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At least 937 records · Page 52
All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

Comptonization in Ultra-Strong Magnetic Fields: Numerical Solution to the Radiative Transfer Problem

We consider the radiative transfer problem in a plane-parallel slab of thermal electrons in the presence of an ultra-strong magnetic field (B approximately greater than B(sub c) approx. = 4.4 x 10(exp 13) G). Under these conditions, the magnetic field behaves like a birefringent medium for the propagating photons, and the electromagnetic radiation is split into two polarization modes, ordinary and extraordinary, that have different cross-sections. When the optical depth of the slab is large, the ordinary-mode photons are strongly Comptonized and the photon field is dominated by an isotropic component. Aims. The radiative transfer problem in strong magnetic fields presents many mathematical issues and analytical or numerical solutions can be obtained only under some given approximations. We investigate this problem both from the analytical and numerical point of view, provide a test of the previous analytical estimates, and extend these results with numerical techniques. Methods. We consider here the case of low temperature black-body photons propagating in a sub-relativistic temperature plasma, which allows us to deal with a semi-Fokker-Planck approximation of the radiative transfer equation. The problem can then be treated with the variable separation method, and we use a numerical technique to find solutions to the eigenvalue problem in the case of a singular kernel of the space operator. The singularity of the space kernel is the result of the strong angular dependence of the electron cross-section in the presence of a strong magnetic field. Results. We provide the numerical solution obtained for eigenvalues and eigenfunctions of the space operator, and the emerging Comptonization spectrum of the ordinary-mode photons for any eigenvalue of the space equation and for energies significantly lesser than the cyclotron energy, which is on the order of MeV for the intensity of the magnetic field here considered. Conclusions. We derived the specific intensity of the ordinary photons, under the approximation of large angle and large optical depth. These assumptions allow the equation to be treated using a diffusion-like approximation.

acceleration of particles↗
NASA NTRS2014

Badhwar-O'Neill 2011 Galactic Cosmic Ray Model Update and Future Improvements

The Badhwar-O'Neill Galactic Cosmic Ray (GCR) Model based on actual GCR measurements is used by deep space mission planners for the certification of microelectronic systems and the analysis of radiation health risks to astronauts in space missions. The BO GCR Model provides GCR flux in deep space (outside the earth's magnetosphere) for any given time from 1645 to present. The energy spectrum from 50 MeV/n - 20 GeV/n is provided for ions from hydrogen to uranium. This work describes the most recent version of the BO GCR model (BO'11). BO'11 determined the GCR flux at a given time applying an emperical time delay function to past sunspot activity. We describe the GCR measurement data used in the BO'11 update - modern data from BESS, PAMELA, CAPRICE, and ACE emphasized more than the older balloon data used for the previous BO model (BO'10). We look at the GCR flux for the last 24 solar minima and show how much greater the flux was for the cycle 24 minimum in 2010. The BO'11 Model uses the traditional, steady-state Fokker-Planck differential equation to account for particle transport in the heliosphere due to diffusion, convection, and adiabatic deceleration. It assumes a radially symmetrical diffusion coefficient derived from magnetic disturbances caused by sunspots carried outward by a constant solar wind. A more complex differential equation is now being tested to account for particle transport in the heliosphere in the next generation BO model. This new model is time-dependent (no longer a steady state model). In the new model, the dynamics and anti-symmetrical features of the actual heliosphere are accounted for so emperical time delay functions will no longer be required. The new model will be capable of simulating the more subtle features of modulation - such as the Sun's polarity and modulation dependence on gradient and curvature drift. This improvement is expected to significantly improve the fidelity of the BO GCR model. Preliminary results of its performance will be presented.

O'Neill, Pat M.↗
NASA NTRS2014

Badhwar-O'Neill 2011 Galactic Cosmic Ray Model Update and Future Improvements

The Badhwar-O'Neill Galactic Cosmic Ray (GCR) Model based on actual GR measurements is used by deep space mission planners for the certification of micro-electronic systems and the analysis of radiation health risks to astronauts in space missions. The BO GCR Model provides GCR flux in deep space (outside the earth's magnetosphere) for any given time from 1645 to present. The energy spectrum from 50 MeV/n-20 GeV/n is provided for ions from hydrogen to uranium. This work describes the most recent version of the BO GCR model (BO'11). BO'11 determines the GCR flux at a given time applying an empirical time delay function to past sunspot activity. We describe the GCR measurement data used in the BO'11 update - modern data from BESS, PAMELA, CAPRICE, and ACE emphasized for than the older balloon data used for the previous BO model (BO'10). We look at the GCR flux for the last 24 solar minima and show how much greater the flux was for the cycle 24 minimum in 2010. The BO'11 Model uses the traditional, steady-state Fokker-Planck differential equation to account for particle transport in the heliosphere due to diffusion, convection, and adiabatic deceleration. It assumes a radially symmetrical diffusion coefficient derived from magnetic disturbances caused by sunspots carried onward by a constant solar wind. A more complex differential equation is now being tested to account for particle transport in the heliosphere in the next generation BO model. This new model is time-dependent (no longer a steady state model). In the new model, the dynamics and anti-symmetrical features of the actual heliosphere are accounted for so empirical time delay functions will no longer be required. The new model will be capable of simulating the more subtle features of modulation - such as the Sun's polarity and modulation dependence on the gradient and curvature drift. This improvement is expected to significantly improve the fidelity of the BO GCR model. Preliminary results of its performance will be presented.

O'Neill, Pat M.↗
DOE OSTI2026

Explicit Monotone Stable Super-Time-stepping Methods for Finite Time Singularities

We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge–Kutta–Legendre (RKL) and Runge–Kutta–Gegenbauer (RKG) super-time-stepping methods were originally developed for nonlinear complex physics problems with diffusion. These are multistage single step second-order, forward-in-time methods with no implicit solves. The advantage is that the time-step size for stability scales with stage number 𝑠 as $\mathcal{O}$⁡(𝑠 2 ). Many interesting nonlinear PDEs have finite-time singularities, and the presence of diffusion often limits one to using implicit or semi-implicit time-step methods for stability constraints. Finite-time singularities are particularly challenging due to the large range of scales that one desires to resolve, often with adaptive spatial grids and adaptive time steps. Here, in this study, we show two examples of nonlinear PDEs for which the self-similar singularity structure has time and space scales that are resolvable using the RKL and RKG methods, without forcing even smaller time steps. Compared to commonly used implicit numerical methods, we achieve a significantly smaller run time while maintaining comparable accuracy. We also prove numerical monotonicity for both the RKL and RKG methods under their linear stability conditions for the constant coefficient heat equation, in the case of infinite domain and periodic boundary condition, leading to a theoretical guarantee of the superiority of the RKL and RKG methods over traditional super-time-stepping methods, such as the Runge-Kutta-Chebyshev and the orthogonal Runge-Kutta-Chebyshev methods. Code can be found at https://github.com/ZT220501/SRK-Singularity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Direct Discontinuous Galerkin methods for the reacting multi-component flow equations

The Direct Discontinuous Galerkin (DDG (Liu and Yan, 2008)) method and a counterpart with Interface Correction (DDGIC (Danis and Yan, 2022)) are extended to compute diffusion terms that arise when solving the compressible multi-component flow equations in thermochemical nonequilibrium. Thermodynamic properties, transport properties, chemical reaction rates, and energy exchange terms are computed using Mutation++ (Scoggins et al., 2020). The DG method is applied on unstructured grids, where the accuracy and convergence rates can be sensitive to the numerical method chosen for parabolic terms. A method for determining the homogeneity tensor of the flow equations required for DDGIC is shown. The convergence properties of the DDG methods are studied and compared to the Interior Penalty (IP) method. A number of numerical experiments are conducted to assess the accuracy and performance of the method. The numerical results and convergence studies indicate that DDG and DDGIC provide accurate solutions and perform well for general flows in thermochemical nonequilibrium.

Diffusion↗
DOE OSTI2024

Fast permeability measurement for tight reservoir cores using only initial data of the one chamber pressure pulse decay test

Here, in this study, a mathematical model for fast determination of the permeabilities of tight rocks using measurements taken from the initial period of the One Chamber Pressure Pulse Decay (OC-PPD) test is presented. The model applies to measurements taken both before and after the pressure pulse front has reached the downstream end of the specimen. The analytical solutions for the pressure decay in the upstream chamber are derived based on a parabolic arc approximation of pore pressure distribution along the test specimen. This approximation allows converting the initial–boundary value problem of fluid diffusion in the specimen, governed by partial differential equations, to a system of ordinary differential equations that can be easily solved by explicit formulae. Thus, an explicit formula for the pressure decay rate is obtained, which enables inverse analysis of the initial experimental data to estimate the rock permeability. The proposed method expedites the pulse decay test as it does not require the system to reach equilibrium. The method is validated with three sets of experimental data of the OC-PPD test using helium as the diffusing fluid, for which the relative error of the permeability is found to be less than 6%. This method is particularly useful if the equilibrium time of the pulse decay test for rock specimens with permeabilities in the range of nano-Darcy takes hours or days.

early-time solution↗
DOE OSTI2020

Heat Loss Correction Factor for Fireball Yield Measurements

Fireball yield calculations are performed using Taylor’s radius equation. However, at early times, the x-ray diffusion process has a significant effect on the size of the fireball, and at late times the shock wave degenerates into an acoustic wave. Thus, earlier research determined that the range of validity for Taylor’s equation was in the scaled time regime of 0.004–0.008 s. So, when performing a yield calculation, the only values that are analyzed are those that lie within that range of validity. While Taylor’s equations offer an approximation of the scaled yield, they also rely on several assumptions. For example, the equations assume that the shock wave is adiabatic, when, in fact, the first light pulse on the nuclear test films, which occurs as the shock wave is forming, suggests that the shock wave is not adiabatic. Furthermore, the amount of heat loss from the shock wave that occurs prior to the scaled time regime of 0.004–0.008 s can change significantly as a function of air density. This may cause the shock wave radius to be smaller relative to the assumed adiabatic shock wave. Therefore, the objective of this project was to determine the correction factor for heat transfer, which should be applied in order to produce a more accurate approximation of the weapon’s yield.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
NASA NTRS1980

Dissolution of multicomponent bubbles

The behavior of an isolated, stationary, multicomponent gas bubble in a glassmelt containing several dissolved gases is considered. The relevant mass-transport equations are formulated and calculations are performed for the case of two diffusing gases using a quasi-stationary model and a numerical solution of the exact mass-transfer equations. The results obtained from these two approaches are compared. The factors which govern the dissolution or growth of a bubble are thermodynamic and kinetic in origin. The tendency of a bubble to grow or shrink at long times is controlled by departure from overall equilibrium, whereas the short-time bubble dynamics may be dominated by kinetic effects. As a result of the existence of these dual influences, maxima and/or minima occur in the functional dependence of the bubble radius on time.

Weinberg, M. C.↗
NASA NTRS2007

Multi-Scale Modeling of Magnetospheric Reconnection

One of the major challenges in modeling the magnetospheric magnetic reconnection is to quantify the interaction between large-scale global magnetospheric dynamics and microphysical processes in diffusion regions near reconnection sites. There is still considerable debate as to what degree microphysical processes on kinetic scales affect the global evolution and how important it is to substitute numerical dissipation and/or ad hoc anomalous resistivity by a physically motivated model of dissipation. Comparative studies of magnetic reconnection in small scale geometries demonstrated that MHD simulations that included non-ideal processes in terms of a resistive term $\eta J$ did not produce the fast reconnection rates observed in kinetic simulations. For a broad range of physical parameters in collisionless magnetospheric plasma, the primary mechanism controlling the dissipation in the vicinity of the reconnection site is non-gyrotropic effects with spatial scales comparable with the particle Larmor radius. We utilize the global MHD code BATSRUS and incorporate nongyrotropic effects in diffusion regions in terms of corrections to the induction equation. We developed an algorithm to search for magnetotail reconnection sites, specifically where the magnetic field components perpendicular to the local current direction approaches zero and form an X-type configuration. Spatial scales of the diffusion region and magnitude of the reconnection electric field are calculated selfconsistently using MHD plasma and field parameters in the vicinity of the reconnection site. The location of the reconnection sites is updated during the simulations. To clarify the role of nongyrotropic effects in diffusion region on the global magnetospheric dynamic we perform simulations with steady southward IMF driving of the magnetosphere. Ideal MHD simulations with magnetic reconnection supported by numerical resistivity produce steady configuration with almost stationary near-earth neutral line (NENL). Simulations with non-gyrotropic corrections demonstrate dynamic quasi-periodic response to the steady driving condition. The loading/unloading cycle in non-gyrotropic MHD results has a non-stationary reconnection site in the magnetotail, with the retreating during the stretching phase and then a new NENL forming in the resulting thin plasma sheet. We expect that this model will lead to improved representations of space weather event in the magnetosphere.

Kuznetsova, M. M.↗
NASA NTRS2008

Spiking Neurons for Analysis of Patterns

Artificial neural networks comprising spiking neurons of a novel type have been conceived as improved pattern-analysis and pattern-recognition computational systems. These neurons are represented by a mathematical model denoted the state-variable model (SVM), which among other things, exploits a computational parallelism inherent in spiking-neuron geometry. Networks of SVM neurons offer advantages of speed and computational efficiency, relative to traditional artificial neural networks. The SVM also overcomes some of the limitations of prior spiking-neuron models. There are numerous potential pattern-recognition, tracking, and data-reduction (data preprocessing) applications for these SVM neural networks on Earth and in exploration of remote planets. Spiking neurons imitate biological neurons more closely than do the neurons of traditional artificial neural networks. A spiking neuron includes a central cell body (soma) surrounded by a tree-like interconnection network (dendrites). Spiking neurons are so named because they generate trains of output pulses (spikes) in response to inputs received from sensors or from other neurons. They gain their speed advantage over traditional neural networks by using the timing of individual spikes for computation, whereas traditional artificial neurons use averages of activity levels over time. Moreover, spiking neurons use the delays inherent in dendritic processing in order to efficiently encode the information content of incoming signals. Because traditional artificial neurons fail to capture this encoding, they have less processing capability, and so it is necessary to use more gates when implementing traditional artificial neurons in electronic circuitry. Such higher-order functions as dynamic tasking are effected by use of pools (collections) of spiking neurons interconnected by spike-transmitting fibers. The SVM includes adaptive thresholds and submodels of transport of ions (in imitation of such transport in biological neurons). These features enable the neurons to adapt their responses to high-rate inputs from sensors, and to adapt their firing thresholds to mitigate noise or effects of potential sensor failure. The mathematical derivation of the SVM starts from a prior model, known in the art as the point soma model, which captures all of the salient properties of neuronal response while keeping the computational cost low. The point-soma latency time is modified to be an exponentially decaying function of the strength of the applied potential. Choosing computational efficiency over biological fidelity, the dendrites surrounding a neuron are represented by simplified compartmental submodels and there are no dendritic spines. Updates to the dendritic potential, calcium-ion concentrations and conductances, and potassium-ion conductances are done by use of equations similar to those of the point soma. Diffusion processes in dendrites are modeled by averaging among nearest-neighbor compartments. Inputs to each of the dendritic compartments come from sensors. Alternatively or in addition, when an affected neuron is part of a pool, inputs can come from other spiking neurons. At present, SVM neural networks are implemented by computational simulation, using algorithms that encode the SVM and its submodels. However, it should be possible to implement these neural networks in hardware: The differential equations for the dendritic and cellular processes in the SVM model of spiking neurons map to equivalent circuits that can be implemented directly in analog very-large-scale integrated (VLSI) circuits.

Huntsberger, Terrance↗
NASA NTRS1984

Computation of three-dimensional viscous flows using a space-marching method

A space-marching method, developed to compute three-dimensional flows for internal geometries, has been utilized to predict viscous flows through a curved duct and over a swept wing. The Navier-Stokes equations have been posed as an initial value problem by neglecting the streamwise viscous diffusion terms and by treating the pressure gradient as a known source term. The resulting equations have been solved by a non-iterative (single pass) algorithm at each streamwise step. The results are compared with earlier computations (based on iterative methods) and the experimental data. The agreement between the present predictions, the experimental data, and the earlier predictions is good for the cases computed. The computation time is only a fraction of the iterative methods.

Murthy, K. N. S.↗
DOE OSTI2021

Improved Prediction of Cold-Air Pools in the Weather Research and Forecasting Model Using a Truly Horizontal Diffusion Scheme for Potential Temperature

The terrain-following vertical coordinate system used by many atmospheric models, including the Weather Research and Forecasting (WRF) Model, is prone to errors in regions of complex terrain. These errors stem, in part, from the calculation of horizontal gradients within the diffusion term of the momentum or scalar evolution equations. In WRF, such gradients can be calculated along coordinate surfaces, or using metric terms that help account for grid skewness. However, neither of these options ensures a truly horizontal gradient calculation, especially if a grid cell is skewed enough that the heights of the neighboring grid points used in the calculation fall outside the vertical range of the cell. In this work, an improved scheme that uses Taylor series approximations to vertically interpolate variables to the level necessary for a truly horizontal gradient calculation is implemented in WRF for the diffusion of potential temperature. The scheme is validated using an atmosphere-at-rest configuration, in which spurious flows develop only as a result of numerical errors and can thus be used as a proxy for model performance. Following validation, the method is applied to the simulation of cold-air pools (CAPs), which occur in regions of complex terrain and are characterized by strong near-surface temperature gradients. Using the truly horizontal scheme, idealized simulations demonstrate reduced numerical mixing in a quiescent CAP, and a realistic case study in the Columbia River basin shows a reduction in positive wind speed bias by up to roughly 20% compared to observations from the Second Wind Forecast Improvement Project.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1979

An elliptic representation of coupled boundary layers and inviscid core for computation of separated internal flows

This report presents a viscous-inviscid calculation method for the prediction of turbulent incompressible flows in diffusers with small regions of stall. Integral turbulent boundary layer equations (BLE) are used to provide boundary conditions for a finite difference representation of the inviscid core. The BLE are applied at the floating displacement-thickness line, resulting in a simulataneous set of nonlinear block tridiagonal equations which are solved iteratively using a sucessive line-relaxation technique. Results of the method have been applied to calculate the performance of a variety of asymmetric stalled diffusers.

Ghose, S.↗
NASA NTRS1992

Simulations of surface winds at the Viking Lander sites using a one-level model

The one-level model developed by Mass and Dempsey for use in predicting surface flows in regions of complex terrain was adapted to simulate surface flows at the Viking lander sites on Mars. In the one-level model, prediction equations for surface winds and temperatures are formulated and solved. Surface temperatures change with time in response to diabatic heating, horizontal advection, adiabatic heating and cooling effects, and horizontal diffusion. Surface winds can change in response to horizontal advection, pressure gradient forces, Coriolis forces, surface drag, and horizontal diffusion. Surface pressures are determined by integration of the hydrostatic equation from the surface to some reference level. The model has successfully simulated surface flows under a variety of conditions in complex-terrain regions on Earth.

Bridger, Alison F. C.↗
NASA NTRS1996

Influence of a Simple Heat Loss Profile on a Pure Diffusion Flame

The presence of soot on the fuel side of a diffusion flame results in significant radiative heat losses. The influence of a fuel side heat loss zone on a pure diffusion flame established between a fuel and an oxidizer wall is investigated by assuming a hypothetical sech(sup 2) heat loss profile. The intensity and width of the loss zone are parametrically varied. The loss zone is placed at different distances from the Burke-Schumann flame location. The migration of the temperature and reactivity peaks are examined for a variety of situations. For certain cases the reaction zone breaks through the loss zone and relocates itself on the fuel side of the loss zone. In all cases the temperature and reactivity peaks move toward the fuel side with increased heat losses. The flame structure reveals that the primary balance for the energy equation is between the reaction term and the diffusion term. Extinction plots are generated for a variety of situations. The heat transfer from the flame to the walls and the radiative fraction is also investigated, and an analytical correlation formula, derived in a previous study, is shown to produce excellent predictions of our numerical results when an O(l) numerical multiplicative constant is employed.

Ray, Anjan↗
NASA NTRS1988

The diffusion of stars through phase space

An orbit-averaged Fokker-Planck equation has been derived to study the secular evolution of stellar systems with regular orbits and the heating of stellar disks. It is shown that a population of stars with an initially Maxwellian peculiar-velocity distribution will remain Maxwellian as it diffuses through orbit space only if: (1) a second-order diffusion tensor is proportional to epicycle energy; and (2) the population's velocity dispersion grows as the square root of time. Scattering by ephemeral spiral waves is able to account for the observed kinematics of the solar neighborhood only if the waves have wavelengths in excess of 9 kpc and constantly drifting pattern speeds.

Binney, James↗
DOE OSTI2026

Langevin and Fokker-Planck analyses for diffusion-mediated passing of circular and discorectangular species in two-dimensional channels

The propensity for pairs of diffusing species to pass each other within narrow channels or pores is of basic interest as a first-passage-type problem. It is also of relevance for solution-phase transport in nanoporous materials, and in particular for catalytic conversion reactions where high yield requires that product species can efficiently pass reactant species to exit the pores. Here, we analyze a two-dimensional model with nonoverlapping circular and discorectangular species confined to a rectangular channel, and where passing is mediated by Brownian dynamics in an implicit solvent. For narrower channels where passing is still possible, the discorectangle must align with the channel to pass the circular species. Behavior of the passing propensity, 𝑃, can be assessed by strongly damped Langevin simulations, or within an equivalent Fokker-Planck equation (FPE) formalism. The latter corresponds to a diffusion problem in a “higher-dimensional channel” with a constriction. We assess the variation of the passing propensity, 𝑃, for a broad range of channel width including its scaling just above the threshold where passing is sterically blocked. Analysis of 𝑃 versus the rotational diffusion coefficient 𝐷 𝑟 of the discorectangle reveals a significant decrease in 𝑃 for lower 𝐷 𝑟 for moderate channel width. This prompts a direct analysis of the regime where 𝐷 𝑟 → 0 , for which the FPE can be reduced to a three-dimensional diffusion problem, precise analysis of which is facilitated by adaptive-mesh finite element methods. The dependence of 𝑃 on the aspect ratio of the discorectangle is also assessed.

Rahman, Md Khaledur [Ames Laboratory (AMES), Ames,↗
NASA NTRS2001

Nonlinearity Effects of Lateral Density Diffusion Coefficient on Gain-Guided VCSEL Performance

Electron and hole diffusions in the plane of semiconductor quantum wells play an important part in the static and dynamic operations of semiconductor lasers. In this paper, we apply a hydrodynamic model developed from the semiconductor Bloch equations to numerically study the effects of nonlinearity in the diffusion coefficient on single mode operation and direct modulation of a gain-guided InGaAs/GaAs multiple quantum well laser, operating not too far from threshold. We found that a small diffusion coefficient is advantageous for lowering the threshold current and increasing the modulation bandwidth. Most importantly, the effects of nonlinearity in the coefficient can be approximately reproduced by replacing the coefficient with an effective constant diffusion coefficient, which corresponds roughly to the half height density of the density distribution.

Li, Jian-Zhong↗