Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport.
Abstract not provided.
Gulian, Mamikon↗
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Results for “anisotropic diffusion”
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A semi-automated algorithm for designing stellarator divertor and limiter plates and application to HSX
We present a semi-automated algorithm for designing three-dimensional divertor or limiter plates targeting low heat loads. The algorithm designs the plates in two stages: firstly, the parallel heat flux distribution is caught on vertically-inclined plates at one or several toroidal locations. Secondly, the power per unit area is reduced by stretching, tilting and bending the plates toroidally. Heat transport is modelled using the EMC3-Lite code, which uses an anisotropic diffusion model. We apply this scheme to HSX, a medium-sized stellarator located at the University of Wisconsin–Madison. Starting from the current machine with an extended vessel wall, we construct plates which are able to effectively catch and spread the heat for three different magnetic configurations. The scheme has a computational cost in the order of tens of CPU-minutes, making it a powerful tool for semi-automated plasma-facing component design in three-dimensional environments.
anisotropic diffusion↗
Overlapping Schwarz Methods Are Not Anisotropy‐Robust Multigrid Smoothers
We analyze overlapping multiplicative Schwarz methods as smoothers in the geometric multigrid solution of two-dimensional anisotropic diffusion problems. For diffusion equations, it is well known that the smoothing properties of point-wise smoothers, such as Gauss Seidel, rapidly deteriorate as the strength of anisotropy increases. On the other hand, global smoothers based on line smoothing are known to generally provide good smoothing for diffusion problems, independent of the anisotropy strength. Here, a natural question is whether global methods are really necessary to achieve good smoothing in such problems, or whether it can be obtained with locally overlapping block smoothers using sufficiently large blocks and overlap. Through local Fourier analysis and careful numerical experimentation, we show that global methods are indeed necessary to achieve anisotropy-robust smoothing. Specifically, for any fixed block size bounded sufficiently far away from the global domain size, we find that the smoothing properties of overlapping multiplicative Schwarz rapidly deteriorate with increasing anisotropy, irrespective of the amount of overlap between blocks. Moreover, our results indicate that anisotropy-robust smoothing requires blocks of diameter 𝒪(𝜖 −1/2 ) for anisotropy ratio 𝜖 ∈(0,1] .
97 MATHEMATICS AND COMPUTING↗
First-principles investigation of lanthanides diffusion in HCP zirconium via vacancy-mediated transport
The diffusion of lanthanide fission products plays an important role in the growth of the fuel-cladding chemical interaction (FCCI) region in metallic fuels. The use of a Zr interdiffusion barrier may mitigate the transport of lanthanides from the fuel to the cladding, but the efficacy of such a liner is not yet known. In this paper, the stability and vacancy-mediated diffusion of La, Ce, Pr, and Nd in hexagonal close-packed (HCP) Zr is investigated via density functional theory (DFT) calculations and self-consistent mean field (SCMF) analysis. DFT is used to calculate the formation, binding, and migration energies of vacancies and vacancy-solute pairs. The DFT energetics are used in the KineCluE code to calculate the Onsager transport coefficients. La is found to be the fastest diffusing species in HCP Zr and experiences an almost isotropic diffusion behavior. The other three species (Ce, Pr, and Nd) demonstrate anisotropic diffusion where the diffusion in the basal planes is significantly faster than that along the c-axis. Further, the calculated lanthanide diffusivities in HCP Zr are fitted to an Arrhenius relation and the activation energies and prefactors are reported for the first time. Furthermore, the vacancy drag and the segregation tendencies were analyzed using the calculated off-diagonal transport coefficients. According to our vacancy-mediated diffusion model, lanthanides are expected to be enriched at vacancy sinks at low temperatures, while at high temperatures, lanthanides are depleted at sinks and will preferably diffuse into the bulk. The enrichment/depletion transition temperature depends on the diffusion direction (basal or axial) and hence will be controlled by the grain texture and orientation.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
On the convection, diffusion, and adiabatic deceleration of cosmic rays in the solar wind
Cosmic ray transport in solar wind generalized with anisotropic diffusion approximation
Jokipii, J. R.↗
High Temperature Degradation Mechanisms in Polymer Matrix Composites
Polymer matrix composites are increasingly used in demanding structural applications in which they may be exposed to harsh environments. The durability of such materials is a major concern, potentially limiting both the integrity of the structures and their useful lifetimes. The goal of the current investigation is to develop a mechanism-based model of the chemical degradation which occurs, such that given the external chemical environment and temperatures throughout the laminate, laminate geometry, and ply and/or constituent material properties, we can calculate the concentration of diffusing substances and extent of chemical degradation as functions of time and position throughout the laminate. This objective is met through the development and use of analytical models, coupled to an analysis-driven experimental program which offers both quantitative and qualitative information on the degradation mechanism. Preliminary analyses using a coupled diffusion/reaction model are used to gain insight into the physics of the degradation mechanisms and to identify crucial material parameters. An experimental program is defined based on the results of the preliminary analysis which allows the determination of the necessary material coefficients. Thermogravimetric analyses are carried out in nitrogen, air, and oxygen to provide quantitative information on thermal and oxidative reactions. Powdered samples are used to eliminate diffusion effects. Tests in both inert and oxidative environments allow the separation of thermal and oxidative contributions to specimen mass loss. The concentration dependency of the oxidative reactions is determined from the tests in pure oxygen. Short term isothermal tests at different temperatures are carried out on neat resin and unidirectional macroscopic specimens to identify diffusion effects. Mass loss, specimen shrinkage, the formation of degraded surface layers and surface cracking are recorded as functions of exposure time. Geometry effects in the neat resin, and anisotropic diffusion effects in the composites, are identified through the use of specimens with different aspect ratios. The data is used with the model to determine reaction coefficients and effective diffusion coefficients. The empirical and analytical correlations confirm the preliminary model results which suggest that mass loss at lower temperatures is dominated by oxidative reactions and that these reaction are limited by diffusion of oxygen from the surface. The mechanism-based model is able to successfully capture the basic physics of the degradation phenomena under a wide range of test conditions. The analysis-based test design is successful in separating out oxidative, thermal, and diffusion effects to allow the determination of material coefficients. This success confirms the basic picture of the process; however, a more complete understanding of some aspects of the physics are required before truly predictive capability can be achieved.
Cunningham, Ronan A.↗
High Temperature Degradation Mechanisms in Polymer Matrix Composites
Polymer matrix composites are increasingly used in demanding structural applications in which they may be exposed to harsh environments. The durability of such materials is a major concern, potentially limiting both the integrity of the structures and their useful lifetimes. The goal of the current investigation is to develop a mechanism-based model of the chemical degradation which occurs, such that given the external chemical environment and temperatures throughout the laminate, laminate geometry, and ply and/or constituent material properties, we can calculate the concentration of diffusing substances and extent of chemical degradation as functions of time and position throughout the laminate. This objective is met through the development and use of analytical models, coupled to an analysis-driven experimental program which offers both quantitative and qualitative information on the degradation mechanism. Preliminary analyses using coupled diffusion/reaction model are used to gain insight into the physics of the degradation mechanisms and to identify crucial material parameters. An experimental program is defined based on the results of the preliminary analysis which allows the determination of the necessary material coefficients. Thermogravimetric analyses are carried out in nitrogen, air, and oxygen to provide quantitative information on thermal and oxidative reactions. Powdered samples are used to eliminate diffusion effects. Tests in both inert and oxidative environments allow the separation of thermal and oxidative contributions to specimen mass loss. The concentration dependency of the oxidative reactions is determined from the tests in pure oxygen. Short term isothermal tests at different temperatures are carried out on neat resin and unidirectional macroscopic specimens to identify diffusion effects. Mass loss, specimen shrinkage, the formation of degraded surface layers and surface cracking are recorded as functions of exposure time. Geometry effects in the neat resin, and anisotropic diffusion effects in the composites, are identified through the use of specimens with different aspect ratios. The data is used with the model to determine reaction coefficients and effective diffusion coefficients. The empirical and analytical correlations confirm the preliminary model results which suggest that mass loss at lower temperatures is dominated by oxidative reactions and that these reaction are limited by diffusion of oxygen from the surface. The mechanism-based model is able to successfully capture the basic physics of the degradation phenomena under a wide range of test conditions. The analysis-based test design is successful in separating out oxidative, thermal, and diffusion effects to allow the determination of material coefficients. This success confirms the basic picture of the process; however, a more complete understanding of some aspects of the physics are required before truly predictive capability can be achieved.
Cunningham, Ronan A.↗
Effects of drift on the transport of cosmic rays. VI - A three-dimensional model including diffusion
The first results are presented from a series of computer simulations of the solar modulation of galactic cosmic rays using a full three-dimensional model which incorporates all known important effects on particle transport, particle drifts, convection with the solar wind, energy loss, and anisotropic diffusion. The model is time-independent in the coordinate frame rotating with the sun, so corotating effects can be studied. Modulation in an interplanetary magnetic field model is considered in which the current sheet separating the northern and southern solar hemispheres is warped and corotating with the sun. The amplitude of the warp is varied to simulate possible solar cycle variation of the magnetic field. Substantial effects due to the warp of the current sheet are found. Comparison of the model results with various data is presented. Among other things, it is shown that the intensity may decrease away from the current sheet for both signs of the magnetic field, as suggested by recent observations, and in contrast with inferences from earlier, more approximate calculations.
Kota, J.↗
Reduced Artifact Approach for Determining Diffusion Coefficients in Time-Resolved Microscopy
Ultrafast microscopy methods traditionally assume a Gaussian profile to extract excited state diffusivities from transport measurements. Although this fitting method recovers accurate diffusion coefficients when the point spread function is well-represented by a Gaussian, even minor spatial aberrations introduced by the imaging system cause significant errors in the determined value. To provide a more accurate measure of excited state transport in nano- and microscale materials systems, in this work an alternative analysis protocol is proposed that numerically convolves the Green’s function solution to the diffusion equation with the experimentally measured point spread function. In contrast to the Gaussian fitting approach, the numerical convolution is shown to be robust against artifacts caused by nonideal point spread functions. Furthermore, the numerical convolution approach is highly effective at resolving anisotropic diffusion in modeled data.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
On Thermodynamic and Kinetic Mechanisms for Stabilizing Surface Solid Solutions
Many processes for energy storage rely on transformations between phases with strong separation tendencies. In these systems, performance limitations can arise from undesirable chemical and mechanical factors associated with the phase separation behavior. Solid solutions represent a desirable alternative, provided the conditions for their formation are known. In the present work, we invoke linear stability theory and diffuse-interface mesoscopic simulations to demonstrate that solid solutions can be stabilized near surface layers of phase-separating systems. Two factors are found to drive surface solid-solution formation: surface relaxation of solution self-strain energy and anisotropy of diffusion mobility. Using a strongly phase-separating LiXFePO4 particle as a model system, we show that the relaxation of the solution self-strain energy competes against the relaxation of the coherency strain energy to stabilize surface solid solutions. Our theoretical understanding also suggests that highly anisotropic diffusion mobility can provide an alternative kinetic route to achieve the same aim, with stabilizing behavior strongly dependent on the specific alignment of the surface orientation. Our findings provide fundamental guidance for manipulating solid-solution behavior in nanoscale structures, in which surface effects become especially significant. Beyond energy storage materials, our findings have important implications for understanding solid-solution formation in other phase-separating systems from metal alloys to ceramics.
25 ENERGY STORAGE↗
Frustrated charge density wave and quasi-long-range bond-orientational order in the magnetic kagome FeGe
The intrinsic frustrated nature of a kagome lattice is amenable to the realization of exotic phases of matter, such as quantum spin liquids or spin ices, and the multiple-q charge density waves (CDW) in the kagome metals. Despite intense efforts to understand the mechanism driving the electronic modulations, its origin is still unknown and obscured by competing interactions and intertwined orders. Here, we identify a dimerization-driven 2D hexagonal charge-diffuse precursor in the antiferromagnetic kagome metal FeGe and demonstrate that the fraction of dimerized/undimerized states is the relevant order parameter of the multiple-q CDW of a continuous phase transition. The pretransitional charge fluctuations with propagation vector q = q M at T CDW < T < T*(125 K) are anisotropic, hence holding a quasi-long-range bond-orientational order. The broken translational symmetry emerges from the anisotropic diffuse precursor, akin to the Ising scenario of antiferromagnetic triangular lattices. The temperature and momentum dependence of the critical scattering show parallels to the stacked hexatic B-phases reported in liquid crystals and transient states of CDWs and highlight the key role of the topological defect-mediated melting of the CDW in FeGe.
Subires, D. [Donostia International Physics Center↗
Atomic-Scale Mechanism of Unidirectional Oxide Growth
A basic knowledge of the unidirectional growth mechanisms is required for precise control on size, shape, and thereby functionalities of nanostructures. The oxidation of many metals results in oxide nanowire growth with a bicrystal grain boundary along the axial direction. Using transmission electron microscopy that spatially and temporally resolves CuO nanowire growth during the oxidation of copper, here we provide direct evidence of the correlation between unidirectional crystal growth and bicrystal grain boundary diffusion. Based on atomic scale observations of the upward growth at the nanowire tip, oscillatory downward growth of atomic layers on the nanowire sidewall and the parabolic kinetics of lengthening, bicrystal grain boundary diffusion is the mechanism by which Cu ions are delivered from the nanowire root to the tip. Together with density-functional theory calculations, we further show that the asymmetry in the corner-crossing barriers promotes the unidirectional oxide growth by hindering the transport of Cu ions from the nanowire tip to the sidewall facets. We anticipate the broader applicability of these results in manipulating the growth of nanostructured oxides by controlling the bicrystal grain boundary structure that favors anisotropic diffusion for unidirectional, one-dimensional crystal growth for nanowires or isotropic diffusion for two-dimensional platelet growth.
36 MATERIALS SCIENCE↗
Diffuse scattering from dynamically compressed single-crystal zirconium following the pressure-induced α → ω phase transition
The prototypical α → ω phase transition in zirconium is an ideal test bed for our understanding of polymorphism under extreme loading conditions. After half a century of study, a consensus had emerged that the transition is realized via one of two distinct displacive mechanisms, depending on the nature of the compression path. However, recent dynamic-compression experiments equipped with diffraction diagnostics performed in the past few years have revealed new transition mechanisms, demonstrating that our understanding of the underlying atomistic dynamics and transition kinetics is in fact far from complete. We present classical molecular dynamics simulations of the α → ω phase transition in single-crystal zirconium shock compressed along the [0001] axis using a machine-learning-class potential. The transition is predicted to proceed primarily via a modified version of the two-stage Usikov-Zilberstein mechanism, whereby the high-pressure ω phase heterogeneously nucleates at boundaries between grains of an intermediate β phase. We further observe the fomentation of atomistic disorder at the junctions between β grains, leading to the formation of highly defective interstitial material between the ω grains. We directly compare synthetic x-ray diffraction patterns generated from our simulations with those obtained using femtosecond diffraction in recent dynamic-compression experiments, and show that the simulations produce the same unique, anisotropic diffuse scattering signal unlike any previously seen from an elemental metal. Our simulations suggest that the diffuse signal arises from a combination of thermal diffuse scattering, nanoparticlelike scattering from residual kinetically stabilized α and β grains, and scattering from interstitial defective structures. Published by the American Physical Society 2024
36 MATERIALS SCIENCE↗
Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations
In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac–Frenkel time-dependent variational principle. In recent years, it has attracted a lot of attention due to its wide applicability. Our schemes are inspired by the three-step procedure used in the rank adaptive version of the unconventional robust integrator (the so called BUG integrator) (Ceruti et al. in BIT Numer Math 62(4):1149–1174, 2022) for DLRA. First, a prediction (basis update) step is made computing the approximate column and row spaces at the next time level. Second, a Galerkin evolution step is invoked using an implicit solves for the small core matrix. Finally, a truncation is made according to a prescribed error threshold. Since the DLRA is evolving the differential equation projected on to the tangent space of the low rank manifold, the error estimate of the BUG integrator contains the tangent projection (modeling) error which cannot be easily controlled by mesh refinement. This can cause convergence issue for equations with cross terms. To address this issue, we propose a simple modification, consisting of merging the row and column spaces from the explicit step truncation method together with the BUG spaces in the prediction step. In addition, we propose an adaptive strategy where the BUG spaces are only computed if the residual for the solution obtained from the prediction space by explicit step truncation method, is too large. Here, we prove stability and estimate the local truncation error of the schemes under assumptions. We benchmark the schemes in several tests, such as anisotropic diffusion, solid body rotation and the combination of the two, to show robust convergence properties.
97 MATHEMATICS AND COMPUTING↗
Evolution of dislocation loops in irradiated α-Uranium: An atomistically-informed cluster dynamics investigation
An atomistically-informed mean field cluster dynamics model has been developed to investigate the nucleation and growth of prismatic loops in irradiated a-Uranium. TEM analysis of neutron irradiated a-Uranium shows the evolution of self-interstitial atom and vacancy loops on (010) and (100) crystallographic planes, respectively, resulting in an anisotropic lattice swelling of its face-centered orthorhombic crystal. To provide model parameters, the crystallography of loops and the binding energy of point defects to these loops were studied using an angular dependent EAM potential and classical molecular dynamics (MD) simulations. Furthermore, using the bond-boost hyperdynamics method, the anisotropic diffusion of interstitials and vacancies in a-Uranium was investigated. Here, the mechanisms of point defect diffusion and the associated migration energies were reported and compared with previous DFT studies. The energetics and kinetic quantities mentioned above were used in the cluster dynamics model to predict the cluster density as a function of dose rate, dose and temperature and the results were compared to the reported neutron irradiation experiments. The model predictions reveal an accumulation of small sized vacancy loops along with a population of large and growing self-interstitial loops, which closely corresponds to the TEM observations.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Phase transformation mechanism in irradiation-induced superlattice formation
Atomic kinetic Monte Carlo simulations were used to model void superlattice formation under irradiation in molybdenum, driven by anisotropic diffusion of self-interstitial atoms. A change in the phase transformation mechanism from nucleation and growth to spinodal decomposition occurred with increasing dose rate, with both mechanisms leading to superlattice formation. Analysis of a rate-theory based analytical model showed that an observed change in the kinetics of vacancy accumulation, the appearance of a region of positive second derivative in the plot of average vacancy concentration versus time, was caused by the onset of spinodal instability. Further, the analytical model showed that for molybdenum and several other metals where void superlattice formation is commonly observed, the phase transformation likely occurs by nucleation and growth. However, nickel may offer the possibility of experimental observation of the transition between phase transformation mechanisms.
36 MATERIALS SCIENCE↗
Unveiling the lithium-ion transport mechanism in Li{sub 2}ZrCl{sub 6} Solid-State Electrolyte {ital via} deep learning-accelerated molecular dynamics simulations.
Lithium zirconium chlorides (LZCs) present a promising class of cost-effective solid electrolytes for next-generation all-solid-state batteries. The unique crystal structure of LZCs plays a crucial role in facilitating lithium-ion mobility, which further affects the electrochemical performance. To understand the underlying mechanism governing ion transport, we employed deep learning-accelerated molecular dynamics simulation on Li2ZrCl6 (trigonal alpha- and monoclinic beta-LZC), focusing specifically on the zirconium coordination environment. Our results reveal that disordered alpha-LZC exhibits the highest ionic conductivity, while beta-LZC demonstrates significantly lower conductivity, closely aligning with experimental findings. The study confirms that across all phases, lithium migration proceeds via the site-to-site hopping mechanism, where variations in site residence times critically impact the overall ionic conductivity. In alpha-LZCs, lithium ions prefer to anisotropically diffuse across interlayers as the result of a lower energy barrier, driven primarily by collective diffusion. In contrast, lithium ions in beta-LZC primarily isotropically diffuse within the intralayer, hindered by higher energy barriers and determined by individual diffusion. The variation in ZrCl6 2- octahedral unit softening, induced by the specific layered arrangement of zirconium atoms, emerges as a critical determinant of the energy barriers across the LZC phases. These atomic-scale insights into the transport processes provide valuable guidance for the rational design and optimization of LZCs-based electrolytes, accelerating their practical application in advanced energy storage technologies.
Guo, Hanzeng↗
Investigating nonlinear magnetohydrodynamics in an optimized, reactor-scale quasi-axisymmetric stellarator
We use the new simulation capabilities of the extended-magnetohydrodynamic (MHD) code, M3D-C1, to investigate the nonlinear MHD properties of a reactor-scale quasisymmetric stellarator equilibrium. Our model captures the self-consistent evolution of the magnetic field, temperature, density, and flow profiles without imposing restrictions on the structure of the first. We include the effects of resistivity using a realistic temperature-dependent Spitzer model, along with a model for heat transport that captures the key physical characteristic, namely, strongly anisotropic diffusion in directions perpendicular and parallel to the magnetic field. We consider a quasi-axisymmetric, finite-pressure equilibrium that was optimized for self-consistent bootstrap current, quasi-symmetry, and energetic particle confinement. Our assessment finds that the equilibrium is highly unstable to interchange-like pressure-driven instabilities near the plasma edge. The initially unstable modes rapidly destabilize other modes in the direction of the N-fold rotational symmetry (toroidal, in this case). For this equilibrium, N = 2, meaning destabilization of a large number of even-numbered toroidal Fourier modes. Thus, field-periodicity is likely to be an important factor in the nonlinear MHD stability characteristics of optimized stellarators.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗