Mean Field Research Articles

Induced cosmological anisotropy by a gauge-gravity interaction

We present a simple model which generates cosmological anisotropies on top of standard FLRW geometry. This is in some sense reminiscent of the mean field approximation, where the mean field cosmological model under consideration would be the standard FLRW, and the anisotropy is a small perturbative correction on top of it. Using a supergravity-inspired model, we confirm that the stable fixed point of our model corresponds to standard FLRW cosmology. We use a Bianchi VII0-type model supplemented with a scalar and U(1) gauge fields, and we show that the anisotropies of the geometry are generated by the non-trivial interaction between the gravity sector and the U(1) gauge sector. Studying the attractor flow, we show that the anisotropies are present at early times (high redshift) and decay asymptotically to an FLRW attractor fixed point. With such a mechanism, observations of non-isotropy are not contradictory to FLRW geometry or indeed the ΛCDM model. Such models could in principle shed some insights on the present cosmological tensions.

Learning Discrete-Time Major-Minor Mean Field Games

Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and cannot model major players that strongly influence other players, severely limiting the class of problems that can be handled. We propose a novel discrete time version of major-minor MFGs (M3FGs), along with a learning algorithm based on fictitious play and partitioning the probability simplex. Importantly, M3FGs generalize MFGs with common noise and can handle not only random exogeneous environment states but also major players. A key challenge is that the mean field is stochastic and not deterministic as in standard MFGs. Our theoretical investigation verifies both the M3FG model and its algorithmic solution, showing firstly the well-posedness of the M3FG model starting from a finite game of interest, and secondly convergence and approximation guarantees of the fictitious play algorithm. Then, we empirically verify the obtained theoretical results, ablating some of the theoretical assumptions made, and show successful equilibrium learning in three example problems. Overall, we establish a learning framework for a novel and broad class of tractable games.

Meta-Inverse Reinforcement Learning for Mean Field Games via Probabilistic Context Variables

Designing suitable reward functions for numerous interacting intelligent agents is challenging in real-world applications. Inverse reinforcement learning (IRL) in mean field games (MFGs) offers a practical framework to infer reward functions from expert demonstrations. While promising, the assumption of agent homogeneity limits the capability of existing methods to handle demonstrations with heterogeneous and unknown objectives, which are common in practice. To this end, we propose a deep latent variable MFG model and an associated IRL method. Critically, our method can infer rewards from different yet structurally similar tasks without prior knowledge about underlying contexts or modifying the MFG model itself. Our experiments, conducted on simulated scenarios and a real-world spatial taxi-ride pricing problem, demonstrate the superiority of our approach over state-of-the-art IRL methods in MFGs.

Constraining a relativistic mean field model using neutron star mass–radius measurements I: nucleonic models

ABSTRACT Measurements of neutron star mass and radius or tidal deformability deliver unique insight into the equation of state (EOS) of cold dense matter. EOS inference is very often done using generalized parametric or non-parametric models, which deliver no information on composition. In this paper, we consider a microscopic nuclear EOS model based on a field theoretical approach. We show that current measurements from NICER and gravitational wave observations constrain primarily the symmetric nuclear matter EOS. We then explore what could be delivered by measurements of mass and radius at the level anticipated for future large-area X-ray timing telescopes. These should be able to place very strong limits on the symmetric nuclear matter EOS, in addition to constraining the nuclear symmetry energy that determines the proton fraction inside the neutron star.

Mean Field Games Master Equations: From Discrete to Continuous State Space

Mean Field Games Master Equations: From Discrete to Continuous State Space

A manifold learning perspective on surrogate modeling of nitrate concentration in the Kansas River

Abstract A non-linear surrogate model of nitrate concentration in the Kansas River (USA) is described. The model is an (almost) Piece-wise Linear response surface that provides a mean field approximation to the dynamics of the measured data for nitrate plus nitrite (target product) correlations to turbidity and chlorophyll-a concentrations (input variables). The method extends the United States Geological Survey’s linear procedures for surrogate data modeling allowing for better approximations for river systems exhibiting algal blooms due to nutrient-rich source waters. The model and visualization procedures illustrated in the Kansas River example should be generally applicable to many medium-size rivers in agricultural regions.

Interrelationship of Electric Double Layer Theory and Microfluidic Microbial Fuel Cells: A Review of Theoretical Foundations and Implications for Performance

Microbial fuel cells and their related microfluidic systems have emerged as promising greener energy alternatives for the exploitation of avenues related to combined power and wastewater treatment operations. Moreover, the potential for their application in biosensing technology is large. However, while the fundamental principles of science that govern the design and operation of microbial fuel cells (MFCs) and microfluidic microbial fuel cells (MMFCs) are similar to those found in colloid science, the literature shows that current research lacks sufficient reference to the electrostatic and electrokinetic aspects, focusing mostly on aspects related to the architecture, design, anodes, microbial growth and metabolism, and electron transfer mechanisms. In this regard, research is yet to consider MFCs and MMFCs in the context of electrostatic and electrokinetic aspects. In this extensive review, we show, for the first time, the interrelationship of MFCs and MMFCs with electric double layer theory. Consequently, we show how the analytical solution to the mean field Poisson–Boltzmann theory relates to these systems. Moreover, we show the interrelationship between MFC and MMFCs’ performance and the electric double layer and the associated electrostatic and electrokinetic phenomena. This extensive review will likely motivate research in this direction.

Characterization of defects in additively manufactured materials from mechanical properties

Minimization of defects in additively manufactured components is essential for material development and the determination of fabrication process windows. Here, a purely mechanical means of quantifying porosity in a material is developed based on the Mori–Tanaka mean field theory. The micromechanics based defect quantification approach developed here links the elastic properties of a material with the specific defect structures that must exist within it to obtain those properties. Laser powder bed fusion is used to fabricate aluminum 6061 with three different processing conditions to produce nominally identical samples with unique defect microstructures. Test samples are imaged with microcomputed X-ray tomography (μCT) and the images are classified with a machine learning method to identify the volume fraction of pores, solidification cracks, and the orientation distribution function of the solidification cracks. Tensile tests are then conducted in the z-axis and within the xy-plane to measure the respective elastic moduli and the Poisson’s ratio. These three commonly measured material properties are the only inputs to the new micromechanics based approach used to infer the same defect descriptors that were extracted from μCT. Excellent agreement is found between defect descriptors obtained with both methods, and quantities derived from the mechanical properties are found to carry substantially lower uncertainty. Full error propagation maps for the micromechanics based technique are calculated. Notably, defect descriptors from the micromechanics based approach are calculated from strain and load measurements, which are measured on much larger length scales than the defect size. This enables simple quantification of defects for materials containing small defects that are challenging to image.

Magnetocaloric effect in Gd1-xCexNi (x = 0–0.6): A cost-effective approach to tuning Curie temperature from 70 K to 30 K

Magnetic refrigeration is a promising alternative to traditional gas compression refrigeration technologies, as it offers significantly higher energy efficiency. One factor hindering the widespread implementation of magnetic refrigeration is the dependence on expensive and critical rare earth elements needed to produce a strong magnetocaloric effect. Inside this work we explore substituting a non-critical rare earth element, Ce, into an established magnetocaloric material of choice, GdNi. Structural characteristics are investigated via x-ray powder diffraction, and the magnetocaloric effect is evaluated indirectly from heat capacity measurements as well as calculated using the mean field method. Our results show that small substitutions of Ce into GdNi results in the dilution of the magnetocaloric effect while maintaining relative cost effectiveness for small substitutions of Ce. As Ce content is increased, the cost effectiveness of the adiabatic temperature change (ΔTad) increases as high as 20% for (Gd0.4Ce0.6)Ni while the magnetic entropy change (-ΔSm) shows minimal improvement in cost effectiveness, falling from 3.93 J/kg*K in GdNi to 1.75 J/kg*K in (Gd0.4Ce0.6)Ni at 1 T applied field. This demonstrates that using Ce substitutions can be a powerful tool in both tuning Curie temperature and mitigating the reliance on critical elements as we look to develop towards a more sustainable future.

Woody semi‐natural habitats modulate the effects of field size and functional crop diversity on farmland birds

Abstract Agricultural intensification has simplified landscape composition and configuration, which has led to biodiversity declines. Increasing landscape‐wide crop heterogeneity can promote farmland biodiversity. However, knowledge is still lacking on how the effects of configurational and compositional crop heterogeneity (i.e. field size and crop diversity) are modulated by the amount of semi‐natural habitats in the landscape, especially across large scales. We tested how mean field size and functional crop diversity affect farmland bird diversity and abundance over three consecutive years, and how these effects are modulated by the amount of small woody features (SWF) in the landscape. We related data from a national bird monitoring scheme to field‐level information from a novel, high‐resolution remote sensing‐based crop type map. Smaller field sizes and higher functional crop diversity were not generally associated with a higher diversity or abundance of farmland birds. Associations varied with species' breeding habitat preferences and were modulated by the amount of SWF. In landscapes with a low SWF amount, species diversity and the abundance of species breeding in field edges or shrubs were negatively associated with increasing field size. However, where the amount of SWF was high, larger field size was associated with higher species diversity and abundance of field and shrub breeders. Diversity increased with higher functional crop diversity, as did the abundance of non‐field breeders in landscapes with a medium to high SWF amount. Field size tended to have a stronger effect on bird diversity and abundance than functional crop diversity. Policy implications: National and EU agricultural policies should adopt a landscape perspective by considering the amount of semi‐natural habitats when designing biodiversity‐enhancing measures that target field size and functional crop diversity. In landscapes with low SWF amount, decreasing field sizes may be particularly effective to promote farmland bird diversity and the abundance of non‐field breeders. In landscapes with a medium to high SWF amount, increasing functional crop diversity is likely more effective than reducing field sizes. Field and shrub breeders may be promoted by maintaining landscapes with large fields, only if these offer a high SWF amount, low agronomic yield potential and low productivity.

Semi-linear parabolic equations on homogenous Lie groups arising from mean field games

AbstractThe existence and the uniqueness of solutions to some semilinear parabolic equations on homogeneous Lie groups, namely, the Fokker–Planck equation and the Hamilton–Jacobi equation, are addressed. The anisotropic geometry of the state space plays a crucial role in our analysis and creates several issues that need to be overcome. Indeed, the ellipticity directions span, at any point, subspaces of dimension strictly less than the dimension of the state space. Finally, the above results are used to obtain the short-time existence of classical solutions to the mean field games system defined on an homogenous Lie group.

A mean field game approach to optimal investment and risk control for competitive insurers

We consider an insurance market consisting of multiple competitive insurers with a mean field interaction via their terminal wealth under the exponential utility with relative performance. It is assumed that each insurer regulates her risk by controlling the number of policies. We respectively establish the constant Nash equilibrium (independent of time) on the investment and risk control strategy for the finite n-insurer game and the constant mean field equilibrium for the corresponding mean field game (MFG) problem (when the number of insurers tends to infinity). Furthermore, we examine the convergence relationship between the constant Nash equilibrium of finite n-insurer game and the mean field equilibrium of the corresponding MFG problem. Our numerical analysis reveals that, for a highly competitive insurance market consisting of many insurers, every insurer will invest more in risky assets and increase the total number of outstanding liabilities to maximize her exponential utility with relative performance.

Compensation and Critical Behaviors of a Mixed-Spin (1/2, 2) Hexagonal Nanotube: Mean Field Study and Monte Carlo Simulation

In this work, we used the mean field approximation and Monte Carlo simulation to study the magnetic properties of a ferrimagnetic mixed-spin (1/2, 2) hexagonal nanotube with core-shell structure. The effects of parameters DS, JS and Jin on the critical and compensation behaviors of the system are investigated. The core, shell and total magnetizations are examined. The results obtained show the appearance of second- and first-order phase transitions and compensation temperatures.

Fluid-solid interaction simulations of an aeroelastic square prism in sinusoidal oscillatory flows

This study numerically investigates the aerodynamic and aeroelastic characteristics of a square prism (aeroelastic model) and wind field around it in sinusoidal oscillatory flows (SOFs). The reliability of the fluid-solid interaction (FSI) simulation is validated by a free vibration test and wind tunnel tests in smooth flow and SOF. The effects of the amplitude and frequency of SOFs are studied at the mean wind speed of vortex-induced resonance. The results show that increasing the amplitude and frequency of SOFs will amplify the root mean square (RMS) along-wind and across-wind base shear forces of the aeroelastic model but decrease the RMS across-wind displacement at the top of the aeroelastic model. The spectral analysis of the base shear forces indicates that the influence of vortex shedding on the across-wind base shear force is reduced by either increasing the amplitude or increasing the frequency of SOFs. The mean and instantaneous wind fields around the aeroelastic model in SOFs and smooth flow are compared, and the wake characteristics of the aeroelastic model in SOFs are analysed by dynamic mode decomposition. It is observed that when the frequency of SOFs is 1.5 times as large as the fundamental natural frequency of the aeroelastic model, the regular vortex shedding process is substantially affected.

Symmetry breaking in vanadium trihalides

In the light of new experimental evidence we study the insulating ground state of the 3d2 -transition metal trihalides VX 3 (X = Cl, I). Based on density functional theory with the Hubbard correction we systematically show how these systems host multiple metastable states characterised by different orbital ordering and electronic behaviour. Our calculations reveal the importance of imposing a precondition in the on site d density matrix and of considering a symmetry broken unit cell to correctly take into account the correlation effects in a mean field framework. Furthermore we ultimately found a ground state with the a1g orbital occupied in a distorted VX 6 octahedra driven by an optical phonon mode.

Mean field game of optimal relative investment with jump risk

Mean field game of optimal relative investment with jump risk

Weak and Renormalized Solutions to a Hypoelliptic Mean Field Games System

Weak and Renormalized Solutions to a Hypoelliptic Mean Field Games System

Ab-initio DFT＋[formula omitted] study on the electronic correlation in multiferroic XY-antiferromagnetic Ba2CoGe2O7

Ab-initio density functional theory (DFT)＋U has been used to study the spin-resolved electronic band structure and the partial density of states of the multiferroic XY-antiferromagnetic Ba2CoGe2O7. Using the constrained random-phase approximation (cRPA) method, the value of Hubbard U and Hund’s coupling JH has been determined and plugged into the further dynamical mean field theory (DMFT) calculations. The strong metal-ligand hybridization between Co-3d and O-2p orbitals in the CoO4 tetrahedron has been demonstrated via DFT and DFT＋DMFT calculations. The calculated indirect band gap in the antiferromagnetic state without and with U (=5 eV) correction is found to be 0.67 and 2.71 eV, respectively. The highest calculated ordered magnetic moment of 2.7 μB/Co2+ is close to the reported experimental value. The presented DFT calculations based on the different orbital models brings the underlying strong electronic correlation in the Ba2CoGe2O7.

Triple points and phase transitions of D-dimensional dyonic AdS black holes with quasitopological electromagnetism in Einstein-Gauss-Bonnet gravity

Triple points and phase transitions of <i>D</i>-dimensional dyonic AdS black holes with quasitopological electromagnetism in Einstein-Gauss-Bonnet gravity

Critical Opalescence and Its Impact on the Jet Quenching Parameter q^

Jet quenching parameter q^ is essential for characterizing the interaction strength between jet partons and nuclear matter. Based on the quark-meson model, we develop a new framework for calculating q^ at finite chemical potentials, in which q^ is related to the spectral function of the chiral order parameter. A mean field perturbative calculation up to the one-loop order indicates that the momentum broadening of jets is enhanced at both high temperature and high chemical potential, and approximately proportional to the parton number density in the partonic phase. We further investigate the behavior of q^ in the vicinity of the critical endpoint (CEP) by coupling our calculation with a recently developed equation of state that includes a CEP in the universality class of the Ising model, from which we discover the partonic critical opalescence, i.e., the divergence of scattering rate of jets and their momentum broadening at the CEP, contributed by scatterings via the σ exchange process. Hence, for the first time, jet quenching is connected with the search of CEP.