Mean-field Modeling Research Articles

Comparative simulations of methanol steam reforming on PdZn alloy using kinetic Monte Carlo and mean-field microkinetic model.

Methanol steam reforming (MSR) is an attractive route for producing clean energy hydrogen. PdZn alloys are extensively studied as potential MSR catalysts for their stability and high CO2 selectivity. Here, we investigated the reaction mechanism using density functional calculations, mean-field microkinetic modeling (MF-MKM), and kinetic Monte Carlo (kMC) simulations. To overcome the over-underestimation of CO2 selectivity by log-kMC, an ads-kMC algorithm is proposed in which the adsorption/desorption rate constants were reduced under certain requirements and the diffusion process was treated by redistributing surface species each time an event occured. The simulations show that the dominant pathway to CO2 at low temperatures is CH3OH → CH3O → CH2O → H2COOH → H2COO → HCOO → CO2. The ads-kMC predicted OH coverage is 2-3 times that of MF-MKM, while they produce similar coverage for other species. Analyses indicate that surface OH promotes the dehydrogenation of CH3OH, CH3O, and H2COOH significantly and plays a key role in the MSR process. The dissociation of water/methanol is the most important rate-limiting/rate-inhibiting step. The CO2 selectivity obtained by the two methods is close to each other and consistent with the experimental trend with temperature. Generally, the ads-kMC results agree with the MF-MKM ones, supporting the previous finding that kMC and MF-MKM predict similar results if the diffusion is very fast and adsorbate interactions are neglected. The present study sheds light on the MSR process on PdZn alloys, and the proposed scheme to overcome the stiff problems in kMC simulations is worthy of being extended to other systems.

Implementing the Blowers-Masel Approximation to Scale Activation Energy Based on Reaction Enthalpy in Mean-Field Microkinetic Modeling for Catalytic Methane Partial Oxidation.

Mean-field microkinetic modeling is a powerful tool for catalyst design and the simulation of catalytic processes. The reaction enthalpies in a microkinetic model often need to be adjusted when changing species' binding energies to model different catalysts, when performing thermodynamic sensitivity analyses, and when fitting experimental data. When altering reaction enthalpies, the activation energies should also be reasonably altered to ensure realistic reaction rates. The Blowers-Masel approximation (BMA) relates the reaction barrier to the reaction enthalpy. Unlike the Brønsted-Evans-Polani relationship, the BMA requires less data because only one parameter, the intrinsic activation energy, needs to be determined. We validate this application of BMA relations to model surface reactions by comparing against density functional theory data taken from the literature. By incorporating the BMA rate description into the open-source Cantera software, we enable a new workflow, demonstrated herein, allowing rapid screening of catalysts using linear scaling relationships and BMA kinetics within the process simulation software. For demonstration purposes, a catalyst screening for catalytic methane partial oxidation on 81 hypothetical metals is conducted. We compared the results with and without BMA-corrected rates. The heat maps of various descriptors (e.g., CH4 conversion, syngas yield) show that using BMA rates instead of Arrhenius rates (with constant activation energies) changes which metals are most active. Heat maps of sensitivity analyses can help identify which reactions or species are the most influential in shaping the descriptor map patterns. Our findings indicate that while using BMA-adjusted rates did not markedly affect the most sensitive reactions, it did change the most influential species.

Speed-accuracy trade-offs in best-of-n collective decision making through heterogeneous mean-field modeling.

To succeed in their objectives, groups of individuals must be able to make quick and accurate collective decisions on the best option among a set of alternatives with different qualities. Group-living animals aim to do that all the time. Plants and fungi are thought to do so too. Swarms of autonomous robots can also be programed to make best-of-n decisions for solving tasks collaboratively. Ultimately, humans critically need it and so many times they should be better at it! Thanks to their mathematical tractability, simple models like the voter model and the local majority rule model have proven useful to describe the dynamics of such collective decision-making processes. To reach a consensus, individuals change their opinion by interacting with neighbors in their social network. At least among animals and robots, options with a better quality are exchanged more often and therefore spread faster than lower-quality options, leading to the collective selection of the best option. With our work, we study the impact of individuals making errors in pooling others' opinions caused, for example, by the need to reduce the cognitive load. Our analysis is grounded on the introduction of a model that generalizes the two existing models (local majority rule and voter model), showing a speed-accuracy trade-off regulated by the cognitive effort of individuals. We also investigate the impact of the interaction network topology on the collective dynamics. To do so, we extend our model and, by using the heterogeneous mean-field approach, we show the presence of another speed-accuracy trade-off regulated by network connectivity. An interesting result is that reduced network connectivity corresponds to an increase in collective decision accuracy.

Mean-field modeling and Phase-field simulation of Grain Growth under Directional driving forces

Directional grain growth is a common phenomenon in the synthetic and natural evolution of various polycrystals. It occurs in the presence of an external driving force, such as a temperature gradient, along which grains show a preferred, yet competitive, growth. Novel additive manufacturing processes, with intense, localized energy deposition, are prominent examples of when directional grain growth can occur, beneath the melting pool. In this work, we derive a phenomenological mean-field model and perform 3D phase-field simulations to investigate the directional grain growth and its underlying physical mechanisms. The effect of the intensity of driving force is simulated and systematically analyzed at the evolving growth front as well as various cross-sections perpendicular to the direction of the driving force. We found that although the directional growth significantly deviates from normal grain growth, it is still governed by a power law relation 〈R〉∝tn, with an exponent n∼ 0.6–0.7. The exponent n exhibits a nontrivial dependence on the magnitude of the directional driving force, such that the lowest growth exponent is observed for intermediate driving forces. We elaborate that this can originate from the fact that the forces at grain boundary junctions evolve out of balance under the influence of the directional driving force. With increasing the driving forces, the growth exponent asymptotically approaches a value of n≈0.63, imposed by the largest possible grain aspect ratio for given grain boundary energies. The current combined mean-field and phase-field framework pave the way for future exploration in broader contexts such as the evolution of complex additively manufactured microstructures.

Memory effects during co-deposition of binary alloys

The possibility of memory effects during the co-deposition of binary alloy with simultaneous phase separation is studied on the atomistic scale by the Stochastic Kinetic Mean-Field method. At first, the morphology map is found for the asymptotic structures obtained under various compositions of deposition flux and various deposition rates, starting from random alloy at the initial atomic plane. Such a map consists of “single-pattern” and “mixed-pattern” regions. At that, a new way of morphology quantification is suggested. The best candidates for keeping memory about the initial morphology (if it is not a random alloy anymore) are the systems from the “mixed-pattern region”. They indeed demonstrate the memory effects at least in mean-field modeling.

Intragranular ferrite nucleation on MX carbonitrides and dislocations

The competing mechanisms of ferrite nucleation on (Ti,V)(C,N) MX carbonitrides and dislocations, as well as their dependence on deformation, are investigated experimentally by thermo-mechanical treatments and via simulation. The impact of recrystallization and the resulting austenite grain size on intragranular ferrite nucleation is evaluated. The austenite-to-ferrite transformation temperatures, affected by different microstructures, are examined by isothermal uniaxial single-hit compression tests on a dilatometer DIL 805 and compared to thermal treatments without deformation. Different resulting microstructures are analyzed by using optical light microscopy. The experimental data is used for the validation of thermo-kinetic simulations with the mean-field modeling software MatCalc using the implemented models for the austenite grain evolution, the on-particle nucleation of ferrite on the surface of MX particles, the dislocation density evolution, and recrystallization.

Combining descriptor-based analyses and mean-field modeling of the electrochemical interface to comprehend trends of catalytic processes at the solid/liquid interface

Electrocatalysis is undergoing a renaissance due to its central importance for a sustainable energy economy, relying on green (electro-)chemical processes to harvest, convert, and store energy. Theoretical considerations by electronic structure methods are key to identify potential material motifs for electrocatalytic processes at the solid/ liquid interface. Most commonly, heuristic concepts in the realm of materials screening by the compilation of volcano plots are used, which rely on a plethora of simplifications and approximations of the complex electrochemical interface. While the investigation of the catalytic processes at the solid/ liquid interface mainly relies on descriptor-based approaches, in the present future article it is discussed that the inclusion of the liquid part of the interface by mean-field models is crucial to elevate screening approaches to the next level.

Understanding the influence of solvents on the Pt-catalyzed hydrodeoxygenation of guaiacol

Bio-oil derived from fast pyrolysis of lignocellulosic biomass needs to be deoxygenated to become a substitute for petroleum fuels. Here, we study the hydrodeoxygenation mechanism of guaiacol, a bio-oil model compound derived from the lignin fraction of biomass, on Pt(111) terrace sites in the presence of water, diethyl ether, 1-butanol, and n-hexane as solvent. Using first-principles periodic density functional theory (DFT) calculations and mean-field microkinetic reactor modeling, a detailed reaction mechanism is investigated targeting various products such as catechol, phenol, anisole, benzene, cyclohexanone, and cyclohexanol. Solvent phase DFT outcomes are mostly similar to that of the vapor phase; however, microkinetic modeling results suggest that rate controlling species and transition states differ somewhat in the various reaction environments. Catechol was found to be the major aromatic product across all reaction environments. Over Pt(111), unsaturated monooxygenate production from catechol is unlikely.

Multiple redox mechanisms for water-gas shift reaction on Fe3O4 (1 1 1) surface: A density functional theory and mean-field microkinetic modeling study

We investigated redox mechanisms for the high temperature (HT) water–gas shift reaction (WGSR) on the Fe3O4 (111) surface using density functional theory (DFT) calculations and mean-field microkinetic modeling (MKM). The redox pathways branched into three Langmuir-Hinshelwood processes (LH1, LH2 and LH3) and one Mars-van-Krevelen (MVK) process (in the presence of oxygen vacancy) from multidentate binding of CO and CO2 over four available reactive sites (Feoct2, Fetet1, Fe bridge, and O1). We found that the LH1 and LH2 processes have CO adsorption at a single iron site (Feoct2 or Fetet1), while the LH3 and MVK processes have stronger chemisorption of CO or CO2 by both the Feoct2 site and the O1 site. From the mechanistic study of these reaction path, we recognized that availability of O1 sites was key to proceed to either CO oxidation by the single site (LH1, LH2) or by the dual site (LH3, MVK). We observed that the reaction energetics were significantly different in the CO oxidation steps, where the single or dual site results in markedly different apparent activation energy (73–281 kJ/mol) and reaction rates (10−3–10−10 mol⋅m−2⋅s−1) among the four reaction mechanisms. The utilization of mean field MKM with DFT reaction energetics helps explain the experimental debates for the catalytic reaction details as well as providing a possible direction to engineer the catalyst with higher activity.

Understanding the Source of Error in First-Principles-Based Micro-Kinetic Modeling: Density Functional Theory Calculations Versus the Mean-Field Approximation

First-principles-based micro-kinetic modeling has become an essential tool in the rational design of heterogeneous catalysts. Currently, most theoretical understandings and predictions are provided by this model, which combines results from density functional theory (DFT) calculations at the generalized gradient approximation level with the simulations using the mean-field micro-kinetic modeling (MF-MKM). In spite of its popularity and success in the catalyst design and screening, sometimes this combination yields undesired predictions that significantly deviate from experimental observations. It is, therefore, important to understand its success and failure and to locate the bottleneck of applying/improving the conventional MF-MKM. To this end, we have compared the errors that come from different DFT functionals with those introduced by the MF approximations against the kinetic Monte Carlo (KMC) results for the Pt-catalyzed water gas shift reaction system. It was found that the shape of the volcano map is less sensitive to the differences in the DFT functionals, even though their predictions of the key energetic parameters are distinctly different. On the other hand, the top of the volcano map, the detailed mechanism, as well as some key kinetic properties are markedly affected by the change of the energetic data. In comparison, the traditional MF-MKM that neglects the adsorbate–adsorbate interactions totally fails to describe the reaction kinetics. The inclusion of the adsorbate–adsorbate interaction effect can significantly improve the performance of the MF-MKM, which results in largely similar predictions to the reference data provided by KMC simulations. Nevertheless, the missing spatial correlation in the MF treatment can lead to an improper description in the high coverage region. Our analyses demonstrate that the accuracy of the MKM might not always be improved by only modifying the DFT-calculated energetic parameters, and close attention should be paid to the kinetic simulation method employed, particularly when quantitative kinetic properties are to be expected.

Analysis of Recrystallization Kinetics Concerning the Experimental, Computational, and Empirical Evaluation of Critical Temperatures for Static Recrystallization in Nb, Ti, and V Microalloyed Steels

Recrystallization kinetics and two critical temperatures—the non-recrystallization temperature TNR and the static recrystallization critical temperature TSRCT—of five Nb, Ti, and V microalloyed steel grades are evaluated. The experimental examination is realized by employing isothermal double-hit compression tests and continuous hot torsion tests, both performed on a Gleeble® 3800 thermo-mechanical simulator. The experimental results are used for the critical assessment of predicted TNR using four empirical equations from the literature, and for the validation of simulated TNR and TSRCT. The thermokinetic computer simulations are realized using the mean-field microstructure modeling software MatCalc. Analysis shows that higher microalloying contents increase both critical temperatures, TNR and TSRCT, whereby the effect of recrystallization retardation of Nb is more pronounced than that of Ti or V. The most accurate reproduction of the experimental recrystallization behavior of the five examined steel grades is realized by the employed physics-based simulation approach.

Filamentary transport in global edge-SOL simulations of ASDEX Upgrade

The understanding and the predictive capability for turbulence in the plasma edge and scrape-off layer (SOL) are crucial for the development of magnetic confinement fusion reactors. To this end, we characterise turbulent transport across the edge and SOL of the diverted ASDEX Upgrade tokamak in attached L-mode conditions by means of validated, global simulations. The collisionality is controlled by the divertor neutrals density, as their ionization increases the plasma density and decreases the temperature. The radial E×B particle and heat transport, quantified by effective diffusivities, rises strongly with collisionality. The modest increase in fluctuation amplitudes is not a sufficient explanation. The reason is shown to be the destabilisation of resistive drift-ballooning modes, resulting in larger phase shifts between the pressure and electrostatic potential. The transport varies both radially and poloidally. Due to its ballooning nature, radial transport is close to zero on the inboard mid-plane. On the outboard mid-plane, significant transport is driven in the SOL by large filaments (blobs) with amplitudes of up to 250% of the mean, propagating ballistically from the separatrix to the wall. This non-local transport leads to large radial variations of diffusivities, as they do not necessarily correlate with the local gradient. Ion temperature fluctuations in the plasma edge are shown to be involved in blob seeding at the separatrix, and are the largest in the SOL. Radial diffusivities peak at the top and bottom of the device, since gradients are flatter there due to the flux expansion while the cross-field flow is sustained by streamers—a feature which should be considered in mean-field transport modeling. The increase of SOL E×B transport with collisionality is likely fostered by the simultaneously decreasing radial electric field, resulting from a flattened electron temperature profile. Large amplitude blobs are a hazard for plasma facing components of fusion reactors, but they could be restrained by control of SOL collisionality.

How Topological Differences between Two Oxide Surfaces Determine Selectivity—The Case of the Dehydra-Decyclization of Tetrahydrofuran

Production of butadiene from biomass-based tetrahydrofuran (THF) is explored as an alternative to the existing petroleum-based processes. Metal oxide catalysts have been shown to exhibit varying product selectivities when reacted with THF. Among those oxides, ZrO2 showed the highest selectivity for butadiene. In contrast, Al2O3 showed the highest selectivity for the competing retro-Prins products, C3H6 and HCHO. The reasons behind the varying selectivity across oxides are unclear. In this work, we employ periodic density functional theory and mean-field microkinetic modeling to investigate the mechanism of the reaction of THF to butadiene and retro-Prins products on t-ZrO2 (101) (dry and hydrous) and on γ-Al2O3 (110). Our simulations reproduce the experimental selectivity trends. High selectivity for butadiene is promoted by the presence of neighboring Lewis acid metal sites that facilitate E1cB hydroxyl elimination from a 3-butenoxide intermediate; on hydrous Al2O3; where such neighboring Lewis acid centers are not available, the butenoxide undergoes E2 elimination and retro-Prins products ensue. The THF ring opening is rate-determining on ZrO2, whereas the γ-proton elimination that yields the 3-butenoxide intermediate is rate controlling on hydroxylated Al2O3. We conclude that the local topology around the active site greatly influences the mechanism and selectivity.

A comprehensive neural simulation of slow-wave sleep and highly responsive wakefulness dynamics.

Hallmarks of neural dynamics during healthy human brain states span spatial scales from neuromodulators acting on microscopic ion channels to macroscopic changes in communication between brain regions. Developing a scale-integrated understanding of neural dynamics has therefore remained challenging. Here, we perform the integration across scales using mean-field modeling of Adaptive Exponential (AdEx) neurons, explicitly incorporating intrinsic properties of excitatory and inhibitory neurons. The model was run using The Virtual Brain (TVB) simulator, and is open-access in EBRAINS. We report that when AdEx mean-field neural populations are connected via structural tracts defined by the human connectome, macroscopic dynamics resembling human brain activity emerge. Importantly, the model can qualitatively and quantitatively account for properties of empirically observed spontaneous and stimulus-evoked dynamics in space, time, phase, and frequency domains. Large-scale properties of cortical dynamics are shown to emerge from both microscopic-scale adaptation that control transitions between wake-like to sleep-like activity, and the organization of the human structural connectome; together, they shape the spatial extent of synchrony and phase coherence across brain regions consistent with the propagation of sleep-like spontaneous traveling waves at intermediate scales. Remarkably, the model also reproduces brain-wide, enhanced responsiveness and capacity to encode information particularly during wake-like states, as quantified using the perturbational complexity index. The model was run using The Virtual Brain (TVB) simulator, and is open-access in EBRAINS. This approach not only provides a scale-integrated understanding of brain states and their underlying mechanisms, but also open access tools to investigate brain responsiveness, toward producing a more unified, formal understanding of experimental data from conscious and unconscious states, as well as their associated pathologies.

Mean Field Modeling of Grain Growth and Zener Pinning

A mean-field model has been developed to simulate curvature-driven grain growth by exploring the evolution of grain size distribution under arbitrary thermal histories. The model was integrated into precipitation module TC-PRISMA, so that the pinning effect of the concurrently precipitated particles on the growing grains can be considered by a modified, location-specific Zener model. The developed model was validated against analytical calculations, and then applied to real alloy systems, fed with assessed grain boundary energy and mobility data. Its capabilities, limitations, and directions to improvements have been discussed.

Modeling precipitation kinetics in multicomponent alloys during deformation

A new mean-field modeling tool is developed to correctly tackle the problem of precipitation during deformation. The model is an extension of a previously developed Langer–Schwartz–Kampmann–Wagner precipitation modeling approach for multicomponent alloys. The latter is now integrated together with Thermo-Calc software and with physically based equations describing the evolution of the dislocation density during hot-working. New equations for the nucleation barrier and the critical size have also been added to correctly simulate the early stages of precipitation. The model is applied to hot compression tests, for which experimental information was available. The model shows the importance of accounting for the overall precipitation kinetics, and not only for constant values of the precipitate volume fraction or size, to investigate the mechanical property evolution. This is due to a complex interplay between the defects and the precipitates’ evolution driven by a competition between thermodynamics and kinetics. Finally, it is highlighted how the strain rate used affects the final microstructure of the material.

Unified mean-field modeling of viscous short-fiber suspensions and solid short-fiber reinforced composites

Mean-field homogenization is an established and computationally efficient method estimating the effective linear elastic behavior of composites. In view of short-fiber reinforced materials, it is important to homogenize consistently during process simulation. This paper aims to comprehensively reflect and expand the basics of mean-field homogenization of anisotropic linear viscous properties and to show the parallelism to the anisotropic linear elastic properties. In particular, the Hill–Mandel condition, which is generally independent of a specific material behavior, is revisited in the context of boundary conditions for viscous suspensions. This study is limited to isothermal conditions, linear viscous and incompressible fiber suspensions and to linear elastic solid composites, both of which consisting of isotropic phases with phase-wise constant properties. In the context of homogenization of viscous properties, the fibers are considered as rigid bodies. Based on a chosen fiber orientation state, different mean-field models are compared with each other, all of which are formulated with respect to orientation averaging. Within a consistent mean-field modeling for both fluid suspensions and solid composites, all considered methods can be recommended to be applied for fiber volume fractions up to 10%. With respect to larger, industrial-relevant, fiber volume fractions up to 20%, the (two-step) Mori–Tanaka model and the lower Hashin–Shtrikman bound are well suited.

Jets from Accretion Disk Dynamos: Consistent Quenching Modes for Dynamo and Resistivity

Astrophysical jets are launched from strongly magnetized systems that host an accretion disk surrounding a central object. The origin of the magnetic field, which is a key component of the launching process, is still an open question. Here we address the question of how the magnetic field required for jet launching is generated and maintained by a dynamo process. By carrying out nonideal MHD simulations (PLUTO code), we investigate how the feedback of the generated magnetic field on the mean-field dynamo affects the disk and jet properties. We find that a stronger quenching of the dynamo leads to a saturation of the magnetic field at a lower disk magnetization. Nevertheless, we find that, while applying different dynamo feedback models, the overall jet properties remain unaffected. We then investigate a feedback model that encompasses a quenching of the magnetic diffusivity. Our modeling considers a more consistent approach for mean-field dynamo modeling simulations, as the magnetic quenching of turbulence should be considered for both a turbulent dynamo and turbulent magnetic diffusivity. We find that, after the magnetic field is saturated, the Blandford–Payne mechanism can work efficiently, leading to more collimated jets, which move, however, with slower speed. We find strong intermittent periods of flaring and knot ejection for low Coriolis numbers. In particular, flux ropes are built up and advected toward the inner disk thereby cutting off the inner disk wind, leading to magnetic field reversals, reconnection and, the emergence of intermittent flares.

Modeling the Snoek peak in bct-martensite

Snoek relaxation in bcc crystals is the delayed strain response to an applied stress resulting from the interaction of the interstitial atoms with the stress field. It is responsible for the Snoek peak observed in internal friction measurements of ferrite. However, although martensite is carbon supersaturated, several authors denied the possibility of Snoek relaxation in bct-martensite. We investigated this matter by means of Monte Carlo simulations and mean-field thermo-kinetic modeling. Our results show that Snoek relaxation does occur in bct-martensite. The computed Snoek profiles of temperature-dependent and frequency-dependent internal friction exhibit unexpected features: both peak height and peak temperature decrease when the carbon content is increased. We explain this behavior in the frame of the linear-response approximation. Our theoretical predictions are in qualitative agreement with experiments.

Erratum to: Progress of Physics-based Mean-field Modeling and Simulation of Steel

Erratum to: Progress of Physics-based Mean-field Modeling and Simulation of Steel