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At least 721 records · Page 40

Consistent boundary conditions for reduced Navier-Stokes (RNS) scheme applied to three-dimensional internal viscous flows

Three-dimensional internal viscous flow problems are presently addressed by a consistent and efficient set of boundary conditions for the multisweep space-marching, pressure-elliptic Reduced Navier-Stokes scheme. Since continuity is by this means directly satisfied at all points in the flow domain, the first-order momentum equations are directly solvable for pressure without the requirement for a Poisson pressure-correction equation. Incompressible flow solutions are obtained for straight and curved ducts of square cross section, in order to validate the procedure. Usefulness is demonstrated for internal flows with strong interactions, as would be found in turbomachine geometries.

Reddy, D. R.↗

Analytical models of calcium binding in a calcium channel

The anomalous mole fraction effect of L-type calcium channels is analyzed using a Fermi like distribution with the experimental data of Almers and McCleskey [J. Physiol. 353, 585 (1984)] and the atomic resolution model of Lipkind and Fozzard [Biochemistry 40, 6786 (2001)] of the selectivity filter of the channel. Much of the analysis is algebraic, independent of differential equations. The Fermi distribution is derived from the configuration entropy of ions and water molecules with different sizes, different valences, and interstitial voids between particles. It allows us to calculate potentials and distances (between the binding ion and the oxygen ions of the glutamate side chains) directly from the experimental data using algebraic formulas. The spatial resolution of these results is comparable with those of molecular models, but of course the accuracy is no better than that implied by the experimental data. The glutamate side chains in our model are flexible enough to accommodate different types of binding ions in different bath conditions. The binding curves of Na{sup +} and Ca{sup 2+} for [CaCl{sub 2}] ranging from 10{sup −8} to 10{sup −2} M with a fixed 32 mM background [NaCl] are shown to agree with published Monte Carlo simulations. The Poisson-Fermi differential equation—that includes both steric and correlation effects—is then used to obtain the spatial profiles of energy, concentration, and dielectric coefficient from the solvent region to the filter. The energy profiles of ions are shown to depend sensitively on the steric energy that is not taken into account in the classical rate theory. We improve the rate theory by introducing a steric energy that lumps the effects of excluded volumes of all ions and water molecules and empty spaces between particles created by Lennard-Jones type and electrostatic forces. We show that the energy landscape varies significantly with bath concentrations. The energy landscape is not constant.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The shifted boundary method for embedded domain computations. Part I: Poisson and Stokes problems

We propose a new finite element method for embedded domain computations, which falls in the category of surrogate/approximate boundary algorithms. The key feature of the proposed approach is the idea of shifting the location where boundary conditions are applied from the true to the surrogate boundary, and to appropriately modify the shifted boundary conditions, enforced weakly, in order to preserve optimal convergence rates of the numerical solution. This process yields a method which, in our view, is simple, efficient, and also robust, since it is not affected by the small-cut-cell problem. Although general in nature, here we apply this new concept to the Poisson and Stokes problems. We present in particular the full analysis of stability and convergence for the case of the Poisson operator, and numerical tests for both the Poisson and Stokes equations, for geometries of progressively higher complexity.

97 MATHEMATICS AND COMPUTING↗

Ion Transport in Charged Membranes: Linking Electric-Field-Driven Mechanisms to Pore Size via Perturbation Analysis

Ion-exchange membranes are a critical component in electrochemical systems. Nevertheless, the understanding and modeling of ion transport within these porous structures have been limited by particular complexity reductions, either ignoring the dimensionality of their porous network architecture or imposing geometric assumptions (i.e., overlapping double layers). Before addressing this morphology-transport gap, a framework that relates the driving forces of transport to the geometry of a single pore is required. In this work, our modeling domain consists of a two-dimensional single pore with charged walls, connecting two identical electrolyte reservoirs. Using the Poisson-Nernst-Planck equations and regular perturbation theory, we decouple the electric fields and analyze the driving forces of ion transport, specifically electromigration and induced electroosmosis within the pore. These processes are described as analytical functions of the interaction aspect ratio, ?, defined as the ratio of the pore radius to the Debye length. Using this parameter, our study (i) describes the interplay between electromigrative and electroosmotic mechanisms that set ionic conductivity, (ii) identifies a dimensionless group of intrinsic electrolyte properties that indicates the predominant driving force, and (iii) provides a qualitative, confinement-dependent perspective on selectivity in ion-conducting membranes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling the electrical double layer at solid-state electrochemical interfaces

Models of the electrical double layer (EDL) at electrode/liquid-electrolyte interfaces no longer hold for all-solid-state electrochemistry. Here we show a more general model for the EDL at a solid-state electrochemical interface based on the Poisson–Fermi–Dirac equation. By combining this model with density functional theory predictions, the interconnected electronic and ionic degrees of freedom in all-solid-state batteries, including the electronic band bending and defect concentration variation in the space-charge layer, are captured self-consistently. Along with a general mathematical solution, the EDL structure is presented in various materials that are thermodynamically stable in contact with a lithium metal anode: the solid electrolyte Li 7 La 3 Zr 2 O 12 (LLZO) and the solid interlayer materials LiF, Li 2 O and Li 2 CO 3 . Here, the model further allows design of the optimum interlayer thicknesses to minimize the electrostatic barrier for lithium ion transport at relevant solid-state battery interfaces.

25 ENERGY STORAGE↗

Contribution of electrolyte in nanoscale electrolysis of pure and buffered water by particulate photocatalysis

Photocatalysis using semiconductor powders in suspension performs reduction and oxidation reactions at nanometer-scale distances. Such short distances between the reduction (cathode) and the oxidation (anode) sites enable photocatalytic water splitting to generate H 2 and O 2 from pure water without a supporting electrolyte, which is otherwise impossible in conventional electrode systems due to the high solution resistance. A CrO x /Pt/SrTiO 3 model photocatalyst achieves high efficiency under UV irradiation in ultra-pure water splitting at rates (>1 μmol-H 2 per cm 2 per h) corresponding to electrocatalysis on the order of mA cm -2 . The introduction of an unbuffered supporting electrolyte did not improve the photocatalytic rates, consistent with the negligible ohmic losses (<1 mV) numerically calculated using the Poisson–Nernst–Planck equations. The Nernstian potential loss resulting from pH gradients became apparent at high photocatalytic rates (>100 mV when rate >1 μmol-H 2 per cm 2 per h) even when the distance between redox sites was below 10 nm. Substantial improvements in photocatalytic rates were observed when buffer ions were introduced into near-neutral pH media by not only circumventing pH gradients but introducing kinetically facile H + reduction to H 2 instead of the kinetically sluggish direct reduction of H 2 O to H 2 . In this work, the quantitative descriptions of the electric potential, concentration gradients, and catalytic performance in nanoscale water electrolysis are presented with emphasis on (1) the advantages of performing redox reactions at the nanoscale, (2) the use of electrolyte engineering at near-neutral pH as a universal and effective strategy, and (3) the effectiveness of transferring knowledge from electrocatalysis to photocatalysis, where the potential is quantitatively defined regarding the former and poorly quantified regarding the latter.

36 MATERIALS SCIENCE↗

Depletion of parallel conducting layers in high mobility In{sub 0.53}Ga{sub 0.47}As/In{sub 0.52}Al{sub 0.48}As modulation doped field effect transistors

Self-consistent calculations for solving the Poisson and Schrödinger equations were performed in order to study parallel conduction in the In{sub 0.52}Al{sub 0.48}As barrier layer in In{sub 0.53}Ga{sub 0.47}As/In{sub 0.52}Al{sub 0.48}As Modulation Doped Field Effect Transistors. It is shown that the parallel conducting layer occupied sub-bands can be entirely depleted by wet chemical etching of the upper part of the un-doped In{sub 0.52}Al{sub 0.48}As Schottky layer without affecting the total carrier concentration at the In{sub 0.53}Ga{sub 0.47}As quantum well.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Large deviations of ionic currents in dilute electrolytes

Here, we evaluate the exponentially rare fluctuations of the ionic current for a dilute electrolyte by means of macroscopic fluctuation theory. We consider the fluctuating hydrodynamics of a fluid electrolyte described by a stochastic Poisson–Nernst–Planck equation. We derive the Euler–Lagrange equations that dictate the optimal concentration profiles of ions conditioned on exhibiting a given current, whose form determines the likelihood of that current in the long-time limit. For a symmetric electrolyte under small applied voltages, number density fluctuations are small, and ionic current fluctuations are Gaussian with a variance determined by the Nernst–Einstein conductivity. Under large applied potentials, the ionic current distribution is generically non-Gaussian. Its structure is constrained thermodynamically by Gallavotti–Cohen symmetry and the thermodynamic uncertainty principle.

Farhadi, Jafar [University of California, Berkeley↗

Fluctuation-enhanced electric conductivity in electrolyte solutions

Significance Using fluctuating hydrodynamics, we demonstrate that thermal fluctuations contribute to charge transport in binary electrolyte solutions. We show the existence of an enhancement, or renormalization, of the electric conductivity due to the coupling between fluctuations of charge and fluid velocity. This coupling results in nontrivial corrections to the classical Poisson–Nernst–Planck equations, which are of the order of the square root of the salt concentration and therefore significant even for dilute solutions. Our calculations predict a cation–anion cross-diffusion coefficient that is in quantitative agreement with experimental measurements. Our findings have important implications for the fields of both mesoscale hydrodynamics and electrolyte transport.

97 MATHEMATICS AND COMPUTING↗

Principal component analysis of modified gravity using weak lensing and peculiar velocity measurements

We perform a principal component analysis to assess ability of future observations to measure departures from General Relativity in predictions of the Poisson and anisotropy equations on linear scales. In particular, we focus on how the measurements of redshift-space distortions (RSD) observed from spectroscopic galaxy redshift surveys will improve the constraints when combined with lensing tomographic surveys. Assuming a Euclid-like galaxy imaging and redshift survey, we find that adding the 3D information decreases the statistical uncertainty by a factor between 3 and 7 compared to the case when only observables from lensing tomographic surveys are used. We also find that the number of well-constrained modes increases by a factor between 3 and 6. Our study indicates the importance of joint galaxy imaging and redshift surveys such as SuMIRe and Euclid to give more stringent tests of the ΛCDM model and to distinguish between various modified gravity and dark energy models.

79 ASTRONOMY AND ASTROPHYSICS↗

Stability of BEC galactic dark matter halos

In this paper we show that spherically symmetric BEC dark matter halos, with the sin r/r density profile, that accurately fit galactic rotation curves and represent a potential solution to the cusp-core problem are unstable. We do this by introducing back the density profiles into the fully time-dependent Gross-Pitaevskii-Poisson system of equations. Using numerical methods to track the evolution of the system, we found that these galactic halos lose mass at an approximate rate of half of its mass in a time scale of dozens of Myr. We consider this time scale is enough as to consider these halos are unstable and unlikely to be formed. We provide some arguments to show that this behavior is general and discuss some other drawbacks of the model that restrict its viability.

79 ASTRONOMY AND ASTROPHYSICS↗

Cosmological perturbation theory for large scale structure in phase space

We develop a framework for Large Scale Structure (LSS) perturbation theory, that solves the Vlasov-Poisson system of equations for the distribution function in full phase space. This approach relaxes the usual apriori assumption of negligible velocity dispersion underlying the Standard Perturbation Theory (SPT). We apply the new method to rederive the usual SPT kernels up to third order in the perturbative expansion. We also show that a counterterm, identical to the one introduced by standard Effective Field Theory (EFT) methods, naturally arises within our framework. We finish by making a precise connection to EFT techniques, which reveals the necessity of the EFTofLSS to self-consistently model the long-wavelength fluid, and illustrates the importance of having theoretical control over short distance fluctuations.

Cosmological perturbation theory in GR and beyond↗

Coupled Charge and Radiation Transport Processes in Thermophotovoltaic and Thermoradiative Cells

Accurate modeling of charge transport and both thermal and luminescent radiation is crucial to the understanding and design of radiative thermal energy converters. Charge-carrier dynamics in semiconductors are well-described by the Poisson-drift-diffusion equations, and thermal radiation in emitter-absorber structures can be computed using multilayer fluctuational electrodynamics. These two types of energy flows interact through radiation absorption or luminescence and charge-carrier generation or recombination. However, past research has typically only assumed limited interaction, with thermal radiation absorption as an input for charge-carrier models to predict device performance. To examine this assumption, we develop a fully coupled iterative model of charge and radiation transport in semiconductor devices, and we use our model to analyze near-field and far-field GaSb thermophotovoltaic and thermoradiative systems. By comparing our results with past methods that do not consider cross-influences between charge and radiation transport, we find that a fully coupled approach is necessary to accurately model photon recycling and near-field enhancement of external luminescence. As these effects can substantially alter device performance, our modeling approach can aid in the design of efficient thermophotovoltaic and thermoradiative systems.

30 DIRECT ENERGY CONVERSION↗

Development of a Physical-Topological Model for the Response of a High-Power Vertical DMOS Transistor to the Effect of Pulsed Gamma-Radiation

A method for developing models of semiconductor devices with two-dimensional nonuniform concentration profiles of donors and acceptors in working regions of a semiconductor device structure is for the first time proposed based on a complex of physical-topological modeling of charge carrier transport and process simulation of the forming processes of the device structure. The application of process simulation is due to the need to correctly define the parameters of the semiconductor device structure, which are used as initial data to calculate the electron transport according to the physical-topological model. The parameters of production processes of ion implantation, diffusion, and lithography, which were refined during process simulation, are determined for a high-power metal—oxide—semiconductor (MOS) transistor forming by the double diffusion method in accordance with known electrical characteristics and measured geometrical sizes of the structure. This results in two-dimensional distribution profiles of donors and acceptors in p–n junctions necessary to calculate the transistor breakdown under the effect of pulsed γ radiation. Breakdown processes are modeled with the help of the physical-topological model based on the Poisson and continuity equations as well as expressions for the diffusion and drift current densities in the transistor. Accounting for carriers formed at the instant of γ irradiation is implemented by the introduction of the dependence of the generation coefficient of electron–hole pairs on the radiation-dose power. The results of calculations correlate well with the experimental data, which makes it possible to give a conclusion regarding the adequacy of the proposed complex model.

36 MATERIALS SCIENCE↗

MOSCATO Development and Integration in Fiscal Year 2022

During FY21, we conducted ongoing development work for the MOSCATO (Molten Salt Chemistry and Transport) solver. The code development work primarily consisted of transitioning capabilities from the original version of the solver, which was written in OpenFOAM, into Nek5000. In doing so, a fast, highly parallelizable solver was created that is capable of complex chemistry and corrosion simulations for engineering-scale molten salt systems. The Nek5000 version of MOSCATO is now fully featured and capable of higher-fidelity simulations than were previously possible. Demonstration cases including a thermal convection loop have been simulated to test these new capabilities. We built upon the work for FY22 and improved the code from several different perspectives. First, we improved the user interface by adding a new component to the official Nek5000 input file (.par). This new part contains documents parameters like, salt properties (density, viscosity, Cp, thermal conductivity), diffusion coefficients, standard potential, etc. Second, we built a conversion script to extract salt properties from the MSTDB-TP salt database and write to MOSCATO input file. Third, we migrated the code to NekRS, which is the GPU branch of Nek5000 and suitable for next generation supercomputers. Verification and Validation (V&V) work was also continued in FY22. Two tasks were performed. The first V&V task involved the validation of the Poisson-Nernst-Planck equation solver and Butler-Volmer electrode kinetics, by comparing with numerical and experimental data about thermoelectric cells. The second task involved the comparisons to corrosion results from a thermal convection loop run during the MSRE era. Satisfactory agreement was obtained from both tasks.

Yuan, Haomin↗

Flow study in the cross sectional planes of a turbine scroll

A numerical study of the nonviscous flow characteristics in the cross-sectional planes of a radial inflow turbine scroll is presented. The velocity potential is used in the formulation to determine the flow velocity in these planes resulting from the continuous mass discharge. The effect of the through flow velocity is simulated by a continuous distribution of source/sink in the cross-section. A special iterative procedure is devised to handle the solution of the resulting Poisson's differential equation with Neumann boundary conditions in a domain with generally curved boundaries. The analysis is used to determine the effects of the radius of curvature, the location of the scroll section and its geometry on the flow characteristics in the turbine scroll.

Hamed, A.↗

A numerical method based on the Fourier-Fourier transform approach for modeling 1-D electron plasma evolution

A numerical method is presented for studying one-dimensional electron plasma evolution under typical interplanetary conditions. The method applies the Fourier-Fourier transform approach to a plasma model that is a generalization of the electrostatic Vlasov-Poisson system of equations. Conservation laws that are modified to include the plasma model generalization and also the boundary effects of nonperiodic solutions are given. A new conservation law for entropy in the transformed space is then introduced. These conservation laws are used to verify the numerical solutions. A discretization error analysis is presented. Two numerical instabilities and the methods used for their suppression are treated. It is shown that in interplanetary plasma conditions, the bump-on-tail instability produces significant excitation of plasma oscillations at the Bohm-Gross frequency and its second harmonic. An explanation of the second harmonic excitation is given in terms of wave-wave coupling during the growth phase of the instability.

Klimas, A. J.↗

Elliptic generation of composite three-dimensional grids about realistic aircraft

An elliptic method for generating composite grids about realistic aircraft is presented. A body-conforming grid is first generated about the entire aircraft by the solution of Poisson's differential equation. This grid has relatively coarse spacing, and it covers the entire physical domain. At boundary surfaces, cell size is controlled and cell skewness is nearly eliminated by inhomogeneous terms, which are found automatically by the program. Certain regions of the grid in which high gradients are expected, and which map into rectangular solids in the computational domain, are then designated for zonal refinement. Spacing in the zonal grids is reduced by adding points with a simple, algebraic scheme. Details of the grid generation method are presented along with results of the present application, a wing-body configuration based on the F-16 fighter aircraft.

Sorenson, R. L.↗