Predictions Of Continuum Models Research Articles

Photogalvanic response in multi-Weyl semimetals

We investigate the dependence of the photogalvanic response of a twofold degenerate multi-Weyl semimetal on its topological charge, tilt, and chemical potential. We derive analytical expressions for the shift and injection conductivities for tilted charge-n Weyl points using a low-energy two-band effective Hamiltonian. We compute the response for more realistic tight-binding models of a double-Weyl semimetal with broken time-reversal symmetry to find significant deviations from the effective low-energy continuum model predictions. We analyze several different limits of these models, describe the nature of these deviations, and provide estimates of their dependence on the frequency and other model parameters. Our analysis provides a simple explanation for the first-principle calculation based frequency dependence of the injection current in SrSi2. We also obtain analytical results for the charge-4 Weyl semimetal using a new approach, providing all relevant information about the nature of its second-order dc response and the precise condition for observing quantized circular photogalvanic effect. This approach can easily be extended to a systematic study of second harmonic generation and first-order optical conductivity in charge-4 Weyl semimetals. Published by the American Physical Society 2024

Multiscale Modeling of Solid Electrolyte Interphase Growth in Lithium-Ion Batteries

Calendar and cycle life of lithium-ion batteries (LIBs) are predominantly dictated by the passivating nature of the solid electrolyte interphase (SEI) film growth on battery anodes. Graphitic anodes exhibit stable SEI growth which enables ubiquitous commercialization of LIBs. In contrast, silicon anodes exhibit poorly passivating SEI characteristics including rapid thickness and composition changes during cycling (“breathing”) and sensitivity to electrolyte composition and surface functionalization. In this work, we develop a chemically complex continuum-level multicomponent, multiphase coupled thermodynamics-reaction-transport SEI model to unravel the mechanisms of SEI growth in LIB anodes. Atomistic calculations in conjunction with experimental datasets are utilized to ascertain the dominant decomposition pathways towards predominant SEI components like Li2EDC, Li2O, Li2CO3, LiMC, LiF etc. and inform the continuum model predictions. Furthermore, experimental voltage-hold measurements are utilized to validate the SEI model parasitic currents/composition evolution profiles enabling prediction of voltage regimes for stable SEI growth with favorable SEI composition. The development of such chemically complex SEI models will aid predictive electrolyte screening for the growth of stable and passivating SEI layers on next generation anodes like silicon.Figure 1(a) shows a schematic of the detailed SEI model incorporating species and charge transport through the pore and solid phases of the SEI for LEDC formation. Figure (b) showcases experimental leakage currents during V-hold at 100 mV and 250 mV for Li-Si half cells and the detailed SEI model fits. Figure (c) shows the SEI composition profiles predicted by the model and the formation of inner inorganic (Li2CO3, Li2O) - outer organic (LEDC) bilayer SEI. Interestingly, inorganic LiF from FEC decomposition is predicted to form throughout the SEI. Figure 1

A continuum model and simulations for large deformation of anisotropic fiber–matrix composites for cardiac tissue engineering

Cardiac patch therapies promise to restore heart function and lower the risk of heart failure after heart attack. Fiber–matrix engineered tissue scaffolds have gained significant attention due to their tunable micro-structures, providing nonlinear mechanical properties similar to native anisotropic heart tissues. Mechanical properties of engineered scaffolds directly affect the stress fields generated inside and around the tissue scaffolds and have significant impact on the tissue functionality. Currently, biomedical cardiac patches are designed through experimentation and there exists a need for an accurate model that will allow micro-structural design optimization and analysis of effectiveness of the implanted patches. We have developed a three-dimensional large strain continuum model that can predict nonlinear, anisotropic mechanical response of engineered tissue scaffolds that have two orientation families of fibers inside a bulk hydrogel matrix. We have validated the predictive capability of our continuum model for the fiber–matrix composite using selected experiments and a suite of detailed finite element analysis that incorporated the micro-structural details of the composites. Comparing the continuum model predictions (1 element) against the representative volume micro-structural geometry finite element simulations (with greater than 4,00,000 elements), we show that the proposed model can accurately predict nonlinear mechanical behavior of highly anisotropic tissue scaffolds in both the longitudinal and transverse directions, as a function of the critical design parameters inter-fiber angle and fiber spacing. We show that the model can also capture native heart tissue’s anisotropic large strain mechanical response. We implemented our model in the finite element software Abaqus by writing a user material subroutine UANISOHYPER and demonstrated its predictive abilities by conducting a full three-dimensional analysis of engineered tissue patch application on an infarcted heart.

Twisted-shape selection of self-assembled Si nanobelts and nanowires

This letter discusses the surface-reconstruction-induced self-twisting behavior of Si〈100〉 nanobelts and nanowires (NWs) with rectangular cross section. Giving a thorough physical interpretation, we explain the reason behind this phenomenon and present a continuum-based model. It is revealed that these structures can self-assemble into both right- and left-handed helicoids depending on their crystal arrangements. More specifically, for NWs with the same number of layers in each of their cross sections directions, two distinct values of torsion angle are possible for each of right- and left-handed twisted morphologies. In conclusion, four modes of torsion can be observed in Si〈100〉 NWs. Furthermore, some atomistic simulations are conducted to substantiate analytical results by utilizing Tersoff’s potential. These results confirm the precision of the analytical discussions and are in good agreement with the continuum model predictions. Finally, the results of Tersoff’s potential are validated by a density functional based tight-binding model.

Comprehensive study of vacancy frank loop unfaulting: atomistic simulations and predictive model

In this study, vacancy Frank loop unfaulting via Shockley partial loop(s) in two model material systems (Al and Ni) has been investigated through comprehensive atomistic simulations combining continuum modeling. A general approach has been outlined and has been demonstrated to enable reliable construction of different dislocation loop configurations. The unfaulting of vacancy Frank loop is shown to occur when the enclosed Shockley loop exceeds a threshold size, independent of the Frank loop radius. A continuum model is then established to quantitatively predict the geometrical parameters of the Shockley loop and threshold condition for unfaulting. The continuum model prediction yields excellent agreement with simulation results, and has been shown to apply in various different unfaulting scenarios involving either single or multiple Shockley loops. Experimentally observed Butterfly and Mercedes hexagon morphologies have been reproduced from our simulations, with the underlying dislocation reactions fully clarified, and a mechanism of competitive growth identified as the cause for their subsequent transformation into normal prismatic dislocation loops. The present study offers generic and flexible computational tools towards understanding defect reactions and evolution mechanism of Frank loops, and more generally secondary defects in quenched and irradiated materials.

A predictive discrete-continuum multiscale model of plasticity with quantified uncertainty

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). 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.

Imaging strain-localized excitons in nanoscale bubbles of monolayer WSe2 at room temperature.

In monolayer transition-metal dichalcogenides, localized strain can be used to design nanoarrays of single photon sources. Despite strong empirical correlation, the nanoscale interplay between excitons and local crystalline structure that gives rise to these quantum emitters is poorly understood. Here, we combine room-temperature nano-optical imaging and spectroscopic analysis of excitons in nanobubbles of monolayer WSe2 with atomistic models to study how strain induces nanoscale confinement potentials and localized exciton states. The imaging of nanobubbles in monolayers with low defect concentrations reveals localized excitons on length scales of around 10 nm at multiple sites around the periphery of individual nanobubbles, in stark contrast to predictions of continuum models of strain. These results agree with theoretical confinement potentials atomistically derived from the measured topographies of nanobubbles. Our results provide experimental and theoretical insights into strain-induced exciton localization on length scales commensurate with exciton size, realizing key nanoscale structure-property information on quantum emitters in monolayer WSe2.

Atomistic simulations of precipitation hardening mechanisms in Mg-Al alloys

Precipitation hardening of Mg-Al alloys primarily comes from the interaction of basal dislocations with Mg17Al12 precipitates. Strengthening of Mg-alloys by precipitation is much less efficient than in other metallic alloys (e.g. Al) and this behaviour has been attributed to geometrical efects, as the Mg17Al12 precipitates grow as thin plates/lozenses or long rod shape parallel to the basal plane. In the present study I focus on the dislocation/precipitate interaction in the athermal limit for both edge and screw type basal dislocations, carried out using molecular statics methodology. In particular, the critical resolved shear stress (CRSS) necessary to overcome the precipitates are determined as a function of the precipitate size and compared with predictions of classical continuum models. These results provide valuable information about the precipitate hardening mechanisms and suggested new avenues to improve the mechanical properties of Mg-Al alloys.

Nanocontacts and Gaussian Filters

The inherent surface roughness at atomic scale contacts has profound effects on their local stresses, contact areas, and so on, which yield deviations from the predictions of continuum models. While these deviations can be interpreted as a breakdown of the models, attempts have been made to reconcile the two via different paths, e.g., proposing new methods for estimating the contact area, or filtering the contact stress fields. The applicability of the latter to randomly rough nanocontacts, however, has not yet been explored hitherto. Here, we show that this new method should be employed with care. Investigating two smooth and rough contacts, we find that the filtering method can make the stresses resemble each other by varying the filter’s resolution. Our results demonstrate that the filtering method improves comparisons between atomistic contacts and Hertz theory, while accounting for roughness in the rough contact results in more accurate solutions.

Reaction engineering approach for modeling single wood particle drying at elevated air temperature

In this paper, a semi-empirical drying model for convective drying of a single wood particle at elevated temperature is developed based on the reaction engineering approach (REA). The parameter of this model is determined and verified against both experimental and numerical data. The method proposed to identify the REA model parameter operates as follows: the evolution of the moisture content of a single wood particle over time is measured accurately by using a magnetic suspension balance. A continuum-scale model that takes into account major transport mechanisms relevant to wood particle drying is developed within the frame of volume averaging approach. Continuum model predictions are successfully assessed against the measurements conducted at four different inlet gas temperatures. A set of numerical simulation results obtained at 120 °C is used to deduce the REA model parameter. The fact that the REA model can fairly well reflect the experimental data at higher drying temperatures, i.e. 140 °C, 160 °C and 180 °C, is used to evaluate the accuracy of the REA model parameter. The REA model is also assessed using the continuum model simulations which are obtained for particles of different dimeters (2–20 mm) in a wide range of drying conditions (initial moisture content varies between 0.3 kg water/kg dry solid and 0.6 kg water/kg dry solid and air velocity between 0.005 m/s and 5 m/s). The results indicate that the REA model parameter is insensitive to variations of the drying conditions with an exception of inlet air velocity. The developed REA model can thus be considered as a simple predictive tool for drying of wood particles in a wide range of process conditions.

Wrinkling in engineering fabrics: a comparison between two different comprehensive modelling approaches.

We consider two ‘comprehensive’ modelling approaches for engineering fabrics. We distinguish the two approaches using the terms ‘semi-discrete’ and ‘continuum’, reflecting their natures. We demonstrate a fitting procedure, used to identify the constitutive parameters of the continuum model from predictions of the semi-discrete model, the parameters of which are in turn fitted to experimental data. We, then, check the effectiveness of the continuum model by verifying the correspondence between semi-discrete and continuum model predictions using test cases not previously used in the identification process. Predictions of both modelling approaches are compared against full-field experimental kinematic data, obtained using stereoscopic digital image correlation techniques, and also with measured force data. Being a reduced order model and being implemented in an implicit rather than an explicit finite-element code, the continuum model requires significantly less computational power than the semi-discrete model and could therefore be used to more efficiently explore the mechanical response of engineering fabrics.

Including surface ligand effects in continuum elastic models of nanocrystal vibrations

The measured low frequency vibrational energies of some quantum dots (QDs) deviate from the predictions of traditional elastic continuum models. Recent experiments have revealed that these deviations can be tuned by changing the ligands that passivate the QD surface. This observation has led to speculation that these deviations are due to a mass-loading effect of the surface ligands. In this article, we address this speculation by formulating a continuum elastic theory that includes the dynamical loading by elastic surface ligands. We demonstrate that this model is capable of accurately reproducing the l = 0 phonon energy across a variety of different QD samples, including cores with different ligand identities and epitaxially grown CdSe/CdS core/shell heterostructures. We highlight that our model performs well even in the small QD regime, where traditional elastic continuum models are especially prone to failure. Furthermore, we show that our model combined with Raman measurements can be used to infer the elastic properties of surface bound ligands, such as sound velocities and elastic moduli, that are otherwise challenging to measure.

On the homogeneous nucleation and propagation of dislocations under shock compression

The dynamic response of crystalline materials subjected to extreme shock compression is not well understood. The interaction between the propagating shock wave and the material’s defect occurs at the sub-nanosecond timescale which makes in situ experimental measurements very challenging. Therefore, computer simulation coupled with theoretical modelling and available experimental data is useful to determine the underlying physics behind shock-induced plasticity. In this work, multiscale dislocation dynamics plasticity (MDDP) calculations are carried out to simulate the mechanical response of copper reported at ultra-high strain rates shock loading. We compare the value of threshold stress for homogeneous nucleation obtained from elastodynamic solution and standard nucleation theory with MDDP predictions for copper single crystals oriented in the [0 0 1]. MDDP homogeneous nucleation simulations are then carried out to investigate several aspects of shock-induced deformation such as; stress profile characteristics, plastic relaxation, dislocation microstructure evolution and temperature rise behind the wave front. The computation results show that the stresses exhibit an elastic overshoot followed by rapid relaxation such that the 1D state of strain is transformed into a 3D state of strain due to plastic flow. We demonstrate that MDDP computations of the dislocation density, peak pressure, dynamics yielding and flow stress are in good agreement with recent experimental findings and compare well with the predictions of several dislocation-based continuum models. MDDP-based models for dislocation density evolution, saturation dislocation density, temperature rise due to plastic work and strain rate hardening are proposed. Additionally, we demonstrated using MDDP computations along with recent experimental reports the breakdown of the fourth power law of Swegle and Grady in the homogeneous nucleation regime.

DEM modelling of shear localization in a plane Couette shear test of granular materials

This paper presents a numerical study of shear localization in granular materials based on a discrete element method. The plane Couette shear test is proposed for this purpose. A numerical model is established to simulate the test. With the flexible side boundaries, it is demonstrated that the plane Couette shear state can be achieved within a granular sample of limited length, and a shear band parallel to the shear direction can be obtained. Numerical results are also presented to show the formation and the development of the shear band. A homogenization procedure is employed for presenting the variation of the field variables such as stress components, the couple stress, the void ratio and the grain rotation. The evolution and the spatial distribution of these quantities are qualitatively in accordance with the Cosserat continuum model predictions. The numerical results also indicate that the Cosserat effect plays a vital role in shear localization zone.

On the ultra-high-strain rate shock deformation in copper single crystals: multiscale dislocation dynamics simulations

Multiscale dislocation dynamics plasticity (MDDP) calculations are carried out to simulate the mechanical response of copper single crystals that have undergone shock loading at high strain rates ranging from 1 × 106 to 1 × 1010 s−1. Plasticity mechanisms associated with both the activation of pre-existing dislocation sources and homogeneous nucleation of glide loops are considered. Our results show that there is a threshold strain rate of 108 s−1 at which the deformation mechanism changes from source activation to homogeneous nucleation. It is also illustrated that the pressure dependence on strain rate follows a one-fourth power law up to 108 s−1 beyond which the relationship assumes a one-half power law. The MDDP computations are in good agreement with recent experimental findings and compare well with the predictions of several dislocation-based continuum models.

Molecular Modeling of Lipid Membrane Curvature Induction by a Peptide: More than Simply Shape

Molecular dynamics simulations of an amphipathic helix embedded in a lipid bilayer indicate that it will induce substantial positive curvature (e.g., a tube of diameter 20 nm at 16% surface coverage). The induction is twice that of a continuum model prediction that only considers the shape of the inclusion. The discrepancy is explained in terms of the additional presence of specific interactions described only by the molecular model. The conclusion that molecular shape alone is insufficient to quantitatively model curvature is supported by contrasting molecular and continuum models of lipids with large and small headgroups (choline and ethanolamine, respectively), and of the removal of a lipid tail (modeling a lyso-lipid). For the molecular model, curvature propensity is analyzed by computing the derivative of the free energy with respect to bending. The continuum model predicts that the inclusion will soften the bilayer near the headgroup region, an effect that may weaken curvature induction. The all-atom predictions are consistent with experimental observations of the degree of tubulation by amphipathic helices and variation of the free energy of binding to liposomes.

Stokes shift dynamics of ionic liquids: Solute probe dependence, and effects of self-motion, dielectric relaxation frequency window, and collective intermolecular solvent modes

In this paper we have used a semi-molecular theory for investigating the probe dependence of Stokes shift dynamics in room temperature ionic liquids (ILs) by considering three different but well-known dipolar solvation probes--coumarin 153, trans-4-dimethylamino-4(')-cyanostilbene, and 4-aminophthalimide. In addition, effects on polar solvation energy relaxation in ILs of solute motion, frequency coverage (frequency window) accessed by dielectric relaxation measurements and collective IL intermolecular modes (CIMs) at tera-hertz range have been explored. Eleven different ILs have been considered for the above theoretical study. Calculated results show better agreement with the recent (fluorescence up-conversion (FLUPS) + time-correlated single photon counting (TCSPC)) experimental results, particularly at short times, when the CIM contribution to the frequency dependent dielectric function (ɛ(ω)) is included. This is done via assigning the missing dispersion in an experimental ɛ(ω) to an IL intermolecular mode at 30 cm(-1). No significant probe dependence has been observed for solvation energy relaxation although the magnitude of dynamic Stokes shift varies with the dipole moment of the excited solute. Calculations using experimental ɛ(ω) measured with broader frequency window generate solvation response functions closer to experiments. However, average solvation rates predicted by using different ɛ(ω) for the same IL do not differ appreciably, implying over-all validity of these dielectric relaxation measurements. Results presented here indicate that inclusion of solvent molecularity via wavenumber dependent static correlations and ion dynamic structure factor relaxation improves significantly the comparison between theory and experiments over the continuum model predictions for polar solvation dynamics in these solvents.

Continuum Computational Fluid Dynamics model of heat transfer in monolith converter

Continuum Computational Fluid Dynamics model of heat transfer in monolith converter Atul Pant,1 Thiyagarajan Paramadayalan2 1Global General Motors R&D, India Science Lab, GM Tech Center (India), Bangalore, India; 2GM Powertrain-India, Engine CAE, GM Tech Center (India), Bangalore, India Abstract: A continuum model representation of transient heat transfer in monoliths with square channels requires solving separate energy balance for gas and solid domains. Comparison of continuum model predictions with results of a full three-dimensional model of distributed square channels shows that besides adequate estimation of effective radial thermal conductivity, heat flux at boundary also needs to be properly assigned. It is shown that solving separate energy balances for solid and fluid domains requires splitting the total boundary heat flux between the two domains. The heat flux can be split based on thermal resistance of the fluid and solid domain in the continuum model. Heat transfer in a monolith with 1024 square channels is simulated using the proposed continuum approach and the direct approach considering each individual channel. The continuum model predicts the radial variation in temperature to within 6°C of that obtained in the actual channel model. Using the model to simulate the heating up of the monolith with hot inlet gas and heat loss at the boundary shows that the heat loss at the monolith boundary does not penetrate to more than three channels near the wall. Keywords: monolith reactors, heat conduction, heat transfer, mathematical modeling, numerical analysis, porous media

Comparing a discrete and continuum model of the intestinal crypt

The integration of processes at different scales is a key problem in the modelling of cell populations. Owing to increased computational resources and the accumulation of data at the cellular and subcellular scales, the use of discrete, cell-level models, which are typically solved using numerical simulations, has become prominent. One of the merits of this approach is that important biological factors, such as cell heterogeneity and noise, can be easily incorporated. However, it can be difficult to efficiently draw generalizations from the simulation results, as, often, many simulation runs are required to investigate model behaviour in typically large parameter spaces. In some cases, discrete cell-level models can be coarse-grained, yielding continuum models whose analysis can lead to the development of insight into the underlying simulations. In this paper we apply such an approach to the case of a discrete model of cell dynamics in the intestinal crypt. An analysis of the resulting continuum model demonstrates that there is a limited region of parameter space within which steady-state (and hence biologically realistic) solutions exist. Continuum model predictions show good agreement with corresponding results from the underlying simulations and experimental data taken from murine intestinal crypts.

Ion-Induced Nanoscale Ripple Patterns on Si Surfaces: Theory and Experiment.

Nanopatterning of solid surfaces by low-energy ion bombardment has received considerable interest in recent years. This interest was partially motivated by promising applications of nanopatterned substrates in the production of functional surfaces. Especially nanoscale ripple patterns on Si surfaces have attracted attention both from a fundamental and an application related point of view. This paper summarizes the theoretical basics of ion-induced pattern formation and compares the predictions of various continuum models to experimental observations with special emphasis on the morphology development of Si surfaces during sub-keV ion sputtering.