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At least 1,009 records · Page 56
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Observation of Weyl exceptional rings in thermal diffusion

A non-Hermitian Weyl equation indispensably requires a three-dimensional (3D) real/synthetic space, and it is thereby perceived that a Weyl exceptional ring (WER) will not be present in thermal diffusion given its purely dissipative nature. Here, we report a recipe for establishing a 3D parameter space to imitate thermal spinor field. Two orthogonal pairs of spatiotemporally modulated advections are employed to serve as two synthetic parameter dimensions, in addition to the inherent dimension corresponding to heat exchanges. We first predict the existence of WER in our hybrid conduction–advection system and experimentally observe the WER thermal signatures verifying our theoretical prediction. When coupling two WERs of opposite topological charges, the system further exhibits surface-like and bulk topological states, manifested as stationary and continuously changing thermal processes, respectively, with good robustness. Our findings reveal the long-ignored topological nature in thermal diffusion and may empower distinct paradigms for general diffusion and dissipation controls.

42 ENGINEERING↗
DOE OSTI2016

A hybridized discontinuous Galerkin method on mapped deforming domains

Here in this paper we present a hybridized discontinuous Galerkin (HDG) discretization for unsteady simulations of convection-dominated flows on mapped deforming domains. Mesh deformation is achieved through an arbitrary Lagrangian-Eulerian transformation with an analytical mapping. We present details of this transformation applied to the HDG system of equations, with focus on the auxiliary gradient equation, viscous stabilization, and output calculation. We discuss conditions under which optimal unsteady output convergence rates can be attained, and we show that both HDG and discontinuous Galerkin (DG) achieve these rates in advection-dominated flows. Results for scalar advection-diffusion and the Euler equations verify the implementation of the mesh motion mapping for both discretizations, show that HDG and DG yield similar results on a given mesh, and demonstrate differences in output convergence rates depending on the choice of HDG viscous stabilization. We note that such similar results bode well for HDG, which has fewer globally-coupled degrees of freedom compared to DG. A simulation of the unsteady compressible Navier-Stokes equations demonstrates again very similar results for HDG and DG and illustrates a pitfall of using steady-state adapted meshes for accurate unsteady simulations.

42 ENGINEERING↗
DOE OSTI2016

Pitch-angle scattering of energetic charged particles in nearly constant magnitude magnetic turbulence

We use a method developed by Roberts that optimizes the phase angles of an ensemble of plane waves with amplitudes determined from a Kolmogorov-like power spectrum, to construct magnetic field vector fluctuations having nearly constant magnitude and large variances in its components. This is a representation of the turbulent magnetic field consistent with that observed in the solar wind. Charged-particle pitch-angle diffusion coefficients are determined by integrating the equations of motion for a large number of charged particles moving under the influence of forces from our predefined magnetic field. We tested different cases by varying the kinetic energy of the particles (E {sub p}) and the turbulent magnetic field variance (σ{sub B}{sup 2}). For each combination of E {sub p} and σ{sub B}{sup 2}, we tested three different models: (1) the so-called “slab” model, where the turbulent magnetic field depends on only one spatial coordinate and has significant fluctuations in its magnitude (b=√(δB{sub x}{sup 2}(z)+δB{sub y}{sup 2}(z)+B{sub 0}{sup 2})); (2) the slab model optimized with nearly constant magnitude b; and (3) the slab model turbulent magnetic field with nearly constant magnitude plus a “variance-conserving” adjustment. In the last case, this model attempts to conserve the variance of the turbulent components (σ{sub Bx}{sup 2}+σ{sub By}{sup 2}), which is found to decrease during the optimization with nearly constant magnitude. We found that there is little or no effect on the pitch-angle diffusion coefficient D{sub μμ} between models 1 and 2. However, the result from model 3 is significantly different. We also introduce a new method to accurately determine the pitch-angle diffusion coefficients as a function of μ.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1988

Cosmic-ray transport in accelerating flows

The quasi-linear transport equation of energetic charged particles is derived, including scattering by Alfven waves propagating parallel and antiparallel to a uniform magnetic field, losses by synchrotron radiation, and acceleration of the cold background fluid supporting the waves. As in the comoving frame equations of radiative transfer, scattering, and loss terms are evaluated in the frame in which the fluid is locally at rest. The diffusion approximation is applied to the resulting equation, yielding a transport equation for the isotropic part of the distribution function and a first-order approximation to the anisotropy. The conditions under which this approximation may be applied are discussed. In the nonrelativistic regime, the standard equation of the diffusion approximation is recovered. As contributions previously investigated, new effects appear from the spatial and temporal variations of the fluid velocity as well as the synchrotron radiation terms. These are discussed in detail.

Kirk, John G.↗
DOE OSTI2017

PARTICLE SCATTERING OFF OF RIGHT-HANDED DISPERSIVE WAVES

Resonant scattering of fast particles off low frequency plasma waves is a major process determining transport characteristics of energetic particles in the heliosphere and contributing to their acceleration. Usually, only Alfvén waves are considered for this process, although dispersive waves are also present throughout the heliosphere. We investigate resonant interaction of energetic electrons with dispersive, right-handed waves. For the interaction of particles and a single wave a variable transformation into the rest frame of the wave can be performed. Here, well-established analytic models derived in the framework of magnetostatic quasi-linear theory can be used as a reference to validate simulation results. However, this approach fails as soon as several dispersive waves are involved. Based on analytic solutions modeling the scattering amplitude in the magnetostatic limit, we present an approach to modify these equations for use in the plasma frame. Thereby we aim at a description of particle scattering in the presence of several waves. A particle-in-cell code is employed to study wave–particle scattering on a micro-physically correct level and to test the modified model equations. We investigate the interactions of electrons at different energies (from 1 keV to 1 MeV) and right-handed waves with various amplitudes. Differences between model and simulation arise in the case of high amplitudes or several waves. Analyzing the trajectories of single particles we find no microscopic diffusion in the case of a single plasma wave, although a broadening of the particle distribution can be observed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Proton diffusion and hydrogen/deuterium exchange in amorphous solid water at temperatures from 114 to 134 K

The reaction coefficient for hydrogen/deuterium (H/D) exchange and the diffusion of hydrated excess protons within amorphous solid water (ASW) are characterized as a function of temperature. For these experiments, water films are deposited on a Pt(111) substrate at 108 K, and reactions with pre-adsorbed hydrogen atoms produce hydrated protons. Upon heating, protons diffuse within the water, and H/D exchange occurs when they encounter D2O probe molecules deposited in the films. The time-dependent concentration of D2O is monitored with infrared spectroscopy, and it indicates the protons diffusion from the substrate and establish an equilibrium distribution prior to significant H/D exchange for temperatures 114 K ≤T≤ 134 K. By controlling the distance between the D2O molecules and the substrate, we probe the distribution of protons within the film. It decays as x−2 for the examined range of x (12–52 nm) due to the electric field that develops between the diffusing protons and their image charges in the metal substrate. This agrees with the theoretical distance scaling for the equilibrated proton concentration in a dielectric near a metal boundary. From the proton concentration and the measured D2O decay rate, a lower bound for the proton diffusion coefficient ranging from 10−20 m2/s at 114 K to 10−18 m2/s at 134 K is estimated. The diffusion coefficient has an activation energy of 0.40 eV, which is comparable to energies reported for molecular translations and rotations of H2O, suggesting they may play a critical role in the proton diffusion mechanism within ASW.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Reaction-diffusive dynamics of number-conserving dissipative quantum state preparation

The use of dissipation for the controlled creation of nontrivial quantum many-body correlated states is of much fundamental and practical interest. What is the result of imposing number conservation, which, in closed system, gives rise to diffusive spreading? For this work, we investigate this question for a paradigmatic model of a two-band system, with dissipative dynamics aiming to empty one band and to populate the other, which had been introduced before for the dissipative stabilization of topological states. Going beyond the mean-field treatment of the dissipative dynamics, we demonstrate the emergence of a diffusive regime for the particle and hole density modes at intermediate length- and timescales, which, interestingly, can only be excited in nonlinear response to external fields. We also identify processes that limit the diffusive behavior of this mode at the longest length- and timescales. Strikingly, we find that these processes lead to a reaction-diffusion dynamics governed by the Fisher-Kolmogorov-Petrovsky-Piskunov equation, making the designed dark state unstable towards a state with a finite particle and hole density.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1967

Nonstationary radiation field

Radiation diffusion without redistribution by frequencies, equations for radiative transfer, and stellar spectrum

DIFFUSION WAVE↗
NASA NTRS1971

An analysis of the flow field near the fuel injection location in a gas core reactor.

An analytical study is presented which shows the effects of large energy release and the concurrent high acceleration of inner stream fluid on the coaxial flow field in a gas core reactor. The governing equations include the assumptions of only radial radiative transport of energy represented as an energy diffusion term in the Euler equations. The method of integral relations is used to obtain the numerical solution. Results show that the rapidly accelerating, heat generating inner stream actually shrinks in radius as it expands axially.

Weinstein, H.↗
NASA NTRS1987

Numerical solution of the radiation transport equation in disk geometry

An efficient numerical method for solving the problem of radiation transport in a dusty medium with two dimensional (2-D) disk geometry is described. It is a generalization of the one-dimensional quasi-diffusion method in which the transport equation is cast in diffusion form and then solved as a boundary value problem. The method should be applicable to a variety of astronomical sources, the dynamics of which are angular-momentum dominated and hence not accurately treated by spherical geometry, e.g., protoplanetary nebulae, circumstellar disks, interstellar molecular clouds, accretion disks, and disk galaxies. The computational procedure and practical considerations for implementing the method are described in detail. To illustrate the effects of 2-D radiation transport, some model results (dust temperature distributions and IR flux spectra) for externally heated, interstellar dust clouds with spherically symmetric and disk geometry are compared.

Spagna, George F., Jr.↗
DOE OSTI2017

Development of a diffusive wave shallow water model with a novel stability condition and other new features

Traditionally, one of the approaches to flood modelling is numerical simulation of the diffusive wave approximation of the shallow water equations. Improving these models in various aspects is still an open area of research. In this study, a new diffusive wave model with explicit time integration was developed which includes some novel features: (1) time steps are determined using a novel stability criterion which resulted in more dynamic time steps (i.e., broader range) compared to the conventional Courant-Friedrichs-Lewy stability condition; (2) stability constraints are reduced, considering the flow processes within surface ponds; (3) besides Manning's formula, which is the common equation for computing velocities in diffusive wave models, the free fall velocity and a new equation for wave-front velocity are employed; and (4) the influence of upstream surface ponds on downstream flow is considered. This paper introduces the enhanced diffusive wave model, the socalled Overland Flow Simulator Cellular Automata (OFS-CA), and its results for five test cases. Available analytical solutions and an experimental study were used for verification. Two other shallow water models were used for comparison and benchmarking. Overall, good agreements were observed and OFS-CA was computationally less expensive compared to the other two shallow water models.

42 ENGINEERING↗
DOE OSTI2024

Quasilinear theory: the lost ponderomotive effects and why they matter

Quasilinear theory (QLT) has been used for modeling wave–plasma interactions for decades but remains largely heuristic. Plasma inhomogeneity, ponderomotive effects, microscopic fluctuations, and collisions are not easily accommodated from first principles in QLT, and typically are ignored entirely, due to the limitations of the standard Fourier–Laplace global-mode approach. This results in inconsistencies, for example, violation of the action conservation for nonresonant waves. However, these issues can be avoided, and the theory can be substantially generalized and corrected, if QLT is formulated using more suitable analytical tools, particularly, the Weyl symbol calculus. Here, an attempt is made to deliver an accessible review of this modern formulation, provide intuitive calculations for special cases, and elaborate on the connection with the ‘oscillation-center QLT’ originally proposed by Dewar (Phys Fluids 16:1102, 1973). A Fokker–Planck equation for a ‘dressed’ distribution is derived from the Klimontovich equation and captures quasilinear diffusion, ponderomotive forces, and interactions with background fields for a generic Hamiltonian, so many known formulations of QLT for specific plasma models become corollaries of a single unifying theory. Also, waves are allowed to be off-shell (not constrained by a dispersion relation), which allows them to accommodate microscopic fluctuations. This leads to a collision integral of the Balescu–Lenard type that has all the usual properties but is not restricted to any specific plasma model. For on-shell waves, a generalized version of the classic oscillation-center QLT is obtained. Finally, combined with the wave-kinetic equation, this formulation not only conserves particles, momentum, and energy, like the classic QLT but also reinstates the action conservation for nonresonant waves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1981

Computing diffuse reflection from particulate planetary surface with a new function

An equation is derived to compute the amount of diffuse light reflected by a particulate surface, such as on Mars or an asteroid. The method traces the paths of rays within an ensemble of randomly shaped grains and finds the eventual probability of emission. The amount of diffuse, unpolarized emitted light is obtained in terms of the real index of refraction, the imaginary index, and the average diameter of particles making up the surface. The equation is used to compute the empirical rule for obtaining the planetary albedo from the slope of its polarization curve. Accuracy of the equation, estimated at + or - 4%, seems justified because of quantitative agreement with experimental measures of the empirical rule. It is also shown that the equation can be applied to bubble-enclosing surfaces such as volcanic foams. Results for the indices of the moon, Mars, Io, and Europa are obtained and compared with other data.

Wolff, M.↗
DOE OSTI2025

Scalar flux transport models for self-similar turbulent mixing

A common approach to closing turbulent species flux in multicomponent Reynolds-averaged Navier-Stokes models is to use the standard gradient diffusion approximation. While such an approach has been shown to work well when applied to many canonical turbulent mixing configurations, a gradient diffusion approach is fundamentally limited in its ability to capture complex phenomena such as countergradient transport. For this reason, complicated mixing applications may benefit by treating the turbulent diffusivity with a model transport equation in a manner analogous to second-moment momentum closure in Reynolds-stress transport models. Here, the present work explores the development and application of two different scalar flux transport (SFT) models. Self-similarity constraints are derived for these models, and they are evaluated against gradient-diffusion-based models in several one- and two-dimensional problems of turbulent mixing. It is found that the new SFT models out-perform gradient diffusion models in problems involving rapid acceleration reversal and in problems involving anisotropic transport of materials. In addition, it is found that even a hybrid-SFT approach, in which an SFT equation is utilized along with a gradient diffusion closure, provides some measure of improvement over models that transport the mass flux rather than the scalar flux.

Reynolds-averaged Navier Stokes↗
DOE OSTI2023

Methane mass transfer in mesoporous silica saturated with liquid hydrocarbons

Mass transfer across gas/liquid interfaces plays a central role in many industrial applications. In particular, gas dissolution and diffusion in liquid hydrocarbon mixtures, confined in nanometer-sized pores, is an essential mechanism during enhanced oil recovery (EOR) from unconventional formations. In this work, we have measured methane (C 1 ) diffusion in n-decane (C 10 ), n-hexadecane (C 16 ), and mixtures of C 10 + C 16 in a mesoporous material with an average pore size of 4 nm at 50 °C and ~ 8 MPa of gas pressure. A key conclusion of this work is that the diffusivities, measured in the bulk phase, for the relevant binary systems, are sufficient to predict the diffusion behavior of the corresponding multicomponent systems in the porous medium by using Wilke’s equation for the evaluation of effective component diffusivities, combined with an accurate equation of state (EOS) representation of the (bulk) phase behavior. This observation can facilitate accurate prediction of recovery processes in unconventional formations and, potentially, guide other applications that entail gas-liquid interface mass transfer in mesoporous materials.

42 ENGINEERING↗
NASA NTRS1984

What Would a Dynamo Theorist like to Know About the Dynamics of the Solar Convection Zone?

Observations about the current status of solar dynamo theory are given. The induction equation for magnetic field is solved using assumed velocities and parametric representations of the inductive or diffusive effects of velocities. The equations of motion governing these flow are not solved in parallel. Results from global compressible convection models are discussed. Differential rotation and convection are also investigated.

Gilman, P. A.↗
NASA NTRS1997

Equivalence of Fluctuation Splitting and Finite Volume for One-Dimensional Gas Dynamics

The equivalence of the discretized equations resulting from both fluctuation splitting and finite volume schemes is demonstrated in one dimension. Scalar equations are considered for advection, diffusion, and combined advection/diffusion. Analysis of systems is performed for the Euler and Navier-Stokes equations of gas dynamics. Non-uniform mesh-point distributions are included in the analyses.

Wood, William A.↗
NASA NTRS1954

Heat transfer, diffusion, and evaporation

Although it has long been known that the differential equations of the heat-transfer and diffusion processes are identical, application to technical problems has only recently been made. In 1916 it was shown that the speed of oxidation of the carbon in iron ore depends upon the speed with which the oxygen of the combustion air diffuses through the core of gas surrounding the carbon surface. The identity previously referred to was then used to calculate the amount of oxygen diffusing to the carbon surface on the basis of the heat transfer between the gas stream and the carbon surface. Then in 1921, H. Thoma reversed that procedure; he used diffusion experiments to determine heat-transfer coefficients. Recently Lohrisch has extended this work by experiment. A technically very important application of the identity of heat transfer and diffusion is that of the cooling tower, since in this case both processes occur simultaneously.

GASES - DIFFUSION↗