Mean Field Research Articles

Evaluation of a New Approach for Entrainment and Detrainment Rate Estimation

AbstractEntrainment and detrainment rates (ε and δ) constitute the most critical free parameters in mass flux schemes commonly employed for cumulus parameterizations. Recently, Zhu et al. (2021) introduced a new approach that utilizes aircraft observations to simultaneously estimate ε and δ for cumulus clouds, overcoming the limitation of other observation‐based approaches that solely yield ε without offering insights into δ. This study aims to comprehensively evaluate the reliability of this new approach. First, evaluation using an Explicit Mixing Parcel Model demonstrates the capability of the new approach to back‐calculate predetermined ε and δ based on the physical properties before and after the entrainment mixing. Second, evaluation using large‐eddy simulations illustrates that the new approach yields consistent ε and δ profiles compared to the traditional approach. Sensitivity tests indicate a weak sensitivity of the estimated δ with the new approach to the entrained air source. A decrease in the proportion of cloudy air in the assumed detrained air leads to a reduction in the estimated δ, while ε remains unaffected. Finally, the most appropriate assumptions for entrained and detrained air are discussed. Estimating ε for cumulus parameterizations involves acquiring ambient air more than 500 m away from the cloud edge as entrained air. Due to implicit mean field approximations in the traditional approach, determining the optimal assumption for detrained air properties proves challenging. This study confirms the reliability of the new approach in estimating ε and δ, providing confidence in its application to extensive observational data and advancement in parameterization.

Exact Numerical Solution of the Fully Connected Classical and Quantum Heisenberg Spin Glass.

We present the mean field solution of the quantum and classical Heisenberg spin glasses, using the combination of a high precision numerical solution of the Parisi full replica symmetry breaking equations and a continuous time quantum MonteCarlo algorithm. We characterize the spin glass order and its low-energy excitations down to zero temperature. The Heisenberg spin glass has a rougher energy landscape than its Ising analog, and exhibits a very slow temperature evolution of its dynamical properties. We extend our analysis to the doped, metallic Heisenberg spin glass, which displays unexpectedly slow spin dynamics, reflecting the proximity to the melting quantum critical point and its associated Sachdev-Ye-Kitaev Planckian dynamics.

Free boundary regularity and support propagation in mean field games and optimal transport

We study the behavior of solutions to the first-order mean field games system with a local coupling, when the initial density is a compactly supported function on the real line. Our results show that the solution is smooth in regions where the density is strictly positive, and that the density itself is globally continuous. Additionally, the speed of propagation is determined by the behavior of the cost function near small values of the density. When the coupling is entropic, we demonstrate that the support of the density propagates with infinite speed. On the other hand, for a power-type coupling, we establish finite speed of propagation, leading to the formation of a free boundary. We prove that under a natural non-degeneracy assumption, the free boundary is strictly convex and enjoys C1,1 regularity. We also establish sharp estimates on the speed of support propagation and the rate of long time decay for the density. Moreover, the density and the gradient of the value function are both shown to be Hölder continuous up to the free boundary. Our methods are based on the analysis of a new elliptic equation satisfied by the flow of optimal trajectories. The results also apply to mean field planning problems, characterizing the structure of minimizers of a class of optimal transport problems with congestion.

A mean field analysis of the role of indirect transmission in emergent infection events

We developed a mathematical model to investigate the role of indirect transmission in the spread of infectious diseases, using the illustrative example of sarcoptic mange as a case study. This disease can be transmitted through direct contact between an infected host and a susceptible one, or indirectly when potential hosts encounter infectious mites and larvae deposited in the environment, commonly referred to as fomites. Our focus is on exploring the potential of these infectious reservoirs as triggers for emerging infection events and as stable reservoirs of the disease. To achieve this, our mean field compartmental model incorporates the epidemiological dynamics driven by indirect transmission via fomites. We identify different types of dynamics that the system can go into, controlled by different levels of direct and indirect transmission. Among these, we find a new regime where the disease can emerge and persist over time solely through fomites, without the necessity for direct transmission. This possibility of the system reveals an evolutionary pathway that could enable the parasite to enhance its fitness beyond host co-evolution. We also define a new threshold based on an effective reproductive number, that enables us to predict the conditions for disease persistence. Our model allows us to assess the potential effectiveness of various disease intervention measures by incorporating a feature observed in real systems. We hope this contributes to a better understanding of infectious disease outbreaks.

A mean field analysis of the role of indirect transmission in emergent infection events

We developed a mathematical model to investigate the role of indirect transmission in the spread of infectious diseases, using the illustrative example of sarcoptic mange as a case study. This disease can be transmitted through direct contact between an infected host and a susceptible one, or indirectly when potential hosts encounter infectious mites and larvae deposited in the environment, commonly referred to as fomites. Our focus is on exploring the potential of these infectious reservoirs as triggers for emerging infection events and as stable reservoirs of the disease. To achieve this, our mean field compartmental model incorporates the epidemiological dynamics driven by indirect transmission via fomites. We identify different types of dynamics that the system can go into, controlled by different levels of direct and indirect transmission. Among these, we find a new regime where the disease can emerge and persist over time solely through fomites, without the necessity for direct transmission. This possibility of the system reveals an evolutionary pathway that could enable the parasite to enhance its fitness beyond host co-evolution. We also define a new threshold based on an effective reproductive number, that enables us to predict the conditions for disease persistence. Our model allows us to assess the potential effectiveness of various disease intervention measures by incorporating a feature observed in real systems. We hope this contributes to a better understanding of infectious disease outbreaks.

Induced cosmological anisotropies and CMB anomalies by a non-abelian gauge-gravity interaction

We present a non-abelian cousin of the model presented in Lee et al. (2024) which induces cosmological anisotropies on top of standard FLRW geometry. This is in some sense doing a cosmological mean field approximation, where the mean field cosmological model under consideration would be the standard FLRW, and the induced anisotropies are small perturbative corrections on top of it. Here we mostly focus on the non-abelian SU(2) gauge fields coupled to the gravity to generate the anisotropies, which can be a viable model for the axion-like particle (ALP) dark sector. The induced anisotropies are consequences of the non-trivial back-reaction of the gauge fields on the gravity sector, and by a clever choice of the parametrization, one can generate the Bianchi model we have studied in this note. We also show that the anisotropies influence the Sachs-Wolfe effect and we discuss the implications.

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.

The dynamical analysis of simplicial SAIS epidemic model with awareness programs by media

In this paper, we propose an SAIS epidemic model with awareness programs by media on higher-order networks to study the impact of media and higher-order networks on disease transmission, in which the simplicial complex is utilized to construct a social network that describes connections between nodes, where a single link can connect more than two individuals. We use the cumulative density of awareness programs to quantify the impact of media and use the Microscopic Markov Chains method to get the probability evolution equation of each node. In order to solve the computational difficulties caused by the excessively high dimension of the equation, we use the mean field method to reduce the dimension of the equation to get the equilibrium of the system. Through dynamical analysis, we obtain the threshold of disease outbreak and conditions for the existence and stability of the disease-free equilibrium and the endemic equilibrium. The numerical simulations of SAIS model prove that the mean field method has good predictive performance. We also obtaine the influence of parameters on threshold and system dynamical behavior through sensitivity analysis. The results show that: on one hand, the introduce of 2-simplex increases the probability of disease transmission in healthy populations, and the system appears discontinuous transition and bistable coexistence of health state and disease epidemic state, on the other hand, awareness programs by media can increase the threshold of disease outbreak, decrease the final density of infected individuals and inhibit the explosive growth of disease, thus effectively control the spread of diseases.

Cryogenic temperature magnetocaloric effect and critical behavior of GdDyErAlM (M=Fe, Co, Ni) high entropy amorphous alloys

High entropy amorphous alloys (HE AMs) have attracted extensive interest lately due to their superior magnetocaloric properties. However, the critical behavior and mechanical properties have received less research, which restricts their applications. This work presented a comprehensive investigation of the magnetocaloric effect (MCE), critical behavior, and mechanical performance of quinary Gd20Dy20Er20Al20M20 (M=Fe, Co, Ni) HE AMs. All samples exhibited distinct spin glass-like behavior below TC and competitive MCE around hydrogen liquefaction temperature range. Excellent MCE was achieved by the HE AMs through a second-order phase transition from paramagnetic state to ferromagnetic state at 79 K for Fe, 41 K for Co, and 36 K for Ni. Among them, the maximum magnetic entropy change (-ΔSM)max of Gd20Dy20Er20Al20Co20 amorphous alloys was 9.59 J kg-1 K-1 under 0-5 T. Furthermore, RC and RCP of Gd20Dy20Er20Al20Fe20 amorphous alloys were respectively 519 J kg-1 and 613 J kg-1, larger than that of most RE-based amorphous alloys. For all samples, the critical behavior of the phase transition approached the mean field model, and this responded to the long-range ordering of the magnetic interaction. The bending plasticity of Gd20Dy20Er20Al20M20 (M=Fe, Co, Ni) HE AMs were 0.78, 1.03, 0.89, respectively. The adjustable Tc, large (-ΔSM), high RCP, and outstanding mechanical properties suggested Gd20Dy20Er20Al20M20 (M=Fe, Co, Ni) HE AMs may find utility as magnetic refrigerants in low-temperature applications.

Magnetorotational dynamo can generate large-scale vertical magnetic fields in 3D GRMHD simulations of accreting black holes

ABSTRACT Jetted astrophysical phenomena with black hole engines, including binary mergers, jetted tidal disruption events, and X-ray binaries, require a large-scale vertical magnetic field for efficient jet formation. However, a dynamo mechanism that could generate these crucial large-scale magnetic fields has not been identified and characterized. We have employed three-dimensional global general relativistic magnetohydrodynamical simulations of accretion discs to quantify, for the first time, a dynamo mechanism that generates large-scale magnetic fields. This dynamo mechanism primarily arises from the non-linear evolution of the magnetorotational instability (MRI). In this mechanism, large non-axisymmetric MRI-amplified shearing wave modes, mediated by the axisymmetric azimuthal magnetic field, generate and sustain the large-scale vertical magnetic field through their non-linear interactions. We identify the advection of magnetic loops as a crucial feature, transporting the large-scale vertical magnetic field from the outer regions to the inner regions of the accretion disc. This leads to a larger characteristic size of the, now advected, magnetic field when compared to the local disc height. We characterize the complete dynamo mechanism with two time-scales: one for the local magnetic field generation, $t_{\rm gen}$, and one for the large-scale scale advection, $t_{\rm adv}$. Whereas the dynamo we describe is non-linear, we explore the potential of linear mean field models to replicate its core features. Our findings indicate that traditional $\alpha$-dynamo models, often computed in stratified shearing box simulations, are inadequate and that the effective large-scale dynamics is better described by the shear current effects or stochastic $\alpha$-dynamos.

Instrumentation for TMS‐EEG Experiment: ArTGen and a Custom EEG Interface

ABSTRACTIn transcranial magnetic stimulation (TMS) and electroencephalography (EEG) experiments, two researchers typically collaborate in the lab. This study addresses the challenge a single researcher faces in managing the TMS experiment's timing while operating the TMS coil. It introduces the Arduino Trigger Generator (ArTGen) to remotely control the timing of TMS experiments using a footswitch pedal. Moreover, a bespoke printed circuit board (PCB) is designed to interface the eegoMylab amplifier with off‐the‐shelf EEG caps. The ArTGen facilitates accurate timing of the TMS stimulator's inter‐pulse intervals (IPIs) through a footswitch pedal, enhancing researchers' control over TMS‐EEG experiments. The PCB interface provides a cost‐effective tool to extend the functionality of the eegoMylab amplifier. The integration of our PCB interface has been validated in a custom TMS‐EEG setup by analyzing TMS‐evoked potentials (TEPs), global mean field power (GMFP), butterfly plots, and event‐related spectral potentials (ERSPs). The PCB reliably preserved EEG signal integrity, ensuring accurate data acquisition. Thorough channel‐wise consistency checks across components confirmed data accuracy. ArTGen's portability and footswitch feature streamline experimental control, aiding TMS‐EEG research and clinical applications. Moreover, our PCB resolves compatibility between the eegoMylab amplifier and the Waveguard EEG cap by extending the amplifier to connect to off‐the‐shelf EEG caps. The ArTGen serves as a robust remote control tool for TMS stimulators, while our PCB interface presents a solution for integrating a customized TMS‐EEG setup. This study addresses the gap in existing TMS‐EEG research by introducing innovative technological enhancements that not only augment experimental flexibility but also streamline procedural workflows.

Convexification Numerical Method for the Retrospective Problem of Mean Field Games

Convexification Numerical Method for the Retrospective Problem of Mean Field Games

Mode analysis of spin field of thermal atomic ensembles

The spin dynamics in a thermal atomic vapor cell have been investigated thoroughly over the past decades and have proven to be successful in quantum metrology and memory owing to their long coherent time and manipulation convenience. The existing mean field analysis of spin dynamics among the whole cell is sometimes inaccurate due to the non-uniformity of the ensemble and spatial coupling of multi-physical fields interacting with the ensembles. Here we perform mode analysis onto the quasi-continuous spin field including atomic thermal motion to derive Bloch mode equations and obtain corresponding analytical solutions in diffusion regime. We demonstrate that the widely used mean field dynamics of thermal gas is a particular case in our solution, corresponding to the uniform spatial mode. This mode analysis approach offers a precise method for analyzing the dynamics of the spin ensemble in greater detail from a field perspective, enabling the effective determination of spatially non-uniform multi-physical fields coupling with the spin ensembles, which cannot be accurately analyzed by the mean field method. Furthermore, this work paves the way to address quantum noises and relaxation mechanisms associated with non-uniform fields and inter-atomic interactions, which limit further improvement of ultra-sensitive spin-based sensors.

Mean Field Games in a Stackelberg Problem with an Informed Major Player

Mean Field Games in a Stackelberg Problem with an Informed Major Player

Insight into structural, electronic, optoelectronic, dynamic, elastic, thermal and magnetic properties of pure and doped LiMgSb by nitrogen: Ab-initio calculations

In this work, ab-initio simulation has been conducted to explore and compare various properties, structural, electronic, optoelectronic, dynamic, elastic and magnetic of the pure bulk unit cell of LiMgSb and substituted by nitrogen (N). Herein, we have optimized the lattice parameter of the structure using the both approximations, generalized gradient approximation (GGA) and self-interaction correction (SIC), finding values of 6.9 and 6.7 Å, respectively. Additionally, the undoped system exhibits characteristics of a non-magnetic P-type semiconductor. The forbidden band of the compound is an indirect one at Γ-X points, aligning with existing literature, and measuring 0.742 eV and 0.95 eV under the GGA and SIC approximations, respectively. We have also investigated how the bandgap varies with the lattice parameter to analyze the influence of atomic interactions on the electronic band structure. Further analyses include the calculation of the energy photon wavelength and refractive index corresponding to the pure LiMgSb band gap. The electronic and dynamic stabilities of the compound have been confirmed through calculations of formation energies and phonon dispersion and total density of states. The bulk modulus, elastic constants, Debye temperature and melting temperature have been determined, indicating elastic stability of the system. Moreover, substitution doping the compound with N in different antisites positions with various concentrations has revealed ferromagnetic stability in Li1-xNxMgSb and LiMg1-xNxSb. Emphasis has been placed on the half-metallic behavior of the doped alloys, with an estimation of the Curie temperature utilizing mean field theory. Hence, the predicted compounds hold potential for multifaceted applications in spintronics and optoelectronics.

A Mean Field to Capture Asynchronous Irregular Dynamics of Conductance-Based Networks of Adaptive Quadratic Integrate-and-Fire Neuron Models.

Mean-field models are a class of models used in computational neuroscience to study the behavior of large populations of neurons. These models are based on the idea of representing the activity of a large number of neurons as the average behavior of mean-field variables. This abstraction allows the study of large-scale neural dynamics in a computationally efficient and mathematically tractable manner. One of these methods, based on a semianalytical approach, has previously been applied to different types of singleneuron models, but never to models based on a quadratic form. In this work, we adapted this method to quadratic integrate-and-fire neuron models with adaptation and conductance-based synaptic interactions. We validated the mean-field model by comparing it to the spiking network model. This mean-field model should be useful to model large-scale activity based on quadratic neurons interacting with conductance-based synapses.

The fate of 17β-estradiol in snowmelt from a field with a history of manure application: A laboratory simulation and field study

17β-estradiol is a naturally occurring estrogen, and livestock manure applied to agricultural fields is a major source to the environment. Liquid swine manure is widely applied to agricultural fields in the Canadian Prairies, a region where the majority of the annual runoff occurs during a brief snowmelt period over frozen soil. Transport of estrogens from manure amendments to soil during this important hydrological period is not well understood but is critical to mitigating the snowmelt-driven offsite transport of estrogens. This study quantified the concentration and load of 17β-estradiol in snowmelt from an agricultural field with a history of manure application under manure application methods: no manure applied, manure applied on the sub-surface, and on the surface, using a laboratory simulation study with flooded intact soil cores and a field study during snowmelt. A higher concentration of 17β-estradiol was in the laboratory simulation than in the field (mean laboratory pore water = 1.65 ± 1.2 μg/L; mean laboratory flood water = 0.488 ± 0.58 μg/L; and mean field snowmelt = 0.0619 ± 0.048 μg/L). There were no significant differences among manure application methods for 17β-estradiol concentration. Laboratory pore water concentrations significantly increased over time, corresponding with changes in pH. In contrast, there was no significant change in the field snowmelt concentrations of 17β-estradiol over time. However, for both laboratory simulation experiments and field-based snowmelt experiments, mean concentrations of 17β-estradiol were higher with subsurface than surface-applied manure, and the cumulative load of 17β-estradiol was significantly higher in the sub-surface than in surface applied. The mean cumulative load from the field study across all treatments (6.91 ± 3.7 ng/m2) approximates the magnitude of 17β-estradiol that could be mobilized from manured fields. The sub-surface application of manure seems to increase the persistence of 17β-estradiol in soil, thus enhancing the potential loss to snowmelt runoff.

Comparison of Mechanical Property Simulations with Results of Limited Flexural Tests of Different Multi-Layer Carbon Fiber-Reinforced Polymer Composites.

This article is focused on the experimental study of flexural properties in different multi-layer carbon fiber-reinforced polymer (CFRP) composites and correlations with the results of finite element method (FEM) simulations of mechanical properties. The comparison of the results shows the possibility of reducing the number of experimental specimens for testing. The experimental study of flexural properties for four types of carbon fiber-reinforced polymer matrix composites with twill weaves (2 × 2) was carried out. As input materials, pre-impregnated carbon laminate GG 204 T and GG 630 T (prepreg) and two types of carbon fiber fabrics (GG 285 T and GG 300 T (fabric)) were used. Multi-layer samples were manufactured from two types of prepregs and two types of fabrics, which were hand-impregnated during sample preparation. The layers were stacked using same orientation. All specimens for flexural test were cut with the longer side in the weft direction. Pre-impregnated carbon laminates were further impregnated with resin DT 121H. Carbon fabrics were hand-impregnated with epoxy matrix LG 120 and hardener HG 700. To fulfill the aim of this research, finite element method (FEM)-based simulations of mechanical properties were performed. The FEM simulations and analysis were conducted in Hexagon's MSC Marc Mentat 2022.3 and Digimat 2022.4 software. This paper presents the results of actual experimental bending tests and the results of simulations of bending tests for different composite materials (mentioned previously). We created material models for simulations based on two methods-MF (Mean Field) and FE (Finite Element), and the comparative results show better agreement with the MF model. The composites (GG 285 T and GG 300 T) showed better flexural results than composites made from pre-impregnated carbon laminates (GG 204 T and GG 630 T). The difference in results for the hand-impregnated laminates was about 15% higher than for prepregs, but this is still within an acceptable tolerance as per the reported literature. The highest percentage difference of 14.25% between the simulation and the real experiment was found for the software tool Digimat FE 2022.4-GG 630 T composite. The lowest difference of 0.5% was found for the software tool Digimat MF 2022.4-GG 204 T composite. By comparing the results of the software tools with the results of the experimental measurements, it was found that the Digimat MF 2022.4 tool is closer to the results of the experimental measurements than the Digimat FE 2022.4 tool.

CDMFT+HFD: An extension of dynamical mean field theory for nonlocal interactions applied to the single band extended Hubbard model

We examine the phase diagram of the extended Hubbard model on a square lattice, for both attractive and repulsive nearest-neighbor interactions, using CDMFT+HFD, a combination of Cluster Dynamical Mean Field theory (CDMFT) and a Hartree-Fock mean-field decoupling of the inter-cluster extended interaction. For attractive non-local interactions, this model exhibits a region of phase separation near half-filling, in the vicinity of which we find islands of d-wave superconductivity, decaying rapidly as a function of doping, with disconnected regions of extended s-wave order at smaller (higher) electron densities. On the other hand, when the extended interaction is repulsive, a Mott insulating state at half-filling is destabilized by hole doping, in the strong-coupling limit, in favor of d-wave superconductivity. At the particle-hole invariant chemical potential, we find a first-order phase transition from antiferromagnetism (AF) to d-wave superconductivity as a function of the attractive nearest-neighbor interaction, along with a deviation of the density from the half-filled limit. A repulsive extended interaction instead favors charge-density wave (CDW) order at half-filling.

Towards parameterizing eddy-mediated transport of Warm Deep Water across the Weddell Sea continental slope

Abstract The transport of Warm Deep Water (WDW) onto the Weddell Sea continental shelf is associated with a heat flux and strongly contributes to the melting of Antarctic ice shelves. The small radius of deformation at high latitudes makes it difficult to accurately represent the eddy-driven component of onshore WDW transport in coarse-resolution ocean models so that a parameterization becomes necessary. The Gent and McWilliams/Redi (GM/Redi) scheme was designed to parameterize mesoscale eddies in the open ocean. Here, it is assessed to what extent the GM/Redi scheme can generate a realistic transport of WDW across the Weddell Sea continental slope. To this end, the eddy parameterization is applied to a coarse-resolution idealized model of the Weddell Sea continental shelf and slope, and its performance is evaluated against a high-resolution reference simulation. With the GM/Redi parameterization applied, the coarse model simulates a shoreward WDW transport with a heat transport that matches the high-resolution reference and both the hydrographic mean fields and the mean slopes of the isopycnals are improved. A successful application of the GM/Redi parameterization is only possible by reducing the GM diffusivity over the continental slope by an order of magnitude compared to the open ocean value to account for the eddy-suppressing effect of the topographic slope. When the influence of topography on the GM diffusivity is neglected, the coarse model with the parameterization either under or overestimates the shoreward heat flux. These results motivate the incorporation of slope-aware eddy parameterizations into regional and global ocean models.