first in the quasi-neutral regime (where the Debye length λ{sub D} vanishes and analytic solutions exist) and then in the general case, which we solve numerically. In the general case, a double layer forms where the illuminated and un-illuminated regions meet, and an approximately quasi-neutral plasma connects the double layer to the wall sheath; in plane geometry, the ions coast through the quasi-neutral section at slightly more than the Bohm speed c{sub s}. The system, although simple, therefore has two novel features: a double layer that does not require counter-streaming ions and electrons, and a quasi-neutral plasma where ions travel in straight lines with at least the Bohm speed. We close with a précis of our asymptotic solutions of this system, and suggest how our theoretical conclusions might be extended and tested in the laboratory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2010

Non-Markovian dynamics of a damped driven two-state system

We study a driven two-state system interacting with a generic structured environment. We outline the derivation of the time-local microscopic non-Markovian master equation, in the limit of weak coupling between the system and the reservoir, and we derive its analytic solution for general reservoir spectra in the regime of validity of the secular approximation. We also consider the non-Markovian master equation without the secular approximation and study the effect of nonsecular terms on the system dynamics for two classes of reservoir spectra: the Ohmic and the Lorentzian reservoir. Finally, we derive the analytic conditions for complete positivity of the dynamical map, with and without the secular approximation. Interestingly, the complete positivity conditions have a transparent physical interpretation in terms of the characteristic time scales of phase diffusion and relaxation processes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗