Moiré fractional Chern insulators. I. First-principles calculations and continuum models of twisted bilayer MoTe 2
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Despite the availability of computational resources and advancements in numerical computing capabilities, the multiscale models core to understanding, predicting the behaviors of, and designing energy and environmental systems involving porous media are still 1.) developed through by-hand derivations and 2.) limited by many methodological assumptions employed during model derivation. As a result, the advancement of effective media models for engineering DOE mission-critical systems (e.g., batteries, flow batteries, electrolyzers, geothermal systems, subsurface chemical storage systems, etc.) is slow (i.e., it takes years for models to traverse from stages of “development” to “practical utilization”), hindering our ability to effectively optimize such systems and stay at the cutting-edge of the energy frontier. In this work, we aimed to address these limitations by 1.) automating and accelerating multiscale model derivation via symbolic computing and 2.) develop a novel multiscale modeling methodology for flow and transport through porous media that avoids the typical assumptions hindering previous models. As a result of our efforts, we 1.) developed a hybrid symbolic-numeric code called Fouriera for fully-automating the implementation of multiphysical and phase-field models via the Fourier spectral method for materials science research, and 2.) advanced a multiscale modeling methodology called The Method of Finite Averages that rigorously predicts the behaviors of flow and transport through heterogeneous porous media under the influence of non-local effects and strong advection. Ultimately, these deliverables provide strong foundations from which further efforts can advance multiscale modeling tools and capabilities that do not intrinsically rely on 1.) the speed and mathematical capabilities of humans, nor 2.) the methodological assumptions limiting current models.
Here we present a two-step method specifically tailored for band structure calculation of the small-angle moiré-pattern materials which contain tens of thousands of atoms in a unit cell. In the first step, the self-consistent field calculation for the ground state is performed with the O(N) Krylov subspace method implemented in openmx. Second, the crystal momentum-dependent Bloch Hamiltonian and overlap matrix are constructed from the results obtained in the first step and only a small number of eigenvalues near the Fermi energy are solved with shift-invert and Lanczos techniques. By systematically tuning two key parameters, the cutoff radius for electron hopping interaction and the dimension of the Krylov subspace, we obtained the band structures for both rigid and corrugated twisted bilayer graphene structures down to the first magic angle (θ = 1.08°) with high enough accuracy at affordable costs. The band structures are in good agreement with those from tight-binding models, continuum models, plane-wave pseudopotential based ab initio calculations, and experimental observations. This method is also shown to be efficient in twisted double-bilayer graphene and bilayer WSe 2 . We think this two-step method can play a crucial role in other twisted two-dimensional materials, especially those with much more complex band structure and where the effective model is hard to construct.
The design of efficient material-handling systems for milled lignocellulosic biomass is challenging due to their complex particle morphologies and frictional interactions. Computational modeling, including the discrete element method (DEM) and continuum-based finite-element/volume methods, may offer scientific insight and predictive capabilities for the flow of milled biomass in hoppers and feeders. Herein, this article (Part II) presents a review of current state-of-the-art continuum models for the flow of milled biomass, whereas DEM models are reviewed in a companion article (Part I). Advances of numerical methods to solve the global governing equations are discussed first, followed by a comprehensive review of constitutive models for granular materials, including Drucker–Prager, hypoplastic, Cambridge-type, inertial-rheology, and nonlocal granular fluidity models. Specifically, we provide in-depth discussion on the suitability of those models for milled lignocellulosic biomass materials in terms of nonlinear elasticity, dependence of flow strength on pressure, density and shear rate, and compaction (dilation) associated with hardening (softening). Furthermore, our study shows that, despite the recent advances in continuum granular flow modeling, the most suitable constitutive models still need further development to account for material parametrization, multiflow regimes, and multiscale behavior before they can be reliably used to optimize the design and operation of biomass handling systems.
Multiscale models of materials, consisting of upscaling discrete simulations to continuum models, are unique in their capability to simulate complex materials behavior. The fundamental limitation in multiscale models is the presence of uncertainty in the computational predictions delivered by them. In this work, a sequential multiscale model has been developed, incorporating discrete dislocation dynamics (DDD) simulations and a strain gradient plasticity (SGP) model to predict the size effect in plastic deformations of metallic micro-pillars. The DDD simulations include uniaxial compression of micro-pillars with different sizes and over a wide range of initial dislocation densities and spatial distributions of dislocations. An SGP model is employed at the continuum level that accounts for the size-dependency of flow stress and hardening rate. Sequences of uncertainty analyses have been performed to assess the predictive capability of the multiscale model. The variance-based global sensitivity analysis determines the effect of parameter uncertainty on the SGP model prediction. The multiscale model is then constructed by calibrating the continuum model using the data furnished by the DDD simulations. A Bayesian calibration method is implemented to quantify the uncertainty due to microstructural randomness in discrete dislocation simulations (density and spatial distribution of dislocations) on the macroscopic continuum model prediction (size effect in plastic deformation). Here, the outcomes of this study indicate that the discrete-continuum multiscale model can accurately simulate the plastic deformation of micro-pillars, despite the significant uncertainty in the DDD results. Additionally, depending on the macroscopic features represented by the DDD simulations, the SGP model can reliably predict the size effect in plasticity responses of the micropillars with below 10% of error.
The upstream of bioenergy industry has suffered from unreliable operations of granular biomass feedstocks in handling equipment. Computational modeling, including continuum-mechanics models and discrete-particle models, offers insightful understandings and predictive capabilities on the flow of milled biomass and can assist equipment design and optimization. This paper presents a benchmark study on the fidelity of the continuum and discrete modeling approaches for predicting granular biomass flow. We first introduce the constitutive law of the continuum-mechanics model and the contact law of the coarse-grained discrete-particle model, with model parameters calibrated against laboratory characterization tests of the milled loblolly pine. Three classical granular material flow systems (i.e., a lab-scale rotating drum, a pilot-scale hopper, and a full-scale inclined plane) are then simulated using the two models with the same initial and boundary conditions as the physical experiments. The close agreement of the numerical predictions with the experimental measurements on the hopper mass flow rate, the hopper critical outlet width, the material stopping thickness on the inclined plane, and the dynamic angle of repose, clearly indicates that the two methods can capture the critical flow behavior of granular biomass. The qualitative comparison shows that the continuum-mechanics model outperforms in parameterization of materials and wall friction, and large-scale systems, while the discrete-particle model is more preferred for discontinuous flow systems at smaller scales. Industry stakeholders can use these findings as guidance for choosing appropriate numerical tools to model biomass material flow in part of the optimization of material handling equipment in biorefineries.
Widespread use of hydrogen energy is contingent on the development of reliable and economical sources of hydrogen. Electrolysis from renewably-derived low-carbon electricity is a potentially viable method of hydrogen generation. Prime among the electrolysis technologies are those utilizing ion-conducting polymers (ionomers) including proton-exchange-membrane water electrolyzer (PEMWE). However, these technologies need to exhibit increased efficiency, performance, and durability to become commercially viable. Like most electrochemical devices, PEMWEs involve multiple components (e.g., catalyst, ionomer, transport layers, membrane, plates) and multiple phases, with phenomena occurring across different time and length scales. Furthermore, it is difficult to experimentally probe many of the species and phenomena during operation. Thus, mathematical modeling at the continuum level has been an invaluable aid in exploring, understanding, and optimizing PEMWE cell and components. Furthermore, this is especially true in the highly coupled and complex physics and chemistries that occur with the membrane-electrode assembly (MEA). The physics in a typical volume-averaged non-isothermal model include multiphase transport in porous media, concentrated-solution theory, Ohm's Law, and Butler-Volmer kinetics, and ion, gas, and water transport in the ionomer.
Solid–water interfaces are crucial for clean water, conventional and renewable energy, and effective nuclear waste management. However, reflecting the complexity of reactive interfaces in continuum-scale models is a challenge, leading to oversimplified representations that often fail to predict real-world behavior. This is because these models use fixed parameters derived by averaging across a wide physicochemical range observed at the molecular scale. Recent studies have revealed the stochastic nature of molecular-level surface sites that define a variety of reaction mechanisms, rates, and products even across a single surface. To bridge the molecular knowledge and predictive continuum-scale models, we propose to represent surface properties with probability distributions rather than with discrete constant values derived by averaging across a heterogeneous surface. This conceptual shift in continuum-scale modeling requires exponentially rising computational power. By incorporating our molecular-scale understanding of solid–water interfaces into continuum-scale models we can pave the way for next generation critical technologies and novel environmental solutions.
Understanding and controlling solid-electrolyte interphase (SEI) formation to stabilize cell performance is a significant challenge for next-generation Li-ion battery technologies. In recent years, computational modeling has become an essential tool in providing fundamental insights into SEI properties and dynamics. However, neither atomistic nor continuum-level approaches alone can capture the complexities of SEI chemistry across all relevant length and time scales. In this work, a continuum-level model is developed that is informed by reaction mechanisms obtained from first-principle calculations. The atomistically informed continuum-level model is used to understand electrolyte degradation, including the decomposition of ethylene carbonate (EC), ethyl methyl carbonate (EMC), and fluoroethylene carbonate (FEC). The model presented here is the most chemically complex continuum-level SEI model in the literature to date. The SEI model is calibrated against experimental irreversible leakage currents and shows qualitative agreement with expected SEI growth trends. The model framework is expected to accelerate fundamental understanding of SEI formation, facilitate mechanism development feedback, and dynamically interact with experimental insights.