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At least 181 records · Page 10

Polysulfide entrapment and retardation in gel electrolyte Li–S batteries: experiments and modeling

Gelling the electrolyte in lithium–sulfur (Li–S) batteries provides advantages in terms of safety and mitigating polysulfide shuttling leading to reduced side reactions and dendrite growth on the anode side. In the current study, organic and ceramic crosslinkers have been used to improve the entrapment of polysulfides and prevent them from shuttling to the anode side. However, the performance of gel electrolytes is still far from being on par with liquid electrolytes in terms of raw capacity. The discharge curves exhibit an extended first plateau for gel electrolyte batteries compared to liquid electrolytes, showing that polysulfides are better trapped in the gel system. Yet, in the conversion of soluble polysulfides into insoluble polysulfides, the second plateau was delayed. Qualitative and quantitative analysis of the polysulfide diffusion in the liquid electrolyte and gel electrolyte systems were also conducted to predict the relative diffusivity ratio between the liquid electrolyte and gel electrolyte for simulation. To probe what happens at the end of the discharge, where the mass transport in the gel electrolyte appears to be slow, a modified discharge procedure was used where the cell is first paused after discharge and then discharged a second time before recharging normally. Coin cell tests for two gel electrolytes in addition to liquid electrolyte show up to 7% capacity recovery after the pause, which indicates that the diffusion of species during the pause is responsible for the failure recovery. Additionally, the recovery is higher for gel electrolytes compared to liquid, for higher C-rates, and for longer pause times. To better understand this behavior, a Li–S numerical model with mass transport limited reactions was used to examine the polysulfide diffusion coefficients expected in different electrolyte systems. The model is able to reproduce the trends seen in experiments and yields a higher recovery for smaller Li 2 S 4 diffusion coefficients, suggesting that insufficient Li 2 S 4 mass transport is responsible for failure at the end of discharge. By identifying the effect that gel electrolytes have on the state of the battery during discharge using both experimental and simulation methods, this work is a step towards leveraging the advantages of gel electrolytes and mitigating their weaknesses.

25 ENERGY STORAGE↗

Mixing by internal gravity waves in stars: assessing numerical simulations against theory

ABSTRACT Here we present a study of radial chemical mixing in non-rotating massive main-sequence stars driven by internal gravity waves (IGWs), based on multidimensional hydrodynamical simulations with the fully compressible code MUSIC. We examine two proposed mechanisms of material mixing in stars by IGWs that are commonly quoted, relating to thermal diffusion and sub-wavelength shearing. Thermal diffusion provides a non-restorative effect to the waves, leaving material displaced from its previous equilibrium, while shearing arising within the waves drives weak localized flows, mixing the fluid there. Using IGW spectra from the simulations, we evaluate theoretical predictions of mixing rates due to these mechanisms. We show, for $20\, \mathrm{M}_\odot$ main-sequence stars, that neither of these mechanisms are likely to create mixing sufficient to correct inaccuracies in current stellar evolution models. Furthermore, we compare these predictions to results obtained from Lagrangian tracer particles, following a method recently used for global simulations of stellar interiors to measure mixing by IGWs in their radiative zones. We demonstrate that tracer particle methods face significant numerical challenges in measuring the small diffusion coefficients predicted by the aforementioned theories, for which they are prone to yielding artificially enhanced coefficients. Diffusion coefficients based on such methods are currently used with stellar evolution codes for asteroseismic studies, but should be viewed with caution. Finally, in a case where tracer particles do not suffer from numerical artefacts, we suggest that a diffusion model is not suitable for time-scales typically considered by 2D numerical simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

The Numerical Computation of Clear-Sky Transmittance and Reflectance of Solar Radiation for the Modeling of PV System Performance

Modeling of photovoltaics (PV) system performance requires numerical computation of plane-of-array (POA) irradiances that are influenced by atmospheric absorption and scattering. Clear-sky transmittance and reflectance of diffuse irradiance are essential for the understanding of solar radiation related to multiple reflection between land surface and clouds. This study analytically solves the radiative transfer equation for clear-sky conditions and numerically computes the transmittance and reflectance of diffuse irradiance as functions of the optical thickness of the atmosphere. The computation will be implemented in all-sky radiative transfer models to improve their computational efficiency.

14 SOLAR ENERGY↗

Improving Solution Accuracy and Convergence for Stochastic Physics Parameterizations with Colored Noise

Stochastic parameterizations are used in numerical weather prediction and climate modeling to help capture the uncertainty in the simulations and improve their statistical properties. Convergence issues can arise when time integration methods originally developed for deterministic differential equations are applied naively to stochastic problems. In previous studies, it has been demonstrated that a correction term, known in stochastic analysis as the Itô correction, can help improve solution accuracy for various deterministic numerical schemes and ensure convergence to the physically relevant solution without substantial computational overhead. The usual formulation of the Itô correction is valid only when the stochasticity is represented by white noise. In this study, a generalized formulation of the Itô correction is derived for noises of any color. The formulation is applied to a test problem described by an advection–diffusion equation forced with a spectrum of fast processes. We present numerical results for cases with both constant and spatially varying advection velocities to show that, for the same time step sizes, the introduction of the generalized Itô correction helps to substantially reduce time integration error and significantly improve the convergence rate of the numerical solutions when the forcing term in the governing equation is rough (fast varying); alternatively, for the same target accuracy, the generalized Itô correction allows for the use of significantly longer time steps and, hence, helps to reduce the computational cost of the numerical simulation.

54 ENVIRONMENTAL SCIENCES↗

Numerical Simulations of Orographic Convection across Multiple Gray Zones

Idealized simulations are used to determine the sensitivity of moist orographic convection to horizontal grid spacing Δ h . In simulated mechanically (MECH) and thermally (THERM) forced convection over an isolated ridge, Δ h is varied systematically over both the deep-convection (Δ h ~ 10 –1 km) and turbulence (Δ h ~ 1 km–100 m) gray zones. To aid physical interpretation, a new parcel-based bulk entrainment/detrainment diagnosis for horizontally heterogeneous flows is developed. Within the deep-convection gray zone, the Δ h sensitivity is dominated by differences in parameterized versus explicit convection; the former initiates convection too far upstream of the ridge (MECH) and too early in the diurnal heating cycle (THERM). These errors stem in part from a large underprediction of parameterized entrainment and detrainment. Within the turbulence gray zone, sensitivities to Δh arise from the representation of both subcloud- and cloud-layer turbulence. As Δ h is decreased, MECH exhibits stronger cloud-layer entrainment to enhance the convective mass flux M co , while THERM exhibits stronger detrainment to suppress Mco and delay convection initiation. The latter is reinforced by increased subcloud turbulence at smaller Δ h , which leads to drying and diffusion of the central updraft responsible for initiating moist convection. Numerical convergence to a robust solution occurs only in THERM, which develops a fully turbulent flow with a resolved inertial subrange (for Δ h ≤ 250 m). In MECH, by contrast, turbulent transition occurs within the orographic cloud, the details of which depend on both physical location and Δ h .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An efficient reconstruction algorithm for diffusion on triangular grids using the nodal discontinuous Galerkin method

High-energy-density (HED) hydrodynamics studies such as those relevant to inertial confinement fusion and astrophysics require highly disparate densities, temperatures, viscosities, and other diffusion parameters over relatively short spatial scales. This presents a challenge for high-order accurate methods to effectively resolve the hydrodynamics at these scales, particularly in the presence of highly disparate diffusion. A significant volume of engineering and physics applications use an unstructured discontinuous Galerkin (DG) method developed based on the finite element mesh generation and algorithmic framework. This work discusses the application of an affine reconstructed nodal DG method for unstructured grids of triangles. Solving the diffusion terms in the DG method is non-trivial due to the solution representations being piecewise continuous. Hence, the diffusive flux is not defined on the interface of elements. The proposed numerical approach reconstructs a smooth solution in a parallelogram that is enclosed by the quadrilateral formed by two adjacent triangle elements. The interface between these two triangles is the diagonal of the enclosed parallelogram. Similar to triangles, the mapping of parallelograms from a physical domain to a reference domain is an affine mapping, which is necessary for an accurate and efficient implementation of the numerical algorithm. Thus, all computations can still be performed on the reference domain, which promotes efficiency in computation and storage. This reconstruction does not make assumptions on choice of polynomial basis. Reconstructed DG algorithms have previously been developed for modal implementations of the convection–diffusion equations. However, to the best of the authors’ knowledge, this is the first practical guideline that has been proposed for applying the reconstructed algorithm on a nodal discontinuous Galerkin method with a focus on accuracy and efficiency. As a result, the algorithm is demonstrated on a number of benchmark cases as well as a challenging substantive problem in HED hydrodynamics with highly disparate diffusion parameters.

Computational efficiency↗

Physics-Informed Neural Network Method for Forward and Backward Advection-Dispersion Equations

Advection-dispersion equations (ADEs) are commonly used to describe transport phenomena in porous media. Even though mature discretization-based numerical methods for ADEs exist, some challenges still remain, especially when it comes to solving advection-dominated forward ADEs and diffusion-dominated backward ADEs. The latter problem usually arises in the source identification context and leads to numerically unstable grid-based solutions that require a form of regularization or should be treated as an inverse problem that is computationally more expensive because it requires solving the forward problem multiple times. In this study, we propose a discretization-free approach based on the physics-informed neural network (PINN) method for solving coupled ADE and Darcy flow equations with space-dependent hydraulic conductivity. In this approach, the hydraulic conductivity, hydraulic head, and concentration fields are approximated with deep neural networks (DNNs). We assume that the conductivity field is given by its values on a grid, and we use these values to train the conductivity DNN. The head and concentration DNNs are trained by minimizing the residuals of the flow equation and ADE and using the initial and boundary conditions as additional constraints. The PINN method is applied to one- and two-dimensional forward ADE problems, where its performance for various P\'{e}clet numbers ($Pe$) is compared with the analytical and numerical solutions. We find that the PINN method is accurate with errors of less than 1\% and outperforms some conventional discretization-based methods for $Pe$ larger that 100. Next, we demonstrate that the PINN method remains accurate for the backward ADEs, with the relative errors in most cases staying under 5\% compared to the reference concentration field. Finally, we show that when available, the concentration measurements can be easily incorporated in the PINN method and significantly improve (by more than 50\% in the considered cases) the accuracy of the PINN solution of the backward ADE.

He, Qizhi↗

Comparing the MELCOR Aerosol Deposition Model with Exact Analytical Solutions

Exact analytical solutions are presented for the evolution of the aerosol particle mass density function in a control volume for particle deposition due to gravitational settling, thermophoresis, and diffusion. The solutions are for arbitrary initial mass density functions and are applied for an initial lognormal density function. Integration of these solutions provides the suspended mass in the control volume as a function of time. These solutions serve as an exact benchmark to assess the accuracy of numerical methods. For the numerical algorithm used in MELCOR, excellent agreement is obtained for gravitational settling, diffusive deposition, and thermophoretic deposition for the suspended aerosol mass. In all cases, the default number of discrete particle size bins of 10 is shown to converge, with hardly any advantage to using 20 size bins.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Capturing the fractocohesive length scale in elastomers through a statistical mechanics-based gradient enhanced damage model

Here, this study aims to examine modeling flaw sensitivity in elastomers. The direct incorporation of polymer chain statistical mechanics considerations into a continuum stretch-based gradient-enhanced damage formulation, in turn, allows a representation of diffuse chain damage and fracture events that align with known micromechanical mechanisms. Through a series of numerical experiments, we simulate crack propagation and extract the fracture energy as an output of the model, while keeping track of the micromechanical signatures of diffuse chain damage that accommodate fracture propagation and eventually influence flaw sensitivity. Finally, by combining the fracture toughness and the work to rupture, we identify a fractocohesive length of the material, corresponding to the full width of the damage process zone. As the damage-to-fracture cascade in the proposed GED model is influenced by the introduction of a length scale associated with network imperfection and long-range load transfer, the emerging relationship of the two length scales is discussed, providing a potential link between microscopic damage mechanisms and the observed macroscopic fracture response.

36 MATERIALS SCIENCE↗

Exploring the impact of hydro-mechanical coupling on compaction localization

In deep subsurface environments, where porous rocks are saturated with fluids, hydromechanical coupling plays a critical role in the formation and propagation of localized deformation zones, such as compaction bands. In this study, we numerically investigate the influence of fluid-rock interactions on the development of compaction localization in fluid-saturated rocks. For this purpose, it uses a numerical framework that adapts the heat equation to model the diffusion of pore pressure caused by deformation. This is achieved with specialized subroutines for material behavior and heat transfer formulated within the ABAQUS platform and by allowing changes in rock permeability during strain localization. The results highlight that hydromechanical coupling significantly alters the compaction behavior compared to dry conditions. Under high confining stress, excess pore pressure inhibits the progression of compaction fronts, while in time-dependent processes like rock creep, pore pressure transients accelerate deformation by creating feedback loops between mechanical forces and fluid flow. These findings underscore the importance of saturation in controlling the dynamics of compaction localization and provide insights into the interplay between pore pressure, deformation, and permeability. The implications of this study extend to applications in geological storage, resource extraction, and subsurface geomechanics, offering a deeper understanding of coupled hydromechanical processes in porous rocks.

58 GEOSCIENCES↗

Relativistic diffusion model for hadron production in p -Pb collisions at energies available at the CERN Large Hadron Collider

We investigate charged-hadron production in relativistic heavy-ion collisions of asymmetric systems within a nonequilibrium-statistical framework. Calculated centrality-dependent pseudorapidity distributions for p-Pb collisions at s NN = 5.02 and 8.16 TeV are compared with data from the Large Hadron Collider. Our approach combines a relativistic diffusion model with formulations based on quantum chromodynamics while utilizing numerical solutions of a Fokker-Planck equation to account for the shift and broadening of the fragmentation sources for particle-production with respect to the stopping (net-baryon) rapidity distributions. To represent the centrality dependence of charged-hadron production in asymmetric systems over a broad region of pseudorapidities, the consideration and precise modeling of the fragmentation sources, along with the central gluon-gluon source, is found to be essential. Specifically, this results in an inversion of the particle-production amplitude from backward to forward dominance when transitioning from central to peripheral collisions, in agreement with recent ATLAS and ALICE p-Pb data at s NN = 5.02 T e V . Published by the American Physical Society 2024

Schulz, Philipp (ORCID:0009000266642148)↗

Learning Optimal Multigrid Smoothers via Neural Networks

Multigrid methods are one of the most efficient techniques for solving large sparse linear systems arising from partial differential equations (PDEs) and graph Laplacians from machine learning applications. One of the key components of multigrid is smoothing, which aims at reducing high-frequency errors on each grid level. However, finding optimal smoothing algorithms is problem-dependent and can impose challenges for many problems. In this paper, we propose an efficient adaptive framework for learning optimized smoothers from operator stencils in the form of convolutional neural networks (CNNs). Here, the CNNs are trained on small-scale problems from a given type of PDEs based on a supervised loss function derived from multigrid convergence theories and can be applied to large-scale problems of the same class of PDEs. Numerical results on anisotropic rotated Laplacian problems and variable coefficient diffusion problems demonstrate improved convergence rates and solution time compared with classical hand-crafted relaxation methods.

97 MATHEMATICS AND COMPUTING↗

Systematic correction of the density functional theory spectra via a quantum Monte Carlo approach

Numerical outputs and driver scripts supporting auxiliary-boson corrected diffusion Monte Carlo (ABCDMC) benchmarks on second-row neutral atoms, cations, and dications, plus a C2 molecule active-space study. Includes NIST reference energies, ABCDMC timestep extrapolation summaries, orbital generation inputs, singles-only CASCI driver scripts, an O-atom basis-set convergence study, and the PyQMC boson code snapshot used for the calculations.

36 MATERIALS SCIENCE↗

On the Spectral Evolution of Hot White Dwarf Stars. II. Time-dependent Simulations of Element Transport in Evolving White Dwarfs with STELUM

White dwarf stars are subject to various element transport mechanisms that can cause their surface composition to change radically as they cool, a phenomenon known as spectral evolution. In this paper, we undertake a comprehensive theoretical investigation of the spectral evolution of white dwarfs. First, we introduce STELUM, a new implementation of the stellar evolutionary code developed at the Université de Montréal. We provide a thorough description of the physical content and numerical techniques of the code, covering the treatment of both stellar evolution and chemical transport. Then, we present two state-of-the-art numerical simulations of element transport in evolving white dwarfs. Atomic diffusion, convective mixing, and mass loss are considered simultaneously as time-dependent diffusive processes and are fully coupled to the cooling. We first model the PG 1159-DO-DB-DQ evolutionary channel: a helium-, carbon-, and oxygen-rich PG 1159 star transforms into a pure-helium DB white dwarf due to gravitational settling and then into a helium-dominated, carbon-polluted DQ white dwarf through convective dredge-up. We also compute for the first time the full DO-DA-DC evolutionary channel: a helium-rich DO white dwarf harboring residual hydrogen becomes a pure-hydrogen DA star through the float-up process and then a helium-dominated, hydrogen-bearing DC star due to convective mixing. We demonstrate that our results are in excellent agreement with available empirical constraints. In particular, our DO-DA-DC simulation perfectly reproduces the lower branch of the bifurcation observed in the Gaia color–magnitude diagram, which can therefore be interpreted as a signature of spectral evolution.

79 ASTRONOMY AND ASTROPHYSICS↗

Correlation Function Approach for Diffusion in Confined Geometries

This paper describes a formalism for extracting spatially varying transport coefficients from simulations of a molecular fluid in a nano channel. This approach is applied to self-diffusion of a Lennard-Jones fluid confined between two parallel surfaces. A numerical grid is laid over the domain confining the fluid, and fluid properties are projected onto the grid cells. The time correlation functions between properties in different grid cells are calculated and can be used as the basis for a fitting procedure for extracting spatially varying diffusion coefficients from the simulation. Results for the Lennard-Jones system show that transport behavior varies sharply near the liquid-solid boundary and that the changes depend on the details of the liquid-solid interaction. A quantitative difference between the reduced and detailed models is discussed. It is found that the difference could be associated with assumptions about the form of the transport equations at molecular scales in lieu of problems with the method itself. The study suggests that this approach to fitting molecular simulations to continuum equations may guide the development of appropriate coarse-grained equations to model transport phenomena at nanometer scales.

Nanoscale flow, Transport, molecular simulation↗

A new approach for simulating inhomogeneous chemical kinetics

Abstract In this paper, inhomogeneous chemical kinetics are simulated by describing the concentrations of interacting chemical species by a linear expansion of basis functions in such a manner that the coupled reaction and diffusion processes are propagated through time efficiently by tailor-made numerical methods. The approach is illustrated through modelling $$\alpha$$ α - and $$\gamma$$ γ -radiolysis in thin layers of water and at their solid interfaces from the start of the chemical phase until equilibrium was established. The method’s efficiency is such that hundreds of such systems can be modelled in a few hours using a single core of a typical laptop, allowing the investigation of the effects of the underlying parameter space. Illustrative calculations showing the effects of changing dose-rate and water-layer thickness are presented. Other simulations are presented which show the approach’s capability to solve problems with spherical symmetry (an approximation to an isolated radiolytic spur), where the hollowing out of an initial Gaussian distribution is observed, in line with previous calculations. These illustrative simulations show the generality and the computational efficiency of this approach to solving reaction-diffusion problems. Furthermore, these example simulations illustrate the method’s suitability for simulating solid-fluid interfaces, which have received a lot of experimental attention in contrast to the lack of computational studies.

97 MATHEMATICS AND COMPUTING↗

Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces

Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, including many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process using exact (as opposed to variational) analysis. We relate the theory to the existing continuous-state Gaussian diffusion as well as other approaches to discrete diffusion, and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce “Blackout Diffusion”, which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10, Binarized MNIST, and CelebA datasets confirm the feasibility of our approach. Generalizing from specific (Gaussian) forward processes to discrete-state processes without a variational approximation sheds light on how to interpret diffusion models, which we discuss.

Santos, Javier E.↗

Synthesis of wafer-scale SWCNT forests with remarkably invariant structural properties in a bulk-diffusion-controlled kinetic regime

Robust synthesis of vertically aligned carbon nanotubes (VACNT) at large scale is required to accelerate deployment of numerous cutting-edge devices to emerging commercial applications. To address this need, this work demonstrates that the structural characteristics of single-walled CNTs (SWCNTs) produced in a growth regime dominated by bulk diffusion of the gaseous carbon precursor are remarkably invariant over a broad range of process conditions (precursor concentration increased up to 30-fold, catalyst substrate area from 1 cm 2 to 180 cm 2 , growth pressure from 20 to 790 mbar, and gas flowrates up to 8-fold). A simple growth kinetics model is derived that accounts for both reactant bulk diffusion and competing byproduct formation in the presence of excess hydrogen, which quantitatively reproduces the experimental data in the entire isothermal parameter space. The model enables critical predictions for process scale-up optimization including a potential 6-fold increase in CNT production rate, a ~90% carbon conversion efficiency in select conditions, and elimination of reaction rate decay observed at high pressures by using a hydrogen-free growth environment. This model-guided opportunity to substantially improve synthesis throughput and efficiency, in conjunction with the remarkably invariant CNT properties, is appealing for reliable VACNT device fabrication at both small and industrial scales.

36 MATERIALS SCIENCE↗