Mean Field Research Articles

A mean field game model of green economy

A mean field game model of green economy

Trends of nuclear matter and neutron-star observables post CREX-PREX-II results within the relativistic mean field model

Trends of nuclear matter and neutron-star observables post CREX-PREX-II results within the relativistic mean field model

The MDW Hα Sky Survey: Data Release 0

The Mittelman–di Cicco–Walker (MDW) Hα Sky Survey is an autonomously operated and ongoing all-sky imaging survey in the narrowband Hα wavelength. The survey was founded by amateur astronomers and is presented here in its first stage of refinement for rigorous scientific use. Each field is exposed through an Hα filter with a 3 nm bandwidth for a total of 4 hr, with a pixel scale of 3.″2. Here, we introduce the first Data Release of the MDW Hα Survey (Data Release 0, or DR0), spanning 238 fields in the region of Orion (∼3100 deg2). DR0 includes: calibrated mean fields, star-removed mean fields, a point-source catalog matched to Data Release 1 of the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS1) and the Isaac Newton Telescope Galactic Plane Survey (IGAPS), and mosaics. 3 3 DR0 components are available at http://mdw.astro.columbia.edu; the DR0 catalog can also be found on the AAS Journals Zenodo repository: doi:10.5281/zenodo.12747455.

Pairing phase favored by magnetic frustration.

The interplay between magnetic frustration and pairing is investigated by adopting a BCS-like pairing mechanism on the frustrated $J_1-J_2$ Ising model on the square lattice. The ground-state and thermal phase transitions of the model are analyzed using a fermionic formulation within a cluster mean-field method. In this approach, the lattice system is divided into identical clusters, where the intracluster dynamic is exactly solved, and the intercluster interactions are replaced by self-consistent mean fields. We introduce a framework with two pairing couplings: an intracluster local coupling, $g$, which controls the electron pairing and its mobility within the clusters, and an intercluster coupling, $g'$, which adjusts the pairing mechanism between clusters. Tuning $g'/g$ allows evaluating how the pairing phase evolves from a weak pairing coupling between clusters (clustered system) to a strong one ($g' \rightarrow g$, homogeneous system). In the range $0 \le g'/g \le 1$, we find that a gradual increase in $g'/g$ favors the pairing phase and induces a change in criticality. In particular, our results reveal the presence of tricriticality for a certain range of $g'/g$. In addition, an increase in competing magnetic interactions weakens the magnetic orders, causing the pairing phase to occur at lower strengths of pairing interactions, especially when $g' = g$. Therefore, our findings support that magnetic frustration favors the pairing phase, contributing to the onset of a superconducting state.

Role of harmonic and anharmonic interactions in controlling the cooperativity of spin-crossover molecular crystals

We present a theoretical model of spin transitions in homogeneous spin-crossover (SCO) materials, based on the description of the interactions between SCO molecules by the Lennard-Jones potential in which the equilibrium distances depend on the spin states of the linked molecules. By expanding the potential to order 3 considering a homogeneous lattice spacing, we demonstrate that the present model is isomorphic with an Ising-like model combining infinite long-range “ferromagnetic-like” interactions, competing with short-range “antiferromagnetic-like” between nearest neighbors in the case of harmonic interactions. When an anharmonic contribution is included, the short-range interaction becomes dependent on the average high-spin fraction, and changes its sign along the spin transition. The thermodynamic properties of the model were first investigated analytically in mean field approximation for both harmonic and anharmonic cases, for which we clarify the conditions for obtaining gradual and first-order transitions. Moreover, we demonstrated that within this approximation, the strength of the antiferromagnetic-like interactions are insufficient to produce multistep transitions. In contrast, the resolution of the previous emerging Ising-like model by Monte Carlo simulations demonstrated the possibility of obtaining gradual, first-order and two-step transitions as a result of the antagonism between long- and short-range interactions. Overall, the obtained results demonstrate the suitability of the present theoretical model to describe cooperative SCO materials. The key message of our paper is that our model can be used to predict complex behavior of spin-crossover crystals. Published by the American Physical Society 2024

Mean field games with major and minor agents: the limiting problem and Nash equilibrium

In this paper, we consider a mean field game (MFG) with a major and N minor agents. We first consider the limiting problem and allow the coefficients to vary with the conditional distribution in a nonlinear way. We use the stochastic maximum principle to transform the limiting control problem into a system of two coupled conditional distribution dependent forward–backward stochastic differential equations (FBSDEs), and prove the existence and uniqueness result of the FBSDEs when the dependence between major agent and minor agents is sufficiently weak. We then use the solution of the limiting problem to construct an O ( N − 1 2 ) -Nash equilibrium for the MFG with a major and N minor agents.

Long-Run Behavior and Convergence of Dynamic Mean Field Equilibria

AbstractWe study the behavior of dynamic equilibria in mean field games with large time horizons in a dynamic consumer choice model. We show that if the stationary equilibrium in the associated infinite horizon game is unique, the dynamic equilibria of the finite horizon games converge to the stationary equilibrium of the infinite horizon game as the time horizon tends to infinity. If the stationary equilibrium is not unique, however, the situation becomes more involved. In this case, we show that in addition to convergence to the stationary equilibria, in the long run, the dynamic equilibria circle around randomized stationary equilibria for certain choices of boundary data.

Numerical Analysis of the Projection Dynamics and Their Associated Mean Field Control

Numerical Analysis of the Projection Dynamics and Their Associated Mean Field Control

Dark energy effects on surface gravitational redshift and Keplerian frequency of neutron stars

Research on the properties of neutron stars with dark energy is a particularly interesting yet unresolved problem in astrophysics. We analyze the influence of dark energy on the equation of state, the maximum mass, the surface gravitational redshift and the Keplerian frequency for the traditional neutron star and the hyperon star matter within the relativistic mean field theory, using the GM1 and TM1 parameter sets by considering the two flavor symmetries of SU(6) and SU(3) combined with the observations of PSR J1614-2230, PSR J0348+0432, PSR J0030+0451, RX J0720.4-3125, and 1E 1207.4-5209. It is found that the existence of dark energy leads to the softened equations of the state of the traditional neutron star and the hyperon star. The radius of a fixed-mass traditional neutron star (or hyperon star) with dark energy becomes smaller, which leads to increased compactness. The existence of dark energy can also enhance the surface gravitational redshift and the Keplerian frequency of traditional neutron stars and hyperon stars. The growth of the Keplerian frequency may cause the spin rate to speed up, which may provide a possible way to understand and explain the pulsar glitch phenomenon. Specifically, we infer that the mass and the surface gravitational redshift of PSR J1748-2446ad without dark energy for the GM1 (TM1) parameter set are 1.141 M ⊙ (1.309 M ⊙) and 0.095 (0.105), respectively. The corresponding values for the GM1 (TM1) parameter set are 0.901 M ⊙ (1.072M ⊙) and 0.079 (0.091) if PSR J1748-2446ad contains dark energy with α = 0.05. PSR J1748-2446ad may be a low-mass pulsar with a lower surface gravitational redshift under our selected models.

Effect of forced lateral vibration on flow and heat transfer performance within an annular fuel element

The investigation into the thermo-hydraulic characteristics of fuel elements under forced vibration conditions is of paramount importance in the design and application of offshore nuclear power platforms. This study employs a mathematical model of fluid-solid coupling and applies the theory of multi-field synergy to numerically analyze the flow and heat transfer features in an annular fuel element with internal and external double-sided cooling under forced lateral vibration conditions. The synergistic relationship of each flow field parameter is scrutinized for vibration conditions with frequencies ranging from 0 to 10 Hz and amplitudes from 0.005 to 0.2 m. The results demonstrate that increased amplitude and frequency contribute to enhancing the homogeneity of the temperature and velocity field distributions. Notably, the field synergy angles α, β, ψ, and γ attain minimal values at the gaps (X = 8 mm, X = 25 mm). Furthermore, the variation of vibration frequency and amplitude decreases the mean synergistic angle ψ by 5.14 % and 7.9 % and increases the mean field synergistic angle θ by 23.18 % and 31.21 %, respectively. It indicates that the vibration parameters have the least effect on the synergistic angle ψ and the greatest effect on the synergistic angle θ.

Modified Debye-Hückel-Onsager theory for electrical conductivity in aqueous electrolyte solutions: Account of ionic charge nonlocality.

This paper presents a mean field theory of electrolyte solutions, extending the classical Debye-Hückel-Onsager theory to provide a detailed description of the electrical conductivity in strong electrolyte solutions. The theory systematically incorporates the effects of ion specificity, such as steric interactions, hydration of ions, and their spatial charge distributions, into the mean-field framework. This allows for the calculation of ion mobility and electrical conductivity, while accounting for relaxation and hydrodynamic phenomena. At low concentrations, the model reproduces the well-known Kohlrausch's limiting law. Using the exponential (Slater-type) charge distribution function for solvated ions, we demonstrate that experimental data on the electrical conductivity of aqueous 1:1, 2:1, and 3:1 electrolyte solutions can be approximated over a broad concentration range by adjusting a single free parameter representing the spatial scale of the nonlocal ion charge distribution. Using the fitted value of this parameter at 298.15K, we obtain good agreement with the available experimental data when calculating electrical conductivity across different temperatures. We also analyze the effects of temperature and electrolyte concentration on the relaxation and electrophoretic contributions to total electrical conductivity, explaining the underlying physical mechanisms responsible for the observed behavior.

Relativistic BEC extracted from a complex FRG flow equation

Abstract Based on the functional renormalization group (FRG) under the local potential approximation, we analyze the Bose-Einstein condensation (BEC) in the relativistic complex scalar theory. This framework leads to a complex flow equation of the effective potential, even with the well-known Litim regulator. In order to evaluate the condensate from such a complex effective potential, we impose a condition between chemical potential and mass, analogously to those in the free theory or the mean field theory. We elucidate that for the strongly (weakly) coupled theory, the phase diagrams computed from the FRG are more (less) deviated from that under the mean field approximation. This result implies that quantum fluctuations strongly affect the nonperturbative formation of the BEC.

Processes Driving the Intermodel Spread of the Southern Hemisphere Hadley Circulation Expansion in CMIP6 Models

AbstractThe Hadley circulation (HC) has been expanding poleward in recent decades. The Coupled Model Intercomparison Project Phase 6 (CMIP6) models predict that the expansion will accelerate in the future, more so in the Southern Hemisphere (SH). However, the extent of the expansion varies widely among the models. We investigate the mechanisms driving the intermodel spread in SH HC expansion predictions. The intermodel spread is obtained by an empirical orthogonal function analysis on the SH HC trend patterns of 16 CMIP6 model simulations using the historical and shared socioeconomic pathway 5–8.5 scenarios. The leading mode, showing a mean meridional stream function anomaly at the poleward SH HC extent, explains 49.73% of the variance and significantly correlates (r = 0.94) with the SH HC expansion. By analyzing the extended Kuo‐Eliassen equation, we find that the intermodel difference in the representation of diabatic heating is responsible for about 14% of the intermodel spread. The meridional eddy momentum and heat fluxes contribute to about 21% and 18% of the intermodel spread, respectively. The models simulating a relatively large SH HC expansion tend to show increased precipitation in the Southern Pacific Convergence Zone, reduced baroclinic instability in the subtropics, and an enhanced poleward shift of jet stream in the midlatitudes. This suggests that the uncertainty in the HC projection may be constrained by reducing the bias in the trend of the mean fields.

G. BERKELEY & F. MATHEWS “LOGOS” ONTOLOGY

The purpose of article’s study is to discover Logos phenomenon which is present in the nature of thinking using an empirical method in the value system of F. Mathews & G. Berkeley from the point of view of modern ethics, historical experience, modern psychology and culture of ecology. “Logos” is considered as a segment of the field of thinking, a certain event in the field of meaning.The meaning of “Logos” as an event in the ontology of F. Mathews is considered from a metaphysical point of view and acquires a special semantic value in the context of G. Berkeley philosophy. In the space-time continuum, “Logos” exists in a moving field of meanings and is opposed to “Nonthought.” In the course of history, the manifestation of “Logos” was absorbed by everyday life and mediocrity, but F. Mathews and G. Berkeley are trying to prevent the disappearance of “Logos” by creating an “Ecological Model of Thinking”, revealing perception from internal semantic structures towards natural phenomena. An ecological model of thinking can prevent the formation of a “perceptual dead zone” where human genius is devalued by self-centered mediocrity. The phenomenon of the integrity of the "Logos" is an ethical expression of intuitive perception.The causes and consequences of "ontological inertia" are also revealed.

Dual symmetries of dense isotopically and chirally asymmetric QCD

In the present paper, the dual symmetries of dense quark matter phase diagram found in some massless three- and two-color NJL models in the mean field approximation have been shown to exist at a more fundamental level as dual transformations of fields and chemical potentials leaving the Lagrangian invariant. As a result, the corresponding dual symmetries of the full phase diagram can be shown without any approximation. And it has been shown not only in the NJL models, but also in framework of two- and three-color massless QCD itself. This is quite interesting, since one might say that it is not very common to show something completely non-perturbatively in QCD.

Block approximations for probabilistic mixtures of elementary cellular automata

Probabilistic Cellular Automata are a generalization of Cellular Automata. Despite their simple definition, they exhibit fascinating and complex behaviours. The stationary behaviour of these models changes when model parameters are varied, making the study of their phase diagrams particularly interesting. The block approximation method, also known in this context as the local structure approach, is a powerful tool for studying the main features of these diagrams, improving upon Mean Field results. This work considers systems with multiple stationary states, aiming to understand how their interactions give rise to the structure of the phase diagram. Additionally, it shows how a simple algorithmic implementation of the block approximation allows for the effective study of the phase diagram even in the presence of several absorbing states.

Mean field responses in disordered systems: an example from nonlinear MHD

Understanding the generation of large-scale magnetic fields and flows in magnetohydro-dynamical (MHD) turbulence remains one of the most challenging problems in astrophysical fluid dynamics. Although much work has been done on the kinematic generation of large-scale magnetic fields by turbulence, relatively little attention has been paid to the much more difficult problem in which fields and flows interact on an equal footing. The aim is to find conditions for long-wavelength instabilities of stationary MHD states. Here, we first revisit the formal exposition of the long-wavelength linear instability theory, showing how long-wavelength perturbations are governed by four mean field tensors; we then show how these tensors may be calculated explicitly under the ‘short-sudden’ approximation for the turbulence. For MHD states with relatively little disorder, the linear theory works well: average quantities can be readily calculated, and stability to long-wavelength perturbations determined. However, for disordered basic states, linear perturbations can grow without bound and the purely linear theory, as formulated, cannot be applied. We then address the question of whether there is a linear response for sufficiently weak mean fields and flows in a dynamical (nonlinear) evolution, where perturbations are guaranteed to be bounded. As a preliminary study, we first address the nature of the response in a series of one-dimensional maps. For the full MHD problem, we show that in certain circumstances, there is a clear linear response; however, in others, mean quantities – and hence the nature of the response – can be difficult to calculate.

Improvement of the Low-Energy Adaptive Clustering Hierarchy Protocol in Wireless Sensor Networks Using Mean Field Games.

The Low-Energy Adaptive Clustering Hierarchy (LEACH) protocol is a widely used method for managing energy consumption in Wireless Sensor Networks (WSNs). However, it has limitations that affect network longevity and performance. This paper presents an improved version of the LEACH protocol, termed MFG-LEACH, which incorporates the Mean Field Game (MFG) theory to optimize energy efficiency and network lifetime. The proposed MFG-LEACH protocol addresses the imbalances in energy consumption by modeling the interactions among nodes as a game, where each node optimizes its transmission energy based on the collective state of the network. We conducted extensive simulations to compare MFG-LEACH with Enhanced Zonal Stable Election Protocol (EZ-SEP), Energy-Aware Multi-Hop Routing (EAMR), and Balanced Residual Energy routing (BRE) protocols. The results demonstrate that MFG-LEACH significantly reduces energy consumption and increases the number of packets received across different node densities, thereby validating the effectiveness of our approach.

Respective Roles of Electron-Phonon and Electron-Electron Interactions in the Transport and Quasiparticle Properties of SrVO_{3}.

The spectral and transport properties of strongly correlated metals, such as SrVO_{3} (SVO), are widely attributed to electron-electron (e-e) interactions, with lattice vibrations (phonons) playing a secondary role. Here, using first-principles electron-phonon (e-ph) and dynamical mean field theory calculations, we show that e-ph interactions play an essential role in SVO: they govern the electron scattering and resistivity in a wide temperature range down to 30K, and induce an experimentally observed kink in the spectral function. In contrast, the e-e interactions control quasiparticle renormalization and low temperature transport, and enhance the e-ph coupling. We clarify the origin of the near T^{2} temperature dependence of the resistivity by analyzing the e-e and e-ph limited transport regimes. Our work disentangles the electronic and lattice degrees of freedom in a prototypical correlated metal, revealing the dominant role of e-ph interactions in SVO.

Spontaneous Magnetization Induced by Antiferromagnetic Toroidal Ordering.

The magnetic toroidal dipole moment, which is induced by a vortex-type spin texture, manifests itself in parity-breaking physical phenomena, such as a linear magnetoelectric effect and nonreciprocal transport. We elucidate that a staggered alignment of the magnetic toroidal dipole can give rise to spontaneous magnetization even under antiferromagnetic structures. We demonstrate the emergence of uniform magnetization by considering the collinear antiferromagnetic structure with the staggered magnetic toroidal dipole moment on a bilayer zigzag chain. Based on the model calculations, we show that the interplay between the collinear antiferromagnetic mean field and relativistic spin-orbit coupling plays an important role in inducing the magnetization.