Mean Field Research Articles

Multiconfigurational Surface Hopping: a Time-Dependent Variational Approach with Momentum-Jump Trajectories.

The Ehrenfest mean field dynamics and trajectory surface hopping have been widely used in nonadiabatic dynamics simulations. Based on the time-dependent variational principle (TDVP), the multiconfigurational Ehrenfest (MCE) method has also been developed and can be regarded as a multiconfigurational extension of the traditional Ehrenfest dynamics. However, it is not straightforward to apply the TDVP to surface hopping trajectories because there exists momentum jump during surface hops. To solve this problem, we here propose a multiconfigurational surface hopping (MCSH) method, where continuous momenta are obtained by linear interpolation and the interpolated trajectories are used to construct the basis functions for TDVP in a postprocessing manner. As demonstrated in a series of representative spin-boson models, MCSH achieves high accuracy with only several hundred trajectory bases and can uniformly improve the performance of surface hopping. In principle, MCSH can be combined with all kinds of mixed quantum-classical trajectories and thus has the potential to properly describe general nonadiabatic dynamics.

The mean field limit for the Vlasov–Poisson system with a point charge

In this paper, we are concerned with the validity problem for the repulsive Vlasov–Poisson system when the initial datum is the sum of a diffuse density and a point charge in the three dimensional space. Our result leads to a derivation of this system from the regularized microscopic N-plasma particle and one point charge system when the Coulomb force between plasma particles needs to be modified with the modified size N − 1 3 + ϵ while the Coulomb force between plasma and point charge does not need to be modified. More precisely, we obtain the convergence rate between the empirical measure associated to the regularized particle system and the solution of the Vlasov–Poisson system with a point charge in terms of the Wasserstein distance.

Advancing Our Understanding of the Excited States of the Tantalum Anion.

Our study provides a comprehensive theoretical examination of the energy levels associated with the neutral tantalum atom and its ions in various charge states (Ta, Ta+, and Ta-), employing the multiconfiguration Dirac-Hartree-Fock (MCDHF) method, and relativistic infinite order two-component (IOTC) method with multiconfiguration complete active space self-consistent field (CASSCF) followed by the second-order single-state multireference perturbation (CASPT2) methods. The effect of spin-orbit (SO) coupling is introduced via the restricted active space state interaction (RASSI) method, utilizing atomic mean field SO integrals (AMFI). Through IOTC CASSCF/CASPT2 RASSI calculations, we determined the electron affinity (EA) of the tantalum atom to be 0.321 eV, which stands among the most accurate theoretical values achieved to date. This result closely aligns with the experimental measurement of 0.329 eV. Our investigation highlights potential discrepancies between the predicted symmetry of the excited states of the tantalum anion and experimental observations. Additionally, we calculated the bonding energies for transitions from Ta- to Ta and identified four potential bound or quasi-bound states in the tantalum anion.

Multimodal and Multifactor Branching Time Active Inference.

Active inference is a state-of-the-art framework for modeling the brain that explains a wide range of mechanisms. Recently, two versions of branching time active inference (BTAI) have been developed to handle the exponential (space and time) complexity class that occurs when computing the prior over all possible policies up to the time horizon. However, those two versions of BTAI still suffer from an exponential complexity class with regard to the number of observed and latent variables being modeled. We resolve this limitation by allowing each observation to have its own likelihood mapping and each latent variable to have its own transition mapping. The implicit mean field approximation was tested in terms of its efficiency and computational cost using a dSprites environment in which the metadata of the dSprites data set was used as input to the model. In this setting, earlier implementations of branching time active inference (namely, BTAIVMP and BTAIBF) underperformed in relation to the mean field approximation (BTAI3MF) in terms of performance and computational efficiency. Specifically, BTAIVMP was able to solve 96.9% of the task in 5.1 seconds, and BTAIBF was able to solve 98.6% of the task in 17.5 seconds. Our new approach outperformed both of its predecessors by solving the task completely (100%) in only 2.559 seconds.

Strategic behaviour in the mean field Ising game

The properties of the mean field version of the Ising game of far-sighted agents on a complete graph are considered. General evolution equation for arbitrary yield of simultaneously decision-making agents is derived. Analytical expressions demonstrating strategic stiffening/cooling in the limits of small and large yield of simultaneously decision-making agents are derived.

On a Differential Generalized Nash Equilibrium Problem with Mean Field Interaction

On a Differential Generalized Nash Equilibrium Problem with Mean Field Interaction

A mean field game approach to equilibrium consumption under external habit formation

This paper studies the equilibrium consumption under external habit formation in a large population of agents. We first formulate problems under two types of conventional habit formation preferences, namely linear and multiplicative external habit formation, in a mean field game framework. In a log-normal market model with the asset specialization, we characterize one mean field equilibrium in analytical form in each problem, allowing us to understand some quantitative properties of the equilibrium strategy and conclude some financial implications caused by consumption habits from a mean-field perspective. In each problem with n agents, we construct an approximate Nash equilibrium for the n-player game using the obtained mean field equilibrium when n is sufficiently large. The explicit convergence order in each problem can also be obtained.

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.

Quenches in the Sherrington–Kirkpatrick model

The Sherrington–Kirkpatrick model is a prototype of a complex non-convex energy landscape. Dynamical processes evolving on such landscapes and locally aiming to reach minima are generally poorly understood. Here, we study quenches, i.e. dynamics that locally aim to decrease energy. We analyse the energy at convergence for two distinct algorithmic classes, single-spin flip and synchronous dynamics, focusing on greedy and reluctant strategies. We provide precise numerical analysis of the finite size effects and conclude that, perhaps counter-intuitively, the reluctant algorithm is compatible with converging to the ground state energy density, while the greedy strategy is not. Inspired by the single-spin reluctant and greedy algorithms, we investigate two synchronous time algorithms, the sync-greedy and sync-reluctant algorithms. These synchronous processes can be analysed using dynamical mean field theory (DMFT), and a new backtracking version of DMFT. Notably, this is the first time the backtracking DMFT is applied to study dynamical convergence properties in fully connected disordered models. The analysis suggests that the sync-greedy algorithm can also achieve energies compatible with the ground state, and that it undergoes a dynamical phase transition.

Near-room-temperature magnetic properties and magnetocaloric effect of polycrystalline and nano-scale manganites Pr(0.65-x)NdxSr0.35MnO3 (x ≤ 0.35)

Here we report investigations of structural, electrical and magnetic properties of bulk and nano-sized Pr0.65-xNdxSr0.35MnO3 compounds (x ≤ 0.35). Polycrystalline compounds were produced by solid – state reaction and nanocrystalline samples were obtained by sol–gel method. Analysis of x-ray diffraction patterns revealed a change in lattice structure from ‘Pbnm’ to ‘R3c’ symmetry, with diminishing cell volume upon increasing Nd ions substitution for all samples. Optical microscopy was used for bulk surface morphology and transmission electron microscopy was implemented for nano-sized samples. Iodometric titration showed oxygen deficiency for bulk compounds and oxygen excess for nano-sized particles. Measurements of resistivity of bulk samples revealed a single peak at temperatures associated with grain boundary conditions and with ferromagnetic/paramagnetic transition and negative magnetoresistivity. Critical magnetic behavior analysis disclosed that the polycrystalline samples are governed by a tricritical mean field and by 3D Heisenberg models while nanocrystalline samples are governed by a mean field model. Curie temperature Tc values remain in near room temperature range for all bulk compounds; they lower with increasing Nd ions substitution from 295 K for the parent bulk compound to 268 K for x = 0.35. Tc is lowered from 255 K for the parent nano-sized compound in small temperature intervals. All compounds exhibit second-order magnetic phase transitions and relatively high magnetic entropy change, with the highest value of 5.74 J/kgK for x = 0.25 bulk sample in μ˳∆H = 4 T. Strong magnetocaloric effect, stability and the possibility of fine-tuning Tc by Nd ions substitution make the investigated bulk polycrystalline compounds promising for application in magnetic refrigeration. Nano-sized samples possess lower magnetic entropy changes of maximum 2.4 J/kgK in μ˳∆H = 4 T for x = 0.15, but wider effective entropy change temperature (δTfwhm) and relative cooling power on par with other manganites, bringing them into the conversation as a viable option in cooling materials.

Mean-field backward stochastic differential equations with mean reflection and nonlinear resistance

The present paper is devoted to the study of the well-posedness of mean field BSDEs with mean reflection and nonlinear resistance. By the contraction mapping argument, we first prove that the mean-field BSDE with mean reflection and nonlinear resistance admits a unique deterministic flat local solution on a small time interval. Moreover, we build the global solution by introducing a two-step approach, which is a combination of stitching method and fixed point method. We further provide an application to the super-hedging problem with risk constraint.

Two-dimensional ideal magnetohydrodynamic waves on a rotating sphere under a non-Malkus field: I. Continuous spectrum and its ray-theoretical interpretation

Two-dimensional ideal incompressible magnetohydrodynamic (MHD) linear waves at the surface of a rotating sphere are studied as a model to imitate the outermost layer of the Earth's core or the solar tachocline. This thin conducting layer is permeated by a toroidal magnetic field the magnitude of which depends only on the latitude. The Malkus background field, which is proportional to the sine of the colatitude, provides two well-known groups of branches; on one branch, retrograde Alfvén waves gradually become fast magnetic Rossby (MR) waves as the field amplitude decreases, and on the other, prograde Alfvén waves undergo a gradual transition into slow MR waves. In the case of non-Malkus fields, we demonstrate that the associated eigenvalue problems can yield a continuous spectrum instead of Alfvén and slow MR discrete modes. The critical latitudes attributed to the Alfvén resonance eliminate these discrete eigenvalues and produce an infinite number of singular eigenmodes. The theory of slowly varying wave trains in an inhomogeneous magnetic field shows that a wave packet related to this continuous spectrum propagates toward a critical latitude corresponding to the wave and is eventually absorbed there. The expected behaviour whereby the retrograde propagating packets pertaining to the continuous spectrum approach the latitudes from the equatorial side and the prograde ones approach from the polar side is consistent with the profiles of their eigenfunctions derived using our numerical calculations. Further in-depth discussions of the Alfvén continuum would develop the theory of the “wave–mean field interaction” in the MHD system and the understanding of the dynamics in such thin layers.

Evolution of 2D Nanostructures on Charged Surfaces through the Precipitation of Hydrolyzable Ions

The significance of surface charge at solid-liquid interfaces extends to crucial roles in diverse chemical processes, including crystallization, self-assembly, fuel cell reactions, and heterogeneous catalysis. Building upon the classical mean field description derived from the Gouy–Chapman model, the electrostatic attraction between a charged interface and counterions in solutions prompts oppositely charged ions from the solution to accumulate at the interface, forming an electric double layer (EDL), with distinct properties from those observed in bulk solutions. While the model accounts for the distribution of ions based on their spatial average perpendicular to the surface, the discussion regarding the lateral structure at the interface, particularly the local molecular-level details, is relatively limited.In this study, we explored the interfacial structure of mica, a mineral with an atomically flat surface and intrinsic negative charge, in electrolytes containing different multi-valent cations, utilizing in-situ liquid phase atomic force microscopy (LP-AFM). We find that, as the solution pH is gradually raised, cations precipitate and form a monolayer hydroxide film on mica surface. Divalent ions such as Mg2+, Ni2+, and Co2+, form large continuous monolayers in a manner that aligns with expectations based on classical nucleation theory. For trivalent ions like Al3+, Fe3+, and Cr3+, hydrolyzed species adsorb in increasing amounts as pH is increased. Instead of exhibiting a random distribution, these ions reveal intricate lateral ordering and eventually evolve into an ordered ion network. Upon further pH increase, the ion network undergoes a transition to a discontinuous film with a persistent network of gaps. The links between the surface nanostructure and local surface charge were investigated using three-dimensional fast force mapping (3D FFM) and complementary streaming potential apparatus (SPA) measurements. As films form, an inversion from negative to positive zeta potential on mica is observed through SPA and is accompanied by the appearance of a long-range tip-sample forces through 3D FFM. These findings suggest that electrostatic interactions between positively charged ions/films and a negatively charged substrate stabilize the surface nanostructure. Furthermore, films created by trivalent ions are more strongly charged compared to those formed by divalent ions.The lateral structure at mica-electrolyte interfaces was simulated using a charge-frustrated lattice gas model, where the ions experience competing interactions between short-range chemical bonding and long-range electrostatic forces. For weak charge effects, the film undergoes a first-order transition from sparse adsorbates to large continuous sheets, aligning with the behavior observed with divalent ions. When the charge effect is sufficiently strong, the surface forms various states, including ordered patterns of ions, ion clusters, and microphase-separated partial films, corresponding to the behavior observed with trivalent ions. This study provides molecular-level understanding of how electric fields control the spontaneous formation of interfacial nanostructures, and offers valuable insights into using electric fields to control crystallization processes for the development of functional materials.

Electrified Nano-Gaps Under AC Field: A Molecular Dynamics Study

Solid-Liquid Interfaces (SLIs) hold immense significance in various areas such as materials science, chemistry, physics, biology and medicine [1]. Many studies aim to decipher the molecular details of SLIs through analytical, computational or experimental methods [2]-[3], each optimized for different aspects of SLIs. Analytical methods are mainly based on the mean field approximation and work best for dilute solutions. Computational methods are bound by their maximum accessible time and length scales, while the limitation of experimental approach tend to lie in minimum values accessible of these scales. The concomitant deployment of both the approaches is a powerful tool in studying SLIs.In the current study both the computational and experimental tools are employed to study the interface of silica with aqueous saline solutions under electric fields. Molecular Dynamics (MD) simulation are utilized to investigate the relative response of the ions and waters exposed to an external AC field in a nanoscale silica-elecrolyte-gold system. Complementary experimental measurements are conducted with atomic force microscopy (AFM) which measures the dielectric force exerted on the nanoscale AFM probe. The impact of external factors such as salt concentration, AC voltage frequency and the system size is systematically investigated.Simulations reveal both the transient and stable response of water and ions as the main component of the system to the AC field. In the transient response, the water electric dipole increases monotonically with the voltage at the first cycle while it takes longer for ions to react to the field, limited by their diffusion time. When the ionic response becomes large enough to screen the field, the dipole moment of water molecules decreases and lead the phase of the applied field. The lag in the ionic response is owing to the time required for the ionic diffusion, while the lead in the water response is due to ionic lag.To obtain the stable response through MD simulation, Fourier transform was deployed with the results showing that electric dipole of ions and water have a periodic behavior with a frequency similar to the AC field and waters in lead and ions in lag. The dipole-voltage plots for ions and waters depicted an energy transfer between water and ions in each cycle. Decreasing the frequency to 10MHz, no energy exchange was observed concomitant to the removal of water lead. Besides, in the frequency range of 100MHz-200MHz in which the water phase lead reaches its maximum value, there is also a maximum in the energy exchange. Thus, there is a direct relation between the water-ion energy exchange and lead in the water response.The stable response is affected by various factors including the separation distance between the surfaces, the ionic concentration and the AC frequency. The MD observations of a decrease in the water lead and ionic lag with reducing the electrolyte gap could explain AFM measurements where the dielectric force appears to decrease for small gaps, a counter-intuitive result if bulk electrolyte properties are assumed. The simulation results also show that the sum of the electric dipole of water and ions is always in phase with the applied voltage implying that the field is totally screened by the combination of both of them. To provide the same amount of screening in larger separation distance the electric dipole of ions has to increase to counteract its larger lag which is observed in the ionic dipole values. As the ionic dipole despite water molecules are caused by translational entropy, larger ionic dipole translates to larger forces which is observed in the AFM experiments.[1] Taketoshi et al. Japanese Journal of Applied Physics (2021).[2] T. Fukuma and R. Garcia, ACS nano (2018).[3] J.M. Andanson and A. Baiker, Chemical Society Reviews (2010).

Magnetic transition magnetocaloric and supercapacitor behavior in synthesized Sn0.6Mn0.1Ge0.3Te alloys

This study comprehensively investigates the structural, microstructural, vibrational, magnetic, and magnetocaloric properties of novelty Sn0.6Mn0.1Ge0.3Te alloys synthesized using the sealed tube solid-state reaction method. The observed magnetic behavior showcases a transition from paramagnetic (PM) to ferromagnetic (FM) phases at the Curie temperature TC = 29 K. Notably, magnetic entropy change (−ΔSM), relative cooling power (RCP), and refrigerant capacity (RC) are calculated as 1.5 J/kg-K, 42.05 J/kg, and 37.39 J/kg, respectively, under a magnetic field of 60 kOe. Arrott curve analysis further validates the magnetic phase transition, affirming a second-order transition between FM and PM phases. Critical exponents (β, γ, and δ) are derived from field-dependent magnetic entropy changes around the second-order transition and strongly agree with the mean field model. These critical exponents establish a clear correlation between critical behavior and magnetocaloric effects, reinforcing the potential of Sn0.6Mn0.1Ge0.3Te alloys for magnetocaloric applications. Investigations into the electrochemical properties of the alloy have indicated that it exhibits a specific capacitance of 152.9 F/g at a scan rate of 20 mV/s, demonstrating a predominantly pseudocapacitive charge storage mechanism. Additionally, the alloy has proven to be highly stable, retaining 94.2 % of its specific capacitance after 10,000 cycles.

Correlation equalities and some upper bounds for the coupling constant implying area decay of Wilson loop for Z 3 lattice gauge theories

Correlation identities are obtained for a Z 3 lattice gauge theory where the bonds of the plaquettes are decorated by generalized three-state Ising variables. Making use of correlation inequalities, we obtain rigorous bounds to the area decay of the Wilson loop observable in a range of the coupling parameter larger than those obtained from mean field theory considerations.

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.

Climate storylines as a tool for interdisciplinary dialogue on risk decision-making: Analyzing a severe drought in southeastern South America

Recently, we are witnessing a growing interest in the study of climate narratives and storylines. These are seen as critical tools both for improving shared understandings involving different stakeholders (including scientists from different disciplines) and guiding initiatives for transformative adaptation actions and decision making. This paper approaches the storylines about a severe drought event that took place in southeastern South America (SESA) in 2008/2009 from an interdisciplinary dialogue between climatologists and anthropologists. This approach responds to the need for a more robust understanding of the event and the responses adopted locally, i.e: not restricted to physical aspects but considering socio-economic and political aspects, with the aim of contributing to the development of socially relevant climatic information for realistic climate risk decision making contexts. In particular it intends to contribute to the decision-making processes of government agencies focused on climate communication and public climate services, such as national and weather services and regional agencies. Considering disciplinary differences, we account for the interpretative polyphony regarding this event, i.e.: what each actor/sector is talking about (for what and to whom they are talking about) when referring to "the drought", and analyze climate storylines as an agonistic field of meanings. This implies recognizing the disputes and contradictions among them, how different storylines promote certain lines of argumentation and meanings to the detriment of others, knowledge gaps, the role of social power relations, socio-political order factors and their impact in terms of the necessary transformations towards an environmentally sustainable and socially just horizon.

Atomristor Mott Theory of Sn Adatom Adlayer on a Si Surface

We use a combination of density functional theory (DFT) and dynamical mean field theory (DMFT) to unveil orbital field-induced electronic structure reconstruction of the atomic Sn layer deposited onto a Si(111) surface (Sn/Si(111)−3×3R30∘), also referred to as α-Sn. Our DFT + DMFT results indicate that α-Sn is an ideal testing ground to explore electric field-driven orbital selectivity and Mott memory behavior, all arising from the close proximity of α-Sn to metal insulator transitions. We discuss the relevance of orbital phase changes for α-Sn in the context of the current–voltage (I−V) characteristic for future silicon-based metal semiconductor atomristors.

First-principles investigation of lanthanides diffusion in HCP zirconium via vacancy-mediated transport

The diffusion of lanthanide fission products plays an important role in the growth of the fuel-cladding chemical interaction (FCCI) region in metallic fuels. The use of a Zr interdiffusion barrier may mitigate the transport of lanthanides from the fuel to the cladding, but the efficacy of such a liner is not yet known. In this paper, the stability and vacancy-mediated diffusion of La, Ce, Pr, and Nd in hexagonal close-packed (HCP) Zr is investigated via density functional theory (DFT) calculations and self-consistent mean field (SCMF) analysis. DFT is used to calculate the formation, binding, and migration energies of vacancies and vacancy-solute pairs. The DFT energetics are used in the KineCluE code to calculate the Onsager transport coefficients. La is found to be the fastest diffusing species in HCP Zr and experiences an almost isotropic diffusion behavior. The other three species (Ce, Pr, and Nd) demonstrate anisotropic diffusion where the diffusion in the basal planes is significantly faster than that along the c-axis. The calculated lanthanide diffusivities in HCP Zr are fitted to an Arrhenius relation and the activation energies and prefactors are reported for the first time. Furthermore, the vacancy drag and the segregation tendencies were analyzed using the calculated off-diagonal transport coefficients. According to our vacancy-mediated diffusion model, lanthanides are expected to be enriched at vacancy sinks at low temperatures, while at high temperatures, lanthanides are depleted at sinks and will preferably diffuse into the bulk. The enrichment/depletion transition temperature depends on the diffusion direction (basal or axial) and hence will be controlled by the grain texture and orientation.