Mean-field Approach Research Articles

The hcp–bcc transition of Be via anisotropy of modulus and sound velocity

Abstract Based on ab initio calculations, we utilize the mean-field potential approach with the quantum modification in conjunction with stress–strain relation to investigate the elastic anisotropies and sound velocities of hcp and bcc Be under high-temperature (0–6000 K) and high-pressure (0–500 GPa) conditions. We propose a general definition of anisotropy for elastic moduli and sound velocities. Results suggest that the elastic anisotropy of Be is more significantly influenced by pressure than by temperature. The pressure-induced increase of c/a ratio makes the anisotropy of hcp Be significantly strengthen. Nevertheless, the hcp Be still exhibits smaller anisotropy than bcc Be in terms of elastic moduli and sound velocities. We suggest that measuring the anisotropy in shear sound velocity may be an approach to distinguishing the hcp–bcc phase transition under extreme conditions.

Ground state properties and bubble structure of the isotopic chains of Z = 125 and 126 using the relativistic mean-field formalism

The ground state properties of Z = 125 and 126 nuclei are investigated, taking the isotopic series from the proton to neutron drip-lines. This analysis uses the relativistic mean-field approach with NL3 and the Relativistic-Hartree–Bogoliubov model with DD-ME2 parameterization. The bulk properties under examination include the binding energy per nucleon, the neutron separation energies, the differential variation of the separation energy, the quadrupole deformation parameter β 2, and the single-particle energy. We observed the stability at N = 172 and 184 over the isotopic chain for both parameter sets. The quadrupole deformation parameter reveals a shape transition from prolate to spherical and back to prolate with mass number. No signature of a super- and/or hyper-deformed structure is found over the isotopic chain. Furthermore, the analysis is extended to examine the bubble structure, revealing a bubble/semi-bubble structure for a few neutron-rich isotopes.

Exploring the limits of the law of mass action in the mean field description of epidemics on Erdös-Rényi networks

The manner epidemics occurs in a social network depends on various elements, with two of the most influential being the relationships among individuals in the population and the mechanism of transmission. In this paper, we assume that the social network has a homogeneous random topology of Erdös-Rényi type. Regarding the contagion process, we assume that the probability of infection is proportional to the proportion of infected neighbours.We consider a constant population, whose individuals are the nodes of the social network, formed by two variable subpopulations: Susceptible and Infected (SI model). We simulate the epidemics on this random network and study whether the average dynamics can be described using a mean field approach in terms of Differential Equations, employing the law of mass action. We show that a macroscopic description could be applied for low average connectivity, adjusting the value of the contagion rate in a precise function. This dependence is illustrated by calculating the transient times for each connectivity.This study contributes valuable insights into the interplay between network connectivity, contagion dynamics, and the applicability of mean-field approximations. The delineation of critical thresholds and the distinctive behaviour at lower connectivity enable a deeper understanding of epidemic dynamics.

A full-field approach for precipitation in metallic alloys. Comparison with a mean-field model

Modeling precipitation in metallic alloys is a topic of great importance in physical metallurgy as the resulting strengthening strongly depends on the precipitate microstructure. We propose here a numerical full-field model for precipitation that describes precipitates with shape functions, thereby allowing to bridge scales between phase-field approaches - that accurately describe the precipitate evolution but require a fine discretization grid - and mean-field approaches - that are computationally very efficient but rely on strong assumptions. Our results demonstrate the capability of the full-field approach to model the different stages of precipitation during isothermal treatments. The comparison with mean-field results allow to discuss the influence of solutal impingement and precipitate coagulations on the evolution of the precipitate microstructure.

Neural mass modelling for the masses: Democratising access to whole-brain biophysical modelling with FastDMF

Abstract Different whole-brain computational models have been recently developed to investigate hypotheses related to brain mechanisms. Among these, the Dynamic Mean Field (DMF) model is particularly attractive, combining a biophysically realistic model that is scaled up via a mean-field approach and multimodal imaging data. However, an important barrier to widespread usage of the DMF model is that current implementations are computationally expensive, supporting only simulations on brain parcellations that consider less than 100 brain regions. Here, we introduce an efficient and accessible implementation of the DMF model: the FastDMF. By leveraging analytical and numerical advances – including a novel estimation of the feedback inhibition control parameter, and a Bayesian optimization algorithm – the FastDMF circumvents various computational bottlenecks of previous implementations, improving interpretability, performance and memory use. Furthermore, these advances allow the FastDMF to increase the number of simulated regions by one order of magnitude, as confirmed by the good fit to fMRI data parcellated at 90 and 1000 regions. These advances open the way to the widespread use of biophysically grounded whole-brain models for investigating the interplay between anatomy, function, and brain dynamics, and to identify mechanistic explanations of recent results obtained from fine-grained neuroimaging recordings.

The dipole moment of supercritical water – local vs. mean-field polarisation contributions

Supercritical water has attracted much attention from both fundamental and technological perspectives, based largely on its ability to solvate other molecules. Predicting and controlling this requires a deeper understanding of water's polarisation behaviour. Using the computationally efficient Self-Consistent Electrostatic Embedding method, we were able to calculate the water dipole moment over an unprecedented range of thermodynamic conditions, covering gas, liquid and supercritical states, with large simulation systems and a high-level quantum mechanical method. We find a discontinuous change in the dipole moment along subcritical isotherms, corresponding to the sharp transition between the vapour and liquid states, with the latter exhibiting induced dipole moments between 0.5 and 0.9 D, depending on the temperature. In contrast, the dipole moment changes continuously from gas-like to liquid-like behaviour in the supercritical regime, allowing the degree of polarisation to be controlled through manipulating temperature and pressure. The dipole moment was found to be linearly related to the average number of hydrogen-bonded neighbours of water, emphasising the key role of local interactions to the polarisation process. Mean-field approaches based on a dielectric continuum representation of the solvent are unable to predict this behaviour due to the neglect of local interactions.

The frustrated bilayer Ising model: A cluster mean-field approach

We investigate the Ising model on the bilayer square lattice with antiferromagnetic interactions between first-(J1) and second-neighbors (J2) inside each layer and a perpendicular antiferromagnetic interaction (Jp) between layers. The roles of frustration and interlayer interactions on the thermal phase transitions are described within a variational cluster mean-field (CMF) approach. For J2/J1<1/2, the model exhibits a Néel antiferromagnetic (AF) ground state and, for J2/J1>1/2, a stripe antiferromagnetic (SAF) ground state takes place. In the absence of interlayer interactions, a tricritical point is found in the phase boundary between SAF and paramagnetic (PM) phases. Our CMF calculations show that the ordering temperature of both AF and SAF phases is enhanced by the interlayer couplings. We also show that, at different levels of frustration, in the strong-interlayer-coupling limit, the ordering temperature is twice the one in the absence of interlayer interactions. At the weak-interlayer-coupling limit, a linear dependence of the ordering temperature with the interlayer interaction is observed, which indicates a shift exponent ϕ=1. Our investigation revealed that the model exhibits tricriticality at all strengths of the interlayer interactions, but the coupling coordinate of the tricritical point (J2/J1)t exhibits a minimum at a finite strength of Jp/J1. However, in the strong interlayer coupling limit, the coupling coordinate of the tricritical point is the same as in the decoupled (Jp=0) limit. Therefore, our CMF study reveals a persistent tricriticality in the frustrated bilayer Ising model.

Landau free energy of small clusters beyond mean-field approach.

Landau free energy determines the landscape of order parameter fluctuations that occur in a physical system at thermal equilibrium and, in particular, characterizes the critical phenomena. We propose a semianalytical approach based on the fluctuating local field method, which allows us to estimate Landau free energy for small clusters with discrete (Ising model) and continuous (Heisenberg model) order parameter.

Robust correlated magnetic moments in end-modified graphene nanoribbons

We conduct a theoretical examination of the electronic and magnetic characteristics of end-modified 7-atom wide armchair graphene nanoribbons (AGNRs). Our investigation is performed within the framework of a single-band Hubbard model, beyond a mean-field approximation. First, we carry out a comprehensive comparison of various approaches for accommodating di-hydrogenation configurations at the AGNR ends. We demonstrate that the application of an on-site potential to the modified carbon atom, coupled with the addition of an electron, replicates phenomena such as the experimentally observed reduction of the bulk-states (BS) gap. These results for the density of states (DOS) and electronic densities align closely with those obtained through a method explicitly designed to account for the orbital properties of hydrogen atoms. Furthermore, our study enables a clear differentiation between magnetic moments already described in a mean-field (MF) approach, which are spatially confined to the same sites as the topological end-states (ES), and correlation-induced magnetic moments, which exhibit localization along all edges of the AGNRs. Notably, we show the robustness of these correlation-induced magnetic moments relative to end modifications, within the scope of the method we employ.

Assessing the forecasting power of mean-field approaches for disease spreading using active systems

The forecasting of the temporal evolution of real-world diseases is systematically performed via mean-field, compartmental models, such as the SIR model and its various variants. Here, we investigate the spreading of SIR dynamics over a system of interacting, active agents – whose dynamics generate random contacts among the agents, as well as temporal and spatial correlation and fluctuations – to assess whether mean-field-like SIR models are able to accurately describe the temporal evolution of an epidemics. We find that such models display temporal dynamics that are intrinsically and fundamentally different from the ones obtained in active agent simulations. Specifically, we numerically prove that no effective mean-field SIR model is consistent with the dynamics that emerge in agent-based simulations. Our results call into question the use of such models to forecast the evolution of real-world epidemics, independently of the method used to estimate the basic reproduction number.

Message-passing approach for percolation on the networked system: A mini-review

Network percolation is one of the core topics in network science, especially in understanding and optimizing the robustness of real-world networks. As a powerful tool, the message-passing approach shows unique advantages in characterizing network percolation compared with the mean-field approach. This approach simulates the behavioural response when the network is damaged by transmitting and updating messages between network nodes, thereby accurately assessing the robustness of the network. This paper reviews the progress of message-passing approaches in network percolation on simple networks, multilayer networks and higher-order networks in recent years and discusses the application of this approach in other research fields. Finally, we discuss future research directions around this approach.

A quantal diffusion approach for multinucleon transfer in heavy-ion collisions

The stochastic mean-field (SMF) approach beyond the time-dependent-Hartree-Fock theory is used to explore the primary production cross sections in Ni64+130Te at the bombarding energy Ec.m.=184.3 MeV and Pb206+118Sn at Ec.m.=436.8 MeV. Secondary production cross-sections in the same systems are calculated using a statistical de-excitation model with GEMINI++ code. The obtained results are compared with available experimental data. Analysis employing SMF and GEMINI++ exhibit a good agreement with the experimental data.

Transboundary pollution control under evolving social norms: a mean-field approach

Transboundary pollution control under evolving social norms: a mean-field approach

Electrolyte effects on the alkaline hydrogen evolution reaction: A mean-field approach

This paper introduces the combination of an advanced double-layer model with electrochemical kinetics to explain electrolyte effects on the alkaline hydrogen evolution reaction. It is known from experimental studies that the alkaline hydrogen evolution current shows a strong dependence on the concentration and identity of cations in the electrolyte, but is independent of pH. To explain these effects, we formulate the faradaic current in terms of the electric potential in the double layer, which is calculated using a mean-field model that takes into account the cation and anion sizes as well as the electric dipole moment of water molecules. We propose that the Volmer step consists of two activated processes: a water reduction sub-step, and a sub-step in which OH− is transferred away from the reaction plane through the double layer. Either of these sub-steps may limit the rate. The proposed models for these sub-steps qualitatively explain experimental observations, including cation effects, pH-independence, and the trend reversal between gold and platinum electrodes. We also assess the quantitative accuracy of the water-reduction-limited current model; we suggest that the predicted functional relationship is valid as long as the hydrogen bonding structure of water near the electrode is sufficiently maintained.

Continuous and explosive synchronization transition in turbulent combustors

Thermoacoustic instabilities in turbulent combustors have disastrous consequences and present notorious challenges in their modeling, prediction, and control. Such instabilities are characterized by self-excited periodic oscillations, arising from a positive feedback between the acoustic pressure and heat release rate fluctuations. We present a mean-field approach to model thermoacoustic transitions. The nonlinear flame response is modeled using an ensemble of phase oscillators constrained to collectively evolve at the rhythm of acoustic fluctuations. Starting from the acoustic wave equation coupled with the phase oscillators, we derive the evolution equations for the amplitude and phase for acoustic oscillations. The model captures abrupt and continuous transitions to thermoacoustic instability observed in disparate combustors. We also discover that continuous and abrupt transitions happen through paradigmatic continuous and explosive synchronization, respectively. Importantly, our approach explains spatiotemporal synchronization and pattern formation underlying the transition to thermoacoustic instability. The versatility of the model in capturing different types of transitions suggests promising prospects for its extension to encompass a wide range of fluid dynamics phenomena.

Strong-coupling mean-field and classical percolation approach to produce the phase diagram of disordered Bose–Hubbard model at fixed n = 1 filling

We perform strong-coupling mean-field along with classical percolation analysis to produce the phase diagram of disordered Bose–Hubbard model with chemical potential disorder in two dimensional square lattice. The phase diagram in the disorder strength (Δ) and the on-site repulsion (U), for two and three dimensional system at fixed n = 1 filling show interesting re-entrant superfluid phase sandwiched between Bose-glass phases, as observed by the previous QMC results. We produce the phase diagram exhibiting the re-entrant phenomenon as well as phenomenologically demonstrate the robustness of the re-entrant phenomena within this method. We also discuss the importance of the method and applicability in further analysis of the same phase diagram.

Beyond Single-Reference Fixed-Node Approximation in Ab Initio Diffusion Monte Carlo Using Antisymmetrized Geminal Power Applied to Systems with Hundreds of Electrons.

Diffusion Monte Carlo (DMC) is an exact technique to project out the ground state (GS) of a Hamiltonian. Since the GS is always bosonic, in Fermionic systems, the projection needs to be carried out while imposing antisymmetric constraints, which is a nondeterministic polynomial hard problem. In practice, therefore, the application of DMC on electronic structure problems is made by employing the fixed-node (FN) approximation, consisting of performing DMC with the constraint of having a fixed, predefined nodal surface. How do we get the nodal surface? The typical approach, applied in systems having up to hundreds or even thousands of electrons, is to obtain the nodal surface from a preliminary mean-field approach (typically, a density functional theory calculation) used to obtain a single Slater determinant. This is known as single reference. In this paper, we propose a new approach, applicable to systems as large as the C60 fullerene, which improves the nodes by going beyond the single reference. In practice, we employ an implicitly multireference ansatz (antisymmetrized geminal power wave function constraint with molecular orbitals), initialized on the preliminary mean-field approach, which is relaxed by optimizing a few parameters of the wave function determining the nodal surface by minimizing the FN-DMC energy. We highlight the improvements of the proposed approach over the standard single-reference method on several examples and, where feasible, the computational gain over the standard multireference ansatz, which makes the methods applicable to large systems. We also show that physical properties relying on relative energies, such as binding energies, are affordable and reliable within the proposed scheme.

Once-in-a-lifetime encounter models for neutrino media: From coherent oscillations to flavor equilibration

Collective neutrino oscillations are typically studied using the lowest-order quantum kinetic equation, also known as the mean-field approximation. However, some recent quantum many-body simulations suggest that quantum entanglement among neutrinos may be important and may result in flavor equilibration of the neutrino gas. In this work, we develop new quantum models for neutrino gases in which any pair of neutrinos can interact at most once in their lifetimes. A key parameter of our models is γ=μΔz, where μ is the neutrino coupling strength, which is proportional to the neutrino density, and Δz is the duration over which a pair of neutrinos can interact each time. Our models reduce to the mean-field approach in the limit γ→0 and achieve flavor equilibration in time t≫(γμ)−1. These models demonstrate the emergence of coherent flavor oscillations from the particle perspective and may help elucidate the role of quantum entanglement in collective neutrino oscillations. Published by the American Physical Society 2024

A comprehensive mean-field approach to simulate the microstructure during the hot forming of Ti-17

Thermomechanical processing of titanium alloys involves several hot forming steps to shape the workpiece and achieve a final microstructure that meets the desired mechanical properties. While mean-field models are commonly used to design the process and understand the influence of the processing route on the final microstructure, they cannot provide detailed spatial information on the local microstructure and stress evolution during the deformation of a workpiece. To address this limitation, we propose a comprehensive approach in which the mean-field model is validated in a region of a cylindrical workpiece at a constant strain rate and temperature during deformation. The validated model is integrated as a material model into a finite element-based software to analyse the effect of the thermomechanical history on the local microstructural and mechanical responses of the α and β phases. The model robustly predicts the role of the α-phase in the microstructural evolution of the β-phase, the α-dynamic globularisation kinetics in regions with different thermomechanical histories, and the influence of strain rate jumps on β-microstructural and mechanical responses. This comprehensive approach provides valuable insights into the intricate interplay between processing parameters, microstructure, and thermomechanical response in titanium alloys.

Computationally Efficient Algorithm for Modeling Grain Growth Using Hillert's Mean-Field Approach.

To investigate the interconnected effects of manufacturing processes on microstructure evolution during hot-rolling, a through process model is required. A novel numerical implementation of the mean-field approach was introduced to efficiently describe the grain growth of larger systems and extended durations. In this approach, each grain is embedded within an average medium and interacts with the average medium, thus avoiding the complexities of individual grain interactions. The proposed upsampling approach dynamically adjusts the simulation grain ensemble, ensuring efficiency and accuracy regardless of the initial number of grains present. This adaptation prevents undersampling artifacts during grain growth. The accuracy of the model is verified against analytical solutions and experimental data, demonstrating high agreement. Moreover, the effects of different initial conditions are successfully investigated, demonstrating the model's versatility. Due to its simplicity and efficiency, the model can be seamlessly integrated into other microstructure evolution models.