Mean-field Predictions Research Articles

The elimination of deviations of the mean-field Landau-type theory from the fancy size effect experiment in nanoscale ferroelectric BaTiO 3 capacitors

A time-dependent mean-field Landau-type model is established based on the dipole energies in epitaxial film in order to investigate thickness dependence of the remanent polarization. It is found that the deviations of the mean-field Landau-type theoretical prediction from the experimental data for size effect can be eliminated in SrRuO 3/BaTiO 3/SrRuO 3 capacitor.

Lattice gas simulations of dynamical geometry in two dimensions

We present a hydrodynamic lattice gas model for two-dimensional flows on curved surfaces with dynamical geometry. This model is an extension to two dimensions of the dynamical geometry lattice gas model previously studied in one dimension. We expand upon a variation of the two-dimensional flat space Frisch-Hasslacher-Pomeau (FHP) model created by Frisch [Phys. Rev. Lett. 56, 1505 (1986)] and independently by Wolfram, and modified by Boghosian [Philos. Trans. R. Soc. London, Ser. A 360, 333 (2002)]. We define a hydrodynamic lattice gas model on an arbitrary triangulation whose flat space limit is the FHP model. Rules that change the geometry are constructed using the Pachner moves, which alter the triangulation but not the topology. We present results on the growth of the number of triangles as a function of time. Simulations show that the number of triangles grows with time as t(1/3), in agreement with a mean-field prediction. We also present preliminary results on the distribution of curvature for a typical triangulation in these simulations.

Loss of nodal quasiparticle integrity in underdoped YBa2Cu3O6+x

Arguably the most intriguing aspect of the physics of cuprates is the close proximity between the record high-Tc superconductivity (HTSC) and the antiferromagnetic charge-transfer insulating state driven by Mott-like electron correlations. These are responsible for the intimate connection between high and low-energy scale physics, and their key role in the mechanism of HTSC was conjectured very early on. More recently, the detection of quantum oscillations in high-magnetic field experiments on YBa2Cu3O6+x (YBCO) has suggested the existence of a Fermi surface of well-defined quasiparticles in underdoped cuprates, lending support to the alternative proposal that HTSC might emerge from a Fermi liquid across the whole cuprate phase diagram. Discriminating between these orthogonal scenarios hinges on the quantitative determination of the elusive quasiparticle weight Z, over a wide range of hole-doping p. By means of angle-resolved photoemission spectroscopy (ARPES) on in situ doped YBCO, and following the evolution of bilayer band-splitting, we show that the overdoped metal electronic structure (0.25<p<0.37) is in remarkable agreement with density functional theory and the Z=2p/(p+1) mean-field prediction. Below p~0.10-0.15, we observe the vanishing of the nodal quasiparticle weight Z_N; this marks a clear departure from Fermi liquid behaviour and -- consistent with dynamical mean-field theory -- is even a more rapid crossover to the Mott physics than expected for the doped resonating valence bond (RVB) spin liquid.

Phase diagram of self-assembled rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a two-dimensional system of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize reversibly into chains with discrete orientational degrees of freedom and, at the same time, undergo a continuous isotropic-nematic (IN) transition. A complete phase diagram was obtained as a function of temperature and density. The numerical results were compared with mean field (MF) and real space renormalization group (RSRG) analytical predictions about the IN transformation. While the RSRG approach supports the continuous nature of the transition, the MF solution predicts a first-order transition line and a tricritical point, at variance with the simulation results.

Fragmented many-body states of definite angular momentum and stability of attractive three-dimensional condensates

A three dimensional attractive Bose-Einstein Condensate (BEC) is expected to collapse, when the number of the particles $N$ in the ground state or the interaction strength $\lambda_0$ exceeds a critical value. We study systems of different particle numbers and interaction strength and find that even if the overall ground state is collapsed there is a plethora of fragmented excited states that are still in the metastable region. Utilizing the \emph{configuration interaction} expansion we determine the spectrum of the ground (`yrast') and excited many-body states with definite total angular momentum quantum numbers $0\leqslant L\leqslant N$ and $-L\leqslant M_L\leqslant L$, and we find and examine states that survive the collapse. This opens up the possibility of realizing a metastable system with overcritical numbers of bosons in a ground state with angular momentum $L\neq0$. The multi-orbital mean-field theory predictions about the existence of fragmented metastable states with overcritical numbers of bosons are verified and elucidated at the many-body level. The descriptions of the total angular momentum within the mean-field and the many-body approaches are compared.

Interfacial layering and capillary roughness in immiscible liquids

The capillary roughness and the atomic density profiles of extended interfaces between immiscible liquids are determined as a function of the interface area by using molecular dynamics and Lennard-Jones (12-6) potentials. We found that with increasing area, the interface roughness diverges logarithmically, thus fitting the theoretical mean-field prediction. In systems small enough for the interfacial roughness not to blur the structural details, atomic density profiles across the fluid interface are layered with correlation length in the range of molecular correlations in liquids. On increasing the system size, the amplitude of the thermally excited position fluctuations of the interface increases, thus causing layering to rapidly vanish, if density profiles are computed without special care. In this work, we present and validate a simple method, operating in the direct space, for extracting from molecular dynamics trajectories the "intrinsic" structure of a fluid interface that is the local density profile of the interface cleaned from capillary wave effects. Estimated values of interfacial properties such as the tension, the intrinsic width, and the lower wavelength limit of position fluctuations are in agreement with results collected from the literature.

Mean-field diffusive dynamics on weighted networks

Diffusion is a key element of a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks. Here, we introduce a general formalism that allows to easily write down mean-field equations for any diffusive dynamics on weighted networks. We also propose the concept of annealed weighted networks, in which such equations become exact. We show the validity of our approach addressing the problem of the random walk process, pointing out a strong departure of the behavior observed in quenched real scale-free networks from the mean-field predictions. Additionally, we show how to employ our formalism for more complex dynamics. Our work sheds light on mean-field theory on weighted networks and on its range of validity, and warns about the reliability of mean-field results for complex dynamics.

Intrinsically limited critical temperatures of highly dopedGa1−xMnxAsthin films

Ga1-xMnxAs films with exceptionally high saturation magnetizations of approximate to 100 emu/cm(3) corresponding to effective Mn concentrations of x(eff)approximate to 0.10 still have a Curie temperature T-C smaller than 195 K contradicting mean-field predictions. The analysis of the critical exponent beta of the remnant magnetization-beta = 0.407(5)-in the framework of the models for disordered/amorphous ferromagnets suggests that this limit on T-C is intrinsic and due to the short range of the ferromagnetic interactions resulting from the small mean-free path of the holes. This result questions the perspective of room-temperature ferromagnetism in highly doped GaMnAs.

SPONTANEOUS SYMMETRY BREAKING IN A MICROTUBULE-LIKE SYSTEM

This paper studies asymmetric exclusion processes on a microtubule-like system with two species of particles. The model is motivated by the structure of microtubules and kinesins and dyneins moving along microtubules in opposite directions. The proposed model is similar to that in J. Phys. A40, 2275 (2007) in which two-channel TASEPs with narrow entrances and parallel update are studied. This paper extended the above-mentioned work to a multiple-channel hollow cylinder case. Thus, each channel has two nearest neighbors in our model. The corresponding rule for narrow entrances is that particles cannot enter the system if either of two nearest-neighbor sites on neighboring channels is occupied by the other species of particles. The phase diagram of the model is obtained from a mean-field approximation and verified by computer simulations. It is shown that the spontaneous symmetry breaking exists with two asymmetric phases: high/low density and low/low density. The flipping process of particles is observed. Bulk density and particle currents are computed. Monte Carlo simulation results deviate from the mean-field prediction when entrance rate α is high, which is due to neglecting correlations among particles in mean-field calculations. The results are also compared with that obtained from two-channel system with one neighbor narrow entrance in parallel update.

Hierarchical Bayesian space-time interpolation versus spatio-temporal BME approach

Abstract. The restrictions of the analysis of natural processes which are observed at any point in space or time to a purely spatial or purely temporal domain may cause loss of information and larger prediction errors. Moreover, the arbitrary combinations of purely spatial and purely temporal models may not yield valid models for the space-time domain. For such processes the variation can be characterized by sophisticated spatio-temporal modeling. In the present study the composite spatio-temporal Bayesian maximum entropy (BME) method and transformed hierarchical Bayesian space-time interpolation are used in order to predict precipitation in Pakistan during the monsoon period. Monthly average precipitation data whose time domain is the monsoon period for the years 1974–2000 and whose spatial domain are various regions in Pakistan are considered. The prediction of space-time precipitation is applicable in many sectors of industry and economy in Pakistan especially; the agricultural sector. Mean field maps and prediction error maps for both methods are estimated and compared. In this paper it is shown that the transformed hierarchical Bayesian model is providing more accuracy and lower prediction error compared to the spatio-temporal Bayesian maximum entropy method; additionally, the transformed hierarchical Bayesian model also provides predictive distributions.

Microwave dielectric study of spin-Peierls and charge-ordering transitions in(TMTTF)2PF6salts

We report a study of the 16.5 GHz dielectric function of hydrogenated and deuterated organic salts (TMTTF)$_2$PF$_6$. The temperature behavior of the dielectric function is consistent with short-range polar order whose relaxation time decreases rapidly below the charge ordering temperature. If this transition has more a relaxor character in the hydrogenated salt, charge ordering is strengthened in the deuterated one where the transition temperature has increased by more than thirty percent. Anomalies in the dielectric function are also observed in the spin-Peierls ground state revealing some intricate lattice effects in a temperature range where both phases coexist. The variation of the spin-Peierls ordering temperature under magnetic field appears to follow a mean-field prediction despite the presence of spin-Peierls fluctuations over a very wide temperature range in the charge ordered state of these salts.

Thermodynamic characteristics of poly(cyclohexylethylene-b -ethylene-co- ethylethylene) block copolymers

A series of poly(cyclohexylethylene-b-ethylene-co-ethylethylene) (C-E/EE) diblock copolymers containing approximately 50% by volume glassy C blocks and varying fraction (x) of EE repeat units, 0.07 ≤ x ≤ 0.90, was synthesized by anionic polymerization and catalytic hydrogenation. The effects of ethyl branch content on the melt state segment–segment (χ) interaction parameter and soft (E/EE) block crystallinity were studied. The percent crystallinity ranged from approximately 30% at x = 0.07 to 0% at about x ≥ 0.30, while the melting temperature changed from 101 °C at x = 0.07 to 44 °C at x = 0.28. Dynamic mechanical spectroscopy was employed to determine the order–disorder transition (ODT) temperatures, from which χ was calculated assuming the mean-field prediction (χNn)ODT = 10.5. Previously published results for the temperature dependent binary interaction parameters for C-E (x = 0.07), C-EE (x = 0.90), and E-EE (x = 0.07 and x = 0.90) fail to account for the quantitative x dependence of χ, based on a simple binary interaction model. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 566–574, 2010

Influence of Hydrogen Bonding on Device Parameters and Field Response in N* and SmC* Phases of a Ferroelectric Liquid Crystal, HBFLC: 12 bpa

Isotropic to chiral nematic (IN*) and chiral nematic to chiral SmC(N*C*) transitions are studied by LF dielectric method in a hydrogen bonded ferroelectric liquid crystal, viz., 12 bpa. They agree with TM and DSC reports. Tilt angle, electro-clinic effect, spontaneous polarization, and dielectric relaxations are investigated and compared with that of an odd homologue 11 bpa. Growth of tilt and spontaneous polarization as order parameters in SmC* phase agree with mean-field prediction. Effect of H-bonding on the growth of tilt and PS order parameters is discussed. Observed large EC-effect is explained by the inclined configuration of soft-covalent interaction. Dielectric dispersion revealed a collective response, viz., Goldstone mode at ∼100 Hz in SmC* and an LF-mode in N* phases. The two HF-relaxations, i.e., Types I and II in N* and SmC* phases are explained through a refined dipole model. Shift of GM with field in SmC* is explained. Off-centred dispersion is explained through the Cole-Davidson relation. HF relaxations are related to the individual dipole reorientation. Shift of fR with T infers higher activation energy for Type I and lower activation energy for Type II relaxations. Soft mode permittivity follows the Curie–Weiss law in the vicinity of TN*C*. Device parameters, viz., thermal stability, tilt angle, and spontaneous polarization in SmC* phase are found to be influenced by H-bonding in FLCs. Results are is discussed and compared with the data reported on 11 bpa and other FE materials.

Measuring the Structure of Epitaxially Assembled Block Copolymer Domains with Soft X-ray Diffraction

The size, shape, and interface structure of poly(styrene-b-methyl methacrylate) block copolymer domains assembled on an epitaxial template are characterized with soft X-ray diffraction. The domain size and shape are deformed when the dimensions of the epitaxial template are incommensurate with the equilibrium dimensions of the block copolymer, producing sidewall angles in the range of 1−2° (±0.2°). The average width of the copolymer interface is (4.9 ± 0.1) nm. Comparison with mean-field theoretic predictions for the structure of block copolymer interfaces suggests a low-frequency variance in the copolymer interface position of 1.2 nm2, or a low-frequency line-edge roughness of approximately 3 nm.

Effective Polyakov loop dynamics for finite temperatureG2gluodynamics

Based on the strong coupling expansion we obtain effective three-dimensional models for the Polyakov loop in finite temperature ${G}_{2}$ gluodynamics. The Svetitsky-Jaffe conjecture relates the resulting continuous spin models with ${G}_{2}$ gluodynamics near phase transition points. In the present work we analyze the effective theory in leading order with the help of a generalized mean-field approximation and with detailed Monte Carlo simulations. In addition we derive a Potts-type discrete spin model by restricting the characters of the Polyakov loops to the three extremal points of the fundamental domain of ${G}_{2}$. Both the continuous and discrete effective models show a rich phase structure with a ferromagnetic, symmetric and several antiferromagnetic phases. The phase diagram contains first and second order transition lines and tricritical points. The modified mean-field predictions compare very well with the results of our simulations.

Habitat conversion, extinction thresholds, and pollination services in agroecosystems

Parallel declines of wild pollinators and pollinator-dependent plants have raised alarms over the loss of pollination services in agroecosystems. A spatially explicit approach is needed to develop specific recommendations regarding the design of agricultural landscapes to sustain wild pollinator communities and the services they provide. I modeled pollination services in agroecosystems using a pair of models: a stochastic individual-based simulation model of wild pollinators, pollinator-dependent plants, and crop pollination; and a set of coupled difference equations designed to capture the nonspatial component of the simulation model. Five spatially explicit models of habitat conversion to crops were simulated, and results for pollination services were compared. Mean-field behavior of the simulation model was in good agreement with analysis of the difference equations. A major feature of the models was the presence of a cusp leading to loss of stability and extinction of pollinators and pollinator-dependent plants beyond a critical amount of habitat loss. The addition of pollen obtained from crop visitation caused a breakdown of the cusp preventing extinction of pollinators, but not of wild pollinator-dependent plants. Spatially restricted foraging and dispersal also altered model outcomes relative to mean-field predictions, in some cases causing extinction under parameter settings that would otherwise lead to persistence. Different patterns of habitat conversion to crops resulted in different levels of pollination services. Most interesting was the finding that optimal pollination services occurred when the size of remnant habitat patches was equal to half the mean foraging and dispersal distance of pollinators and the spacing between remnant patches was equal to the mean foraging and dispersal distance. Conservation of wild pollinators and pollinator-dependent plants in agroecosystems requires careful attention to thresholds in habitat conversion and spatial pattern and scale of remnant habitats. Maximization of pollination services was generally incompatible with conservation of wild pollinator-dependent plants. My prediction is that pollination services will be maximized by providing islands of nesting habitat where interisland distance matches mean foraging distances of wild pollinators.

Conserved-mass aggregation model with mass-dependent diffusion rate on complex networks

We investigate the condensation phenomena of conserved-mass aggregation (CA) with mass-dependent diffusion rate on scale-free networks (SFNs). In the model, the mass m of a node isotropically diffuses to one of directly linked nodes with rate D(m)=m(-alpha), where alpha>0. With rate omega , unit mass is chipped from the mass and also isotropically diffuses. It was shown that no condensation phase transitions occur on regular lattices. However, on SFNs with degree distribution P(k) approximately k(-gamma), we show from mean-field approximation that the model exhibits various types of condensation phenomena according to alpha and gamma . There exists crossover alphac=(gamma-2)/(gamma-1) over which a system undergoes the same type of the condensation as that of zero-range process with jumping rate p(m)=mdelta regardless of gamma(>2). We find delta=1-alpha for alphac<or=alpha<1 and delta=0 for alpha>or=1. For alpha<alphac, however, the diffusion of masses cannot be ignored and so a system exhibits different behavior according to the network structure, i.e., gamma. For gamma>3, a system exhibits the behavior on regular lattice. For gamma<or=3, the condensation always occurs for any density with non-power-law background mass distribution. We also numerically confirm the mean-field predictions. Therefore, the network structure leads to the various condensation phenomena of the CA model unlike on regular lattices.

Neutron star properties in density-dependent relativistic Hartree-Fock theory

With the equations of state provided by the newly developed density dependent relativistic Hartree-Fock (DDRHF) theory for hadronic matter, the properties of the static and $\beta$-equilibrium neutron stars without hyperons are studied for the first time, and compared to the predictions of the relativistic mean field (RMF) models and recent observational data. The influences of Fock terms on properties of asymmetric nuclear matter at high densities are discussed in details. Because of the significant contributions from the $\sigma$- and $\omega$-exchange terms to the symmetry energy, large proton fractions in neutron stars are predicted by the DDRHF calculations, which strongly affect the cooling process of the star. The critical mass about 1.45 $M_\odot$, close to the limit 1.5 $M_\odot$ determined by the modern soft X-ray data analysis, is obtained by DDRHF with the effective interactions PKO2 and PKO3 for the occurrence of direct Urca process in neutron stars. The maximum masses of neutron stars given by the DDRHF calculations lie between 2.45 M$_\odot$ and 2.49 M$_\odot$, which are in reasonable agreement with high pulsar mass $2.08 \pm 0.19 M_\odot$ from PSR B1516+02B. It is also found that the mass-radius relations of neutron stars determined by DDRHF are consistent with the observational data from thermal radiation measurement in the isolated neutron star RX J1856, QPOs frequency limits in LMXBs 4U 0614+09 and 4U 1636-536, and redshift determined in LMXBs EXO 0748-676.

Equilibrium morphologies of nonionic lipid–nanoparticle mixtures in water: A self-consistent mean-field prediction

We model an aqueous system which comprises a mixture of lipid molecules and hydrophobic nanoparticles, by means of a self-consistent mean-field theory (SCMFT). Lipids are modeled as nonlinear/branched copolymers with a single hydrophilic head group and a double hydrophobic tail, whereas nanoparticles are modeled as hard-spheres of a particular size. The mixture of lipids and nanoparticles leads to a formation of core–shell micellar structures where the hydrophobic nanoparticles and lipid tails form the core of the micelle, and the hydrophilic lipid head groups form the shell. Different micellar morphologies are found depending on the total concentration of lipid molecules and nanoparticles, as well as the relative size of nanoparticles. There exist three distinct equilibrium morphologies of lipid–nanoparticle micelles: circular micelles (CM), ellipsoidal micelles (EM), and bilayer/lamellar structures (BL). We observed some smooth morphological transitions and phase coexistences by evaluating the excess free energy of micelles.

Recognition ability of the fully connected Hopfield neural network under a persistent stimulus field

We investigate the pattern recognition ability of the fully connected Hopfield model of a neural network under the influence of a persistent stimulus field. The model considers a biased training with a stronger contribution to the synaptic connections coming from a particular stimulated pattern. Within a mean-field approach, we computed the recognition order parameter and the full phase diagram as a function of the stimulus field strength h , the network charge α and a thermal-like noise T . The stimulus field improves the network capacity in recognizing the stimulated pattern while weakening the first-order character of the transition to the non-recognition phase. We further present simulation results for the zero temperature case. A finite-size scaling analysis provides estimates of the transition point which are very close to the mean-field prediction.