Anisotropic diffusion of solar cosmic rays.
Anisotropic diffusion of solar cosmic rays due to interplanetary magnetic field
INTERPLANETARY MAGNETIC FIELD↗
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Results for “anisotropic diffusion”
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A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields
We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial boundary value problem. A discrete formulation is presented using operator splitting in time with the summation by parts finite difference approximation of spatial derivatives for the perpendicular diffusion operator. Weak penalty procedures are derived for implementing both boundary conditions and parallel diffusion operator obtained by field line tracing. We prove that the fully-discrete approximation is unconditionally stable. Discrete energy estimates are shown to match the continuous energy estimate given the correct choice of penalty parameters. A nonlinear penalty parameter is shown to provide an effective method for tuning the parallel diffusion penalty and significantly minimises rounding errors. Several numerical experiments, using manufactured solutions, the “NIMROD benchmark” problem and a single island problem, are presented to verify numerical accuracy, convergence, and asymptotic preserving properties of the method. Finally, we present a magnetic field with chaotic regions and islands and show the contours of the anisotropic diffusion equation reproduce key features in the field.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Effect of charge and anisotropic diffusivity on ion exchange kinetics in nuclear waste form materials
Motifs of radionuclide absorption particles (absorbers or fillers) for the nuclear waste treatment usually have crystal structures with nano-sized tunnels for fast ion diffusion. On the other hand, the accumulation of ions generates an electric field which affects the ion diffusion. Therefore, the strong anisotropic kinetic properties and the electric field affect ion exchange kinetics, especially in an assembly of these particles which may block the fast diffusion tunnels for each other. In this work, we developed a mesoscale model to describe the effect of anisotropic kinetic properties and electric field on ion exchange kinetics. With the model we simulated the effect of anisotropic diffusivity, electrochemical potential, particle morphology, size and aggregation on ion exchange kinetics during batch experiments. Here, tt is found that 1) ion exchange results in charge accumulation inside the particle because different ions have different diffusivities and different diffusion driving forces. The electric neutrality is not preserved; 2) the electric field speeds up the slower diffusion ions (either uptake or release) and slows down the faster diffusion ions to reduce charge accumulation and maintains charge neutrality; 3) the ion exchange becomes very slow at the later stages because a) diffusion driving force (electrochemical gradient, Cs + concentration in the solution and Na + inside the particle) continuously decreases, as observed in batch experiments; and b) the diffusivity decreases due to the Cs + concentration dependence of ion diffusivity. This can explain the observed experimental phenomena that the radionuclide capacity usually cannot be reached; 4) for needle-like particle and their clusters, both surface area and diffusion distance along the direction with the fastest diffusivities have significant impact on the ion exchange kinetics.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Superior discretizations and AMG solvers for extremely anisotropic diffusion via hyperbolic operators [Slides]
Diffusion in magnetic confinement fusion is extremely anisotropic in the direction of field lines. Rewrote diffusion system based on directional gradients, apply discretization and solver techniques developed for advection. Orders of magnitude decrease in error and solve wallclock time vs. traditional methods. The next steps include: (1) incorporate into larger MHD simulations, (2) better solvers for closed field lines or mixed regimes, and (3) possibly other extremely anisotropic equations.
97 MATHEMATICS AND COMPUTING↗
Renormalization group analysis of anisotropic diffusion in turbulent shear flows
The renormalization group is applied to compute anisotropic corrections to the scalar eddy diffusivity representation of turbulent diffusion of a passive scalar. The corrections are linear in the mean velocity gradients. All model constants are computed theoretically. A form of the theory valid at arbitrary Reynolds number is derived. The theory applies only when convection of the velocity-scalar correlation can be neglected. A ratio of diffusivity components, found experimentally to have a nearly constant value in a variety of shear flows, is computed theoretically for flows in a certain state of equilibrium. The theoretical value is well within the fairly narrow range of experimentally observed values. Theoretical predictions of this diffusivity ratio are also compared with data from experiments and direct numerical simulations of homogeneous shear flows with constant velocity and scalar gradients.
Rubinstein, Robert↗
Mesh refinement for anisotropic diffusion in magnetized plasmas
Highly accurate simulation of plasma transport is needed to drive the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers that are expensive to resolve. Here, this work investigates how various mesh refinement strategies might reduce that expense to allow for more efficient simulation by comparing standard variable refinement approaches that use a field quantity to an adaptive approach that uses an error estimator. It is first verified that higher order discretization only realizes the proper rate of convergence once the mesh resolves the thin boundary layer, therefore motivating the focusing of refinement on the boundary layer. For three two-dimensional test cases that contain characteristic features of tokamak magnetic fields, an exponential refinement strategy based on the magnetic flux function, which is the standard refinement approach in the field, is compared to an adaptive strategy utilizing the established Zienwiekicz and Zhu error estimator. The adaptive mesh refinement strategy consistently achieves the same accuracy using orders of magnitude less degrees of freedom than either exponential or uniform refinement. This result makes the adaptive refinement strategy more efficient than the exponential refinement strategy while also being more generalizable to problems with complex magnetic geometries. Scaling laws are derived that quantify the improvement in cost of the adaptive refinement strategy over other refinement approaches in 2D and 3D.
97 MATHEMATICS AND COMPUTING↗
Advances in HDG Methods for Strongly Anisotropic Diffusion
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Mathematics and Computing↗
Generating a Simulated Fluid Flow Over an Aircraft Surface Using Anisotropic Diffusion
A fluid-flow simulation over a computer-generated aircraft surface is generated using a diffusion technique. The surface is comprised of a surface mesh of polygons. A boundary-layer fluid property is obtained for a subset of the polygons of the surface mesh. A pressure-gradient vector is determined for a selected polygon, the selected polygon belonging to the surface mesh but not one of the subset of polygons. A maximum and minimum diffusion rate is determined along directions determined using a pressure gradient vector corresponding to the selected polygon. A diffusion-path vector is defined between a point in the selected polygon and a neighboring point in a neighboring polygon. An updated fluid property is determined for the selected polygon using a variable diffusion rate, the variable diffusion rate based on the minimum diffusion rate, maximum diffusion rate, and angular difference between the diffusion-path vector and the pressure-gradient vector.
Rodriguez, David L.↗
Generating a Simulated Fluid Flow over a Surface Using Anisotropic Diffusion
A fluid-flow simulation over a computer-generated surface is generated using a diffusion technique. The surface is comprised of a surface mesh of polygons. A boundary-layer fluid property is obtained for a subset of the polygons of the surface mesh. A gradient vector is determined for a selected polygon, the selected polygon belonging to the surface mesh but not one of the subset of polygons. A maximum and minimum diffusion rate is determined along directions determined using the gradient vector corresponding to the selected polygon. A diffusion-path vector is defined between a point in the selected polygon and a neighboring point in a neighboring polygon. An updated fluid property is determined for the selected polygon using a variable diffusion rate, the variable diffusion rate based on the minimum diffusion rate, maximum diffusion rate, and the gradient vector.
Rodriguez, David L.↗
Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport
We analyze the well-posedness of an anisotropic, nonlocal diffusion equation. Establishing an equivalence between weighted and unweighted anisotropic nonlocal diffusion operators in the vein of unified nonlocal vector calculus, we apply our analysis to a class of fractional-order operators and present rigorous estimates for the solution of the corresponding anisotropic anomalous diffusion equation. Furthermore, we extend our analysis to the anisotropic diffusion-advection equation and prove well-posedness for fractional orders s ∊ [0.5, 1). We also present an application of the advection-diffusion equation to anomalous transport of solutes.
97 MATHEMATICS AND COMPUTING↗
Anisotropic carrier diffusion in single MAPbI 3 grains correlates to their twin domains
The anisotropic charge carrier diffusion coupled to ferroelastic twin domains in methylammonium lead iodide opens possibilities for further optimization of perovskite solar cells and optoelectronic devices via strain engineering and heat treatments.
36 MATERIALS SCIENCE↗
Anisotropic thermal diffusivity and conductivity in SiC/SiC tubes studied by infrared imaging and X-ray computed tomography
Traditional flash diffusivity evaluation of thermal diffusivity/conductivity of composite tubes require machining of specimens. For a thin-wall tube, this method can only be used to obtain through-thickness transport property. A novel method to evaluate anisotropic thermal diffusivity in a composite tube has been developed. Braided SiC/SiC composite tubes were subjected to a xenon flash heating pulse. A high-speed, high-sensitivity infrared camera was used to measure surface temperature changes as a function of time and nondestructively detect subsurface defects/damages, such as macroscopic pores. Standard reference material (Pyroceram 9606) and curved SiC/SiC composite tube specimens were used to validate thermal diffusivity obtained from infrared imaging. Unlike the traditional method, there is no need prepare special specimens, and thermal diffusivity values in three orientations are obtained after a single flash. A finite element analysis model based on x-ray computed tomography scans was developed to simulate the heat transfer. In conclusion, this technique is significant in assessing thermal conductivity and inspecting the health of ceramic tubes during and after service.
36 MATERIALS SCIENCE↗
Visualizing Anisotropic Oxygen Diffusion in Ceria under Activated Conditions
Oxygen reactivity plays a key role in the performance of ceria-based catalysts. Aberration-corrected transmission electron microscopy and molecular dynamics simulations were used to study the oxygen atom diffusion in ceria under activated conditions. Reactive oxygen atom and its real-time diffusion were visualized. Additionally, the interplay between cerium and oxygen atoms originating from a Coulomb interaction was revealed by the out-of-plane buckling of cerium atoms associated with oxygen transport. Anisotropic oxygen atom diffusion that depends on crystal orientations was discovered, demonstrating a preferential [001] crystallographic diffusion pathway. These findings reveal prospects for applications of anisotropic orientation-relevant fluorite-structured oxides.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Directional diffusion coefficients of solar protons inside and outside the bow shock.
The directional diffusion coefficients of low-energy (greater than or equal to 0.3 MeV) solar protons inside and outside the bow shock are examined during the solar flare event of Jan. 24, 1969. The data are derived from simultaneous observations obtained by Explorer 33 inside the magnetosheath and by Explorer 35 in the interplanetary medium. Although the gross properties of the spin-averaged intensities on a diffusion-type plot appear to be the same in both media, the directional intensities show significant variations. It is shown that directional intensities of low-energy protons can be described reasonably well by anisotropic diffusion with an associated diffusion coefficient. Directional diffusion coefficients are found to differ by a factor of as much as three among different directions in space, and from the spin-averaged diffusion coefficient. This suggests that anisotropic diffusion does indeed take place and that so called 'isotropic' diffusion coefficients derived in the past from spin-averaged intensities may actually be directional diffusion coefficients in cases where substantial anisotropies (greater than 50%) exist.
Verzariu, P.↗
Evaluation of Moderate-Resolution Imaging Spectroradiometer (MODIS) Snow Albedo Product (MCD43A) over Tundra
This study assesses the MODIS standard Bidirectional Reflectance Distribution Function (BRDF)/Albedo product, and the daily Direct Broadcast BRDF/Albedo algorithm at tundra locations under large solar zenith angles and high anisotropic diffuse illumination and multiple scattering conditions. These products generally agree with ground-based albedo measurements during the snow cover period when the Solar Zenith Angle (SZA) is less than 70deg. An integrated validation strategy, including analysis of the representativeness of the surface heterogeneity, is performed to decide whether direct comparisons between field measurements and 500- m satellite products were appropriate or if the scaling of finer spatial resolution airborne or spaceborne data was necessary. Results indicate that the Root Mean Square Errors (RMSEs) are less than 0.047 during the snow covered periods for all MCD43 albedo products at several Alaskan tundra areas. The MCD43 1- day daily albedo product is particularly well suited to capture the rapidly changing surface conditions during the spring snow melt. Results also show that a full expression of the blue sky albedo is necessary at these large SZA snow covered areas because of the effects of anisotropic diffuse illumination and multiple scattering. In tundra locations with dark residue as a result of fire, the MODIS albedo values are lower than those at the unburned site from the start of snowmelt.
Wang, Zhuosen↗