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Results for “diffusion equation”

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 1,405 records · Page 78
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Evolution of a proto-neutron star with a nuclear many-body equation of state: Neutrino luminosity and gravitational wave frequencies

In a core-collapse supernova, a huge amount of energy is released in the Kelvin-Helmholtz phase subsequent to the explosion, when the proto-neutron star cools and deleptonizes as it loses neutrinos. Most of this energy is emitted through neutrinos, but a fraction of it can be released through gravitational waves. We model the evolution of a proto-neutron star in the Kelvin-Helmholtz phase using a general relativistic numerical code, and a recently proposed finite temperature, many-body equation of state; from this we consistently compute the diffusion coefficients driving the evolution. To include the many-body equation of state, we develop a new fitting formula for the high density baryon free energy at finite temperature and intermediate proton fraction. Here, we estimate the emitted neutrino signal, assessing its detectability by present terrestrial detectors, and we determine the frequencies and damping times of the quasinormal modes which would characterize the gravitational wave signal emitted in this stage.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Microwave gas breakdown in elliptical waveguides

This paper analyzes the microwave gas discharge within elliptical waveguides excited by the fundamental mode. The Rayleigh-Ritz method has been applied to solve the continuity equation. The eigenvalue problem defined by the breakdown condition has been solved and the effective diffusion length of the elliptical waveguide has been calculated, what is used to find the corona threshold. This paper extends the microwave breakdown model developed for circular waveguides and shows the better corona withstanding capabilities of elliptical waveguides. The corona breakdown electric field threshold obtained with the variational method has been compared with the one calculated with the Finite Elements Method, showing excellent agreement.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Technical Note: Analytical Solution for Transient Partitioning and Reaction of a Condensing Vapor Species in a Droplet

We present the exact analytical solution of the transient equation of gas-phase diffusion of a condensing vapor to, and diffusion and reaction in, an aqueous droplet. Droplet-phase reaction is represented by first-order chemistry. The solution facilitates study of the dynamic nature of the vapor uptake process as a function of droplet size, Henry’s law coefficient, and first-order reaction rate constant for conversion in the droplet phase.

Liu, Albert T.↗
DOE OSTI2020

SubTSBR to tackle high noise and outliers for data-driven discovery of differential equations

Data-driven discovery of differential equations has been an emerging research topic. We propose a novel algorithm subsampling-based threshold sparse Bayesian regression (SubTSBR) to tackle high noise and outliers. The subsampling technique is used for improving the accuracy of the Bayesian learning algorithm. It has two parameters: subsampling size and the number of subsamples. When the subsampling size increases with fixed total sample size, the accuracy of our algorithm goes up and then down. When the number of subsamples increases, the accuracy of our algorithm keeps going up. We demonstrate how to use our algorithm step by step and compare our algorithm with threshold sparse Bayesian regression (TSBR) for the discovery of differential equations. We show that our algorithm produces better results. We also discuss the merits of discovering differential equations from data and demonstrate how to discover models with random initial and boundary condition as well as models with bifurcations. The numerical examples are: (1) predator-prey model with noise, (2) shallow water equations with outliers, (3) heat diffusion with random initial and boundary condition, and (4) fish-harvesting problem with bifurcations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Mixed quantum classical calculation of proton transfer reaction rates: From deep tunneling to over the barrier regimes

We present mixed quantum classical calculations of the proton transfer (PT) reaction rates represented by a double well system coupled to a dissipative bath. The rate constants are calculated within the so called nontraditional view of the PT reaction, where the proton motion is quantized and the solvent polarization is used as the reaction coordinate. Quantization of the proton degree of freedom results in a problem of non-adiabatic dynamics. By employing the reactive flux formulation of the rate constant, the initial sampling starts from the transition state defined using the collective reaction coordinate. Dynamics of the collective reaction coordinate is treated classically as over damped diffusive motion, for which the equation of motion can be derived using the path integral, or the mixed quantum classical Liouville equation methods. The calculated mixed quantum classical rate constants agree well with the results from the numerically exact hierarchical equation of motion approach for a broad range of model parameters. Moreover, we are able to obtain contributions from each vibrational state to the total reaction rate, which helps to understand the reaction mechanism from the deep tunneling to over the barrier regimes. The numerical results are also compared with those from existing approximate theories based on calculations of the non-adiabatic transmission coefficients. It is found that the two-surface Landau-Zener formula works well in calculating the transmission coefficients in the deep tunneling regime, where the crossing point between the two lowest vibrational states dominates the total reaction rate. When multiple vibrational levels are involved, including additional crossing points on the free energy surfaces is important to obtain the correct reaction rate using the Landau-Zener formula.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Water in protoplanetary disks: Deuteration and turbulent mixing

We investigate water and deuterated water chemistry in turbulent protoplanetary disks. Chemical rate equations are solved with the diffusion term, mimicking turbulent mixing in a vertical direction. Water near the midplane is transported to the disk atmosphere by turbulence and is destroyed by photoreactions to produce atomic oxygen, while the atomic oxygen is transported to the midplane and reforms water and/or other molecules. We find that this cycle significantly decreases column densities of water ice at r ≲ 30 AU, where dust temperatures are too high to reform water ice effectively. The radial extent of such region depends on the desorption energy of atomic hydrogen. Our model indicates that water ice could be deficient even outside the sublimation radius. Outside this radius, the cycle decreases the deuterium-to-hydrogen (D/H) ratio of water ice from ∼2 × 10{sup –2}, which is set by the collapsing core model, to 10{sup –4}-10{sup –2} in 10{sup 6} yr, without significantly decreasing the water ice column density. The resultant D/H ratios depend on the strength of mixing and the radial distance from the central star. Our finding suggests that the D/H ratio of cometary water (∼10{sup –4}) could be established (i.e., cometary water could be formed) in the solar nebula, even if the D/H ratio of water ice delivered to the disk was very high (∼10{sup –2}).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Reprocessing of ices in turbulent protoplanetary disks: Carbon and nitrogen chemistry

We study the influence of the turbulent transport on ice chemistry in protoplanetary disks, focusing on carbon- and nitrogen-bearing molecules. Chemical rate equations are solved with the diffusion term, mimicking the turbulent mixing in the vertical direction. Turbulence can bring ice-coated dust grains from the midplane to the warm irradiated disk surface, and the ice mantles are reprocessed by photoreactions, thermal desorption, and surface reactions. The upward transport decreases the abundance of methanol and ammonia ices at r ≲ 30 AU because warm dust temperature prohibits their reformation on grain surfaces. This reprocessing could explain the smaller abundances of carbon and nitrogen bearing molecules in cometary coma than those in low-mass protostellar envelopes. We also show the effect of mixing on the synthesis of complex organic molecules (COMs) in two ways: (1) transport of ices from the midplane to the disk surface and (2) transport of atomic hydrogen from the surface to the midplane. The former enhances the COMs formation in the disk surface, while the latter suppresses it in the midplane. Then, when mixing is strong, COMs are predominantly formed in the disk surface, while their parent molecules are (re)formed in the midplane. This cycle expands the COMs distribution both vertically and radially outward compared with that in the non-turbulent model. We derive the timescale of the sink mechanism by which CO and N{sub 2} are converted to less volatile molecules to be depleted from the gas phase and find that the vertical mixing suppresses this mechanism in the inner disks.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

DIRECT FORMATION OF SUPERMASSIVE BLACK HOLES IN METAL-ENRICHED GAS AT THE HEART OF HIGH-REDSHIFT GALAXY MERGERS

We present novel 3D multi-scale smoothed particle hydrodynamics (SPH) simulations of gas-rich galaxy mergers between the most massive galaxies at z ∼ 8–10, designed to scrutinize the direct collapse formation scenario for massive black hole seeds proposed in Mayer et al. The simulations achieve a resolution of 0.1 pc, and include both metallicity-dependent optically thin cooling and a model for thermal balance at high optical depth. We consider different formulations of the SPH hydrodynamical equations, including thermal and metal diffusion. When the two merging galaxy cores collide, gas infall produces a compact, optically thick nuclear disk with densities exceeding 10{sup −10} g cm{sup 3}. The disk rapidly accretes higher angular momentum gas from its surroundings reaching ∼5 pc and a mass of ≳10{sup 9} M{sub ⊙} in only a few 10{sup 4} years. Outside ≳2 pc it fragments into massive clumps. Instead, supersonic turbulence prevents fragmentation in the inner parsec region, which remains warm (∼3000–6000 K) and develops strong non-axisymmetric modes that cause prominent radial gas inflows (>10{sup 4} M{sub ⊙} yr{sup −1}), forming an ultra-dense massive disky core. Angular momentum transport by non-axisymmetric modes should continue below our spatial resolution limit, quickly turning the disky core into a supermassive protostar which can collapse directly into a massive black hole of mass 10{sup 8}–10{sup 9} M{sub ⊙} via the relativistic radial instability. Such a “cold direct collapse” explains naturally the early emergence of high-z QSOs. Its telltale signature would be a burst of gravitational waves in the frequency range of 10{sup −4}–10{sup −1} Hz, possibly detectable by the planned eLISA interferometer.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Atomistic simulations of the thermal conductivity of liquids

We present a method based on sinusoidal approach to equilibrium molecular dynamics (SAEMD) to compute the thermal conductivity of liquids Similar to nonequilibrium molecular dynamics, and unlike equilibrium simulations based on the Green-Kubo formalism, the method only requires the calculation of forces and total energies. The evaluation of heat fluxes and energy densities is not necessary, thus offering the promise of efficiently implementing first principles simulations based on density functional theory or deep molecular dynamics. Our approach is a generalization of SAEMD for solids, where the thermal conductivity is computed in the steady state, instead of a transient regime, thus properly taking into account diffusive terms in the heat equation. We present results for liquid water at ambient conditions and under pressure and discuss simulation requirements to obtain converged values of the thermal conductivity as a function of size and simulation time.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Small-angle scattering of particle assemblies

Small-angle scattering formulae for crystalline assemblies of arbitrary particles are derived from powder diffraction theory using the decoupling approximation. To do so, the pseudo-lattice factor is defined, and methods to overcome the limitations of the decoupling approximation are investigated. Further, approximated equations are suggested for the diffuse scattering from various defects of the first kind due to non-ideal particles, including size polydispersity, orientational disorder and positional fluctuation about their ideal positions. Calculated curves using the formalism developed herein are compared with numerical simulations computed without any approximation. For a finite-sized assembly, the scattering from the whole domain of the assembly must also be included, and this is derived using the correlation function approach.

assembly↗
DOE OSTI2013

BISON Theory Manual: The Equations behind Nuclear Fuel Analysis

BISON is a finite element-based nuclear fuel performance code applicable to a variety of fuel forms including light water reactor fuel rods, TRISO particle fuel, and metallic rod and plate fuel. It solves the fully-coupled equations of thermomechanics and species diffusion, for either 1D spherical, 2D axisymmetric or 3D geometries. Fuel models are included to describe temperature and burnup dependent thermal properties, fission product swelling, densification, thermal and irradiation creep, fracture, and fission gas production and release. Plasticity, irradiation growth, and thermal and irradiation creep models are implemented for clad materials. Models are also available to simulate gap heat transfer, mechanical contact, and the evolution of the gap/plenum pressure with plenum volume, gas temperature, and fission gas addition. BISON is based on the MOOSE framework and can therefore efficiently solve problems using standard workstations or very large high-performance computers. This document describes the theoretical and numerical foundations of BISON.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2016

BISON Theory Manual The Equations behind Nuclear Fuel Analysis

BISON is a finite element-based nuclear fuel performance code applicable to a variety of fuel forms including light water reactor fuel rods, TRISO particle fuel, and metallic rod and plate fuel. It solves the fully-coupled equations of thermomechanics and species diffusion, for either 2D axisymmetric or 3D geometries. Fuel models are included to describe temperature and burnup dependent thermal properties, fission product swelling, densification, thermal and irradiation creep, fracture, and fission gas production and release. Plasticity, irradiation growth, and thermal and irradiation creep models are implemented for clad materials. Models are also available to simulate gap heat transfer, mechanical contact, and the evolution of the gap/plenum pressure with plenum volume, gas temperature, and fission gas addition. BISON is based on the MOOSE framework and can therefore efficiently solve problems using standard workstations or very large high-performance computers. This document describes the theoretical and numerical foundations of BISON.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2017

DCMIP2016: a review of non-hydrostatic dynamical core design and intercomparison of participating models

Abstract. Atmospheric dynamical cores are a fundamental component of global atmospheric modeling systems and are responsible for capturing the dynamical behavior of the Earth's atmosphere via numerical integration of the Navier–Stokes equations. These systems have existed in one form or another for over half of a century, with the earliest discretizations having now evolved into a complex ecosystem of algorithms and computational strategies. In essence, no two dynamical cores are alike, and their individual successes suggest that no perfect model exists. To better understand modern dynamical cores, this paper aims to provide a comprehensive review of 11 non-hydrostatic dynamical cores, drawn from modeling centers and groups that participated in the 2016 Dynamical Core Model Intercomparison Project (DCMIP) workshop and summer school. This review includes a choice of model grid, variable placement, vertical coordinate, prognostic equations, temporal discretization, and the diffusion, stabilization, filters, and fixers employed by each system.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1974

User's instructions for the 41-node thermoregulatory model (steady state version)

A user's guide for the steady-state thermoregulatory model is presented. The model was modified to provide conversational interaction on a remote terminal, greater flexibility for parameter estimation, increased efficiency of convergence, greater choice of output variable and more realistic equations for respiratory and skin diffusion water losses.

Leonard, J. I.↗
NASA NTRS1978

Closure of a kinetic model of plasma in strong turbulence by relaxation

A Fokker-Planck kinetic equation for a turbulent plasma is derived by a repeated cascade decomposition. Calculation of the propagator and the kinetic equation determine the transport coefficients (diffusivity and turbulent viscosity) by means of a closure based on a relaxation procedure governing the approach to equilibrium. The k to the minus third power spectral law is obtained, which governs the coupling between the velocity and the electrostatic field fluctuations.

Tchen, C. M.↗
NASA NTRS1979

A kinetic approach to compressible turbulence

A kinetic theory of strong turbulence is developed by decomposing fluctuation of distribution function into scaled components, or ranks, to represent three transport processes: macroscopic evolution, transport property and relaxation. Closure is obtained by formulating a relaxation process for the approach of eddy diffusivity to equilibrium. The kinetic equation is solved and three transport functions of turbulence in adiabatic gas are derived: two transfer functions describe turbulent mode transfer, and a coupling function describes the build-up of kinetic energy at the expense of internal energy. The energy balance in the inertial subrange of homogeneous and isotropic turbulence in an adiabatic gas yields a k to the -3rd law, in agreement with numerical computations from one dimensional model of compressible turbulence.

Tchen, C. M.↗
NASA NTRS1981

Relationships between diffuse reflectance and vegetation canopy variables based on the radiative transfer theory

Out of the lengthy original expression of the diffuse reflectance formula, simple working equations were derived by employing characteristic parameters, which are independent of the canopy coverage and identifiable by field observations. The typical asymptotic nature of reflectance data that is usually observed in biomass studies was clearly explained. The usefulness of the simplified equations was demonstrated by the exceptionally close fit of the theoretical curves to two separately acquired data sets for alfalfa and shortgrass prairie canopies.

Park, J. K.↗