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DOE OSTI2021

Odd Diffusivity of Chiral Random Motion

Diffusive transport is characterized by a diffusivity tensor which may, in general, contain both a symmetric and an antisymmetric component. Although the latter is often neglected, we derive Green-Kubo relations showing it to be a general characteristic of random motion breaking time-reversal and parity symmetries, as encountered in chiral active matter. In analogy with the odd viscosity appearing in chiral active fluids, we term this component the odd diffusivity. Furthermore, we show how odd diffusivity emerges in a chiral random walk model, and demonstrate the applicability of the Green-Kubo relations through molecular dynamics simulations of a passive tracer particle diffusing in a chiral active bath.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Effect of transport mechanism on the coarsening of bicontinuous structures: A comparison between bulk and surface diffusion

Here, coarsening of bicontinuous microstructures is observed in a variety of systems, such as nanoporous metals and mixtures that have undergone spinodal decomposition. To better understand the morphological evolution of these structures during coarsening, we compare the morphologies resulting from two different coarsening mechanisms, surface and bulk diffusion. We perform phase-field simulations of coarsening via each mechanism in a two-phase mixture at nominal volume fractions of 50%-50% and 36%-64%, and the simulated structures are characterized in terms of topology (genus density), the interfacial shape distribution, structure factor, and autocorrelations of phase and mean curvature. We observe self-similar evolution of morphology and topology and agreement with the expected power laws for dynamic scaling, in which the characteristic length scale increases over time proportionally to t 1/4 for surface diffusion and t 1/3 for bulk diffusion. While we observe the expected difference in the coarsening kinetics, we find that differences in self-similar morphology due to coarsening mechanism are relatively small, although typically they are larger at 36% volume fraction than at 50% volume fraction. In particular, we find that bicontinuous structures coarsened via surface diffusion have lower scaled genus densities than structures coarsened via bulk diffusion. We also compare the self-similar morphologies to those in literature and to two model bicontinuous structures, namely, constant-mean-curvature surfaces based on the Schoen G minimal surface and random leveled-wave structures. The average scaled mean curvatures of these model structures agree reasonably with those of the coarsened structures at both 36% and 50%, but we find substantial disagreements in the scaled genus densities and the standard deviations of mean curvature.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Phosphorus Doping of Polycrystalline CdTe by Diffusion

Phosphorus diffusion in single crystal and polycrystalline CdTe material is explored using various methods. Dynamic secondary ion mass spectroscopy (SIMS) is used to determine 1D P diffusion profiles. A 2D diffusion model is used to determine the expected cross-sectional distribution of P in CdTe after diffusion anneals. Time of flight SIMS and cross-sectional cathodoluminescence corroborates expected P distributions. Devices fabricated with diffused P exhibit hole concentrations up to low 1015 cm-3, however a subsequent activation anneal enabled hole concentrations greater than 1016 cm-3. CdCl2 treatments and Cu based contacts were also explored in conjunction with the P doping process.

14 SOLAR ENERGY↗
DOE OSTI2016

Hindered cytoplasmic diffusion of inositol trisphosphate restricts its cellular range of action

The range of action of intracellular messengers is determined by their rates of diffusion and degradation. Previous measurements in oocyte cytoplasmic extracts indicated that the Ca 2+ -liberating second messenger inositol trisphosphate (IP 3 ) diffuses with a coefficient (~280 μm 2 s -1 ) similar to that in water, corresponding to a range of action of ~25 μm. Consequently, IP 3 is generally considered a “global” cellular messenger. We also reexamined this issue by measuring local IP 3 -evoked Ca 2+ puffs to monitor IP 3 diffusing from spot photorelease in neuroblastoma cells. Fitting these data by numerical simulations yielded a diffusion coefficient (≤10 μm 2 s -1 ) about 30-fold slower than that previously reported. Here, we propose that diffusion of IP 3 in mammalian cells is hindered by binding to immobile, functionally inactive receptors that were diluted in oocyte extracts. The predicted range of action of IP 3 (<5 μm) is thus smaller than the size of typical mammalian cells, indicating that IP 3 should better be considered as a local rather than a global cellular messenger.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Effect of Ion Streaming on Diffusion of Dust Grains in Dissipative System

The presence of strong electric fields in the sheath region of laboratory complex plasma induces an ion drift and perturbs the field around dust grains. The downstream focusing of ions leads to the formation of oscillatory kind of attractive wake potential which superimpose with the normal Debye-Hückel (DH) potential. The structural properties of complex plasma and diffusion coefficient of dust grains in the presence of such a wake potential have been investigated using Langevin dynamics simulation in the subsonic regime of ion flow. The study reveals that the diffusion of dust grains is strongly affected by the ion flow, so that the diffusion changes its character in the wake potential to the DH potential dominant regimes. The dependence of the diffusion coefficient on the parameters, such as the neutral pressure, dust grain size, ion flow velocity, and Coulomb coupling parameter, have been calculated for the subsonic regime by using the Green-Kubo expression, which is based on the integrated velocity autocorrelation function. It is found that the diffusion and the structural property of the system is intimately connected with the interaction potential and significantly get affected in the presence of ion flow in the subsonic regime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion

Reproducing kernel (RK) approximations are meshfree methods that construct shape functions from sets of scattered data. We present an asymptotically compatible (AC) RK collocation method for nonlocal diffusion models with Dirichlet boundary condition. The numerical scheme is shown to be convergent to both nonlocal diffusion and its corresponding local limit as nonlocal interaction vanishes. The analysis is carried out on a special family of rectilinear Cartesian grids for a linear RK method with designed kernel support. The key idea for the stability of the RK collocation scheme is to compare the collocation scheme with the standard Galerkin scheme, which is stable. In addition, assembling the stiffness matrix of the nonlocal problem requires costly computational resources because high-order Gaussian quadrature is necessary to evaluate the integral. We thus provide a remedy to the problem by introducing a quasi-discrete nonlocal diffusion operator for which no numerical quadrature is further needed after applying the RK collocation scheme. The quasi-discrete nonlocal diffusion operator combined with RK collocation is shown to be convergent to the correct local diffusion problem by taking the limits of nonlocal interaction and spatial resolution simultaneously. The theoretical results are then validated with numerical experiments. We additionally illustrate a connection between the proposed technique and an existing optimization based approach based on generalized moving least squares.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A Probabilistic Scheme for Semilinear Nonlocal Diffusion Equations with Volume Constraints

This work presents a probabilistic scheme for solving semilinear nonlocal diffusion equations with volume constraints and integrable kernels. The nonlocal model of interest is defined by a time-dependent semilinear partial integro-differential equation (PIDE), in which the integro-differential operator consists of both local convection-diffusion and nonlocal diffusion operators. Here, our numerical scheme is based on the direct approximation of the nonlinear Feynman–Kac formula that establishes a link between nonlinear PIDEs and stochastic differential equations. The exploitation of the Feynman–Kac representation avoids solving dense linear systems arising from nonlocal operators. Compared with existing stochastic approaches, our method can achieve first-order convergence after balancing the temporal and spatial discretization errors, which is a significant improvement of existing probabilistic/stochastic methods for nonlocal diffusion problems. Error analysis of our numerical scheme is established. The effectiveness of our approach is shown in two numerical examples. The first example considers a three-dimensional nonlocal diffusion equation to numerically verify the error analysis results. The second example presents a physics problem motivated by the study of heat transport in magnetically confined fusion plasmas.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Numerical Solution of Moving Phase Boundary and Diffusion-Induced Stress of Sn Anode in the Lithium-Ion Battery

Here, we have previously observed a large transient stress in Sn film anodes at the beginning of the Sn-Li 2 Sn 5 phase transformation. To understand this behavior, we use numerical modeling to simulate the kinetics of the 1-D moving boundary and Li diffusion in the Sn anodes. A mixture of diffusion-controlled and interface-controlled kinetics is found. The Li concentration in the Li 2 Sn 5 phase remains near a steady-state profile as the phase boundary propagates, whereas the Li diffusion in Sn is more complicated. Li continuously diffuses into the Sn layer and produces a supersaturation; the Li can then diffuse toward the Sn/Li 2 Sn 5 interface and contribute to further phase transformation. Finally, the evolution of Li concentration in the Sn induces strain which involves rate-dependent plasticity and elastic unloading, resulting in the complex stress evolution that is observed. In the long term, the measured stress is dominated by the stress in the growing Li 2 Sn 5 phase.

25 ENERGY STORAGE↗
DOE OSTI2020

Transmural Remodeling of Cardiac Microstructure in Aged Spontaneously Hypertensive Rats by Diffusion Tensor MRI

The long-standing high blood pressure (also known as hypertension) overworks the heart. Microstructural remodeling is a key factor of hypertensive heart disease progression. Diffusion tensor magnetic resonance imaging (DT-MRI) is a powerful tool for the rapid noninvasive nondestructive delineation of the cardiomyocyte organization. The spontaneously hypertensive rat (SHR) is a well-established model of genetic hypertension. The goal of this study was to employ high-resolution DT-MRI and the SHR animal model to assess the transmural layer-specific remodeling of myocardial microstructure associated with hypertension. Ex vivo experiments were performed on excised formalin-fixed hearts of aged SHRs (n = 4) and age-matched controls (n = 4). The DT-MRI-derived fractional anisotropy (FA), longitudinal diffusivity (λ L ), transversal diffusivity (λ T ), and mean diffusivity (MD) served as the readout parameters investigated at three transmural zones (i.e., endocardium, mesocardium, and epicardium). The helix angles (HAs) of the aggregated cardiomyocytes and the orientation of laminar sheetlets were also studied. Compared with controls, the SHRs exhibited decreased epicardial FA, while FA changes in the other two transmural regions were insignificant. No substantial differences were observed in the diffusivity parameters and the transmural course of HAs between the two groups. A consistent distribution pattern of laminar sheetlet orientation was not identified for either group. Our findings are in line with the known cellular microstructure from early painstaking histological studies. Biophysical explanations of the study outcomes are provided. In conclusion, our experimental findings indicate that the epicardial microstructure is more vulnerable to high blood pressure leading to more pronounced changes in this region during remodeling. DT-MRI is well-suited for elucidating these alterations. The revealed transmural nonuniformity of myocardial reorganization may shed light on the mechanisms of the microstructure-function relationship in hypertension progression. Our results provide insights into the management of patients with systemic arterial hypertension, thus prevent the progression toward heart failure. The findings of this study should be acknowledged by electromechanical models of the heart that simulate the specific cardiac pathology.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

DIFFUSE AURORA ON GANYMEDE DRIVEN BY ELECTROSTATIC WAVES

The role of electrostatic electron cyclotron harmonic (ECH) waves in producing diffuse auroral emission O i 1356 Å on Ganymede is investigated. Electron precipitation flux entering the atmosphere of Ganymede due to pitch-angle diffusion by ECH waves into the atmospheric loss-cone is calculated. The analytical yield spectrum approach for electron energy degradation in gases is used for calculating diffuse auroral intensities. It is found that calculated O i 1356 Å intensity resulting from the precipitation of magnetospheric electrons observed near Ganymede is insufficient to account for the observed diffuse auroral intensity. This is in agreement with estimates made in earlier works. Heating and acceleration of ambient electrons by ECH wave turbulence near the magnetic equator on the field line connecting Ganymede and Jupiter are considered. Two electron distribution functions are used to simulate the heating effect by ECH waves. Use of a Maxwellian distribution with temperature 100 eV can produce about 50–70 Rayleigh O i 1356 Å intensities, and the kappa distribution with characteristic energy 50 eV also gives rise to intensities with similar magnitude. Numerical experiments are performed to study the effect of ECH wave spectral intensity profile, ECH wave amplitude, and temperature/characteristic energy of electron distribution functions on the calculated diffuse auroral intensities. The proposed missions, joint NASA/ESA Jupiter Icy Moon Explorer and the present JUNO mission to Jupiter, would provide new data to constrain the ECH wave and other physical parameters near Ganymede. These should help confirm the findings of the present study.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Diffusion and Clustering of Carbon Dioxide on Non-porous Amorphous Solid Water

Observations by ISO and Spitzer toward young stellar objects showed that CO{sub 2} segregates in the icy mantles covering dust grains. Thermal processing of the ice mixture was proposed as being responsible for the segregation. Although several laboratories studied thermally induced segregation, a satisfying quantification is still missing. We propose that the diffusion of CO{sub 2} along pores inside water ice is the key to quantify segregation. We combined Temperature Programmed Desorption and Reflection Absorption InfraRed Spectroscopy to study how CO{sub 2} molecules interact on a non-porous amorphous solid water (np-ASW) surface. We found that CO{sub 2} diffuses significantly on an np-ASW surface above 65 K and clusters are formed at well below one monolayer. A simple rate equation simulation finds that the diffusion energy barrier of CO{sub 2} on np-ASW is 2150 ± 50 K, assuming a diffusion pre-exponential factor of 10{sup 12} s{sup −1}. This energy should also apply to the diffusion of CO{sub 2} on the wall of pores. The binding energy of CO{sub 2} from CO{sub 2} clusters and CO{sub 2} from H{sub 2}O ice has been found to be 2415 ± 20 K and 2250 ± 20 K, respectively, assuming the same prefactor for desorption. CO{sub 2}–CO{sub 2} interaction is stronger than CO{sub 2}–H{sub 2}O interaction, in agreement with the experimental finding that CO{sub 2} does not wet the np-ASW surface. For comparison, we carried out similar experiments with CO on np-ASW, and found that the CO–CO interaction is always weaker than CO–H{sub 2}O. As a result, CO wets the np-ASW surface. This study should be of help to uncover the thermal history of CO{sub 2} on the icy mantles of dust grains.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Toward Space-like Photometric Precision from the Ground with Beam-shaping Diffusers

We demonstrate a path to hitherto unachievable differential photometric precisions from the ground, both in the optical and near-infrared (NIR), using custom-fabricated beam-shaping diffusers produced using specialized nanofabrication techniques. Such diffusers mold the focal plane image of a star into a broad and stable top-hat shape, minimizing photometric errors due to non-uniform pixel response, atmospheric seeing effects, imperfect guiding, and telescope-induced variable aberrations seen in defocusing. This PSF reshaping significantly increases the achievable dynamic range of our observations, increasing our observing efficiency and thus better averages over scintillation. Diffusers work in both collimated and converging beams. We present diffuser-assisted optical observations demonstrating 62{sub −16}{sup +26} ppm precision in 30 minute bins on a nearby bright star 16 Cygni A (V = 5.95) using the ARC 3.5 m telescope—within a factor of ∼2 of Kepler's photometric precision on the same star. We also show a transit of WASP-85-Ab (V = 11.2) and TRES-3b (V = 12.4), where the residuals bin down to 180{sub −41}{sup +66} ppm in 30 minute bins for WASP-85-Ab—a factor of ∼4 of the precision achieved by the K2 mission on this target—and to 101 ppm for TRES-3b. In the NIR, where diffusers may provide even more significant improvements over the current state of the art, our preliminary tests demonstrated 137{sub −36}{sup +64} ppm precision for a K {sub S} = 10.8 star on the 200 inch Hale Telescope. These photometric precisions match or surpass the expected photometric precisions of TESS for the same magnitude range. This technology is inexpensive, scalable, easily adaptable, and can have an important and immediate impact on the observations of transits and secondary eclipses of exoplanets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Simple Analytical Forms of the Perpendicular Diffusion Coefficient for Two-component Turbulence. III. Damping Model of Dynamical Turbulence

In several astrophysical applications one needs analytical forms of cosmic-ray diffusion parameters. Some examples are studies of diffusive shock acceleration and solar modulation. In the current article we explore perpendicular diffusion based on the unified nonlinear transport theory. While we focused on magnetostatic turbulence in Paper I, we included the effect of dynamical turbulence in Paper II of the series. In the latter paper we assumed that the temporal correlation time does not depend on the wavenumber. More realistic models have been proposed in the past, such as the so-called damping model of dynamical turbulence. In the present paper we derive analytical forms for the perpendicular diffusion coefficient of energetic particles in two-component turbulence for this type of time-dependent turbulence. We present new formulas for the perpendicular diffusion coefficient and we derive a condition for which the magnetostatic result is recovered.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Cosmic-Ray Diffusion Coefficients throughout the Inner Heliosphere from a Global Solar Wind Simulation

We use a three-dimensional magnetohydrodynamic simulation of the solar wind to calculate cosmic-ray diffusion coefficients throughout the inner heliosphere (2 R{sub ⊙}−3 au). The simulation resolves large-scale solar wind flow, which is coupled to small-scale fluctuations through a turbulence model. Simulation results specify background solar wind fields and turbulence parameters, which are used to compute diffusion coefficients and study their behavior in the inner heliosphere. The parallel mean free path (mfp) is evaluated using quasi-linear theory, while the perpendicular mfp is determined from nonlinear guiding center theory with the random ballistic interpretation. Several runs examine varying turbulent energy and different solar source dipole tilts. We find that for most of the inner heliosphere, the radial mfp is dominated by diffusion parallel to the mean magnetic field; the parallel mfp remains at least an order of magnitude larger than the perpendicular mfp, except in the heliospheric current sheet, where the perpendicular mfp may be a few times larger than the parallel mfp. In the ecliptic region, the perpendicular mfp may influence the radial mfp at heliocentric distances larger than 1.5 au; our estimations of the parallel mfp in the ecliptic region at 1 au agree well with the Palmer “consensus” range of 0.08–0.3 au. Solar activity increases perpendicular diffusion and reduces parallel diffusion. The parallel mfp mostly varies with rigidity (P) as P{sup .33}, and the perpendicular mfp is weakly dependent on P. The mfps are weakly influenced by the choice of long-wavelength power spectra.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

On the anisotropic advection-diffusion equation with time dependent coefficients

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlation functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Diffusion, atomic transport, and ordering in Al-Zr alloys: FCC and liquid phases

Additive manufacturing of materials with controlled microstructure demands knowledge of atomic scale properties near the solid-liquid transition state. Many of these properties are not affordable by experimental techniques and computer modeling is the possible solution to the problem. In this paper, we present the results of an extended atomistic study of intrinsic atomic transport due to vacancy diffusion in FCC and L12 solid phases and diffusion in the liquid phase of Al-Zr alloys. A deceleration of the overall self-diffusion was observed when Zr was added to Al. The effect was stronger in the solid and weaker in the liquid. Additionally, the effect was strongly temperature dependent in the solid phases, but not in the liquid. Atomic transport was chemically biased: transport of Zr atoms was significantly slower than that of Al atoms, and this bias effect was stronger in the solid phases. The overall diffusion and chemical ordering processes in the liquid state were five to six orders in magnitude faster than in the solid. Chemical short-range order parameters in the liquid saturated at values close to those in the ordered L12 structure of Al3Zr. Chemical and structural ordering in the solid phases was negligible over the modeled microsecond time scale. Here, the results are discussed in view of optimizing additive manufacturing parameters for the controlled formation of metastable L1 2 precipitates.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Enhanced Diffusive Transport in Fluctuating Porous Media

Mass transport within porous structures is a ubiquitous process in biological, geological, and technological systems. Despite the importance of these phenomena, there is no comprehensive theory that describes the complex and diverse transport behavior within porous environments. While the porous matrix itself is generally considered a static and passive participant, many porous environments are in fact dynamic, with fluctuating walls, pores that open and close, and dynamically changing cross-links. While diffusion has been measured in fluctuating structures, notably in model biological systems, it is rarely possible to isolate the effect of fluctuations because of the absence of control experiments involving an identical static counterpart, and it is generally impossible to observe the dynamics of the structure. In this paper, we present a direct comparison of the diffusion of nanoparticles of various sizes within a trackable, fluctuating porous matrix and a geometrically equivalent static matrix, in conditions spanning a range of regimes from obstructed to highly confined. The experimental system comprised a close-packed layer of colloidal spheres that were either immobilized to a planar surface or allowed to fluctuate locally, within the space defined by their nearest neighbors. Interestingly, the effective long-time diffusion coefficient was approximately 35–65% greater in the fluctuating porous matrix than in the static one (depending on the size of the nanoparticle probes), regardless of the geometric regime. This was explained by considering the enhancing effects of matrix fluctuations on the short-time diffusion coefficient and cooperative “gate-opening” motions of matrix particles and nanoparticle probes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Thin Film RuO 2 Lithiation: Fast Lithium‐Ion Diffusion along the Interface

Abstract Although lithium‐ion batteries that run on the conversion reaction have high capacity, their cyclability remains problematic due to large volume changes and material pulverization. Dimensional confinement, such as 2D thin film or nanodots in a conductive matrix, is proposed as a way of improving the cyclic stability, but the lithiation mechanism of such dimensionally controlled materials remains largely unknown. Here, by in situ transmission electron microscopy, lithiation of thin RuO 2 films with different thicknesses and directions of lithium‐ion diffusion are observed at atomic resolution to monitor the reactions. From the side‐wall diffusion in ≈4 nm RuO 2 film, the ion‐diffusion and reaction are fast, called “interface‐dominant” mode. In contrast, in ≈12 nm film, the ion diffusion–reaction only occurs at the interface where there is a high density of defects due to misfits between the film and substrate, called the “interface‐to‐film” mode. Compared to the side‐wall diffusion, the reaction along the normal direction of the thin film are found to be sluggish (“layer‐to‐layer” mode). Once lithiation speed is higher, the volume expansion is larger and the intercalation stage becomes shorter. Such observation of preferential lithiation direction in 2D‐like RuO 2 thin film provides useful insights to develop dimensionally confined electrodes for lithium‐ion batteries.

Kim, Sungkyu↗