Mean-field Model Research Articles

Study on the magnetic properties and critical behavior of CoFe2−x Al x O4 (x = 1.0 and 1.2) spinel ferrite

Abstract We have examined the behavior of CoFe2−x Al x O4 (x = 1.0 and 1.2) ferrite close to the transition from ferromagnetic to paramagnetic phases (T C). The findings indicate that at a temperature of T C = 314 K (x = 1.0) and T C = 224 K (x = 1.2), there is a second order magnetic phase transition. We used various methods, including modified Arrott plot, Kouvel–Fisher method, and critical isotherm analysis, to determine the critical exponents which were found to be similar to those expected for the Tricritical Mean-field model (β = 0.288, γ = 1.057, and δ = 4.665) for the x = 1.0 sample. The critical exponents for the x = 1.2 sample (β = 0.771, γ = 1.081, and δ = 2.403) belonged to a different universality class. These results suggest that the replacement of Fe ions with non-magnetic Al ions decreases the Co–Fe, Fe–Fe, Co–Co interaction sites in the CoFe2O4 spinel ferrite, increasing magnetic disorder.

Simulation of time-crystal-like behavior for a few-boson chiral soliton model in a ring

We present numerical simulations for a chiral soliton model with N=2,3 bosons in a ring, which is a few-particle version of our previous mean-field model for a quantum time crystal. Following Syrwid, Kosior, and Sacha (SKS), the notion is that a precise position measurement of one particle can lead to spontaneous formation of a bright soliton that in a time crystal should rotate intact for at least a few revolutions around the ring. In their work SKS found spontaneous formation of a soliton due to the position measurement, but quantum fluctuations cause the soliton to subsequently decay before it has a chance to perform even one revolution of the ring. Based on this, they concluded that time-crystal dynamics are impossible for Wilczek's model of a bright soliton in a ring. In contrast, for our few-boson chiral soliton model, allowing for imprecise (weak) measurements of the particle position, we show that time-crystal-like behavior is possible, allowing for several revolutions of the spontaneously formed soliton around the ring. Published by the American Physical Society 2024

The Emergence of Order in Many Element Systems

Our work is dedicated to the introduction and investigation of a new asymptotic correlation relation in the field of mean field models and limits. This new notion, order (as opposed to chaos), revolves around a tendency for self organisation in a given system and is expected to be observed in biological and societal models. Beyond the definition of this new notion, our work will show its applicability, and propagation, in the so-called choose the Leader model.

Comparative simulations of methanol steam reforming on PdZn alloy using kinetic Monte Carlo and mean-field microkinetic model.

Methanol steam reforming (MSR) is an attractive route for producing clean energy hydrogen. PdZn alloys are extensively studied as potential MSR catalysts for their stability and high CO2 selectivity. Here, we investigated the reaction mechanism using density functional calculations, mean-field microkinetic modeling (MF-MKM), and kinetic Monte Carlo (kMC) simulations. To overcome the over-underestimation of CO2 selectivity by log-kMC, an ads-kMC algorithm is proposed in which the adsorption/desorption rate constants were reduced under certain requirements and the diffusion process was treated by redistributing surface species each time an event occured. The simulations show that the dominant pathway to CO2 at low temperatures is CH3OH → CH3O → CH2O → H2COOH → H2COO → HCOO → CO2. The ads-kMC predicted OH coverage is 2-3 times that of MF-MKM, while they produce similar coverage for other species. Analyses indicate that surface OH promotes the dehydrogenation of CH3OH, CH3O, and H2COOH significantly and plays a key role in the MSR process. The dissociation of water/methanol is the most important rate-limiting/rate-inhibiting step. The CO2 selectivity obtained by the two methods is close to each other and consistent with the experimental trend with temperature. Generally, the ads-kMC results agree with the MF-MKM ones, supporting the previous finding that kMC and MF-MKM predict similar results if the diffusion is very fast and adsorbate interactions are neglected. The present study sheds light on the MSR process on PdZn alloys, and the proposed scheme to overcome the stiff problems in kMC simulations is worthy of being extended to other systems.

Field Theory for Mechanical Criticality in Disordered Fiber Networks.

Strain-controlled criticality governs the elasticity of jamming and fiber networks. While the upper critical dimension of jamming is believed to be d_{u}=2, non-mean-field exponents are observed in numerical studies of 2D and 3D fiber networks. The origins of this remains unclear. In this study we propose a minimal mean-field model for strain-controlled criticality of fiber networks. We then extend this to a phenomenological field theory, in which non-mean-field behavior emerges as a result of the disorder in the network structure. We predict that the upper critical dimension for such systems is d_{u}=4 using a Gaussian approximation. Moreover, we identify an order parameter for the phase transition, which has been lacking for fiber networks to date.

EEG-fMRI in awake rat and whole-brain simulations show decreased brain responsiveness to sensory stimulations during absence seizures

In patients suffering absence epilepsy, recurring seizures can significantly decrease their quality of life and lead to yet untreatable comorbidities. Absence seizures are characterized by spike-and-wave discharges on the electroencephalogram associated with a transient alteration of consciousness. However, it is still unknown how the brain responds to external stimuli during and outside of seizures. This study aimed to investigate responsiveness to visual and somatosensory stimulation in Genetic Absence Epilepsy Rats from Strasbourg (GAERS), a well-established rat model for absence epilepsy. Animals were imaged under non-curarized awake state using a quiet, zero echo time, functional magnetic resonance imaging (fMRI) sequence. Sensory stimulations were applied during interictal and ictal periods. Whole-brain hemodynamic responses were compared between these two states. Additionally, a mean-field simulation model was used to explain the changes of neural responsiveness to visual stimulation between states. During a seizure, whole-brain responses to both sensory stimulations were suppressed and spatially hindered. In the cortex, hemodynamic responses were negatively polarized during seizures, despite the application of a stimulus. The mean-field simulation revealed restricted propagation of activity due to stimulation and agreed well with fMRI findings. Results suggest that sensory processing is hindered or even suppressed by the occurrence of an absence seizure, potentially contributing to decreased responsiveness during this absence epileptic process.

Exploring spatial segregation induced by competition avoidance as driving mechanism for emergent coexistence in microbial communities.

This study investigates the role of spatial segregation, prompted by competition avoidance, as a key mechanism for emergent coexistence within microbial communities. Recognizing these communities as complex adaptive systems, we challenge the sufficiency of mean-field pairwise interaction models, and we consider the impact of spatial dynamics. We developed an individual-based spatial simulation depicting bacterial movement through a pattern of random walks influenced by competition avoidance, leading to the formation of spatially segregated clusters. This model was integrated with a Lotka-Volterra metapopulation framework focused on competitive interactions. Our findings reveal that spatial segregation combined with low diffusion rates and high compositional heterogeneity among patches can lead to emergent coexistence in microbial communities. This reveals a novel mechanism underpinning the formation of stable, coexisting microbe clusters, which is nonetheless incapable of promoting coexistence in the case of isolated pairs of species. This study underscores the importance of considering spatial factors in understanding the dynamics of microbial ecosystems.

EEG-fMRI in awake rat and whole-brain simulations show decreased brain responsiveness to sensory stimulations during absence seizures.

In patients suffering absence epilepsy, recurring seizures can significantly decrease their quality of life and lead to yet untreatable comorbidities. Absence seizures are characterized by spike-and-wave discharges on the electroencephalogram associated with a transient alteration of consciousness. However, it is still unknown how the brain responds to external stimuli during and outside of seizures. This study aimed to investigate responsiveness to visual and somatosensory stimulation in Genetic Absence Epilepsy Rats from Strasbourg (GAERS), a well-established rat model for absence epilepsy. Animals were imaged under non-curarized awake state using a quiet, zero echo time, functional magnetic resonance imaging (fMRI) sequence. Sensory stimulations were applied during interictal and ictal periods. Whole-brain hemodynamic responses were compared between these two states. Additionally, a mean-field simulation model was used to explain the changes of neural responsiveness to visual stimulation between states. During a seizure, whole-brain responses to both sensory stimulations were suppressed and spatially hindered. In the cortex, hemodynamic responses were negatively polarized during seizures, despite the application of a stimulus. The mean-field simulation revealed restricted propagation of activity due to stimulation and agreed well with fMRI findings. Results suggest that sensory processing is hindered or even suppressed by the occurrence of an absence seizure, potentially contributing to decreased responsiveness during this absence epileptic process.

Diffusion and pattern formation in spatial games.

Diffusion plays an important role in a wide variety of phenomena, from bacterial quorum sensing to the dynamics of traffic flow. While it generally tends to level out gradients and inhomogeneities, diffusion has nonetheless been shown to promote pattern formation in certain classes of systems. Formation of stable structures often serves as a key factor in promoting the emergence and persistence of cooperative behavior in otherwise competitive environments, however, an in-depth analysis on the impact of diffusion on such systems is lacking. We therefore investigate the effects of diffusion on cooperative behavior using a cellular automaton (CA) model of the noisy spatial iterated prisoner's dilemma (IPD), physical extension, and stochasticity being unavoidable characteristics of several natural phenomena. We further derive a mean-field (MF) model that captures the three-species predation dynamics from the CA model and highlight how pattern formation arises in this new model, then characterize how including diffusion by interchange similarly enables the emergence of large scale structures in the CA model as well. We investigate how these emerging patterns favors cooperative behavior for parameter space regions where IPD error rates classically forbid such dynamics. We thus demonstrate how the coupling of diffusion with nonlinear dynamics can, counterintuitively, promote large-scale structure formation and in return establish new grounds for cooperation to take hold in stochastic spatial systems.

Renormalization-group approach to ordered phases in music.

The organization of disordered sounds into the ordered structures of music can be understood through an analogy to the emergent ordering of physical systems undergoing phase transitions. This work builds off a prior mean-field model for pitch in music [J. Berezovsky, Sci. Adv. 5, eaav8490 (2019)2375-254810.1126/sciadv.aav8490] by using renormalization-group techniques to study the effects of dimensionality and local correlations. We corroborate the results of the mean-field model by showing convergence of the phase diagram as lattice dimension is increased, while also uncovering new phases which the mean-field model does not reveal. We also compute the nearest-neighbor correlations and provide comparisons to the mean-field model, as well as historical tuning systems used by different groups of musicians. The new phases and resulting correlations revealed in this work suggest a number of possible avenues for further exploration, including generating new music using the pitch distributions suggested by the model.

Critical behavior of quasi-two-dimensional ferromagnet Cr1.04Te2

Abstract The self-intercalation of Cr into pristine two-dimensional (2D) van der Waals ferromagnetic CrTe2, which forms chromium tellurides (Cr x Te2), has garnered interest due to their remarkable magnetic characteristics and the wide variety of chemical compositions available. Here, comprehensive basic characterization and magnetic studies are conducted on quasi-2D ferromagnetic Cr1.04Te2 crystals. Measurements of the isothermal magnetization curves are conducted around the critical temperature to systematically investigate the critical behavior. Specifically, the critical exponents β = 0.2399, γ = 0.859, and δ = 4.3498, as well as the Curie temperature T C = 249.56 K, are determined using various methods, including the modified Arrott plots, the Kouvel–Fisher method, the Widom scaling method, and the critical isotherm analysis. These results indicate that the tricritical mean-field model accurately represents the critical behavior of Cr1.04Te2. A magnetic phase diagram with tricritical phenomenon is thus constructed. Further investigations confirm that the critical exponents obtained conform to the scalar equation near T C, indicating their self-consistency and reliability. Our work sheds light on the magnetic properties of quasi-2D Cr1.04Te2, broadening the scope of the van der Waals crystals for developments of future spintronic devices operable at room temperature.

Breaking Consensus in Kinetic Opinion Formation Models on Graphons

In this work, we propose and investigate a strategy to prevent consensus in kinetic models for opinion formation. We consider a large interacting agent system and assume that agent interactions are driven by compromise as well as self-thinking dynamics and also modulated by an underlying static social network. This network structure is included using so-called graphons, which modulate the interaction frequency in the corresponding kinetic formulation. We then derive the corresponding limiting Fokker–Planck equation and analyze its large time behavior. This microscopic setting serves as a starting point for the proposed control strategy, which steers agents away from mean opinion and is characterized by a suitable penalization depending on the properties of the graphon. We show that this minimalist approach is very effective by analyzing the quasi-stationary solution mean-field model in a plurality of graphon structures. Several numerical experiments are also provided to show the effectiveness of the approach in preventing the formation of consensus steering the system toward a declustered state.

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.

Bethe M-layer construction on the Ising model

In statistical physics, one of the standard methods to study second order phase transitions is the renormalization group that usually leads to an expansion around the corresponding fully connected solution. Unfortunately, often in disordered models, some important finite dimensional second-order phase transitions are qualitatively different or absent in the corresponding fully connected model: in such cases the standard expansion fails. Recently, a new method, the M-layer one, has been introduced that performs an expansion around a different soluble mean field model: the Bethe lattice one. This new method has been already used to compute the upper critical dimension DU of different disordered systems such as the Random Field Ising model or the Spin glass model with field. If then one wants to go beyond and construct an expansion around DU to understand how critical quantities get renormalized, the actual computation of all the numerical factors is needed. This next step has still not been performed, being technically more involved. In this paper we perform this computation for the ferromagnetic Ising model without quenched disorder, in finite dimensions: we show that, at one-loop order inside the M-layer approach, we recover the continuum quartic field theory and we are able to identify the coupling constant g and the other parameters of the theory, as a function of macroscopic and microscopic details of the model such as the lattice spacing, the physical lattice dimension and the temperature. This is a fundamental step that will help in applying in the future the same techniques to more complicated systems, for which the standard field theoretical approach is impracticable.

Optimal control of oscillatory neuronal models with applications to communication through coherence

Macroscopic oscillations in the brain are involved in various cognitive and physiological processes, yet their precise function is not completely understood. Communication through coherence (CTC) theory proposes that these rhythmic electrical patterns might serve to regulate the information flow between neural populations. Thus, to communicate effectively, neural populations must synchronize their oscillatory activity, ensuring that input volleys from the presynaptic population reach the postsynaptic one at its maximum phase of excitability. We consider an Excitatory–Inhibitory (E–I) network whose macroscopic activity is described by an exact mean-field model. The E–I network receives periodic inputs from either one or two external sources, for which effective communication will not be achieved in the absence of control. We explore strategies based on optimal control theory for phase–amplitude dynamics to design a periodic control that sets the target population in the optimal phase to synchronize its activity with a specific presynaptic input signal and establish communication. The control mechanism resembles the role of a higher cortical area in the context of selective attention. To design the control, we use the phase–amplitude reduction of a limit cycle and leverage recent developments in this field in order to find the most effective control strategy regarding a defined cost function. Furthermore, we present results that guarantee the local controllability of the system close to the limit cycle.

Investigation of the structural and magnetic properties of the GdCoC compound featuring excellent cryogenic magnetocaloric performance

Magnetic refrigeration (MR) based on the magnetocaloric effect (MCE) has been recognized as an environmentally benign and energy-efficient cooling technology. Exploring suitable magnetocaloric materials is a crucial prerequisite for practical MR applications. We have herein provided a systematic investigation of the crystal structure, microstructure, electronic structure, magnetic phase transition, critical behavior, and MCE of the GdCoC compound featuring excellent cryogenic magnetocaloric performance by means of experimental determination and theoretical calculation. The GdCoC compound is crystallized in a simple layered tetragonal crystal structure with a P42/mmc space group and undergoes two successive ferromagnetic (FM) transitions along with a low-temperature weak antiferromagnetic (AFM) transition under low magnetic fields. Density functional theory calculations confirms the FM coupling of the Gd and Co intra-sublattice interactions, whereas AFM coupling for their inter-sublattice interaction. The magnetic transitions are merged in to one under high magnetic fields which has been confirmed to be second-order type and its critical behavior can be understood in the framework of tri-critical mean-field model, whereas the low-temperature weak AFM transition is belonging to the first-order type. The excellent magnetocaloric performance of the GdCoC compound was identified by the parameters of magnetic entropy change, adiabatic temperature change, temperature-averaged entropy change, relative cooling power, and refrigerant capacity, which are superior to most of the well-known magnetocaloric materials with similar working temperatures, making it attractive for practical cryogenic MR applications.

On the performance evaluation of distributed join-idle-queue load balancing with and without token withdrawals

Distributed Join-Idle-Queue load balancing is known to achieve vanishing waiting times in the large-scale limit provided that the number of dispatchers remains fixed, while the number of servers tends to infinity. When the number of dispatchers m scales to infinity together with the number of servers n, such that r=n/m remains fixed, the large-scale performance of Join-Idle-Queue load balancing is less clear as waiting times no longer vanish.In this paper we first discuss some existing mean field models for distributed Join-Idle-Queue load balancing with r=n/m fixed and explain why the well-known model introduced in Lu et al. (2011) is not exact in the large-scale limit. The inexactness is caused by mixing two variants of distributed Join-Idle-Queue load balancing: a variant with and one without token withdrawals. Next we introduce mean field models for Join-Idle-Queue load balancing with and without token withdrawals, where an idle server places a token at a dispatcher with the shortest among d randomly chosen dispatchers.The introduced mean field models in case of token withdrawals imply that for phase type distributed service times and a total job arrival rate of λn<n, the response time of a job corresponds to that in a standard M/PH/1 queue with load λq0. The value of q0 can be determined numerically and depends on λ,r and d, but not on the job size distribution (apart from its mean). This simple behavior is lost if token withdrawals do not take place. For the models without withdrawals we develop fast numerical algorithms to determine the performance. We present simulation experiments that suggest that the unique fixed point of the introduced mean field models provides exact results in the large-scale limit.

Modelling the growth of the network value

We investigate the evolution of network effects, specifically focusing on the emerging paradigm of third-generation networks known as group-forming networks (GFNs). In contrast to traditional views where network value adheres to Metcalfe’s quadratic growth or Sarnoff’s linear growth, GFNs, such as social networks and community-centric platforms like Apple, Microsoft, and Google, exhibit a distinct exponential growth pattern in network value as postulated by Reed’s hypothesis.Unlike conventional network science, economic perspectives on network effects do not necessitate precise knowledge of the network topology. Instead, they often align with mean-field models akin to those found in statistical physics. Recent empirical studies challenge earlier assumptions, revealing that many GFNs have undergone exponential or notably superquadratic growth, deviating significantly from established models based solely on user and link counts.This paper introduces a simplified model aimed at capturing the growth dynamics of marketable groups within a network comprising n users. The model explores various hypothetical mechanisms governing the expansion of these groups, and through rigorous analysis and simulation, we uncover compelling evidence that the observed growth in GFNs surpasses traditional quadratic models. Our findings challenge existing notions, suggesting a new framework for understanding the intricacies of network growth dynamics, and providing solid analytical and conceptual foundations for the recent explosive processes of economic and financial value growth of networks that exploit the formation of groups.

Mapping Brain Synergy Dysfunction in Schizophrenia: Understanding Individual Differences and Underlying Molecular Mechanisms.

To elucidate the brain-wide information interactions that vary and contribute to individual differences in schizophrenia (SCZ), an information-resolved method is employed to construct individual synergistic and redundant interaction matrices based on regional pairwise BOLD time-series from 538 SCZ and 540 normal controls (NC). This analysis reveals a stable pattern of regionally-specific synergy dysfunction in SCZ. Furthermore, a hierarchical Bayesian model is applied to deconstruct the patterns of whole-brain synergy dysfunction into three latent factors that explain symptom heterogeneity in SCZ. Factor 1 exhibits a significant positive correlation with Positive and Negative Syndrome Scale (PANSS) positive scores, while factor 3 demonstrates significant negative correlations with PANSS negative and general scores. By integrating the neuroimaging data with normative gene expression information, this study identifies that each of these three factors corresponded to a subset of the SCZ risk gene set. Finally, by combining data from NeuroSynth and open molecular imaging sources, along with a spatially heterogeneous mean-field model, this study delineates three SCZ synergy factors corresponding to distinct symptom profiles and implicating unique cognitive, neurodynamic, and neurobiological mechanisms.

Unified neutron star equations of state calibrated to nuclear properties

Recently, a dataset of several equations of state (EOSs) for purely nucleonic stellar matter based on a nonlinear relativistic mean-field model prescription and constrained to properties of nuclear matter, state-of-the-art chiral effective-field theory calculations for low-density neutron matter, and astrophysical data were proposed. In this work, 21 unified neutron star EOSs were chosen from that dataset in such a way that a large range of values of the slope of the symmetry energy at saturation is covered. Several quantities are calculated and discussed, such as the proton fraction and the direct Urca behavior, the density dependence of the speed of sound and the trace anomaly, the crust-core transition properties, the compatibility with astrophysical observations, and the neutron matter properties from chiral effective-field theory calculations and pQCD constraints. We construct unified EOSs where the outer crust is given by the BSk22 functional and the inner crust is calculated from a compressible liquid drop approximation. The core is purely nucleonic; made of protons, neutrons, electrons, and muons; under charge neutrality; and in beta -equilibrium conditions. The correlation of the slope of the symmetry energy at saturation with the crust-core transition density and proton fraction is analyzed, and equations that translate these relations are proposed. Moreover, the spectral representation for all the EOSs is given, which is a convenient representation to study quasi-periodic oscillations with realistic EOSs. We show that several of these EOSs have in the center of the most massive neutron star a speed of sound squared on the order of $ 0.5$. Most of the EOSs predict a maximum central density on the order of about six times the nuclear saturation density. Three of the EOSs satisfy all of the constraints imposed. The 21 unified EOSs are available in the zenodo platform.