Mean-field Model Research Articles

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

Mean-field analysis of synaptic alterations underlying deficient cortical gamma oscillations in schizophrenia.

Deficient gamma oscillations in the prefrontal cortex (PFC) of individuals with schizophrenia (SZ) are proposed to arise from alterations in the excitatory drive to fast-spiking interneurons (E I) and in the inhibitory drive from these interneurons to excitatory neurons (I E). Consistent with this idea, prior postmortem studies showed lower levels of molecular and structural markers for the strength of E I and I E synapses and also greater variability in E I synaptic strength in PFC of SZ. Moreover, simulating these alterations in a network of quadratic integrate-and-fire (QIF) neurons revealed a synergistic effect of their interactions on reducing gamma power. In this study, we aimed to investigate the dynamical nature of this synergistic interaction at macroscopic level by deriving a mean-field description of the QIF model network that consists of all-to-all connected excitatory neurons and fast-spiking interneurons. Through a series of numerical simulations and bifurcation analyses, findings from our mean-field model showed that the macroscopic dynamics of gamma oscillations are synergistically disrupted by the interactions among lower strength of E I and I E synapses and greater variability in E I synaptic strength. Furthermore, the two-dimensional bifurcation analyses showed that this synergistic interaction is primarily driven by the shift in Hopf bifurcation due to lower E I synaptic strength. Together, these simulations predict the nature of dynamical mechanisms by which multiple synaptic alterations interact to robustly reduce PFC gamma power in SZ, and highlight the utility of mean-field model to study macroscopic neural dynamics and their alterations in the illness.

Criticality-enhanced precision in phase thermometry

Temperature estimation of interacting quantum many-body systems is both a challenging task and topic of interest in quantum metrology, given that critical behavior at phase transitions can boost the metrological sensitivity. Here we study noninvasive quantum thermometry of a finite, two-dimensional Ising spin lattice based on measuring the dephasing dynamics of a spin probe coupled to the lattice. We demonstrate a strong critical enhancement of the achievable precision in terms of the quantum Fisher information, which depends on the coupling range and the interrogation time. Our numerical simulations are compared to instructive analytic results for the critical scaling of the sensitivity in the Curie-Weiss model of a fully connected lattice and to the mean-field description in the thermodynamic limit, both of which fail to describe the critical spin fluctuations on the lattice the spin probe is sensitive to. Phase metrology could thus help to investigate the critical behavior of finite many-body systems beyond the validity of mean-field models. Published by the American Physical Society 2024

Re-visiting the role of short-range correlations on neutron-star properties

The impact of short-range correlations (SRCs) on neutron star (NS) properties are re-examined across various classes of relativistic mean-field (RMF) models. The coupling strengths of the models are so adjusted that the low-density part of the equation of state (EoS), complemented with saturation properties such as binding energy of symmetric nuclear matter and nuclear symmetry energy responsible for the bulk properties of finite nuclei, remains practically unaffected with the inclusion of SRCs. The EoS for symmetric nuclear matter and the nuclear symmetry energy at supra-saturation densities which governs the EoS for NS matter become softer or stiffer in the presence of the SRCs, depending on the type of RMF model considered. These distinct effects of SRCs are observed to be more significant at higher densities, as expected, when behaviour of the EoS at low densities, which govern the finite nuclei physics, is not compromised. For most of the models with self-couplings of scalar and vector mesons, the EoS of symmetric nuclear matter stiffens, with a slight effect on nuclear symmetry energy with the inclusion of SRCs. Conversely, in the models incorporating cross-couplings between mesons, the addition of SRCs leads to softer symmetry energy, compensating the stiffening effect of the EoS of symmetric nuclear matter. With the inclusion of SRCs, the values of radius and tidal deformability of canonical mass star and maximum mass of NSs for realistic EoSs align well the present constraints on astrophysical observations.

An AI-Driven Model of Consciousness, Its Disorders, and Their Treatment.

Understanding the neural signatures of consciousness and the mechanisms underlying its disorders, such as coma and unresponsive wakefulness syndrome, remains a critical challenge in neuroscience. In this study, we present a novel computational approach for the in silico discovery of neural correlates of consciousness, the mechanisms driving its disorders, and potential treatment strategies. Inspired by generative adversarial networks, which have driven recent advancements in generative artificial intelligence (AI), we trained deep neural networks to detect consciousness across multiple brain areas and species, including humans. These networks were then integrated with a genetic algorithm to optimize a brain-wide mean-field model of neural electrodynamics. The result is a realistic simulation of conscious brain states and disorders of consciousness (DOC), which not only recapitulates known mechanisms of unconsciousness but also predicts novel causes expected to lead to these conditions. Beyond simulating DOC, our model provides a platform for exploring therapeutic interventions, specifically deep brain stimulation (DBS), which has shown promise in improving levels of awareness in DOC in over five decades of study. We systematically applied simulated DBS to various brain regions at a wide range of frequencies to identify an optimal paradigm for reigniting consciousness in this cohort. Our findings suggest that in addition to previously studied thalamic and pallidal stimulation, high-frequency stimulation of the subthalamic nucleus, a relatively underexplored target in DOC, may hold significant promise for restoring consciousness in this set of disorders.

Magnetic structures of PrMn7O12 : Intersublattice magnetoelastic coupling and incommensurate spin canting

We report on the magnetic structures of PrMn7O12, resolving both a high-temperature structure in common with the other R3+Mn7O12 systems and an additional low-temperature phase characterized by a superposed incommensurate (ICM) spin canting. A phenomenological model is developed to account for large magnetoelastic coupling immediately below the Curie temperature, demonstrating that A′B exchange is primarily responsible for the ferrimagnetic structures observed across the R3+Mn7O12 family. Finally, an analytical mean-field minimal model is presented that successfully accounts for all magnetic structures observed in this family of materials, including the canted commensurate and ICM ground states. Published by the American Physical Society 2024

Pseudoscalar mesons from a PNJL model at zero temperature

We study pseudoscalar π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi $$\\end{document}, K and η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta $$\\end{document} meson properties, such as masses and couplings, in dense matter at zero temperature. We use a recently proposed phenomenological quark model, known as the PNJL0, which takes into account the confinement/deconfinement phase transition by means of the traced Polyakov loop (Φ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varPhi $$\\end{document}) which serves as an order parameter at zero temperature. We consider two different scenarios, namely, symmetric quark matter with equal chemical potentials for all the flavors, and the beta equilibrated matter. In the latter case the hadron-quark phase transition is implemented by a two model approach. For the hadron side we use a relativistic mean-field model with density dependent couplings. We show that Φ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varPhi $$\\end{document} induces abrupt changes in the mesons properties with gap sizes regulated by the phenomenological gluonic sector of the model.

Quasi-stationary alpha-states from non-Hermitian Hamiltonians of even-even heavy isotones

Three isotone groups (N=128,130,132) with alpha-decaying, short-lifetime even-even nuclei of large mass number are studied in order to show that the tunneling phase of the alpha decay process is appropriately describable by a specific non-hermitian mean-field model. In this model the mean-field lifetime of the alpha cluster is extracted directly by the complex diagonalization of the non-hermitian Hamiltonian of the system. In this paper, we demonstrate that by calculating the mean-field width of the alpha clusters, in each isotone groups, by non-perturbative complex spectral calculations, then, due to the distinct patterns the isotones are naturally organized into with respect to the half-life and proton number, the total width of the alpha-decay can be approximated by matching the calculated results to experimental data.

Tuning the magnetocaloric and structural properties of La0.67Sr0.28Pr0.05Mn1–xCoxO3 refrigeration materials

Abstract The structural, magnetic and magnetocaloric properties of perovskite manganites La0.67Sr0.28Pr0.05Mn1−x Co x O3 (x = 0.05, 0.075 and 0.10) (LSPMCO) are investigated. LSPMCO crystallizes as a rhombohedral structure with R-3c space group. As the Co content increases, the cell volume expands, the Mn–O–Mn bond angle reduces and the length of the Mn–O bond increases. The samples show irregular submicron particles under a Zeiss scanning electron microscopy. The particle size becomes larger with increasing doping. The chemical composition of the samples is confirmed by x-ray photoelectron spectroscopy (XPS). The ferromagnetic (FM) to paramagnetic (PM) phase transition occurs near the Curie temperature (T C), and all transitions are second-order phase transitions (SMOPT) characterized by minimal thermal and magnetic hystereses. Critical behavior analysis indicates that the critical parameters of LSPMCO closely align with those predicted by the mean-field model. The T C declines with Co doping and reaches near room temperature (302 K) at x = 0.075. The maximum magnetic entropy change ( − Δ S M max ) at x = 0.05 is 4.27 J/kg⋅K, and the relative cooling power (RCP) peaks at 310.81 J/K. Therefore, the system holds significant potential for development as a magnetic refrigeration material, meriting further professional and objective evaluation.

Effect of dark matter interaction on hybrid star in the light of the recent astrophysical observations

We have explored the effect of dark matter interaction on hybrid star (HS) in the light of recent astrophysical observational constraints. The presence of dark matter is assumed to be there in both the hadron as well as the quark sector. The dark matter particle interacts with both hadron and quark matter through the exchange of a scalar as well as a vector meson. The equation of state (EOS) of the hadron part is computed using the NL3 version of the relativistic mean field(RMF) model, whereas the quark part is taken care of using the well-known MIT Bag model with the vector interaction. We investigate the effect of the dark matter density and the mass of the dark matter particle on various observables like mass, radius, tidal deformability of the dark matter admixed hybrid star(DMAHS).In this study, we have noted an intriguing aspect that is the speed of sound in the DMAHS is insensitive to both the mass as well as the density of dark matter. We also observe a striking similarity in the variation of transition mass and its corresponding radius, as well as the maximum mass of neutron stars, with dark matter density and mass. We employ observational constraints from neutron stars to narrow down the allowed range of the parameters of dark matter.

The Role of Meridional Flow in the Generation of Solar/Stellar Magnetic Fields and Cycles

Meridional flow is crucial in generating the solar poloidal magnetic field by facilitating poleward transport of the field from decayed bipolar magnetic regions (BMRs). As the meridional circulation changes with the stellar rotation rate, the properties of stellar magnetic cycles are expected to be influenced by this flow. In this study, we explore the role of meridional flow in generating magnetic fields in the Sun and Sun-like stars using the STABLE (surface flux transport and Babcock–Leighton) dynamo model. We find that a moderate meridional flow increases the polar field by efficiently driving the trailing polarity flux toward the pole, while a strong flow tends to transport both polarities of BMRs poleward, potentially reducing the polar field. Our findings are in perfect agreement with what one can expect from the surface flux transport model. Similarly, the toroidal field initially increases with moderate flow speeds and then decreases beyond a certain value. This trend is due to the competitive effects of shearing and diffusion. Furthermore, our study highlights the impact of meridional flow on the strength and duration of stellar cycles. By including the meridional flow from a mean-field hydrodynamics model in STABLE, we show that the magnetic field strength initially increases with the stellar rotation rate and then declines in rapidly rotating stars, offering an explanation of the observed variation of stellar magnetic field with rotation rate.

Temperature inversion in a confined plasma atmosphere: coarse-grained effect of temperature fluctuations at its base

Prompted by the relevant problem of temperature inversion (i.e. gradient of density anti-correlated to the gradient of temperature) in astrophysics, we introduce a novel method to model a gravitationally confined multi-component collisionless plasma in contact with a fluctuating thermal boundary. We focus on systems with anti-correlated (inverted) density and temperature profiles, with applications to solar physics. The dynamics of the plasma is analytically described via the coupling of an appropriated coarse-grained distribution function and a temporally coarse-grained Vlasov dynamics. We derive a stationary solution of the system and predict the inverted density and temperature profiles of the two species for scenarios relevant for the corona. We validate our method by comparing the analytical results with kinetic numerical simulations of the plasma dynamics in the context of the two-species Hamiltonian mean-field model. Finally, we apply our theoretical framework to the problem of the temperature inversion in the solar corona, obtaining density and temperature profiles in remarkably good agreement with the observations.

Magnetocaloric effect, magnetotransport and magnetic properties of polycrystalline Pr(0.65-x)GdxSr0.35MnO3 (x ≤ 0.3) compounds

Polycrystalline Pr0.65-xGdxSr0.35MnO3 (x = 0.01, 0.05, 0.1, 0.2, 0.3) manganites were prepared by conventional solid-state method. Structural analysis has revealed a change in structure with x = 0.2, from Rhombohedral (R-3c) to Orthorhombic (Pbnm) symmetry. Small oxygen deficiency was found in the samples. The electrical measurements revealed typical colossal magnetoresistance (CMR) behavior, with single metal–insulator peak at Tp for all investigated samples. The small polaron hopping (SPH) and variable-range hopping (VRH) models were used to describe the electrical conduction above Tp. Magnetic measurements show an increase in magnetization below the Curie temperature, TC. Values of Tc diminish with increasing Gd3+ content. Isothermal measurements around critical points suggest a possible interaction between the 4f-ions and Mn-sublattice The magnetic critical behavior analysis established the tri-critical mean-field model to be the governing model for the series. Large magnetic entropy change ΔSM at near room temperature (278 K) was exhibited by the x = 0.01 sample at 2.2 J/kgK in μ0ΔH = 1 T and 5.36 J/kgK in μ0ΔH = 4 T. The largest |ΔSM| value was shown by the x = 0.1 sample. The values of the relative cooling power (RCP) and the temperature-averaged entropy change (TEC) increased with substitution qualifying these compounds as magnetocaloric materials.

Semiclassical Equivalence of Two White Dwarf Models as Ground States of the Relativistic Hartree–Fock and Vlasov–Poisson energies

AbstractWe are concerned with the semi-classical limit for ground states of the relativistic Hartree–Fock energies (HF) under a mass constraint, which are considered as the quantum mean-field model of white dwarfs (Lenzmann and Lewin in Duke Math J 152:257–315, 2010). In Jang and Seok (Kinet Relat Models 15:605–620, 2022), fermionic ground states of the relativistic Vlasov–Poisson energy (VP) are constructed as a classical mean-field model of white dwarfs, and are shown to be equivalent to the classical Chandrasekhar model. In this paper, we prove that as the reduced Planck constant $$\hbar $$ ħ goes to the zero, the $$\hbar $$ ħ -parameter family of the ground energies and states of (HF) converges to the fermionic ground energy and state of (VP) with the same mass constraint.

Exploring the macroscopic properties of proto-neutron stars: Effects of entropy and lepton fraction

Neutron stars (NSs) have generally been considered as cold, zero-temperature entities. Recent progress in computational methods and theoretical modelling has opened up the exploration of finite temperature effects, marking an important research frontier. We examine the macroscopic properties of Proto-Neutron Stars (PNS) using different parametrizations of relativistic mean field (RMF) models. We adopt a constant entropy approach by fixing entropy per baryon, S=1 and 2. Higher S elevates the maximum mass for PNS and flattens the mass-radius curves. The higher lepton fraction (Yl) leads to a decrease in maximum mass and an increase in the canonical radius. Furthermore, both the S and Yl influence the dimensionless tidal deformability (Λ). We note that the f-mode frequencies in PNSs increase as S decreases and the Yl increases at maximum mass. We find that the macroscopic properties of the PNS exhibit the same trend, irrespective of the parameter sets employed for the variation of S and Yl.

Direct Measurement of the Differential Capacitance of Deep Eutectic Solvents on Platinum and Glassy Carbon Electrodes.

Differential capacitance is a crucial parameter that connects the experimental observation of electrical double-layer behavior with theoretical models. However, the current number of reported differential capacitance values for deep eutectic solvents remains limited, making it challenging to verify or refute existing models. In this study, we systematically investigate the differential capacitance in deep eutectic solvents using chronoamperometry. By comparing metal and glassy carbon electrodes across various liquid combinations and ion concentrations, we observed a range of distinct capacitance characteristics. While some findings align with the existing mean-field model for ionic liquids, others clearly reflect the influence of electrode materials, with certain cases resisting full explanation by current theoretical models. These results underscore the importance of selecting appropriate electrode materials in experimental studies of such electrolytes and highlight the need for further theoretical advancements in understanding this complex liquid system.

Predicting the firing behaviour of neural network through the bifurcation analysis of derivative mean-field model

The mean-field model is an important method for understanding the complex dynamics of the nervous system at different spatial levels and for simulating and theoretically analysing the collective dynamic behaviour of large neural populations. In the work, we construct an improved mean-field system of neural networks coupled with quadratic integrate-and-fire neurons and examine the discharge patterns for networks by analysing such a model, which is a three-dimensional smooth differential system. Bifurcation analysis of the mean-field model is conducted from both theoretical and simulation perspectives, we obtain the bifurcation conditions of some co-dimension-two bifurcations and divide the parameter space into different regimes by simulating two parameters bifurcation diagrams. We find a close correspondence, though with some variance, between the mean-field model and neural network when comparing the firing patterns of the two models in various parameter regimes. In summary, the obtained mean-field description builds the bridge between the parameters of neurons or networks and that of a mean-field system to ensure we can compare them and understand the connections between them. Specifically, the mean-field model can reflect the dynamics of neural networks from a macroscopic perspective, and its bifurcation can predict the behaviour of neural networks to a certain extent and understand the mechanisms behind them, such as bursting dynamics of neural networks.

Establishing universality in entropy change and critical behavior for magnetocaloric effect in Si-substituted Mn50Ni40Sn10 inverse Heusler alloy

Magnetic refrigeration working based on the magnetocaloric effect can be the perfect replacement of the conventional gas compression-based refrigeration technology and reduces its harmful effects on the environment. The boundary between a first-order and a second-order phase transition would be where the perfect magnetocaloric material would be found. Therefore, establishing the sequence of phase transitions clearly is essential for the characterization of other phase change materials and for applied magnetocaloric research. A quantitative fingerprint of second-order thermomagnetic phase transitions is reported here in Si-substituted high content Mn-based inverse Heusler alloy systems, which are found to be crystallized in cubic structures. The second-order nature of the phase transition has been confirmed from the Arrott plot analysis and a correlation between magnetocaloric effect and local exponent is established. Using the Arrott plot, the critical exponents are evaluated employing different techniques such as modified Arrott plot, Kouvel–Fisher method, and critical isotherm. Their values are found to be in great agreement with each other and follow the mean-field model signifying the presence of long-range ordering in the materials. The high value of isothermal magnetic entropy change and the reversibility justifies the suitability of the reported materials in the practical application as magnetic refrigerants.

A mean-field game model of price formation with price-dependent agent behavior

A mean-field game model of price formation with price-dependent agent behavior

A Physically Based Mean Field Model for Strain‐Induced Precipitation and Recrystallization in High‐Strength Low‐Alloy Steels

A physically based mean field model developed to predict the microstructural evolution during the thermomechanical control process of X70 high‐strength low‐alloy (HSLA) steels is presented. The physically based mean field model incorporates a new integrated precipitation and recrystallization model developed to describe the interaction between strain‐induced precipitation of niobium and titanium carbonitrides and static recrystallization of austenite. The integrated model considers an effective Zener pinning force for the multimodal particle size distribution (PSD) of precipitates, an effective grain‐boundary mobility for the solute drag effect of niobium, and an inhomogeneous stored energy for austenite recrystallization. Given a processing route, the model predicts the variation of austenite grain size, recrystallized and precipitated fractions, and evolution of PSDs of precipitates. Model predictions reveal an excellent agreement with experimental grain size measurements and a final average ferrite grain size of 3.81 μm is achieved. The proposed model considers the heterogeneous nature of recrystallization and precipitation and can contribute to the process design of the HSLA and microalloyed steels.