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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 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Modulation of low energy cosmic rays

The power spectrum of the interplanetary magnetic field were tested, as well as the power spectrum-cosmic diffusion ray coefficient relation at low energies. A first order perturbation solution of the Fokker-Planck equation governing the diffusion, convection, and adiabatic deceleration of galactic cosmic rays in the solar medium was found to relate intensity fluctuations of low energy cosmic rays to local changes in the propagation parameters. Diffusion coefficients and their day to day variations were calculated from interplanetary magnetic field data obtained by Pioneer 6 in 1965/1966. These are compared to simultaneous observations by IMP 3 of the proton flux in three energy channels (20 to 40, 40 to 60, 60 to 80 MeV).

Sari, J. W.↗
NASA NTRS1990

Compact scheme for systems of equations applied to fundamental problems of mechanics of continua

Compact scheme formulation was used in the treatment of boundary conditions for a system of coupled diffusion and Poisson equations. Models and practical solutions of specific engineering problems arising in solid mechanics, chemical engineering, heat transfer and fuid mechanics are described and analyzed for efficiency and accuracy. Only 2-D cases are discussed and a new method of numerical treatment of boundary conditions common in the fundamental problems of mechanics of continua is presented.

Klimkowski, Jerzy Z.↗
NASA NTRS1981

A computer program for the simulation of heat and moisture flow in soils

A computer program that simulates the flow of heat and moisture in soils is described. The space-time dependence of temperature and moisture content is described by a set of diffusion-type partial differential equations. The simulator uses a predictor/corrector to numerically integrate them, giving wetness and temperature profiles as a function of time. The simulator was used to generate solutions to diffusion-type partial differential equations for which analytical solutions are known. These equations include both constant and variable diffusivities, and both flux and constant concentration boundary conditions. In all cases, the simulated and analytic solutions agreed to within the error bounds which were imposed on the integrator. Simulations of heat and moisture flow under actual field conditions were also performed. Ground truth data were used for the boundary conditions and soil transport properties. The qualitative agreement between simulated and measured profiles is an indication that the model equations are reasonably accurate representations of the physical processes involved.

Camillo, P.↗
DOE OSTI2023

Modelling and simulation of brinicle formation

Below the Arctic sea ice, under the right conditions, a flux of icy brine flows down into the sea. The icy brine has a much lower fusion point and is denser than normal seawater. As a result, it sinks while freezing everything around it, forming an ice channel called a brinicle (also known as ice stalactite). In this paper, we develop a mathematical model for this phenomenon, assuming cylindrical symmetry. The fluid is considered to be viscous and quasi-stationary. The heat and salt transport are weakly coupled to the fluid motion and are modelled with the corresponding conservation equations, accounting for diffusive and convective effects. Finite-element discretization is employed to solve the coupled system of partial differential equations. We find that the model can capture the general behaviour of the physical system and generate brinicle-like structures while also recovering dendrite composition, which is a physically expected feature aligned with previous experimental results. This represents, to our knowledge, the first complete model proposed that captures the global structure of the physical phenomenon even though it has some discrepancies, such as brine accumulation.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Radial diffusion of low-energy plasma ions in Saturn's magnetosphere

Radial diffusion of low-energy plasma ions in Saturn's magnetosphere is investigated using a comprehensive set of equations for radial diffusion that incorporate distributed sources and sinks of ions. The results of calculations indicate that the radial-diffusion transport of low-energy O(+) ions with a source in the neutral H2O cloud of the satellites Dione and Tethys can account for Voyager observations of thermal heavy ions in Saturn's magnetosphere. The source rate was calculated to be about 10 to the 26th O(+) ions/sec, in good agreement with the sputtering calculations of Johnson et al. (1989). It is estimated that, due to fast radial diffusion, the residence time of O(+) ions in the Dione-Tethys torus is about 30 days, sufficiently short to account for the plasma density observed there. The densities of hot H(+) and N(+) resulting from the ionization and pickup of Titan's neutral clouds in the outer magnetosphere can also be accounted for within the framework of diffusive ion transport.

Barbosa, D. D.↗
DOE OSTI2017

Multilevel Sequential Monte Carlo Samplers for Normalizing Constants

This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the discrete approximation error must be balanced. A multilevel strategy is utilized to substantially reduce the cost to obtain a given error level in the approximation as compared to standard estimators. Two estimators are considered and relative variance bounds are given. The theoretical results are numerically illustrated for two Bayesian inverse problems arising from elliptic partial differential equations (PDEs). The examples involve the inversion of observations of the solution of (i) a 1-dimensional Poisson equation to infer the diffusion coefficient, and (ii) a 2-dimensional Poisson equation to infer the external forcing.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

The application of far IR lasers to the investigation of the optical properties of materials

The effect of diffusion on the saturation and absorption properties of molecular gases is considered. The analysis starts with a simple derivation of the multi-level rate equations. Incorporating the diffusion term, calculations are carried out both for the homogeneous and inhomogeneous broadening cases. Both graphical and analytical solutions are obtained for the absorption coefficient and the saturation intensity. It is shown that the effect of diffusion is characterized by a diffusion function, which varies inversely with the radius of the beam at low pressures and small beam sizes. The analysis is done in terms of two parameters k1a and k2a, which are simple functions of the intensity of the beam I, the effective relaxation rate w, and the effective diffusion constant D the a is designated as the radius of the beam.

Stafsudd, O. M.↗
DOE OSTI2017

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications

This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simple ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Where did the tumor start? An inverse solver with sparse localization for tumor growth models

In this work, we present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction–diffusion partial differential equation (PDE) for the tumor concentration. We use a PDE-constrained optimization formulation for the inverse problem. The unknown parameters are the reaction coefficient (proliferation), the diffusion coefficient (infiltration), and the initial condition field for the tumor PDE. Segmentation of magnetic resonance imaging (MRI) scans drive the inverse problem where segmented tumor regions serve as partial observations of the tumor concentration. Like most cases in clinical practice, we use data from a single time snapshot. Moreover, the precise time relative to the initiation of the tumor is unknown, which poses an additional difficulty for inversion. We perform a frozen-coefficient spectral analysis and show that the inverse problem is severely ill-posed. We introduce a biophysically motivated regularization on the structure and magnitude of the tumor initial condition. In particular, we assume that the tumor starts at a few locations (enforced with a sparsity constraint on the initial condition of the tumor) and that the initial condition magnitude in the maximum norm is equal to one. We solve the resulting optimization problem using an inexact quasi-Newton method combined with a compressive sampling algorithm for the sparsity constraint. Our implementation uses PETSc and AccFFT libraries. We conduct numerical experiments on synthetic and clinical images to highlight the improved performance of our solver over a previously existing solver that uses standard two-norm regularization for the calibration parameters. The existing solver is unable to localize the initial condition. Our new solver can localize the initial condition and recover infiltration and proliferation. In clinical datasets (for which the ground truth is unknown), our solver results in qualitatively different solutions compared to the two-norm regularized solver.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

Vapor transport processes of Ge-chalcogenides under normal and reduced gravity conditions

Experimental and theoretical studies of the GeSe-GeI4 system revealed the multicomponent, multireaction nature of this system and the existence of a diffusion boundary layer; they also yielded equations for the prediction of diffusion limited mass transport rates. Vapor transport and crystal growth experiments of the GeSe-GeI4 and GeSe-Xe systems on earth and in a microgravity environment demonstrated the effects of convection and of microgravity on mass flux and crystal morphology. The surface and bulk morphology of GeSe crystals obtained for both systems in microgravity is considerably improved relative to ground-based specimens. Unexpected crystal growth phenomena were observed for the GeSe-Xenon system on recent Shuttle flights.

Wiedemeier, H.↗
NASA NTRS1989

Evolution of the sun's polar fields during sunspot cycle 21 - Poleward surges and long-term behavior

Longitudinally averaged observations of the photospheric field during 1976-1986 are analyzed using a flux transport model. The way in which source eruptions, supergranular diffusion, and meridional flow collaborate to produce strong, highly concentrated polar fields near sunspot minimum is clarified as follows: (1) widespread eruptions of individual bipolar magnetic regions, with their leading polarity flux equatorward of their trailing polarity flux, collectively establish a large-scale separation of polarities in latitude; (2) the low-latitude, leading polarity flux diffuses across the equator and merges with its opposite hemisphere counterpart; and (3) meridional flow carries the resulting surplus of trailing polarity flux to the poles, and concentrates it there against the spreading effect of diffusion. Episodic 'surges' of flux to the poles are induced by fluctuations in the source eruption rate. Simulations indicate that relatively weak, trailing polarity surges may occur even in a steady flow field. However, in order to account for the giant surges of alternating polarity and the resulting oscillations in the polar field strength observed during 1980-1982, both accelerated flow and enhanced eruption rates are required.

Wang, Y.-M.↗
NASA NTRS1986

Convective diffusion in protein crystal growth

A protein crystal modeled as a flat plate suspended in the parent solution, with the normal to the largest face perpendicular to gravity and the protein concentration in the solution adjacent to the plate taken to be the equilibrium solubility, is studied. The Navier-Stokes equation and the equation for convective diffusion in the boundary layer next to the plate are solved to calculate the flow velocity and the protein mass flux. The local rate of growth of the plate is shown to vary significantly with depth due to the convection. For an aqueous solution of lysozyme at a concentration of 40 mg/ml, the boundary layer at the top of a 1-mm-high crystal has a thickness of 80 microns at 1 g, and 2570 microns at 10 to the -6th g.

Baird, J. K.↗
NASA NTRS1986

The Martian climate and energy balance models with CO2/H2O atmospheres

The analysis begins with a seasonal energy balance model (EBM) for Mars. This is used to compute surface temperature versus x = sin(latitude) and time over the seasonal cycle. The core model also computes the evolving boundaries of the CO2 icecaps, net sublimational/condensation rates, and the resulting seasonal pressure wave. Model results are compared with surface temperature and pressure history data at Viking lander sites, indicating fairly good agreement when meridional heat transport is represented by a thermal diffusion coefficient D approx. 0.015 W/sq. m/K. Condensational wind distributions are also computed. An analytic model of Martian wind circulation is then proposed, as an extension of the EMB, which incorporates vertical wind profiles containing an x-dependent function evaluated by substitution in the equation defining the diffusion coefficient. This leads to a parameterization of D(x) and of the meridional circulation which recovers the high surface winds predicted by dynamic Mars atmosphere models (approx. 10 m/sec). Peak diffusion coefficients, D approx. 0.6 w/sq m/K, are found over strong Hadley zones - some 40 times larger than those of high-latitude baroclinic eddies. When the wind parameterization is used to find streamline patterns over Martian seasons, the resulting picture shows overturning hemispheric Hadley cells crossing the equator during solstices, and attaining peak intensities during the south summer dust storm season, while condensational winds are most important near the polar caps.

Hoffert, M. I.↗
DOE OSTI2025

From clutter to clarity: Emergent neural operators via questionnaire metrics

Real-world datasets in chemical engineering and bioengineering processes—such as those from catalytic reactors, multiphase flows, polymerization reactors, bioreactors, and clinical trials—can often be unlabeled or disorganized, rendering the training of existing supervised learning models ineffective at learning the underlying dynamics. To salvage these datasets for decision-making, we first seek to obtain clarity from the cluttered data. Here, we present a framework for developing “structural” generative models, discovering emergent equations, and constructing efficient emulators from scrambled datasets by integrating unsupervised organizational learning techniques (Questionnaires) with advanced deep learning architectures (Deep Hidden Physics Models and Deep Operator Networks). Our approach is demonstrated on two illustrative model systems: (a) a 1D advection–diffusion partial differential equation representing a winding underground pipe and (b) an ensemble of Stuart–Landau oscillators, an agent-based system of coupled ordinary differential equations. In both cases, we successfully reconstruct meaningful spatial, temporal, and parameter embeddings from scrambled data, enabling good predictions of system dynamics. As a result, we highlight the framework’s potential for broader applications, enabling data-driven system identification in fields with inherently disorganized or hidden parameter spaces.

42 ENGINEERING↗
DOE OSTI2018

Large-scale Compression Acceleration during Magnetic Reconnection in a Low- β Plasma

In solar flares and other astrophysical systems, a major challenge for solving the particle acceleration problem associated with magnetic reconnection is the enormous scale separation between kinetic scales and the observed reconnection scale. Because of this, it has been difficult to draw any definite conclusions by just using kinetic simulations. A particle acceleration model that solves the energetic particle transport equation can capture the main acceleration physics found in kinetic simulations and thus provide a practical way to make observable predictions and directly compare model results with observations. Here we study compression particle acceleration in magnetic reconnection by solving the Parker (diffusion–advection) transport equation using velocity and magnetic fields from two-dimensional magnetohydrodynamics (MHD) simulations of a low-β high-Lundquist-number reconnection layer. We show that the compressible reconnection layer can give significant particle acceleration, leading to the formation of power-law particle energy distributions. We analyze the acceleration rate and find that the acceleration in the reconnection layer is a mixture of first- and second-order Fermi processes. When including a guide field, we find that the spectrum becomes steeper and both the power-law cutoff energy and maximum particle energy decrease as plasma becomes less compressible. This model produces a 2D particle distribution that one can use to generate a radiation map and directly compare with solar flare observations. This provides a framework to explain particle acceleration at large-scale astrophysical reconnection sites, such as solar flares.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1977

Simple analytical solutions for spherically symmetric production and modulation of energetic solar particles

Exact analytical solutions are presented for the standard time-independent spherically symmetric convection-diffusion-adiabatic deceleration equation governing the transport of cosmic rays in the interplanetary medium for the case in which particles are produced with spherical symmetry at the sun. It is assumed that the solar-wind speed is constant and radial, and that the spatial diffusion coefficient has a power-law dependence on momentum. The Green's function describing the modulation of a monoenergetic production of particles is presented. The solutions provide a useful basis for the study of time-integrated properties of energetic solar-flare particle spectra.

Gross, M. W.↗
DOE OSTI2019

Fuel Loading Optimization and Planning for the Versatile Test Reactor

The Versatile Test Reactor (VTR) mission is to enable accelerated testing of advanced reactor fuels and materials required for advanced reactor technologies. In service of this duty, the goal of the design is to maximize the peak fast flux and the experimental volume exposed to a fast flux above 4.0 × 1015n/cms s. Delivering the desired neutron fluence for each experiment requires the capability to optimize the fuel loading to achieve a specified cycle length and flux, while also satisfying other criteria such as thermal hydraulic design constraints. To achieve the desired conditions and cycle length, several measures may be taken, including optimization of the fuel loading pattern, moving partially-burned assemblies back and forth between the core and the in-vessel storage, and potentially shuffling fuel within the core. Optimizing in a "brute-force" manner by solving a wholecore transport equation for hundreds of configurations would be inefficient. A sufficiently refined DIF3D-VARIANT solution for the whole core requires on the order of 1 hour. Instead, we seek an approximate evaluation of the parameters for many variations on a base core configuration without directly solving a diffusion or transport equation for each.

fuel loading optimization↗