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Sample records for mean-field theory

  1. Algebraic Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Dankova, T. S.; Rosensteel, G.

    1998-10-01

    Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.

  2. Relativistic mean-field theory

    NASA Astrophysics Data System (ADS)

    Meng, Jie; Ring, Peter; Zhao, Pengwei

    In this chapter, the covariant energy density functional is constructed with both the meson-exchange and the point-coupling pictures. Several widely used functionals with either nonlinear or density-dependent effective interactions are introduced. The applications of covariant density functional theory are demonstrated for infinite nuclear matter and finite nuclei with spherical symmetry, axially symmetric quadrupole deformation, and triaxial quadrupole shapes. Finally, a relativistic description of the nuclear landscape has been discussed, which is not only important for nuclear structure, but also important for nuclear astrophysics, where we are facing the problem of a reliable extrapolation to the very neutron-rich nuclei.

  3. The Mean-Field Flux Pinning Theory

    NASA Astrophysics Data System (ADS)

    Stejic, George

    We develop the Mean-Field Flux Pinning Theory, designed to model the flux line lattice (FLL) as it interacts with itself, the flux pinning centers and the geometry of the superconductor. Like other mean-field theories, the mean-field flux pinning theory does not attempt to model the FLL completely. Instead, it utilizes a simplified model for the FLL, termed the mean-field FLL, in which the FLL is modelled as a continuous vector field rather than as discrete fluxons as in other theories. By so doing, the interactions of the FLL are greatly simplified and more easily modelled. One application of the mean-field flux pinning theory is to predict J_{c} from microstructural data, which we use to determine the optimal Nb-Ti microstructures with (1) alpha -Ti pinning centers and (2) Nb pinning centers. The microstructure is modelled on a grid in which the local values of T_{c} and kappa reflect the spatial distribution of the pinning centers and the superconductor. Using this model, we solve the G-L equations and calculate the pinning potential defined as the vortex free energy as a function of position. We conclude that the ideal Nb-Ti microstructure with alpha-Ti pinning centers would require 40 volume percent of alpha -Ti and have 6nm thick pinning centers. In the Nb pinning center case, the ideal microstructure requires 50 volume percent of Nb and would have 6nm pinning centers. Another application for the mean-field flux pinning theory is to model the FLL as it interacts with the penetrating magnetic fields within lambda of the superconducting surface. Using this theory, we study the effects of sample geometry on the FLL and J _{c} for the thin film geometry. We find that the FLL becomes increasingly distorted as the film thickness is reduced and that J_{c } increases sharply for dimensions less that lambda. These predictions are experimentally evaluated in Nb-Ti thin films. Our results show that J_{c} values as high as 1/3 of J_{d} and a strong orientational

  4. Beyond mean field theory: statistical field theory for neural networks

    PubMed Central

    Buice, Michael A; Chow, Carson C

    2014-01-01

    Mean field theories have been a stalwart for studying the dynamics of networks of coupled neurons. They are convenient because they are relatively simple and possible to analyze. However, classical mean field theory neglects the effects of fluctuations and correlations due to single neuron effects. Here, we consider various possible approaches for going beyond mean field theory and incorporating correlation effects. Statistical field theory methods, in particular the Doi–Peliti–Janssen formalism, are particularly useful in this regard. PMID:25243014

  5. Machine Learning for Dynamical Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Arsenault, Louis-Francois; Lopez-Bezanilla, Alejandro; von Lilienfeld, O. Anatole; Littlewood, P. B.; Millis, Andy

    2014-03-01

    Machine Learning (ML), an approach that infers new results from accumulated knowledge, is in use for a variety of tasks ranging from face and voice recognition to internet searching and has recently been gaining increasing importance in chemistry and physics. In this talk, we investigate the possibility of using ML to solve the equations of dynamical mean field theory which otherwise requires the (numerically very expensive) solution of a quantum impurity model. Our ML scheme requires the relation between two functions: the hybridization function describing the bare (local) electronic structure of a material and the self-energy describing the many body physics. We discuss the parameterization of the two functions for the exact diagonalization solver and present examples, beginning with the Anderson Impurity model with a fixed bath density of states, demonstrating the advantages and the pitfalls of the method. DOE contract DE-AC02-06CH11357.

  6. Mean field theory for long chain molecules

    NASA Astrophysics Data System (ADS)

    Pereira, Gerald G.

    1996-06-01

    We provide a mathematical formalism for a self-consistent mean field treatment of long chain molecules. The formalism is applied to the case of a neutral polymer under the excluded volume interaction. Upon scaling the problem in the N→∞ limit we find the natural scaling length RN, of the polymer, which is made up of (N+1) monomers or beads, is RN˜N3/5, the well known Flory result. The asymptotics of the problem is dominated by the neighborhood of the turning point, so that a uniformly valid Green's function solution of the differential equations is necessary. In the neighborhood of a point y* the scaled polymer density fN(x), is found to decay sharply. If we let x denote the scaled distance from one end of the chain to a point in space we obtain, for y*-x≳O(N-2/15), a closed form expression for the polymer density viz., fN(x)˜{1/2x2[fN(x)-fN(y*)]1/2} while for x-y*≳O(N-2/15) the density is shown to be, to leading order, zero. Although our results imply the rate of decay of the density at y* is O(N1/5) we are unable to verify this explicitly by calculating fN'(y*). We believe this is due to the inability of the WKB theory to correctly approximate solutions in regions of rapid variation. We suggest remedies for this, so that a complete self-consistent solution may be obtained.

  7. Mean Field Theory for Nonequilibrium Network Reconstruction

    NASA Astrophysics Data System (ADS)

    Roudi, Yasser; Hertz, John

    2011-01-01

    There has been recent progress on inferring the structure of interactions in complex networks when they are in stationary states satisfying detailed balance, but little has been done for nonequilibrium systems. Here we introduce an approach to this problem, considering, as an example, the question of recovering the interactions in an asymmetrically coupled, synchronously updated Sherrington-Kirkpatrick model. We derive an exact iterative inversion algorithm and develop efficient approximations based on dynamical mean-field and Thouless-Anderson-Palmer equations that express the interactions in terms of equal-time and one-time-step-delayed correlation functions.

  8. Mean-field theory of echo state networks

    NASA Astrophysics Data System (ADS)

    Massar, Marc; Massar, Serge

    2013-04-01

    Dynamical systems driven by strong external signals are ubiquitous in nature and engineering. Here we study “echo state networks,” networks of a large number of randomly connected nodes, which represent a simple model of a neural network, and have important applications in machine learning. We develop a mean-field theory of echo state networks. The dynamics of the network is captured by the evolution law, similar to a logistic map, for a single collective variable. When the network is driven by many independent external signals, this collective variable reaches a steady state. But when the network is driven by a single external signal, the collective variable is non stationary but can be characterized by its time averaged distribution. The predictions of the mean-field theory, including the value of the largest Lyapunov exponent, are compared with the numerical integration of the equations of motion.

  9. Mean-field theory of echo state networks.

    PubMed

    Massar, Marc; Massar, Serge

    2013-04-01

    Dynamical systems driven by strong external signals are ubiquitous in nature and engineering. Here we study "echo state networks," networks of a large number of randomly connected nodes, which represent a simple model of a neural network, and have important applications in machine learning. We develop a mean-field theory of echo state networks. The dynamics of the network is captured by the evolution law, similar to a logistic map, for a single collective variable. When the network is driven by many independent external signals, this collective variable reaches a steady state. But when the network is driven by a single external signal, the collective variable is non stationary but can be characterized by its time averaged distribution. The predictions of the mean-field theory, including the value of the largest Lyapunov exponent, are compared with the numerical integration of the equations of motion. PMID:23679475

  10. Development of mean-field electrical double layer theory

    NASA Astrophysics Data System (ADS)

    Yike, Huang; Xiaohong, Liu; Shu, Li; Tianying, Yan

    2016-01-01

    In order to understand the electric interfacial behavior, mean field based electric double layer (EDL) theory has been continuously developed over the past 150 years. In this article, we briefly review the development of the EDL model, from the dimensionless Gouy-Chapman model to the symmetric Bikerman-Freise model, and finally toward size-asymmetric mean field theory models. We provide the general derivations within the framework of Helmholtz free energy of the lattice-gas model, and it can be seen that the above-mentioned models are consistent in the sense that the interconversion among them can be achieved by reducing the basic assumptions. Project supported by the National Natural Science Foundation of China (Grant Nos. 21421001, 21373118, and 21203100), the Natural Science Foundation of Tianjin, China (Grant No. 13JCQNJC06700), the MOE Innovation Team of China (Grant No. IRT13022), and NFFTBS (Grant No. J1103306).

  11. Advanced mean-field theory of the restricted Boltzmann machine

    NASA Astrophysics Data System (ADS)

    Huang, Haiping; Toyoizumi, Taro

    2015-05-01

    Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean-field theory based on the Bethe approximation. Our theory provides an efficient message-passing-based method that evaluates not only the partition function (free energy) but also its gradients without requiring statistical sampling. The results are compared with those obtained by the computationally expensive sampling-based method.

  12. Mean-field theory of a recurrent epidemiological model.

    PubMed

    Nagy, Viktor

    2009-06-01

    Our purpose is to provide a mean-field theory for the discrete time-step susceptible-infected-recovered-susceptible (SIRS) model on uncorrelated networks with arbitrary degree distributions. The effect of network structure, time delays, and infection rate on the stability of oscillating and fixed point solutions is examined through analysis of discrete time mean-field equations. Consideration of two scenarios for disease contagion demonstrates that the manner in which contagion is transmitted from an infected individual to a contacted susceptible individual is of primary importance. In particular, the manner of contagion transmission determines how the degree distribution affects model behavior. We find excellent agreement between our theoretical results and numerical simulations on networks with large average connectivity. PMID:19658562

  13. Mean-field theory of a recurrent epidemiological model

    NASA Astrophysics Data System (ADS)

    Nagy, Viktor

    2009-06-01

    Our purpose is to provide a mean-field theory for the discrete time-step susceptible-infected-recovered-susceptible (SIRS) model on uncorrelated networks with arbitrary degree distributions. The effect of network structure, time delays, and infection rate on the stability of oscillating and fixed point solutions is examined through analysis of discrete time mean-field equations. Consideration of two scenarios for disease contagion demonstrates that the manner in which contagion is transmitted from an infected individual to a contacted susceptible individual is of primary importance. In particular, the manner of contagion transmission determines how the degree distribution affects model behavior. We find excellent agreement between our theoretical results and numerical simulations on networks with large average connectivity.

  14. Spin and orbital exchange interactions from Dynamical Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Secchi, A.; Lichtenstein, A. I.; Katsnelson, M. I.

    2016-02-01

    We derive a set of equations expressing the parameters of the magnetic interactions characterizing a strongly correlated electronic system in terms of single-electron Green's functions and self-energies. This allows to establish a mapping between the initial electronic system and a spin model including up to quadratic interactions between the effective spins, with a general interaction (exchange) tensor that accounts for anisotropic exchange, Dzyaloshinskii-Moriya interaction and other symmetric terms such as dipole-dipole interaction. We present the formulas in a format that can be used for computations via Dynamical Mean Field Theory algorithms.

  15. Mean-field theory of planar absorption of RNA molecules

    NASA Astrophysics Data System (ADS)

    Nguyen, Toan; Bruinsma, Robijn; Gelbart, William

    2006-03-01

    Interaction between the viral RNA and the protective protein capsid plays a very important role in the cell infection and self-assembly process of a virus. To better understand this interaction, we study a similar problem of absorption of RNA on an attractive wall. It is known that the secondary structure of a folded RNA molecules without pseudo-knots has the same topology as that of a branched polymer. We use a mean-field theory for branched polymers to analytically calculate the RNA concentration profile. The results are compared to known exact scaling calculations and computer simulations.

  16. Applicability of self-consistent mean-field theory

    SciTech Connect

    Guo Lu; Sakata, Fumihiko; Zhao Enguang

    2005-02-01

    Within the constrained Hartree-Fock (CHF) theory, an analytic condition is derived to estimate whether a concept of the self-consistent mean field is realized in the level repulsive region. The derived condition states that an iterative calculation of the CHF equation does not converge when the quantum fluctuations coming from two-body residual interaction and quadrupole deformation become larger than a single-particle energy difference between two avoided crossing orbits. By means of numerical calculation, it is shown that the analytic condition works well for a realistic case.

  17. The application of mean field theory to image motion estimation.

    PubMed

    Zhang, J; Hanauer, G G

    1995-01-01

    Previously, Markov random field (MRF) model-based techniques have been proposed for image motion estimation. Since motion estimation is usually an ill-posed problem, various constraints are needed to obtain a unique and stable solution. The main advantage of the MRF approach is its capacity to incorporate such constraints, for instance, motion continuity within an object and motion discontinuity at the boundaries between objects. In the MRF approach, motion estimation is often formulated as an optimization problem, and two frequently used optimization methods are simulated annealing (SA) and iterative-conditional mode (ICM). Although the SA is theoretically optimal in the sense of finding the global optimum, it usually takes many iterations to converge. The ICM, on the other hand, converges quickly, but its results are often unsatisfactory due to its "hard decision" nature. Previously, the authors have applied the mean field theory to image segmentation and image restoration problems. It provides results nearly as good as SA but with much faster convergence. The present paper shows how the mean field theory can be applied to MRF model-based motion estimation. This approach is demonstrated on both synthetic and real-world images, where it produced good motion estimates. PMID:18289956

  18. The effectiveness of mean-field theory for avalanche distributions

    NASA Astrophysics Data System (ADS)

    Lee, Edward; Raju, Archishman; Sethna, James

    We explore the mean-field theory of the pseudogap found in avalanche systems with long-range anisotropic interactions using analytical and numerical tools. The pseudogap in the density of low-stability states emerges from the competition between stabilizing interactions between spins in an avalanche and the destabilizing random movement towards the threshold caused by anisotropic couplings. Pazmandi et al. have shown that for the Sherrington-Kirkpatrick model, the pseudogap scales linearly and produces a distribution of avalanche sizes with exponent t=1 in contrast with that predicted from RFIM t=3/2. Lin et al. have argued that the scaling exponent ? of the pseudogap depends on the tail of the distribution of couplings and on non-universal values like the strain rate and the magnitude of the coupling strength. Yet others have argued that the relationship between the pseudogap scaling and the distribution of avalanche sizes is dependent on dynamical details. Despite the theoretical arguments, the class of RFIM mean-field models is surprisingly good at predicting the distribution of avalanche sizes in a variety of different magnetic systems. We investigate these differences with a combination of theory and simulation.

  19. Cluster dynamical mean field theory of the Mott transition.

    PubMed

    Park, H; Haule, K; Kotliar, G

    2008-10-31

    We address the nature of the Mott transition in the Hubbard model at half-filling using cluster dynamical mean field theory (DMFT). We compare cluster-DMFT results with those of single-site DMFT. We show that inclusion of the short-range correlations on top of the on-site correlations does not change the order of the transition between the paramagnetic metal and the paramagnetic Mott insulator, which remains first order. However, the short range correlations reduce substantially the critical U and modify the shape of the transition lines. Moreover, they lead to very different physical properties of the metallic and insulating phases near the transition point. Approaching the transition from the metallic side, we find an anomalous metallic state with very low coherence scale. The insulating state is characterized by the narrow Mott gap with pronounced peaks at the gap edge. PMID:18999845

  20. More is the Same; Phase Transitions and Mean Field Theories

    NASA Astrophysics Data System (ADS)

    Kadanoff, Leo P.

    2009-12-01

    This paper is the first in a series that will look at the theory of phase transitions from the perspectives of physics and the philosophy of science. The series will consider a group of related concepts derived from condensed matter and statistical physics. The key technical ideas go under the names of "singularity", "order parameter", "mean field theory", "variational method", "correlation length", "universality class", "scale changes", and "renormalization". The first four of these will be considered here. In a less technical vein, the question here is how can matter, ordinary matter, support a diversity of forms. We see this diversity each time we observe ice in contact with liquid water or see water vapor (steam) come up from a pot of heated water. Different phases can be qualitatively different in that walking on ice is well within human capacity, but walking on liquid water is proverbially forbidden to ordinary humans. These differences have been apparent to humankind for millennia, but only brought within the domain of scientific understanding since the 1880s. A phase transition is a change from one behavior to another. A first order phase transition involves a discontinuous jump in some statistical variable. The discontinuous property is called the order parameter. Each phase transition has its own order parameter. The possible order parameters range over a tremendous variety of physical properties. These properties include the density of a liquid-gas transition, the magnetization in a ferromagnet, the size of a connected cluster in a percolation transition, and a condensate wave function in a superfluid or superconductor. A continuous transition occurs when the discontinuity in the jump approaches zero. This article is about statistical mechanics and the development of mean field theory as a basis for a partial understanding of phase transition phenomena. Much of the material in this review was first prepared for the Royal Netherlands Academy of Arts and

  1. Multiagent model and mean field theory of complex auction dynamics

    NASA Astrophysics Data System (ADS)

    Chen, Qinghua; Huang, Zi-Gang; Wang, Yougui; Lai, Ying-Cheng

    2015-09-01

    Recent years have witnessed a growing interest in analyzing a variety of socio-economic phenomena using methods from statistical and nonlinear physics. We study a class of complex systems arising from economics, the lowest unique bid auction (LUBA) systems, which is a recently emerged class of online auction game systems. Through analyzing large, empirical data sets of LUBA, we identify a general feature of the bid price distribution: an inverted J-shaped function with exponential decay in the large bid price region. To account for the distribution, we propose a multi-agent model in which each agent bids stochastically in the field of winner’s attractiveness, and develop a theoretical framework to obtain analytic solutions of the model based on mean field analysis. The theory produces bid-price distributions that are in excellent agreement with those from the real data. Our model and theory capture the essential features of human behaviors in the competitive environment as exemplified by LUBA, and may provide significant quantitative insights into complex socio-economic phenomena.

  2. Mean-field theory of four species in cyclic competition

    NASA Astrophysics Data System (ADS)

    Durney, C. H.; Case, S. O.; Pleimling, M.; Zia, R. K. P.

    2011-03-01

    We consider a simple model of cyclic competition of M species: When a pair of individuals from species k and k + 1 interact, the latter transforms into the former. Even with no spatial structure, such systems often display interesting and counterintuitive behavior. With possible applications in both biological systems (e.g., Min proteins, E. Coli, lizards) and game theory (e.g., rock-paper-scissors), the M = 3 case has attracted considerable recent attention. We study a M = 4 system (with no spatial structure) and find major differences, e.g., (1) the presence of macroscopically many absorbing states, (2) coexistence of species, and (3) violation of the ``law'' of survival of the weakest - a central theme in the M = 3 case. Like the game of Bridge, the system typically ends with ``partner pairs.'' After describing the full stochastic model and its master equation, we present the mean-field approximation. Several exact, analytic predictions will be shown. Their limitations and implications for the stochastic system will also be discussed. Supported in part by NSF-DMR-0705152, 0904999, 1005417.

  3. Effects of δ mesons in relativistic mean field theory

    NASA Astrophysics Data System (ADS)

    Singh, Shailesh K.; Biswal, S. K.; Bhuyan, M.; Patra, S. K.

    2014-04-01

    The effect of δ- and ω-ρ-meson cross couplings on asymmetry nuclear systems are analyzed in the framework of an effective field theory motivated relativistic mean field formalism. The calculations are done on top of the G2 parameter set, where these contributions are absent. To show the effect of δ meson on the nuclear system, we split the isospin coupling into two parts: (i) gρ due to ρ meson and (ii) gδ for δ meson. Thus, our investigation is based on varying the coupling strengths of the δ and ρ mesons to reproduce the binding energies of the nuclei Ca48 and Pb208. We calculate the root mean square radius, binding energy, single particle energy, density, and spin-orbit interaction potential for some selected nuclei and evaluate the Lsym and Esym coefficients for nuclear matter as function of δ- and ω-ρ-meson coupling strengths. As expected, the influence of these effects are negligible for the symmetric nuclear system, but substantial for the contribution with large isospin asymmetry.

  4. Real-space renormalized dynamical mean field theory

    NASA Astrophysics Data System (ADS)

    Kubota, Dai; Sakai, Shiro; Imada, Masatoshi

    2016-05-01

    We propose real-space renormalized dynamical mean field theory (rr-DMFT) to deal with large clusters in the framework of a cluster extension of the DMFT. In the rr-DMFT, large clusters are decomposed into multiple smaller clusters through a real-space renormalization. In this work, the renormalization effect is taken into account only at the lowest order with respect to the intercluster coupling, which nonetheless reproduces exactly both the noninteracting and atomic limits. Our method allows us large cluster-size calculations which are intractable with the conventional cluster extensions of the DMFT with impurity solvers, such as the continuous-time quantum Monte Carlo and exact diagonalization methods. We benchmark the rr-DMFT for the two-dimensional Hubbard model on a square lattice at and away from half filling, where the spatial correlations play important roles. Our results on the spin structure factor indicate that the growth of the antiferromagnetic spin correlation is taken into account beyond the decomposed cluster size. We also show that the self-energy obtained from the large-cluster solver is reproduced by our method better than the solution obtained directly for the smaller cluster. When applied to the Mott metal-insulator transition, the rr-DMFT is able to reproduce the reduced critical value for the Coulomb interaction comparable to the large cluster result.

  5. Hot and dense matter beyond relativistic mean field theory

    NASA Astrophysics Data System (ADS)

    Zhang, Xilin; Prakash, Madappa

    2016-05-01

    Properties of hot and dense matter are calculated in the framework of quantum hadrodynamics by including contributions from two-loop (TL) diagrams arising from the exchange of isoscalar and isovector mesons between nucleons. Our extension of mean field theory (MFT) employs the same five density-independent coupling strengths which are calibrated using the empirical properties at the equilibrium density of isospin-symmetric matter. Results of calculations from the MFT and TL approximations are compared for conditions of density, temperature, and proton fraction encountered in the study of core-collapse supernovae, young and old neutron stars, and mergers of compact binary stars. The TL results for the equation of state (EOS) of cold pure neutron matter at sub- and near-nuclear densities agree well with those of modern quantum Monte Carlo and effective field-theoretical approaches. Although the high-density EOS in the TL approximation for cold and β -equilibrated neutron-star matter is substantially softer than its MFT counterpart, it is able to support a 2 M⊙ neutron star required by recent precise determinations. In addition, radii of 1.4 M⊙ stars are smaller by ˜1 km than those obtained in MFT and lie in the range indicated by analysis of astronomical data. In contrast to MFT, the TL results also give a better account of the single-particle or optical potentials extracted from analyses of medium-energy proton-nucleus and heavy-ion experiments. In degenerate conditions, the thermal variables are well reproduced by results of Landau's Fermi-liquid theory in which density-dependent effective masses feature prominently. The ratio of the thermal components of pressure and energy density expressed as Γth=1 +(Pth/ɛth) , often used in astrophysical simulations, exhibits a stronger dependence on density than on proton fraction and temperature in both MFT and TL calculations. The prominent peak of Γth at supranuclear density found in MFT is, however, suppressed in

  6. Dynamical mean-field theory for transition metal dioxide molecules

    NASA Astrophysics Data System (ADS)

    Lin, Nan; Zgid, Dominika; Marianetti, Chris; Reichman, David; Millis, Andrew

    2012-02-01

    The utility of the dynamical mean-field approximation in quantum chemistry is investigated in the context of transition metal dioxide molecules including TiO2 and CrO2. The choice of correlated orbitals and correlations to treat dynamically is discussed. The dynamical mean field solutions are compared to state of the art quantum chemical calculations. The dynamical mean-field method is found to capture about 50% of the total correlation energy, and to produce very good results for the d-level occupancies and magnetic moments. We also present the excitation spectrum in these molecules which is inaccessible in many wave-function based methods. Conceptual and technical difficulties will be outlined and discussed.

  7. Mean field theory for scale-free random networks

    NASA Astrophysics Data System (ADS)

    Barabási, Albert-László; Albert, Réka; Jeong, Hawoong

    1999-10-01

    Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information is available display scale-free features. Here we study the scaling properties of the recently introduced scale-free model, that can account for the observed power-law distribution of the connectivities. We develop a mean-field method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the scaling exponents. The mean-field method can be used to address the properties of two variants of the scale-free model, that do not display power-law scaling.

  8. Calorimetric glass transition in a mean-field theory approach

    PubMed Central

    Mariani, Manuel Sebastian; Parisi, Giorgio; Rainone, Corrado

    2015-01-01

    The study of the properties of glass-forming liquids is difficult for many reasons. Analytic solutions of mean-field models are usually available only for systems embedded in a space with an unphysically high number of spatial dimensions; on the experimental and numerical side, the study of the properties of metastable glassy states requires thermalizing the system in the supercooled liquid phase, where the thermalization time may be extremely large. We consider here a hard-sphere mean-field model that is solvable in any number of spatial dimensions; moreover, we easily obtain thermalized configurations even in the glass phase. We study the 3D version of this model and we perform Monte Carlo simulations that mimic heating and cooling experiments performed on ultrastable glasses. The numerical findings are in good agreement with the analytical results and qualitatively capture the features of ultrastable glasses observed in experiments. PMID:25675523

  9. Small-World Network Spectra in Mean-Field Theory

    NASA Astrophysics Data System (ADS)

    Grabow, Carsten; Grosskinsky, Stefan; Timme, Marc

    2012-05-01

    Collective dynamics on small-world networks emerge in a broad range of systems with their spectra characterizing fundamental asymptotic features. Here we derive analytic mean-field predictions for the spectra of small-world models that systematically interpolate between regular and random topologies by varying their randomness. These theoretical predictions agree well with the actual spectra (obtained by numerical diagonalization) for undirected and directed networks and from fully regular to strongly random topologies. These results may provide analytical insights to empirically found features of dynamics on small-world networks from various research fields, including biology, physics, engineering, and social science.

  10. Avalanche shape and exponents beyond mean-field theory

    NASA Astrophysics Data System (ADS)

    Dobrinevski, Alexander; Le Doussal, Pierre; Jörg Wiese, Kay

    2014-12-01

    Elastic systems, such as magnetic domain walls, density waves, contact lines, and cracks, are pinned by substrate disorder. When driven, they move via avalanches, with power law distributions of size, duration and velocity. Their exponents, and the shape of an avalanche, defined as its mean velocity as a function of time, were studied. They are known approximatively from experiments and simulations, and were predicted from mean-field models, such as the Brownian force model (BFM), where each point of the elastic interface sees a force field which itself is a random walk. As we showed in EPL, 97 (2012) 46004, the BFM is the starting point for an \\varepsilon = d\\text{c}-d expansion around the upper critical dimension, with d\\text{c}=4 for short-ranged elasticity, and d\\text{c}=2 for long-ranged elasticity. Here we calculate analytically the O}(\\varepsilon) , i.e. 1-loop, correction to the avalanche shape at fixed duration T, for both types of elasticity. The exact expression, though different from the phenomenological form presented by Laurson et al. in Nat. Commun., 4 (2013) 2927, is well approximated by ≤ft< \\dot u(t=x T)\\right>_T≃ [ Tx(1-x)]γ-1 \\exp≤ft( A}≤ft[\\frac12-x\\right]\\right) , 0 < x < 1. The asymmetry A}≈ - 0.336 (1-d/d\\text{c}) is negative for d close to d\\text{c} , skewing the avalanche towards its end, as observed in numerical simulations in d = 2 and 3. The exponent γ=(d+\\zeta)/z is given by the two independent exponents at depinning, the roughness ζ and the dynamical exponent z. We propose a general procedure to predict other avalanche exponents in terms of ζ and z. We finally introduce and calculate the shape at fixed avalanche size, not yet measured in experiments or simulations.

  11. Comparisons and connections between mean field dynamo theory and accretion disc theory

    NASA Astrophysics Data System (ADS)

    Blackman, E. G.

    2010-01-01

    The origin of large scale magnetic fields in astrophysical rotators, and the conversion of gravitational energy into radiation near stars and compact objects via accretion have been subjects of active research for a half century. Magnetohydrodynamic turbulence makes both problems highly nonlinear, so both subjects have benefitted from numerical simulations.However, understanding the key principles and practical modeling of observations warrants testable semi-analytic mean field theories that distill the essential physics. Mean field dynamo (MFD) theory and alpha-viscosity accretion disc theory exemplify this pursuit. That the latter is a mean field theory is not always made explicit but the combination of turbulence and global symmetry imply such. The more commonly explicit presentation of assumptions in 20th century textbook MFDT has exposed it to arguably more widespread criticism than incurred by 20th century alpha-accretion theory despite complementary weaknesses. In the 21st century however, MFDT has experienced a breakthrough with a dynamical saturation theory that consistently agrees with simulations. Such has not yet occurred in accretion disc theory, though progress is emerging. Ironically however, for accretion engines, MFDT and accretion theory are presently two artificially uncoupled pieces of what should be a single coupled theory. Large scale fields and accretion flows are dynamically intertwined because large scale fields likely play a key role in angular momentum transport. I discuss and synthesize aspects of recent progress in MFDT and accretion disc theory to suggest why the two likely conspire in a unified theory.

  12. Mean-Field Theory of the Solar Dynamo

    NASA Astrophysics Data System (ADS)

    Schmitt, D.

    The generation of the solar magnetic field is generally ascribed to dynamo processes in the convection zone. The dynamo effects, differential rotation (Omega-effect) and helical turbulence (alpha-effect) are explained, and the basic properties of the mean-field dynamo equations are discussed in view of the observed properties of the solar cycle. Problems of the classical picture of a dynamo in the convection zone (fibril state of magnetic flux, field strength, magnetic buoyancy, polarity rules, differential rotation and butterfly diagram) are addressed and some alternatives to overcome these problems are presented. A possibility to make up for the missing radial gradient of rotation in the convection zone is an alpha^2-Omega-dynamo with an anisotropic alpha-tensor. Dynamo solutions then might have the characteristics of the butterfly diagram. Another approach involves meridional circulation as the cause of the migration of a dynamo wave. Another suggestion is that the solar dynamo operates in the overshoot region at the base of the convection zone where strong fields, necessary to explain the polarity rules, can be stored and radial gradients in the angular velocity occur. As an alternative to the turbulent alpha-effect a dynamic alpha-effect based on magnetostrophic waves driven by a magnetic buoyancy instability of a magnetic flux layer is introduced. Model calculations which use the internal rotation of the Sun as deduced from helioseismology only show solar cycle behaviour if the turbulent diffusivity is reduced in the layer and the alpha-effect is concentrated near the equator. Another possibility is a combined model. The non-uniform rotation and most of the azimuthal magnetic flux are confined to a thin layer at the bottom of the convection zone where turbulent diffusion is greatly reduced, with the convective region above containing only weak fields for which the alpha-effect and turbulent diffusion operate in the conventional manner. The dynamo takes on the

  13. Mean-field theory of the solar dynamo

    NASA Astrophysics Data System (ADS)

    Schmitt, Dieter

    The generation of the solar magnetic field is generally ascribed to dynamo processes in the convection zone. The dynamo effects, differential rotation (Ω-effect and helical turbulence (α-effect are explained, and the basic properties of the mean-field dynamo equations are discussed in view of the observed properties of the solar cycle. Problems of the classical picture of a dynamo in the convection zone (fibril state of magnetic flux, field strength, magnetic buoyancy, polarity rules, differential rotation and butterfly diagram) are addressed and some alternatives to overcome these problems are presented. A possibility to make up for the missing radial gradient of rotation in the convection zone is an α2 Ω-dynamo with an anisotropic a-tensor. Dynamo solutions then might have the characteristics of the butterfly diagram. Another approach involves meridional circulation as the cause of the migration of a dynamo wave. Another suggestion is that the solar dynamo operates in the overshoot region at the base of the convection zone where strong fields, necessary to explain the polarity rules, can be stored and radial gradients in the angular velocity occur. As an alternative to the turbulent α-effect a dynamic α-effect based on magnetostrophic waves driven by a magnetic buoyancy instability of a magnetic flux layer is introduced. Model calculations which use the internal rotation of the Sun as deduced from helioseismology only show solar cycle behaviour if the turbulent diffusivity is reduced in the layer and the a-effect is concentrated near the equator. Another possibility is a combined model. The non-uniform rotation and most of the azimuthal magnetic flux are confined to a thin layer at the bottom of the convection zone where turbulent diffusion is greatly reduced, with the convective region above containing only weak fields for which the α-effect and turbulent diffusion operate in the conventional manner. The dynamo takes on the character of a surface wave at

  14. Mean-field theory for Bose-Hubbard model under a magnetic field

    SciTech Connect

    Oktel, M. Oe.; Tanatar, B.; Nita, M.

    2007-01-15

    We consider the superfluid-insulator transition for cold bosons under an effective magnetic field. We investigate how the applied magnetic field affects the Mott transition within mean-field theory and find that the critical hopping strength (t/U){sub c} increases with the applied field. The increase in the critical hopping follows the bandwidth of the Hofstadter butterfly at the given value of the magnetic field. We also calculate the magnetization and superfluid density within mean-field theory.

  15. Field Theory On the World Sheet: Mean Field Expansion And Cutoff Dependence

    SciTech Connect

    Bardakci, Korkut; Bardakci, Korkut

    2007-01-10

    Continuing earlier work, we apply the mean field method to the world sheet representation of a simple field theory. In particular, we study the higher order terms in the mean field expansion, and show that their cutoff dependence can be absorbed into a running coupling constant. The coupling constant runs towards zero in the infrared, and the model tends towards a free string. One cannot fully reach this limit because of infrared problems, however, one can still apply the mean field method to the high energy limit (high mass states) of the string.

  16. Existence of a solution to an equation arising from the theory of Mean Field Games

    NASA Astrophysics Data System (ADS)

    Gangbo, Wilfrid; Święch, Andrzej

    2015-12-01

    We construct a small time strong solution to a nonlocal Hamilton-Jacobi equation (1.1) introduced in [48], the so-called master equation, originating from the theory of Mean Field Games. We discover a link between metric viscosity solutions to local Hamilton-Jacobi equations studied in [2,19,20] and solutions to (1.1). As a consequence we recover the existence of solutions to the First Order Mean Field Games equations (1.2), first proved in [48], and make a more rigorous connection between the master equation (1.1) and the Mean Field Games equations (1.2).

  17. On the gap problem for the Mott--Hubbard transition within Dynamical Mean-Field Theory

    NASA Astrophysics Data System (ADS)

    Noack, Reinhard M.; Gebhard, Florian

    1998-03-01

    Within the Dynamical Mean-Field Theory, the zero temperature Mott-Hubbard metal-to-insulator transition has been proposed to be discontinuous in the sense that the gap jumps to a finite value at the transition.(A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Rev. Mod. Phys. 68), 13 (1996). We use the Random Dispersion Approximation to the Hubbard model,(F. Gebhard, The Mott Metal-Insulator Transition), Springer Tracts in Modern Physics 137 (Springer, Berlin, 1997). which becomes equivalent to the Dynamical Mean-Field Theory in the thermodynamic limit, to show that the charge gap opens continuously at the critical interaction strength which is of the size of the bandwidth. Therefore, our results support the idea^2 that the Dynamical Mean Field Theory provides a generic description of the Mott--Hubbard transition as a continuous quantum phase transition.

  18. Configuration Interaction as an Impurity Solver: Benchmark Dynamical Mean-Field Theory for the Hubbard Model

    NASA Astrophysics Data System (ADS)

    Go, Ara; Millis, Andrew J.

    2013-03-01

    The configuration interaction technique has been widely used in quantum chemistry to solve quantum many body systems with lower computational costs than exact diagonalization and was introduced by Dominika Zgid, Emanuel Gull, and Garnet Kin-Lic Chan [Phys. Rev. B 86, 165128 (2012)] as a solver for the impurity models of dynamical mean field theory. We extend their work, demonstrating for the one and two dimensional Hubbard model how the method reproduces the known results and allows convergence with bath size to be studied in cluster dynamical mean field theory. As an example of the power of the method, cluster dynamical mean field studies of the three band copper-oxygen model are presented. This work was supported by the CMCSN program of the US Department of Energy.

  19. Mean-field theory of spin-glasses with finite coordination number

    NASA Technical Reports Server (NTRS)

    Kanter, I.; Sompolinsky, H.

    1987-01-01

    The mean-field theory of dilute spin-glasses is studied in the limit where the average coordination number is finite. The zero-temperature phase diagram is calculated and the relationship between the spin-glass phase and the percolation transition is discussed. The present formalism is applicable also to graph optimization problems.

  20. Phase transition studies of BiMnO{sub 3}: Mean field theory approximations

    SciTech Connect

    Lakshmi Priya, K. B.; Natesan, Baskaran

    2015-06-24

    We studied the phase transition and magneto-electric coupling effect of BiMnO{sub 3} by employing mean field theory approximations. To capture the ferromagnetic and ferroelectric transitions of BiMnO{sub 3}, we construct an extended Ising model in a 2D square lattice, wherein, the magnetic (electric) interactions are described in terms of the direct interactions between the localized magnetic (electric dipole) moments of Mn ions with their nearest neighbors. To evaluate our model, we obtain magnetization, magnetic susceptibility and electric polarization using mean field approximation calculations. Our results reproduce both the ferromagnetic and the ferroelectric transitions, matching very well with the experimental reports. Furthermore, consistent with experimental observations, our mean field results suggest that there is indeed a coupling between the magnetic and electric ordering in BiMnO{sub 3}.

  1. Time-odd mean fields in covariant density functional theory: Rotating systems

    NASA Astrophysics Data System (ADS)

    Afanasjev, A. V.; Abusara, H.

    2010-09-01

    Time-odd mean fields (nuclear magnetism) and their impact on physical observables in rotating nuclei are studied in the framework of covariant density functional theory (CDFT). It is shown that they have profound effect on the dynamic and kinematic moments of inertia. Particle number, configuration, and rotational frequency dependencies of their impact on the moments of inertia have been analyzed in a systematic way. Nuclear magnetism can also considerably modify the band crossing features such as crossing frequencies and the properties of the kinematic and dynamic moments of inertia in the band crossing region. The impact of time-odd mean fields on the moments of inertia in the regions away from band crossing only weakly depends on the relativistic mean-field parametrization, reflecting good localization of the properties of time-odd mean fields in CDFT. The moments of inertia of normal-deformed nuclei considerably deviate from the rigid-body value. On the contrary, superdeformed and hyperdeformed nuclei have the moments of inertia which are close to rigid-body value. The structure of the currents in rotating frame, their microscopic origin, and the relations to the moments of inertia have been systematically analyzed. The phenomenon of signature separation in odd-odd nuclei, induced by time-odd mean fields, has been analyzed in detail.

  2. Mean-field theory of atomic self-organization in optical cavities

    NASA Astrophysics Data System (ADS)

    Jäger, Simon B.; Schütz, Stefan; Morigi, Giovanna

    2016-08-01

    Photons mediate long-range optomechanical forces between atoms in high-finesse resonators, which can induce the formation of ordered spatial patterns. When a transverse laser drives the atoms, the system undergoes a second-order phase transition that separates a uniform spatial density from a Bragg grating maximizing scattering into the cavity and is controlled by the laser intensity. Starting from a Fokker-Planck equation describing the semiclassical dynamics of the N -atom distribution function, we systematically develop a mean-field model and analyze its predictions for the equilibrium and out-of-equilibrium dynamics. The validity of the mean-field model is tested by comparison with the numerical simulations of the N -body Fokker-Planck equation and by means of a Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. The mean-field theory predictions well reproduce several results of the N -body Fokker-Planck equation for sufficiently short times and are in good agreement with existing theoretical approaches based on field-theoretical models. The mean field, on the other hand, predicts thermalization time scales which are at least one order of magnitude shorter than the ones predicted by the N -body dynamics. We attribute this discrepancy to the fact that the mean-field ansatz discards the effects of the long-range incoherent forces due to cavity losses.

  3. Time-odd mean fields in covariant density functional theory: Rotating systems

    SciTech Connect

    Afanasjev, A. V.; Abusara, H.

    2010-09-15

    Time-odd mean fields (nuclear magnetism) and their impact on physical observables in rotating nuclei are studied in the framework of covariant density functional theory (CDFT). It is shown that they have profound effect on the dynamic and kinematic moments of inertia. Particle number, configuration, and rotational frequency dependencies of their impact on the moments of inertia have been analyzed in a systematic way. Nuclear magnetism can also considerably modify the band crossing features such as crossing frequencies and the properties of the kinematic and dynamic moments of inertia in the band crossing region. The impact of time-odd mean fields on the moments of inertia in the regions away from band crossing only weakly depends on the relativistic mean-field parametrization, reflecting good localization of the properties of time-odd mean fields in CDFT. The moments of inertia of normal-deformed nuclei considerably deviate from the rigid-body value. On the contrary, superdeformed and hyperdeformed nuclei have the moments of inertia which are close to rigid-body value. The structure of the currents in rotating frame, their microscopic origin, and the relations to the moments of inertia have been systematically analyzed. The phenomenon of signature separation in odd-odd nuclei, induced by time-odd mean fields, has been analyzed in detail.

  4. Hidden Fermi liquid, scattering rate saturation, and Nernst effect: a dynamical mean-field theory perspective.

    PubMed

    Xu, Wenhu; Haule, Kristjan; Kotliar, Gabriel

    2013-07-19

    We investigate the transport properties of a correlated metal within dynamical mean-field theory. Canonical Fermi liquid behavior emerges only below a very low temperature scale T(FL). Surprisingly the quasiparticle scattering rate follows a quadratic temperature dependence up to much higher temperatures and crosses over to saturated behavior around a temperature scale T(sat). We identify these quasiparticles as constituents of the hidden Fermi liquid. The non-Fermi-liquid transport above T(FL), in particular the linear-in-T resistivity, is shown to be a result of a strongly temperature dependent band dispersion. We derive simple expressions for the resistivity, Hall angle, thermoelectric power and Nernst coefficient in terms of a temperature dependent renormalized band structure and the quasiparticle scattering rate. We discuss possible tests of the dynamical mean-field theory picture of transport using ac measurements. PMID:23909344

  5. Mean field theory of the linear sigma-model: chiral solitons

    SciTech Connect

    Kahana, S.; Ripka, G.

    1983-01-01

    The mean field theory of the chiral invariant sigma-model is outlined. bound states (solitons) of valence quarks are obtained self-consistently using a hedgehog shape for the pion field. A schematic model for the coupled fermion-boson fields is presented. Renormalization is worked out for the fermion one-loop corrections and numerical results presented for the purely scalar-field case. The interpretation of the baryon number of the perturbed vacuum is considered.

  6. From effective field theories to effective density functionals in and beyond the mean field

    NASA Astrophysics Data System (ADS)

    Grasso, M.; Lacroix, D.; van Kolck, U.

    2016-06-01

    Since the 1975 Nobel Prize in Physics, nuclear theory has evolved along two main directions. On the one hand, the energy–density functional (EDF) theory was established, which presently encompasses (by enlarging the EDF framework) all the mean-field and beyond-mean-field theories based on energy functionals produced by effective phenomenological interactions. Highly sophisticated structure and reaction models are currently available for the treatment of medium-mass and heavy nuclei. On the other hand, effective field theories (EFTs) have rendered possible the formulation of QCD as a low-energy hadronic theory. Ab initio methods have recently achieved remarkable success in the application of EFT or EFT-inspired potentials to structure analyses of light nuclei. Different but complementary competences have been developed during the past few decades in the EDF and EFT communities. Bridges and connections have in some cases been identified and constructed. We review here some of the developments that have been performed within the EDF theory and the EFT during recent years, with some emphasis on analogies and connections that may one day provide a unified picture of the two theories. Illustrations are given for infinite matter and finite nuclei.

  7. Spin Chain in Magnetic Field: Limitations of the Large-N Mean-Field Theory

    SciTech Connect

    Wohlfeld, K.; Chen, Cheng-Chien; van Veenendaal, M. ; Devereaux, T. P.

    2015-02-01

    Motivated by the recent success in describing the spin and orbital spectrum of a spin-orbital chain using a large-N mean-field approximation [Phys. Rev. B 91, 165102 (2015)], we apply the same formalism to the case of a spin chain in the external magnetic field. It occurs that in this case, which corresponds to N=2 in the approximation, the large-N mean-field theory cannot qualitatively reproduce the spin excitation spectra at high magnetic fields, which polarize more than 50% of the spins in the magnetic ground state. This, rather counterintuitively, shows that the physics of a spin chain can under some circumstances be regarded as more complex than the physics of a spin-orbital chain.

  8. Spin Chain in Magnetic Field: Limitations of the Large-N Mean-Field Theory

    DOE PAGESBeta

    Wohlfeld, K.; Chen, Cheng-Chien; van Veenendaal, M.; Devereaux, T. P.

    2015-02-01

    Motivated by the recent success in describing the spin and orbital spectrum of a spin-orbital chain using a large-N mean-field approximation [Phys. Rev. B 91, 165102 (2015)], we apply the same formalism to the case of a spin chain in the external magnetic field. It occurs that in this case, which corresponds to N=2 in the approximation, the large-N mean-field theory cannot qualitatively reproduce the spin excitation spectra at high magnetic fields, which polarize more than 50% of the spins in the magnetic ground state. This, rather counterintuitively, shows that the physics of a spin chain can under some circumstancesmore » be regarded as more complex than the physics of a spin-orbital chain.« less

  9. Proton and neutron skins of light nuclei within the relativistic mean field theory

    NASA Astrophysics Data System (ADS)

    Geng, L. S.; Toki, H.; Ozawa, A.; Meng, J.

    2004-01-01

    The relativistic mean field (RMF) theory is applied to the analysis of ground-state properties of Ne, Na, Cl and Ar isotopes. In particular, we study the recently established proton skin in Ar isotopes and neutron skin in Na isotopes as a function of the difference between the proton and the neutron separation energy. We use the TMA effective interaction in the RMF Lagrangian, and describe pairing correlation by the density-independent delta-function interaction. We calculate single neutron and proton separation energies, quadrupole deformations, nuclear matter radii and differences between proton radii and neutron radii, and compare these results with the recent experimental data.

  10. The D-D¯ mesons matter in Walecka's mean field theory

    NASA Astrophysics Data System (ADS)

    de Farias Freire, M. L.; Rodrigues da Silva, R.

    2010-11-01

    We study the D-D¯ mesons matter in the framework of σ and ω meson exchange model using Walecka's mean field theory. We choose the equal number of D and anti-D meson then we get <ω0> = 0 and the <σ> field exhibits a critical temperature around 1.2 GeV. We investigate effective mass and pressure. We conclude that this matter is a gas and these results are not favorable for the existence of D-D¯ bound state.

  11. Double occupancy in dynamical mean-field theory and the dual boson approach

    NASA Astrophysics Data System (ADS)

    van Loon, Erik G. C. P.; Krien, Friedrich; Hafermann, Hartmut; Stepanov, Evgeny A.; Lichtenstein, Alexander I.; Katsnelson, Mikhail I.

    2016-04-01

    We discuss the calculation of the double occupancy using dynamical mean-field theory in finite dimensions. The double occupancy can be determined from the susceptibility of the auxiliary impurity model or from the lattice susceptibility. The former method typically overestimates, whereas the latter underestimates the double occupancy. We illustrate this for the square-lattice Hubbard model. We propose an approach for which both methods lead to identical results by construction and which resolves this ambiguity. This self-consistent dual boson scheme results in a double occupancy that is numerically close to benchmarks available in the literature.

  12. Simple Mean-Field Theory for a Zero-Temperature Fermionic Gas at a Feshbach Resonance

    SciTech Connect

    Javanainen, Juha; Kostrun, Marijan; Carmichael, Andrew; Mackie, Matt

    2005-09-09

    We present a simple two-channel mean-field theory for a zero-temperature two-component Fermi gas in the neighborhood of a Feshbach resonance. Our results agree with recent experiments on the bare-molecule fraction as a function of magnetic field [Partridge et al., Phys. Rev. Lett. 95, 020404 (2005)]. Even in this strongly coupled gas of {sup 6}Li, the experimental results depend on the structure of the molecules formed in the Feshbach resonance and, therefore, are not universal.

  13. Two-color spectroscopy of fermions in mean-field BCS-BEC crossover theory

    SciTech Connect

    Kostrun, Marijan; Cote, Robin

    2006-04-15

    We calculate two-photon Raman spectra for fermionic atoms with interactions described by a single-mode mean-field BCS-BEC crossover theory. We compare calculated spectra of interacting and noninteracting systems and find that interactions lead to the appearance of correlated atomic pair signal due to Cooper pairs; splitting of peaks in the spectroscopic signal due to the gap in fermionic dispersion; and attenuation of signal due to the partial conversion of fermions into the corresponding single-mode dimer. By exploring the behavior of these effects, one can obtain quantitative estimates of the BCS parameters from the spectra.

  14. Mean field theory of ionic free energy using scaled binding energies

    NASA Astrophysics Data System (ADS)

    Bhattacharya, Chandrani; Menon, S. V. G.

    2009-03-01

    A mean field model for ionic free energy is developed using the scaled binding energy formula. The model is evaluated using experimental data on Hugoniot, phase diagrams, melting curves, and other thermodynamic parameters of several solids. Predictions of the model are also compared with the Debye-Gruneisen theory, which is also based on the same binding energy formula. The binding energy formulation employs just four parameters, all corresponding to ambient condition—density, bulk modulus, its pressure derivative, and cohesive energy. These are obtained either from experiments or electronic structure theory. The Debye-Gruneisen theory compares better with available data for the phase diagrams of iron, zirconium, and titanium. However, the Hugoniot and melting curves obtained using both models yield similar results.

  15. Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles

    NASA Astrophysics Data System (ADS)

    Chou, Yen-Liang; Ihle, Thomas

    2015-02-01

    Recently, Hanke et al. [Phys. Rev. E 88, 052309 (2013), 10.1103/PhysRevE.88.052309] showed that mean-field kinetic theory fails to describe collective motion in soft active colloids and that correlations must not be neglected. Correlation effects are also expected to be essential in systems of biofilaments driven by molecular motors and in swarms of midges. To obtain correlations in an active matter system from first principles, we derive a ring-kinetic theory for Vicsek-style models of self-propelled agents from the exact N -particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle precollisional correlations and cluster formation, which are both important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small-density expansion of the collision operator and derive the first two equations of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. An algorithm is presented that numerically solves the evolution equation for the two-particle correlations on a lattice. Agent-based simulations are performed and informative quantities such as orientational and density correlation functions are compared with those obtained by ring-kinetic theory. Excellent quantitative agreement between simulations and theory is found at not-too-small noises and mean free paths. This shows that there are parameter ranges in Vicsek-like models where the correlated closure of the BBGKY hierarchy gives correct and nontrivial results. We calculate the dependence of the orientational correlations on distance in the disordered phase and find that it seems to be consistent with a power law with an exponent around -1.8 , followed by an exponential decay. General limitations of the kinetic theory and its numerical solution are discussed.

  16. Double counting in the density functional plus dynamical mean-field theory of transition metal oxides

    NASA Astrophysics Data System (ADS)

    Dang, Hung

    2015-03-01

    Recently, the combination of density functional theory (DFT) and dynamical mean-field theory (DMFT) has become a widely-used beyond-mean-field approach for strongly correlated materials. However, not only is the correlation treated in DMFT but also in DFT to some extent, a problem arises as the correlation is counted twice in the DFT+DMFT framework. The correction for this problem is still not well-understood. To gain more understanding of this ``double counting'' problem, I provide a detailed study of the metal-insulator transition in transition metal oxides in the subspace of oxygen p and transition metal correlated d orbitals using DFT+DMFT. I will show that the fully charge self-consistent DFT+DMFT calculations with the standard ``fully-localized limit'' (FLL) double counting correction fail to predict correctly materials such as LaTiO3, LaVO3, YTiO3 and SrMnO3 as insulators. Investigations in a wide range of the p- d splitting, the d occupancy, the lattice structure and the double counting correction itself will be presented to understand the reason behind this failure. I will also show that if the double counting correction is chosen to reproduce the p- d splitting consistent with experimental data, the DFT+DMFT approach can still give reasonable results in comparison with experiments.

  17. Implementing the density matrix embedding theory with the hierarchical mean-field approach

    NASA Astrophysics Data System (ADS)

    Qin, Jingbo; Jie, Quanlin; Fan, Zhuo

    2016-07-01

    We show an implementation of density matrix embedding theory (DMET) for the spin lattice of infinite size. It is indeed a special form of hierarchical mean-field (HMF) theory. In the method, we divide the lattice into a small part and a large part. View the small part as an impurity, embedding in the large part, which is viewed as the environment. We deal the impurity with a high accuracy method. But treat the environment with a low-level method: the states of the environment nearby the impurity are expressed by a set of multiple block product states, while the distant parts are treated by mean-field consideration. Our method allows for the computation of the ground state of the infinite two-dimensional quantum spin systems. In the text, we take the frustrated Heisenberg model as an example to test our method. The ground state energy we calculated can reach a high accuracy. We also calculate the magnetization, and the fidelity to study the quantum phase transitions.

  18. Bose-Hubbard models in confining potentials: Inhomogeneous mean-field theory

    NASA Astrophysics Data System (ADS)

    Pai, Ramesh V.; Kurdestany, Jamshid Moradi; Sheshadri, K.; Pandit, Rahul

    2012-06-01

    We present an extensive study of Mott insulator (MI) and superfluid (SF) shells in Bose-Hubbard (BH) models for bosons in optical lattices with harmonic traps. For this we apply the inhomogeneous mean-field theory developed by Sheshadri [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.75.4075 75, 4075 (1995)]. Our results for the BH model with one type of spinless bosons agree quantitatively with quantum Monte Carlo simulations. Our approach is numerically less intensive than such simulations, so we are able to perform calculations on experimentally realistic, large three-dimensional systems, explore a wide range of parameter values, and make direct contact with a variety of experimental measurements. We also extend our inhomogeneous mean-field theory to study BH models with harmonic traps and (a) two species of bosons or (b) spin-1 bosons. With two species of bosons, we obtain rich phase diagrams with a variety of SF and MI phases and associated shells when we include a quadratic confining potential. For the spin-1 BH model, we show, in a representative case, that the system can display alternating shells of polar SF and MI phases, and we make interesting predictions for experiments in such systems.

  19. Criterion for DNA melting in the mean-field modified self-consistent phonon theory

    NASA Astrophysics Data System (ADS)

    Feng, Y.; Prohofsky, E. W.

    1991-04-01

    We have examined the validity of the first-order-perturbation method in calculating eigenfunctions and the criterion for helix melting of mean-field polymers in the modified self-consistent phonon approach (MSPA) theory. It is found that the instability in the self-consistent solution is due to the breakdown of the first-order perturbation. The instability as a criterion for helix melting is therefore techniquely inappropriate. However, the breakdown of the perturbation is due to facts that are directly related to the onset of softening. Previously predicted melting temperatures for various sequence DNA polymers may still represent good estimates to the actual melting temperatures. An alternative criterion is required to define the melting temperature of the polymer DNA double helix in the MSPA theory.

  20. Compression induced phase transition of nematic brush: A mean-field theory study

    NASA Astrophysics Data System (ADS)

    Tang, Jiuzhou; Zhang, Xinghua; Yan, Dadong

    2015-11-01

    Responsive behavior of polymer brush to the external compression is one of the most important characters for its application. For the flexible polymer brush, in the case of low grafting density, which is widely studied by the Gaussian chain model based theory, the compression leads to a uniform deformation of the chain. However, in the case of high grafting density, the brush becomes anisotropic and the nematic phase will be formed. The normal compression tends to destroy the nematic order, which leads to a complex responsive behaviors. Under weak compression, chains in the nematic brush are buckled, and the bending energy and Onsager interaction give rise to the elasticity. Under deep compression, the responsive behaviors of the nematic polymer brush depend on the chain rigidity. For the compressed rigid polymer brush, the chains incline to re-orientate randomly to maximize the orientational entropy and its nematic order is destroyed. For the compressed flexible polymer brush, the chains incline to fold back to keep the nematic order. A buckling-folding transition takes place during the compressing process. For the compressed semiflexible brush, the chains are collectively tilted to a certain direction, which leads to the breaking of the rotational symmetry in the lateral plane. These responsive behaviors of nematic brush relate to the properties of highly frustrated worm-like chain, which is hard to be studied by the traditional self-consistent field theory due to the difficulty to solve the modified diffusion equation. To overcome this difficulty, a single chain in mean-field theory incorporating Monte Carlo simulation and mean-field theory for the worm-like chain model is developed in present work. This method shows high performance for entire region of chain rigidity in the confined condition.

  1. Compression induced phase transition of nematic brush: A mean-field theory study

    SciTech Connect

    Tang, Jiuzhou; Zhang, Xinghua; Yan, Dadong

    2015-11-28

    Responsive behavior of polymer brush to the external compression is one of the most important characters for its application. For the flexible polymer brush, in the case of low grafting density, which is widely studied by the Gaussian chain model based theory, the compression leads to a uniform deformation of the chain. However, in the case of high grafting density, the brush becomes anisotropic and the nematic phase will be formed. The normal compression tends to destroy the nematic order, which leads to a complex responsive behaviors. Under weak compression, chains in the nematic brush are buckled, and the bending energy and Onsager interaction give rise to the elasticity. Under deep compression, the responsive behaviors of the nematic polymer brush depend on the chain rigidity. For the compressed rigid polymer brush, the chains incline to re-orientate randomly to maximize the orientational entropy and its nematic order is destroyed. For the compressed flexible polymer brush, the chains incline to fold back to keep the nematic order. A buckling-folding transition takes place during the compressing process. For the compressed semiflexible brush, the chains are collectively tilted to a certain direction, which leads to the breaking of the rotational symmetry in the lateral plane. These responsive behaviors of nematic brush relate to the properties of highly frustrated worm-like chain, which is hard to be studied by the traditional self-consistent field theory due to the difficulty to solve the modified diffusion equation. To overcome this difficulty, a single chain in mean-field theory incorporating Monte Carlo simulation and mean-field theory for the worm-like chain model is developed in present work. This method shows high performance for entire region of chain rigidity in the confined condition.

  2. Multisite mean-field theory for cold bosonic atoms in optical lattices

    NASA Astrophysics Data System (ADS)

    McIntosh, T.; Pisarski, P.; Gooding, R. J.; Zaremba, E.

    2012-07-01

    We present a detailed derivation of a multisite mean-field theory (MSMFT) used to describe the Mott-insulator to superfluid transition of bosonic atoms in optical lattices. The approach is based on partitioning the lattice into small clusters which are decoupled by means of a mean-field approximation. This approximation invokes local superfluid order parameters defined for each of the boundary sites of the cluster. The resulting MSMFT grand potential has a nontrivial topology as a function of the various order parameters. An understanding of this topology provides two different criteria for the determination of the Mott insulator superfluid phase boundaries. We apply this formalism to d-dimensional hypercubic lattices in one, two, and three dimensions and demonstrate the improvement in the estimation of the phase boundaries when MSMFT is utilized for increasingly larger clusters, with the best quantitative agreement found for d=3. The MSMFT is then used to examine a linear dimer chain in which the onsite energies within the dimer have an energy separation of Δ. This system has a complicated phase diagram within the parameter space of the model, with many distinct Mott phases separated by superfluid regions.

  3. Quantum correlated cluster mean-field theory applied to the transverse Ising model

    NASA Astrophysics Data System (ADS)

    Zimmer, F. M.; Schmidt, M.; Maziero, Jonas

    2016-06-01

    Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there has been a surge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.

  4. Coagulation kinetics beyond mean field theory using an optimised Poisson representation

    NASA Astrophysics Data System (ADS)

    Burnett, James; Ford, Ian J.

    2015-05-01

    Binary particle coagulation can be modelled as the repeated random process of the combination of two particles to form a third. The kinetics may be represented by population rate equations based on a mean field assumption, according to which the rate of aggregation is taken to be proportional to the product of the mean populations of the two participants, but this can be a poor approximation when the mean populations are small. However, using the Poisson representation, it is possible to derive a set of rate equations that go beyond mean field theory, describing pseudo-populations that are continuous, noisy, and complex, but where averaging over the noise and initial conditions gives the mean of the physical population. Such an approach is explored for the simple case of a size-independent rate of coagulation between particles. Analytical results are compared with numerical computations and with results derived by other means. In the numerical work, we encounter instabilities that can be eliminated using a suitable "gauge" transformation of the problem [P. D. Drummond, Eur. Phys. J. B 38, 617 (2004)] which we show to be equivalent to the application of the Cameron-Martin-Girsanov formula describing a shift in a probability measure. The cost of such a procedure is to introduce additional statistical noise into the numerical results, but we identify an optimised gauge transformation where this difficulty is minimal for the main properties of interest. For more complicated systems, such an approach is likely to be computationally cheaper than Monte Carlo simulation.

  5. The electronic mean-field configuration interaction method. I. Theory and integral formulas

    NASA Astrophysics Data System (ADS)

    Cassam-Chenaï, Patrick

    2006-05-01

    In this article, we introduce a new method for solving the electronic Schrödinger equation. This new method follows the same idea followed by the mean-field configuration interaction method already developed for molecular vibrations; i.e., groups of electronic degrees of freedom are contracted together in the mean field of the other degrees. If the same partition of electronic degrees of freedom is iterated, a self-consistent field method is obtained. Making coarser partitions (i.e., including more degrees in the same groups) and discarding the high energy states, the full configuration interaction limit can be approached. In contrast with the usual group function theory, no strong orthogonality condition is enforced. We have made use of a generalized version of the fundamental formula defining a Hopf algebra structure to derive Hamiltonian and overlap matrix element expressions which respect the group structure of the wave function as well as its fermionic symmetry. These expressions are amenable to a recursive computation.

  6. Atomically flat superconducting nanofilms: multiband properties and mean-field theory

    NASA Astrophysics Data System (ADS)

    Shanenko, A. A.; Aguiar, J. Albino; Vagov, A.; Croitoru, M. D.; Milošević, M. V.

    2015-05-01

    Recent progress in materials synthesis enabled fabrication of superconducting atomically flat single-crystalline metallic nanofilms with thicknesses down to a few monolayers. Interest in such nano-thin systems is attracted by the dimensional 3D-2D crossover in their coherent properties which occurs with decreasing the film thickness. The first fundamental aspect of this crossover is dictated by the Mermin-Wagner-Hohenberg theorem and concerns frustration of the long-range order due to superconductive fluctuations and the possibility to track its impact with an unprecedented level of control. The second important aspect is related to the Fabri-Pérot modes of the electronic motion strongly bound in the direction perpendicular to the nanofilm. The formation of such modes results in a pronounced multiband structure that changes with the nanofilm thickness and affects both the mean-field behavior and superconductive fluctuations. Though the subject is very rich in physics, it is scarcely investigated to date. The main obstacle is that there are no manageable models to study a complex magnetic response in this case. Full microscopic consideration is rather time consuming, if practicable at all, while the standard Ginzburg-Landau theory is not applicable. In the present work we review the main achievements in the subject to date, and construct and justify an efficient multiband mean-field formalism which allows for numerical and even analytical treatment of nano-thin superconductors in applied magnetic fields.

  7. Mean-Field Theory of Intra-Molecular Charge Ordering in (TTM--TTP)I3

    NASA Astrophysics Data System (ADS)

    Omori, Yukiko; Tsuchiizu, Masahisa; Suzumura, Yoshikazu

    2011-02-01

    We examine an intra-molecular charge-ordered (ICO) state in the multi-orbital molecular compound (TTM--TTP)I3 on the basis of an effective two-orbital model derived from ab initio calculations. Representing the model in terms of the fragment molecular-orbital (MO) picture, the ICO state is described as the charge disproportionation on the left and right fragment MOs. By applying the mean-field theory, the phase diagram of the ground state is obtained as a function of the inter-molecular Coulomb repulsion and the intra-molecular transfer integral. The ICO state is stabilized by large inter-fragment Coulomb interactions, and the small intra-molecular transfer energy between two fragment MOs. Furthermore, we examine the finite-temperature phase diagram. The relevance to the experimental observations in the molecular compound of (TTM--TTP)I3 is also discussed.

  8. Temperature Dependence of the Molar Heat Capacity for Ferromagnets Within the Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Fernández Rodríguez, J.; Blanco, J. A.

    2005-01-01

    We describe, using the Mean Field Theory, a detailed analysis of the magnetic contribution to the molar heat capacity Cmag for ferromagnetic systems. This calculation is designed to be used as a teaching homework problem for physics undergraduates. The description emphasises that Cmag at the transition temperature TC is characterised by the existence of a simple jump discontinuity anomaly, but when the temperature is lowered down to 0 K the shape of Cmag depends strongly on the magnitude of the spin S. In fact, the appearance of a shoulder in Cmag for S > 3/2 is expected. The origin of this shoulder could be understood as a Schottky-like anomaly in the ordered state. These physical results are in good agreement with those from real systems, and give the student a valuable insight into the behaviour of the thermodynamical response of a ferromagneticmaterial.

  9. Application of relativistic mean field and effective field theory densities to scattering observables for Ca isotopes

    NASA Astrophysics Data System (ADS)

    Bhuyan, M.; Panda, R. N.; Routray, T. R.; Patra, S. K.

    2010-12-01

    In the framework of relativistic mean field (RMF) theory, we have calculated the density distribution of protons and neutrons for Ca40,42,44,48 with NL3 and G2 parameter sets. The microscopic proton-nucleus optical potentials for p+Ca40,42,44,48 systems are evaluated from the Dirac nucleon-nucleon scattering amplitude and the density of the target nucleus using relativistic-Love-Franey and McNeil-Ray-Wallace parametrizations. We have estimated the scattering observables, such as the elastic differential scattering cross section, analyzing power and the spin observables with the relativistic impulse approximation (RIA). The results have been compared with the experimental data for a few selective cases and we find that the use of density as well as the scattering matrix parametrizations are crucial for the theoretical prediction.

  10. Application of relativistic mean field and effective field theory densities to scattering observables for Ca isotopes

    SciTech Connect

    Bhuyan, M.; Panda, R. N.; Routray, T. R.; Patra, S. K.

    2010-12-15

    In the framework of relativistic mean field (RMF) theory, we have calculated the density distribution of protons and neutrons for {sup 40,42,44,48}Ca with NL3 and G2 parameter sets. The microscopic proton-nucleus optical potentials for p+{sup 40,42,44,48}Ca systems are evaluated from the Dirac nucleon-nucleon scattering amplitude and the density of the target nucleus using relativistic-Love-Franey and McNeil-Ray-Wallace parametrizations. We have estimated the scattering observables, such as the elastic differential scattering cross section, analyzing power and the spin observables with the relativistic impulse approximation (RIA). The results have been compared with the experimental data for a few selective cases and we find that the use of density as well as the scattering matrix parametrizations are crucial for the theoretical prediction.

  11. The mean field theory in EM procedures for blind Markov random field image restoration.

    PubMed

    Zhang, J

    1993-01-01

    A Markov random field (MRF) model-based EM (expectation-maximization) procedure for simultaneously estimating the degradation model and restoring the image is described. The MRF is a coupled one which provides continuity (inside regions of smooth gray tones) and discontinuity (at region boundaries) constraints for the restoration problem which is, in general, ill posed. The computational difficulty associated with the EM procedure for MRFs is resolved by using the mean field theory from statistical mechanics. An orthonormal blur decomposition is used to reduce the chances of undesirable locally optimal estimates. Experimental results on synthetic and real-world images show that this approach provides good blur estimates and restored images. The restored images are comparable to those obtained by a Wiener filter in mean-square error, but are most visually pleasing. PMID:18296192

  12. Strange hadronic stars in relativistic mean-field theory with the FSUGold parameter set

    SciTech Connect

    Wu Chen; Ren Zhongzhou

    2011-02-15

    Relativistic mean-field theory with parameter set FSUGold that includes the isoscalar-isovector cross interaction term is extended to study the properties of neutron star matter in {beta} equilibrium by including hyperons. The influence of the attractive and repulsive {Sigma} potential on the properties of neutron star matter and the maximum mass of neutron stars is examined. We also investigate the equations of state for pure neutron matter and for nonstrange hadronic matter for comparison. For a pure neutron star, the maximum mass is about 1.8M{sub sun}, while for a strange (nonstrange) hadronic star in {beta} equilibrium, the maximum mass is around 1.35M{sub sun} (1.7M{sub sun}).

  13. Stability of inhomogeneous superstructures from renormalized mean-field theory of the t-J model

    NASA Astrophysics Data System (ADS)

    Poilblanc, Didier

    2005-08-01

    Using the t-J model (which can also include Coulomb repulsion) and the “plain vanilla” renormalized mean-field theory of Zhang, [Supercond. Sci. Technol. 1, 36 (1988)], stability of inhomogeneous 4a×4a superstructures, such as those observed in cuprates superconductors around 1/8 hole doping is investigated. We find a nonuniform 4a×4a bond order wave involving simultaneously small (˜10-2t) inhomogeneous staggered plaquette currents as well as a small charge-density modulation similar to pair density wave order. On the other hand, no supersolid phase involving a decoupling in the superconducting particle-particle channel is found.

  14. Green's function method for single-particle resonant states in relativistic mean field theory

    NASA Astrophysics Data System (ADS)

    Sun, T. T.; Zhang, S. Q.; Zhang, Y.; Hu, J. N.; Meng, J.

    2014-11-01

    Relativistic mean field theory is formulated with the Green's function method in coordinate space to investigate the single-particle bound states and resonant states on the same footing. Taking the density of states for free particles as a reference, the energies and widths of single-particle resonant states are extracted from the density of states without any ambiguity. As an example, the energies and widths for single-neutron resonant states in 120Sn are compared with those obtained by the scattering phase-shift method, the analytic continuation in the coupling constant approach, the real stabilization method, and the complex scaling method. Excellent agreements with these methods are found for the energies and widths of single-neutron resonant states.

  15. Mean-Field Theory of the Symmetry Breaking Model for X Chromosome Inactivation

    NASA Astrophysics Data System (ADS)

    Scialdone, A.; Barbieri, M.; Pallotti, D.; Nicodemi, M.

    X Chromosome Inactivation (XCI) is the process in mammal femalecells whereby one of the X chromosomes is silenced to compensate dosage with respect to males. It is still mysterious how precisely one X chromosome is randomly chosen for inactivation. We discuss here a mean-field theory of the Symmetry Breaking (SB) model of XCI, a Statistical Mechanics model introduced to explain that process. The SB model poses that a single regulatory factor, an aggregate of molecules, is produced which acts to preserve from inactivation one of the X's. The model illustrates a physical mechanism, originating from a thermodynamic phase transition, for the self-assembling of such a single super-molecular aggregate which can spontaneously break the binding symmetry of equivalent targets. This results in a sharp, yet stochastic, regulatory mechanism of XCI. In particular, we focus here on how the model can predict the effects of genetic deletions.

  16. A mean-field theory on the differential capacitance of asymmetric ionic liquid electrolytes

    NASA Astrophysics Data System (ADS)

    Han, Yining; Huang, Shanghui; Yan, Tianying

    2014-07-01

    The size of ions significantly influences the electric double layer structure of room temperature ionic liquid (IL) electrolytes and their differential capacitance (Cd). In this study, we extended the mean-field theory (MFT) developed independently by Kornyshev (2007J. Phys. Chem. B 111 5545-57) and Kilic, Bazant, and Ajdari (2007 Phys. Rev. E 75 021502) (the KKBA MFT) to take into account the asymmetric 1:1 IL electrolytes by introducing an additional parameter ξ for the anion/cation volume ratio, besides the ionic compressibility γ in the KKBA MFT. The MFT of asymmetric ions becomes KKBA MFT upon ξ = 1, and further reduces to Gouy-Chapman theory in the γ → 0 limit. The result of the extended MFT demonstrates that the asymmetric ILs give rise to an asymmetric Cd, with the higher peak in Cd occurring at positive polarization for the smaller anionic size. At high potential, Cd decays asymptotically toward KKBA MFT characterized by γ for the negative polarization, and characterized by ξγ for the positive polarization, with inverse-square-root behavior. At low potential, around the potential of zero charge, the asymmetric ions cause a higher Cd, which exceeds that of Gouy-Chapman theory.

  17. A mean-field theory on the differential capacitance of asymmetric ionic liquid electrolytes.

    PubMed

    Han, Yining; Huang, Shanghui; Yan, Tianying

    2014-07-16

    The size of ions significantly influences the electric double layer structure of room temperature ionic liquid (IL) electrolytes and their differential capacitance (Cd). In this study, we extended the mean-field theory (MFT) developed independently by Kornyshev (2007J. Phys. Chem. B 111 5545-57) and Kilic, Bazant, and Ajdari (2007 Phys. Rev. E 75 021502) (the KKBA MFT) to take into account the asymmetric 1:1 IL electrolytes by introducing an additional parameter ξ for the anion/cation volume ratio, besides the ionic compressibility γ in the KKBA MFT. The MFT of asymmetric ions becomes KKBA MFT upon ξ = 1, and further reduces to Gouy-Chapman theory in the γ → 0 limit. The result of the extended MFT demonstrates that the asymmetric ILs give rise to an asymmetric Cd, with the higher peak in Cd occurring at positive polarization for the smaller anionic size. At high potential, Cd decays asymptotically toward KKBA MFT characterized by γ for the negative polarization, and characterized by ξγ for the positive polarization, with inverse-square-root behavior. At low potential, around the potential of zero charge, the asymmetric ions cause a higher Cd, which exceeds that of Gouy-Chapman theory. PMID:24920102

  18. State-of-the-art of beyond mean field theories with nuclear density functionals

    NASA Astrophysics Data System (ADS)

    Egido, J. Luis

    2016-07-01

    We present an overview of different beyond mean field theories (BMFTs) based on the generator coordinate method (GCM) and the recovery of symmetries used in many body nuclear physics with effective forces. In a first step a short reminder of the Hartree–Fock–Bogoliubov (HFB) theory is given. A general discussion of the shortcomings of any mean field approximation (MFA), stemming either from the lack of the elementary symmetries (like particle number and angular momentum) or the absence of fluctuations around the mean values, is presented. The recovery of the symmetries spontaneously broken in the HFB approach, in particular the angular momentum, is necessary, among others, to describe excited states and transitions. Particle number projection is also needed to guarantee the right number of protons and neutrons. Furthermore a projection before the variation prevents the pairing collapse in the weak pairing regime. A whole chapter is devoted to illustrate with examples the convenience of recovering symmetries and the differences between the projection before and after the variation. The lack of fluctuations around the average values of the MFA is a big shortcoming inherent to this approach. To build in correlations in BMFT one selects the relevant degrees of freedom of the atomic nucleus. In the low energy part of the spectrum these are the quadrupole, octupole and the pairing vibrations as well as the single particle degrees of freedom. In the GCM the operators representing these degrees of freedom are used as coordinates to generate, by the constrained (projected) HFB theory, a collective subspace. The highly correlated GCM wave function is finally written as a linear combination of a projected basis of this space. The variation of the coefficients of the linear combination leads to the Hill–Wheeler equation. The flexibility of the GCM Ansatz allows to describe a whole palette of physical situations by conveniently choosing the generator coordinates. We

  19. Coagulation kinetics beyond mean field theory using an optimised Poisson representation

    SciTech Connect

    Burnett, James; Ford, Ian J.

    2015-05-21

    Binary particle coagulation can be modelled as the repeated random process of the combination of two particles to form a third. The kinetics may be represented by population rate equations based on a mean field assumption, according to which the rate of aggregation is taken to be proportional to the product of the mean populations of the two participants, but this can be a poor approximation when the mean populations are small. However, using the Poisson representation, it is possible to derive a set of rate equations that go beyond mean field theory, describing pseudo-populations that are continuous, noisy, and complex, but where averaging over the noise and initial conditions gives the mean of the physical population. Such an approach is explored for the simple case of a size-independent rate of coagulation between particles. Analytical results are compared with numerical computations and with results derived by other means. In the numerical work, we encounter instabilities that can be eliminated using a suitable “gauge” transformation of the problem [P. D. Drummond, Eur. Phys. J. B 38, 617 (2004)] which we show to be equivalent to the application of the Cameron-Martin-Girsanov formula describing a shift in a probability measure. The cost of such a procedure is to introduce additional statistical noise into the numerical results, but we identify an optimised gauge transformation where this difficulty is minimal for the main properties of interest. For more complicated systems, such an approach is likely to be computationally cheaper than Monte Carlo simulation.

  20. Neutron stars in the Bogomol'nyi-Prasad-Sommerfield Skyrme model: Mean-field limit versus full field theory

    NASA Astrophysics Data System (ADS)

    Adam, C.; Naya, C.; Sanchez-Guillen, J.; Vazquez, R.; Wereszczynski, A.

    2015-08-01

    Using a solitonic model of nuclear matter, the Bogomol'nyi-Prasad-Sommerfield (BPS) Skyrme model, we compare neutron stars obtained in the full field theory, where gravitational backreaction is completely taken into account, with calculations in a mean-field approximation using the Tolman-Oppenheimer-Volkoff approach. In the latter case, a mean-field-theory equation of state is derived from the original BPS field theory. We show that in the full field theory, where the energy density is nonconstant even at equilibrium, there is no universal and coordinate-independent equation of state of nuclear matter, in contrast to the mean-field approximation. We also study how neutron star properties are modified by going beyond mean-field theory and find that the differences between mean-field theory and exact results can be considerable. Further, we compare both exact and mean-field results with some theoretical and phenomenological constraints on neutron star properties, demonstrating thus the relevance of our model even in its most simple version.

  1. Macromolecular Stabilization by Excluded Cosolutes: Mean Field Theory of Crowded Solutions.

    PubMed

    Sapir, Liel; Harries, Daniel

    2015-07-14

    We propose a mean field theory to account for the experimentally determined temperature dependence of protein stabilization that emerges in solutions crowded by preferentially excluded cosolutes. Based on regular solution theory and employing the Flory-Huggins approximation, our model describes cosolutes in terms of their size, and two temperature-dependent microscopic parameters that correspond to macromolecule-cosolute and bulk solution interactions. The theory not only predicts a "depletion force" that can account for the experimentally observed stabilization of protein folding or association in the presence of excluded cosolutes but also predicts the full range of associated entropic and enthalpic components. Remarkably, depending on cosolute identity and in accordance with experiments, the theory describes entropically as well as enthalpically dominated depletion forces, even those disfavored by entropy. This emerging depletion attraction cannot be simply linked to molecular volumes. Instead, the relevant parameter is an effective volume that represents an interplay between solvent, cosolute, and macromolecular interactions. We demonstrate that the apparent depletion free energy is often accompanied by significant yet compensating entropy and enthalpy terms that, although having a net zero contribution to stabilization, can obscure the underlying molecular mechanism. This study underscores the importance of including often-neglected free energy terms that correspond to solvent-cosolute and cosolute-macromolecule interactions, which for most typical cosolutes are expected to be temperature dependent. We propose that experiments specifically aimed at resolving the temperature-dependence of cosolute exclusion from macromolecular surfaces should help reveal the full range of the underlying molecular mechanisms of the depletion force. PMID:26575781

  2. Higgs-Yukawa model with higher dimension operators via extended mean field theory

    NASA Astrophysics Data System (ADS)

    Akerlund, Oscar; de Forcrand, Philippe

    2016-02-01

    Using extended mean field theory (EMFT) on the lattice, we study properties of the Higgs-Yukawa model as an approximation of the standard model Higgs sector, and the effect of higher dimension operators. We remark, as has been noted before, that the discussion of vacuum stability is completely modified in the presence of a ϕ6 term, and that the Higgs mass no longer appears fine tuned. We also study the finite temperature transition. Without higher dimension operators the transition is found to be second order (crossover with gauge fields) for the experimental value of the Higgs mass Mh=125 GeV . By taking a ϕ6 interaction in the Higgs potential as a proxy for a UV completion of the standard model, the transition becomes stronger and turns first order if the scale of new physics, i.e., the mass of the lightest mediator particle, is around 1.5 TeV. This implies that electroweak baryogenesis may be viable in models which introduce new particles around that scale.

  3. Mean field theory for biology inspired duplication-divergence network model

    NASA Astrophysics Data System (ADS)

    Cai, Shuiming; Liu, Zengrong; Lee, H. C.

    2015-08-01

    The duplication-divergence network model is generally thought to incorporate key ingredients underlying the growth and evolution of protein-protein interaction networks. Properties of the model have been elucidated through numerous simulation studies. However, a comprehensive theoretical study of the model is lacking. Here, we derived analytic expressions for quantities describing key characteristics of the network—the average degree, the degree distribution, the clustering coefficient, and the neighbor connectivity—in the mean-field, large-N limit of an extended version of the model, duplication-divergence complemented with heterodimerization and addition. We carried out extensive simulations and verified excellent agreement between simulation and theory except for one partial case. All four quantities obeyed power-laws even at moderate network size ( N ˜104 ), except the degree distribution, which had an additional exponential factor observed to obey power-law. It is shown that our network model can lead to the emergence of scale-free property and hierarchical modularity simultaneously, reproducing the important topological properties of real protein-protein interaction networks.

  4. Analytic models of regularly branched polymer brushes using the self-consistent mean field theory

    NASA Astrophysics Data System (ADS)

    LeSher, Daniel

    2015-10-01

    Polymer brushes consist of multiple monomers connected together with one of the polymer chain's ends attached to a surface. Polymer brushes have shown great promise for a wide variety of applications including drug delivery dendrimer systems and as tunable brushes that can change their shape and physical properties in response to changes in their environment. Regularly branched polymer brushes which are structured as a function of their chemical indices are investigated here using the self-consistent mean field theory for electrically neutral polymers. The brushes were described using weighting functions, f(n), were n was the fewest number of monomers from a specified location to a free end. Brushes with weighting functions of the form f(n)=nb, f(n)=ebn, as well as f(n)=dan when d 2 and alpha > 2 were found to match the parabolic free chain end profile expected, while it was determined that polymer brushes described using f(n)=n b must be very small in order to remain in equilibrium. However, brushes described by f(n)=2G(N-n) N and f(n)2n were found to be unstable for real, positive values of the potential of the system.

  5. On the Connection Between Mean Field Dynamo Theory and Flux Tubes

    NASA Astrophysics Data System (ADS)

    Choudhuri, Arnab Rai

    2003-07-01

    Mean field dynamo theory deals with various mean quantities and does not directly throw any light on the question of existence of flux tubes. We can, however, draw important conclusions about flux tubes in the interior of the Sun by combining additional arguments with the insights gained from solar dynamo solutions. The polar magnetic field of the Sun is of order 10 G, whereas the toroidal magnetic field at the bottom of the convection zone has been estimated to be 100000 G. Simple order-of-magnitude estimates show that the shear in the tachocline is not sufficient to stretch a 10 G mean radial field into a 100000 G mean toroidal field. We argue that the polar field of the Sun must get concentrated into intermittent flux tubes before it is advected to the tachocline. We estimate the strengths and filling factors of these flux tubes. Stretching by shear in the tachocline is then expected to produce a highly intermittent magnetic configuration at the bottom of the convection zone. The meridional flow at the bottom of the convection zone should be able to carry this intermittent magnetic field equatorward, as suggested recently by Nandy and Choudhuri (2002). When a flux tube from the bottom of the convection zone rises to a region of pre-existing poloidal field at the surface, we point out that it picks up a twist in accordance with the observations of current helicities at the solar surface.

  6. Diffuse phase transition in ferroelectrics with mesoscopic heterogeneity: Mean-field theory

    SciTech Connect

    Li, S.; Eastman, J.A.; Newnham, R.E.; Cross, L.E.

    1997-05-01

    The diffuse phase transition in ferroelectrics with mesoscopic heterogeneity has been discussed within the context of a superparaelectric model by using the Ginzburg-Landau formalism. In the Curie region ferroelectrics with mesoscopic heterogeneity are treated as {open_quotes}superparaelectrics{close_quotes} consisting of a mass of polar clusters, each of which has Ising character. Based on the mean-field theory, the influence of the finite-size effects of polar clusters on their structural instability has been discussed by considering a coherent lattice coupling between two structurally different regions. In particular, we have analytically derived the explicit solutions of the distribution of local polarizations. In turn, the processes of polar nanophase precipitation and coarsening have been also discussed in conjunction with the local chemical or structural inhomogeneity. Moreover, we have also analyzed the relationship between the local polarization distribution and the static dielectric susceptibility in ferroelectrics with the nanometric scale heterogeneity. The width of the Curie region is dependent upon the distribution of the sum of localized correlation length, which reflects the size distribution of heterogeneity. The presented analysis reveals that the diffuse phase transition is closely associated with the existence of nanometric polar clusters and their physical size distribution. Intriguingly, our theoretical results bear a very close resemblance to most experimental observations. {copyright} {ital 1997} {ital The American Physical Society}

  7. Mean field theory for biology inspired duplication-divergence network model.

    PubMed

    Cai, Shuiming; Liu, Zengrong; Lee, H C

    2015-08-01

    The duplication-divergence network model is generally thought to incorporate key ingredients underlying the growth and evolution of protein-protein interaction networks. Properties of the model have been elucidated through numerous simulation studies. However, a comprehensive theoretical study of the model is lacking. Here, we derived analytic expressions for quantities describing key characteristics of the network-the average degree, the degree distribution, the clustering coefficient, and the neighbor connectivity-in the mean-field, large-N limit of an extended version of the model, duplication-divergence complemented with heterodimerization and addition. We carried out extensive simulations and verified excellent agreement between simulation and theory except for one partial case. All four quantities obeyed power-laws even at moderate network size ( N∼10(4)), except the degree distribution, which had an additional exponential factor observed to obey power-law. It is shown that our network model can lead to the emergence of scale-free property and hierarchical modularity simultaneously, reproducing the important topological properties of real protein-protein interaction networks. PMID:26328557

  8. Embedding dynamical mean-field theory for superconductivity in layered materials and heterostructures

    NASA Astrophysics Data System (ADS)

    Petocchi, Francesco; Capone, Massimo

    2016-06-01

    We study layered systems and heterostructures of s -wave superconductors by means of a suitable generalization of dynamical mean-field theory. In order to reduce the computational effort, we consider an embedding scheme in which a relatively small number of active layers is embedded in an effective potential accounting for the effect of the rest of the system. We introduce a feedback of the active layers on the embedding potential that improves on previous approaches and essentially eliminates the effects of the finiteness of the active slab allowing for cheap computation of very large systems. We extend the method to the superconducting state, and we benchmark the approach by means of simple paradigmatic examples showing some examples on how an interface affects the superconducting properties. As examples, we show that superconductivity can penetrate from an intermediate coupling superconductor into a weaker coupling one for around ten layers, and that the first two layers of a system with repulsive interaction can turn superconducting by proximity effects even when charge redistribution is inhibited.

  9. Particle creation in Bose-Einstein condensates: Theoretical formulation based on conserving gapless mean-field theory

    SciTech Connect

    Kurita, Yasunari; Kobayashi, Michikazu; Ishihara, Hideki; Tsubota, Makoto

    2010-11-15

    We formulate particle-creation phenomena in Bose-Einstein condensates in terms of conserving gapless mean-field theory for weakly interacting Bose gases. The particle-creation spectrum is calculated by rediagonalizing the Bogoliubov-de Gennes (BdG) Hamiltonian in mean-field theory. The conservation implies that quasiparticle creation is accompanied by quantum back reaction to the condensates. Particle creation in this mean-field theory is found to be equivalent to that in quantum field theory (QFT) in curved space-time. An expression is obtained for an effective metric affected by quantum back reaction. The formula for the particle-creation spectrum obtained in terms of QFT in curved space-time is shown to be the same as that given by rediagonalizing the BdG Hamiltonian.

  10. Cluster radioactive decay within the preformed cluster model using relativistic mean-field theory densities

    SciTech Connect

    Singh, BirBikram; Patra, S. K.; Gupta, Raj K.

    2010-07-15

    We have studied the (ground-state) cluster radioactive decays within the preformed cluster model (PCM) of Gupta and collaborators [R. K. Gupta, in Proceedings of the 5th International Conference on Nuclear Reaction Mechanisms, Varenna, edited by E. Gadioli (Ricerca Scientifica ed Educazione Permanente, Milano, 1988), p. 416; S. S. Malik and R. K. Gupta, Phys. Rev. C 39, 1992 (1989)]. The relativistic mean-field (RMF) theory is used to obtain the nuclear matter densities for the double folding procedure used to construct the cluster-daughter potential with M3Y nucleon-nucleon interaction including exchange effects. Following the PCM approach, we have deduced empirically the preformation probability P{sub 0}{sup emp} from the experimental data on both the alpha- and exotic cluster-decays, specifically of parents in the trans-lead region having doubly magic {sup 208}Pb or its neighboring nuclei as daughters. Interestingly, the RMF-densities-based nuclear potential supports the concept of preformation for both the alpha and heavier clusters in radioactive nuclei. P{sub 0}{sup a}lpha{sup (emp)} for alpha decays is almost constant (approx10{sup -2}-10{sup -3}) for all the parent nuclei considered here, and P{sub 0}{sup c(emp)} for cluster decays of the same parents decrease with the size of clusters emitted from different parents. The results obtained for P{sub 0}{sup c(emp)} are reasonable and are within two to three orders of magnitude of the well-accepted phenomenological model of Blendowske-Walliser for light clusters.

  11. General model of phospholipid bilayers in fluid phase within the single chain mean field theory

    SciTech Connect

    Guo, Yachong; Baulin, Vladimir A.; Pogodin, Sergey

    2014-05-07

    Coarse-grained model for saturated phospholipids: 1,2-didecanoyl-sn-glycero-3-phosphocholine (DCPC), 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC), 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) and unsaturated phospholipids: 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1,2- dioleoyl-sn-glycero-3-phosphocholine (DOPC) is introduced within the single chain mean field theory. A single set of parameters adjusted for DMPC bilayers gives an adequate description of equilibrium and mechanical properties of a range of saturated lipid molecules that differ only in length of their hydrophobic tails and unsaturated (POPC, DOPC) phospholipids which have double bonds in the tails. A double bond is modeled with a fixed angle of 120°, while the rest of the parameters are kept the same as saturated lipids. The thickness of the bilayer and its hydrophobic core, the compressibility, and the equilibrium area per lipid correspond to experimentally measured values for each lipid, changing linearly with the length of the tail. The model for unsaturated phospholipids also fetches main thermodynamical properties of the bilayers. This model is used for an accurate estimation of the free energies of the compressed or stretched bilayers in stacks or multilayers and gives reasonable estimates for free energies. The proposed model may further be used for studies of mixtures of lipids, small molecule inclusions, interactions of bilayers with embedded proteins.

  12. Revival of oscillation from mean-field-induced death: Theory and experiment.

    PubMed

    Ghosh, Debarati; Banerjee, Tanmoy; Kurths, Jürgen

    2015-11-01

    The revival of oscillation and maintaining rhythmicity in a network of coupled oscillators offer an open challenge to researchers as the cessation of oscillation often leads to a fatal system degradation and an irrecoverable malfunctioning in many physical, biological, and physiological systems. Recently a general technique of restoration of rhythmicity in diffusively coupled networks of nonlinear oscillators has been proposed in Zou et al. [Nat. Commun. 6, 7709 (2015)], where it is shown that a proper feedback parameter that controls the rate of diffusion can effectively revive oscillation from an oscillation suppressed state. In this paper we show that the mean-field diffusive coupling, which can suppress oscillation even in a network of identical oscillators, can be modified in order to revoke the cessation of oscillation induced by it. Using a rigorous bifurcation analysis we show that, unlike other diffusive coupling schemes, here one has two control parameters, namely the density of the mean-field and the feedback parameter that can be controlled to revive oscillation from a death state. We demonstrate that an appropriate choice of density of the mean field is capable of inducing rhythmicity even in the presence of complete diffusion, which is a unique feature of this mean-field coupling that is not available in other coupling schemes. Finally, we report the experimental observation of revival of oscillation from the mean-field-induced oscillation suppression state that supports our theoretical results. PMID:26651763

  13. Revival of oscillation from mean-field-induced death: Theory and experiment

    NASA Astrophysics Data System (ADS)

    Ghosh, Debarati; Banerjee, Tanmoy; Kurths, Jürgen

    2015-11-01

    The revival of oscillation and maintaining rhythmicity in a network of coupled oscillators offer an open challenge to researchers as the cessation of oscillation often leads to a fatal system degradation and an irrecoverable malfunctioning in many physical, biological, and physiological systems. Recently a general technique of restoration of rhythmicity in diffusively coupled networks of nonlinear oscillators has been proposed in Zou et al. [Nat. Commun. 6, 7709 (2015), 10.1038/ncomms8709], where it is shown that a proper feedback parameter that controls the rate of diffusion can effectively revive oscillation from an oscillation suppressed state. In this paper we show that the mean-field diffusive coupling, which can suppress oscillation even in a network of identical oscillators, can be modified in order to revoke the cessation of oscillation induced by it. Using a rigorous bifurcation analysis we show that, unlike other diffusive coupling schemes, here one has two control parameters, namely the density of the mean-field and the feedback parameter that can be controlled to revive oscillation from a death state. We demonstrate that an appropriate choice of density of the mean field is capable of inducing rhythmicity even in the presence of complete diffusion, which is a unique feature of this mean-field coupling that is not available in other coupling schemes. Finally, we report the experimental observation of revival of oscillation from the mean-field-induced oscillation suppression state that supports our theoretical results.

  14. Mean-Field Theory is Exact for the Random-Field Model with Long-Range Interactions

    NASA Astrophysics Data System (ADS)

    Tsuda, Junichi; Nishimori, Hidetoshi

    2014-07-01

    We study the classical spin model in random fields with long-range interactions and show the exactness of the mean-field theory under certain mild conditions. This is a generalization of the result of Mori for the non-random and spin-glass cases. To treat random fields, we evoke the self-averaging property of a function of random fields, without recourse to the replica method. The result is that the mean-field theory gives the exact expression of the canonical free energy for systems with power-decaying interactions if the power is smaller than or equal to the spatial dimension.

  15. Scattering from a two-dimensional array of flux tubes: A study of the validity of mean field theory

    NASA Astrophysics Data System (ADS)

    Kiers, Ken; Weiss, Nathan

    1994-02-01

    Mean field theory has been extensively used in the study of systems of anyons in two spatial dimensions. In this paper we study the physical grounds for the validity of this approximatoion by considering the quantum mechanical scattering of a charged particle from a two-dimensional array of magnetic flux tubes. The flux tubes are arranged on a regular lattice which is infinitely long in the y direction but which has a (small) finite number of columns in the x direction. Their physical size is assumed to be infinitesimally small. We develop a method for computing the scattering angle as well as the reflection and transmission coefficients to lowest order in the Aharonov-Bohm interaction. The results of our calculation are compared to the scattering of the same particle from a region of constant magnetic field whose magnitude is equal to the mean field of all the flux tubes. For an incident plane wave, the mean field approximation is shown to be valid provided the flux in each tube is much less than a single flux quantum. This is precisely the regime in which mean field theory for anyons is expected to be valid. When the flux per tube becomes of order 1, mean field theory is no longer valid.

  16. Nuclear matter properties in the relativistic mean-field theory at finite temperature with interaction between sigma-omega mesons

    SciTech Connect

    Costa, R. S.; Duarte, S. B.; Oliveira, J. C. T.; Chiapparini, M.

    2010-05-21

    We study the nuclear matter properties in the regime of high temperatures using a relativistic mean-field theory. Contrasting with the usual linear Walecka model, we include the sigma-omega meson coupling in order to investigate the role of this interaction in the nucleon effective mass behavior. Some numerical results are presented and discussed.

  17. Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations

    SciTech Connect

    Kelly, Aaron; Markland, Thomas E.; Brackbill, Nora

    2015-03-07

    In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.

  18. Phase Transitions in Social Sciences:. Two-Population Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Contucci, Pierluigi; Gallo, Ignacio; Menconi, Giulia

    A new mean field statistical mechanics model of two interacting groups of spins is introduced, and the phase transition is studied in terms of their relative size. A jump of the average magnetization is found for large values of the mutual interaction when the relative percentage of the two populations crosses a critical threshold. It is shown how the critical percentage depends on internal interactions and on the initial magnetizations. The model is interpreted as a prototype of resident-immigrant cultural interaction, and conclusions from the social sciences perspectives are drawn.

  19. Quantum de Finetti theorems and mean-field theory from quantum phase space representations

    NASA Astrophysics Data System (ADS)

    Trimborn, F.; Werner, R. F.; Witthaut, D.

    2016-04-01

    We introduce the number-conserving quantum phase space description as a versatile tool to address fundamental aspects of quantum many-body systems. Using phase space methods we prove two alternative versions of the quantum de Finetti theorem for finite-dimensional bosonic quantum systems, which states that a reduced density matrix of a many-body quantum state can be approximated by a convex combination of product states where the error is proportional to the inverse particle number. This theorem provides a formal justification for the mean-field description of many-body quantum systems, as it shows that quantum correlations can be neglected for the calculation of few-body observables when the particle number is large. Furthermore we discuss methods to derive the exact evolution equations for quantum phase space distribution functions as well as upper and lower bounds for the ground state energy. As an important example, we consider the Bose-Hubbard model and show that the mean-field dynamics is given by a classical phase space flow equivalent to the discrete Gross-Pitaevskii equation.

  20. On the equation of state of athermal lattice chains: Test of mean-field and scaling theories in two dimensions

    NASA Astrophysics Data System (ADS)

    Dickman, Ronald

    1989-07-01

    A recently devised method for determining the pressure in lattice simulations is applied to two-dimensional, athermal chains of 40, 80, and 160 segments, over the full range of fluid densities, from dilute solution to dense melt. The results are used to test Bawendi and Freed's correction to Flory-Huggins mean-field theory, and the des Cloizeaux scaling law. The scaling of the mean-square end-to-end distance with density is also discussed.

  1. Hyperdeformation in the cranked relativistic mean field theory: The Z=40-58 region of the nuclear chart

    SciTech Connect

    Afanasjev, A. V.; Abusara, H.

    2008-07-15

    The systematic investigation of hyperdeformation (HD) at high spin in the Z=40-58 region of the nuclear chart was performed in the framework of the cranked relativistic mean-field theory. The properties of the moments of inertia of the HD bands, the role of the single-particle and necking degrees of freedom at HD, the spins at which the HD bands become yrast, the possibility to observe discrete HD bands, and so on are discussed in detail.

  2. MEAN-FIELD THEORY AND COMPUTATION OF ELECTROSTATICS WITH IONIC CONCENTRATION DEPENDENT DIELECTRICS *

    PubMed Central

    LI, BO; WEN, JIAYI; ZHOU, SHENGGAO

    2015-01-01

    We construct a mean-field variational model to study how the dependence of dielectric coefficient (i.e., relative permittivity) on local ionic concentrations affects the electrostatic interaction in an ionic solution near a charged surface. The electrostatic free-energy functional of ionic concentrations, which is the key object in our model, consists mainly of the electrostatic potential energy and the ionic ideal-gas entropy. The electrostatic potential is determined by Poisson’s equation in which the dielectric coefficient depends on the sum of concentrations of individual ionic species. This dependence is assumed to be qualitatively the same as that on the salt concentration for which experimental data are available and analytical forms can be obtained by the data fitting. We derive the first and second variations of the free-energy functional, obtain the generalized Boltzmann distributions, and show that the free-energy functional is in general nonconvex. To validate our mathematical analysis, we numerically minimize our electrostatic free-energy functional for a radially symmetric charged system. Our extensive computations reveal several features that are significantly different from a system modeled with a dielectric coefficient independent of ionic concentration. These include the non-monotonicity of ionic concentrations, the ionic depletion near a charged surface that has been previously predicted by a one-dimensional model, and the enhancement of such depletion due to the increase of surface charges or bulk ionic concentrations. PMID:26877718

  3. LETTER TO THE EDITOR: Mean-field dynamical density functional theory

    NASA Astrophysics Data System (ADS)

    Dzubiella, J.; Likos, C. N.

    2003-02-01

    We examine the out-of-equilibrium dynamical evolution of density profiles of ultrasoft particles under time-varying external confining potentials in three spatial dimensions. The theoretical formalism employed is the dynamical density functional theory (DDFT) of Marini, Bettolo, Marconi and Tarazona (1999 J. Chem. Phys. 110 8032), supplied by an equilibrium excess free energy functional that is essentially exact. We complement our theoretical analysis by carrying out extensive Brownian dynamics simulations. We find excellent agreement between theory and simulations for the whole time evolution of density profiles, demonstrating thereby the validity of the DDFT when an accurate equilibrium free energy functional is employed.

  4. Dynamic mean field theory of condensation and evaporation processes for fluids in porous materials: application to partial drying and drying.

    PubMed

    Edison, J R; Monson, P A

    2010-01-01

    We study the dynamics of evaporation for lattice gas models of fluids in porous materials using a recently developed dynamic mean field theory. The theory yields a description of the dynamics that is consistent with the mean field theory of the thermodynamics at equilibrium. The nucleation processes associated with phase changes in the pore are emergent features of the dynamics. Our focus is on situations where there is partial drying or drying in the system, associated with weakly attractive or repulsive interactions between the fluid and the pore walls. We consider two systems in this work: (i) a two-dimensional slit pore geometry relevant to the study of adsorption/desorption or intrusion/extrusion dynamics for fluids in porous materials and (ii) a three dimensional slit pore modeling a pair of square plates in a bath of liquid as used in recent theoretical studies of dewetting processes between hydrophobic surfaces. We assess the theory by comparison with a higher order approximation to the dynamics that yields the Bethe-Peierls or quasi-chemical approximation at equilibrium. PMID:21043421

  5. Mott Multiferroics and Ferroelectric Metals from Dynamical Mean-Field Theory combined with Density-Functional Theory

    NASA Astrophysics Data System (ADS)

    Capone, Massimo

    2015-03-01

    Multiferroic materials, in which ferroelectricity and long-range magnetic ordering coexist, are natural candidates for applications. In this perspective, the most promising compounds are those in which the two phenomena do not simply coexist, but they influence each other through a magnetoelectric coupling. We present different applications of Density Functional Theory combined with Dynamical Mean-Field Theory in which electron-electron correlation effects are crucial in the stabilization of multiferroic behavior and in the magnetoelectric coupling. Within this wide family we can distinguish different cases. In Sr0.5Ba0.5MnO3 the multiferroic behavior is associated with a Mott insulating state in which the Mn half-filled t2g orbitals are responsible of the magnetic properties and the value of the polarization is strongly affected by the magnetic state. LiOsO3 shares the same electronic configuration with half-filled Os t2g orbitals. Despite this configuration enhances the effect of electron-electron interactions, the material remains metallic and represents a peculiar ferroelectric metal. We propose however how to turn this non-magnetic polar metal into a multiferroic through the design of a superlattice, which increases the degree of correlation, leading to Mott localization of the Os orbitals. In completely different systems, such as organic crystals like (TMTTF)2-X, strong correlations can lead to multiferroicity in organic crystals such as (TMTTF)2-X, where charge ordering promotes a polarization which is favored by an antiferromagnetic ordering. We finally discuss how strong correlations can play a major role away from half-filling when the Hund's coupling is sizable in compounds with a nominal valence of, e.g., two electrons in the three t2g orbitals. Such ``Hund's metals'' are correlated despite being far from Mott localization. This physical regime can be a fertile ground to obtain other ferroelectric metals. This work is supported by ERC/FP7 through the

  6. Spectral properties of transition metal pnictides and chalcogenides: Angle-resolved photoemission spectroscopy and dynamical mean-field theory

    NASA Astrophysics Data System (ADS)

    van Roekeghem, Ambroise; Richard, Pierre; Ding, Hong; Biermann, Silke

    2016-01-01

    Electronic Coulomb correlations lead to characteristic signatures in the spectroscopy of transition metal pnictides and chalcogenides: quasi-particle renormalizations, lifetime effects or incoherent badly metallic behavior above relatively low coherence temperatures are measures of many-body effects due to local Hubbard and Hund's couplings. We review and compare the results of angle-resolved photoemission spectroscopy experiments (ARPES) and of combined density functional/dynamical mean-field theory (DFT+DMFT) calculations. We emphasize the doping-dependence of the quasi-particle mass renormalization and coherence properties.

  7. Generalized gradient expansion for inhomogeneous dynamical mean-field theory: Application to ultracold atoms in a harmonic trap

    NASA Astrophysics Data System (ADS)

    Freericks, J. K.; Han, Shuyang; Mikelsons, Karlis; Krishnamurthy, H. R.

    2016-08-01

    We develop a generalized gradient expansion of the inhomogeneous dynamical mean-field theory method for determining properties of ultracold atoms in a trap. This approach goes beyond the well-known local density approximation and at higher temperatures, in the normal phase, it shows why the local density approximation works so well, since the local density and generalized gradient approximations are essentially indistinguishable from each other (and from the exact solution within full inhomogeneous dynamical mean-field theory). But because the generalized gradient expansion only involves nearest-neighbor corrections, it does not work as well at low temperatures, when the systems enter into ordered phases. This is primarily due to the problem that ordered phases often satisfy some global constraints, which determine the spatial ordering pattern, and the local density and generalized gradient approximations are not able to impose those kinds of constraints; they also overestimate the tendency to order. The theory is applied to phase separation of different mass fermionic mixtures represented by the Falicov-Kimball model and to determining the entropy per particle of a fermionic system represented by the Hubbard model. The generalized gradient approximation is a useful diagnostic for the accuracy of the local density approximation—when both methods agree, they are likely accurate, when they disagree, neither is likely to be correct.

  8. Density functional plus dynamical mean-field theory of the spin-crossover molecule Fe(phen)2(NCS)2

    NASA Astrophysics Data System (ADS)

    Chen, Jia; Millis, Andrew J.; Marianetti, Chris A.

    2015-06-01

    We study the spin-crossover molecule Fe(phen) 2(NCS) 2 using density functional theory (DFT) plus dynamical mean-field theory, which allows access to observables not attainable with traditional quantum chemical or electronic structure methods. The temperature dependent magnetic susceptibility, electron addition and removal spectra, and total energies are calculated and compared to experiment. We demonstrate that the proper quantitative energy difference between the high-spin and low-spin state, as well as reasonably accurate values of the magnetic susceptibility can be obtained when using reasonable interaction parameters. Comparisons to DFT and DFT+U calculations demonstrate that dynamical correlations are critical to the energetics of the low-spin state. Additionally, we elucidate the differences between DFT+U and spin density functional theory (SDFT) plus U methodologies, demonstrating that DFT+U can recover SDFT+U results for an appropriately chosen on-site exchange interaction.

  9. Hartree–Fock mean-field theory for trapped dirty bosons

    NASA Astrophysics Data System (ADS)

    Khellil, Tama; Pelster, Axel

    2016-06-01

    Here we work out in detail a non-perturbative approach to the dirty boson problem, which relies on the Hartree–Fock theory and the replica method. For a weakly interacting Bose gas within a trapped confinement and a delta-correlated disorder potential at finite temperature, we determine the underlying free energy. From it we determine via extremization self-consistency equations for the three components of the particle density, namely the condensate density, the thermal density, and the density of fragmented local Bose–Einstein condensates within the respective minima of the random potential landscape. Solving these self-consistency equations in one and three dimensions in two other publications has revealed how these three densities change for increasing disorder strength.

  10. Analysis of surface segregation in polymer mixtures: A combination of mean field and statistical associated fluid theories

    NASA Astrophysics Data System (ADS)

    Krawczyk, Jaroslaw; Croce, Salvatore; Chakrabarti, Buddhapriya; Tasche, Jos

    The surface segregation in polymer mixtures remains a challenging problem for both academic exploration as well as industrial applications. Despite its ubiquity and several theoretical attempts a good agreement between computed and experimentally observed profiles has not yet been achieved. A simple theoretical model proposed in this context by Schmidt and Binder combines Flory-Huggins free energy of mixing with the square gradient theory of wetting of a wall by fluid. While the theory gives us a qualitative understanding of the surface induced segregation and the surface enrichment it lacks the quantitative comparison with the experiment. The statistical associating fluid theory (SAFT) allows us to calculate accurate free energy for a real polymeric materials. In an earlier work we had shown that increasing the bulk modulus of a polymer matrix through which small molecules migrate to the free surface causes reduction in the surface migrant fraction using Schmidt-Binder and self-consistent field theories. In this work we validate this idea by combining mean field theories and SAFT to identify parameter ranges where such an effect should be observable. Department of Molecular Physics, Łódź University of Technology, Żeromskiego 116, 90-924 Łódź, Poland.

  11. Investigation of Blend Miscibility of a Ternary PS/PCHMA/PMMA System Using SIMS and Mean-Field Theory

    SciTech Connect

    Harton,S.; Koga, T.; Stevie, F.; Araki, T.; Ade, H.

    2005-01-01

    Poly(cyclohexyl methacrylate) (PCHMA) and polystyrene (PS) are miscible with each other, but each is highly immiscible with PMMA. Identifiable by the asymmetries in the binary mean-field interaction parameters {chi}, PS preferentially segregates to the PCHMA/PMMA interface. Secondary ion mass spectrometry was used to provide real-space depth profiles of deuterated PS (dPS) in a miscible blend with PCHMA. The initial dPS concentration was varied from 5 to 20% (v/v), and the blend film was annealed at 150 C on a film of PMMA for 42 h. X-ray reflectometry was used to determine the interfacial width between PCHMA and PMMA at 150 C. Using self-consistent mean-field theory, good agreement was found between the experimental and theoretical interfacial excess Z* of dPS at each concentration. Because of their similar glass transition temperatures ({approx}100 C for PS and PCHMA) and the ability of PS and PCHMA to be controllably synthesized with low polydispersities, we anticipate this blend to be a model system for future investigations of such phenomena as diffusion in miscible blends and diffusion near surfaces and interfaces.

  12. The spectrum of random magnetic fields in the mean field dynamo theory of the Galactic magnetic field

    NASA Technical Reports Server (NTRS)

    Kulsrud, Russell M.; Anderson, Stephen W.

    1992-01-01

    The fluctuation spectrum that must arise in a mean field dynamo generation of galactic fields if the initial field is weak is considered. A kinetic equation for its evolution is derived and solved. The spectrum evolves by transfer of energy from one magnetic mode to another by interaction with turbulent velocity modes. This kinetic equation is valid in the limit that the rate of evolution of the magnetic modes is slower than the reciprocal decorrelation time of the turbulent modes. This turns out to be the case by a factor greater than 3. Most of the fluctuation energy concentrates on small scales, shorter than the hydrodynamic turbulent scales. The fluctuation energy builds up to equipartition with the turbulent energy in times that are short compared to the e-folding time of the mean field. The turbulence becomes strongly modified before the dynamo amplification starts. Thus, the kinematic assumption of the mean dynamo theory is invalid. Thus, the galactic field must have a primordial origin, although it may subsequently be modified by dynamo action.

  13. Density functional plus dynamical mean-field theory of the metal-insulator transition in early transition-metal oxides

    NASA Astrophysics Data System (ADS)

    Dang, Hung T.; Ai, Xinyuan; Millis, Andrew J.; Marianetti, Chris A.

    2014-09-01

    The combination of density functional theory and single-site dynamical mean-field theory, using both Hartree and full continuous-time quantum Monte Carlo impurity solvers, is used to study the metal-insulator phase diagram of perovskite transition-metal oxides of the form ABO3 with a rare-earth ion A =Sr, La, Y and transition metal B =Ti, V, Cr. The correlated subspace is constructed from atomiclike d orbitals defined using maximally localized Wannier functions derived from the full p-d manifold; for comparison, results obtained using a projector method are also given. Paramagnetic DFT + DMFT computations using full charge self-consistency along with the standard "fully localized limit" (FLL) double counting are shown to incorrectly predict that LaTiO3, YTiO3, LaVO3, and SrMnO3 are metals. A more general examination of the dependence of physical properties on the mean p-d energy splitting, the occupancy of the correlated d states, the double-counting correction, and the lattice structure demonstrates the importance of charge-transfer physics even in the early transition-metal oxides and elucidates the factors underlying the failure of the standard approximations. If the double counting is chosen to produce a p-d splitting consistent with experimental spectra, single-site dynamical mean-field theory provides a reasonable account of the materials properties. The relation of the results to those obtained from "d-only" models in which the correlation problem is based on the frontier orbital p-d antibonding bands is determined. It is found that if an effective interaction U is properly chosen the d-only model provides a good account of the physics of the d1 and d2 materials.

  14. Parametric Smoothness and Self- Scaling of the Statistical Properties of a Minimal Climate Model: what beyond mean field theories?

    NASA Astrophysics Data System (ADS)

    Lucarini, V.; Speranza, A.; Vitolo, R.

    2009-04-01

    A quasi-geostrophic intermediate complexity model of the mid-latitude atmospheric circulation is considered, featuring simplified baroclinic conversion and barotropic convergence processes. The model undergoes baroclinic forcing towards a given latitudinal temperature profile controlled by the forced equator-to-pole temperature difference Te. When Te increases, a transition takes place from a stationary regime-Hadley equilibrium-to a periodic regime, and eventually to a chaotic regime where evolution takes place on a strange attractor. The attractor dimension, metric entropy, and bounding box volume in phase space have a smooth dependence on Te which results in power-law scaling properties. Power-law scalings are detected also for the statistical properties of global physical observables — the total energy of the system and the averaged zonal wind. The scaling laws, which constitute the main novel result of the present work, can be thought to result from the presence of a statistical process of baroclinic adjustment, which tends to decrease the equator-to-pole temperature difference and determines the properties of the attractor of the system. The self-similarity could be of great help in setting up a theory for the overall statistical properties of the general circulation of the atmosphere and in guiding-on a heuristic basis-both data analysis and realistic simulations, going beyond the unsatisfactory mean field theories and /brute force/ approaches. A leading example for this would be the possibility of estimating the sensitivity of the output of the system with respect to changes in the parameters. Ref: Valerio Lucarini, Antonio Speranza, Renato Vitolo, Parametric smoothness and self-scaling of the statistical properties of a minimal climate model: What beyond the mean field theories?, Physica D, 234 (2007), 105-123

  15. Quasi-continuous-time impurity solver for the dynamical mean-field theory with linear scaling in the inverse temperature.

    PubMed

    Rost, D; Assaad, F; Blümer, N

    2013-05-01

    We present an algorithm for solving the self-consistency equations of the dynamical mean-field theory (DMFT) with high precision and efficiency at low temperatures. In each DMFT iteration, the impurity problem is mapped to an auxiliary Hamiltonian, for which the Green function is computed by combining determinantal quantum Monte Carlo (BSS-QMC) calculations with a multigrid extrapolation procedure. The method is numerically exact, i.e., yields results which are free of significant Trotter errors, but retains the BSS advantage, compared to direct QMC impurity solvers, of linear (instead of cubic) scaling with the inverse temperature. The new algorithm is applied to the half-filled Hubbard model close to the Mott transition; detailed comparisons with exact diagonalization, Hirsch-Fye QMC, and continuous-time QMC are provided. PMID:23767655

  16. Incommensurate phase of a triangular frustrated Heisenberg model studied via Schwinger-boson mean-field theory

    NASA Astrophysics Data System (ADS)

    Li, Peng; Su, Haibin; Dong, Hui-Ning; Shen, Shun-Qing

    2009-08-01

    We study a triangular frustrated antiferromagnetic Heisenberg model with nearest-neighbor interactions J1 and third-nearest-neighbor interactions J3 by means of Schwinger-boson mean-field theory. By setting an antiferromagnetic J3 and varying J1 from positive to negative values, we disclose the low-temperature features of its interesting incommensurate phase. The gapless dispersion of quasiparticles leads to the intrinsic T2 law of specific heat. The magnetic susceptibility is linear in temperature. The local magnetization is significantly reduced by quantum fluctuations. We address possible relevance of these results to the low-temperature properties of NiGa2S4. From a careful analysis of the incommensurate spin wavevector, the interaction parameters are estimated as J1≈-3.8755 K and J3≈14.0628 K, in order to account for the experimental data.

  17. Dynamical Mean-Field Theory Study of Correlated Electronic Structures and the Phase Diagram of Hydrocarbon Superconductors

    NASA Astrophysics Data System (ADS)

    Kim, Minjae; Choi, Hong Chul; Shim, Ji Hoon; Min, B. I.

    2014-03-01

    We have studied correlated electronic structures and the phase diagram of electron-doped hydrocarbon molecular solids, based on the dynamical mean-field theory. We have determined the phase diagram of hydrocarbon molecular solids as functions of doping and energy parameters including the Coulomb correlation, the Hund coupling, and the molecular-orbital (MO) energy level splitting. We have found that the hydrocarbon superconductors (electron-doped picene and coronene) belong to the multi-band Fermi liquid state, while non-superconducting electron-doped pentacene belongs to the single-band state in the proximity of the metal-insulator transition. The size of the MO energy level splitting plays an important role in deriving the superconductivity of electron-doped hydrocarbon solids. The multi-band nature of hydrocarbon solids from the small MO energy level splitting boosts the superconductivity through the enhanced density of states at the Fermi level.

  18. Single-proton resonant states and the isospin dependence investigated by Green’s function relativistic mean field theory

    NASA Astrophysics Data System (ADS)

    Sun, T. T.; Niu, Z. M.; Zhang, S. Q.

    2016-08-01

    The relativistic mean field theory formulated with Green’s function method (RMF-GF) is applied to investigate single-proton resonant states and isospin dependence. The calculated energies and widths for the single-proton resonant states in {}120{{Sn}} are in good agreement with previous investigations. The single-proton resonant states of the Sn isotopes and the N = 82 isotones are systematically studied and it is shown that the calculated energies and widths decrease monotonically with the increase of neutron number while increase monotonically with the increase of proton number. To further examine the evolutions of the single-proton resonant states, their dependence on the depth, radius and diffuseness of nuclear potential is investigated with the help of an analytic Woods-Saxon potential, and it is found that the increase of radius plays the most important role in the cross phenomenon appearing in the single-proton resonant states of the Sn isotopes.

  19. Adapting Poisson-Boltzmann to the self-consistent mean field theory: Application to protein side-chain modeling

    NASA Astrophysics Data System (ADS)

    Koehl, Patrice; Orland, Henri; Delarue, Marc

    2011-08-01

    We present an extension of the self-consistent mean field theory for protein side-chain modeling in which solvation effects are included based on the Poisson-Boltzmann (PB) theory. In this approach, the protein is represented with multiple copies of its side chains. Each copy is assigned a weight that is refined iteratively based on the mean field energy generated by the rest of the protein, until self-consistency is reached. At each cycle, the variational free energy of the multi-copy system is computed; this free energy includes the internal energy of the protein that accounts for vdW and electrostatics interactions and a solvation free energy term that is computed using the PB equation. The method converges in only a few cycles and takes only minutes of central processing unit time on a commodity personal computer. The predicted conformation of each residue is then set to be its copy with the highest weight after convergence. We have tested this method on a database of hundred highly refined NMR structures to circumvent the problems of crystal packing inherent to x-ray structures. The use of the PB-derived solvation free energy significantly improves prediction accuracy for surface side chains. For example, the prediction accuracies for χ1 for surface cysteine, serine, and threonine residues improve from 68%, 35%, and 43% to 80%, 53%, and 57%, respectively. A comparison with other side-chain prediction algorithms demonstrates that our approach is consistently better in predicting the conformations of exposed side chains.

  20. Plane-wave based electronic structure calculations for correlated materials using dynamical mean-field theory and projected local orbitals

    NASA Astrophysics Data System (ADS)

    Amadon, B.; Lechermann, F.; Georges, A.; Jollet, F.; Wehling, T. O.; Lichtenstein, A. I.

    2008-05-01

    The description of realistic strongly correlated systems has recently advanced through the combination of density functional theory in the local density approximation (LDA) and dynamical mean field theory (DMFT). This LDA+DMFT method is able to treat both strongly correlated insulators and metals. Several interfaces between LDA and DMFT have been used, such as ( Nth order) linear muffin-tin orbitals or maximally localized Wannier functions. Such schemes are, however, either complex in use or additional simplifications are often performed (i.e., the atomic sphere approximation). We present an alternative implementation of LDA+DMFT , which keeps the precision of the Wannier implementation, but which is lighter. It relies on the projection of localized orbitals onto a restricted set of Kohn-Sham states to define the correlated subspace. The method is implemented within the projector augmented wave and within the mixed-basis pseudopotential frameworks. This opens the way to electronic structure calculations within LDA+DMFT for more complex structures with the precision of an all-electron method. We present an application to two correlated systems, namely, SrVO3 and β -NiS (a charge-transfer material), including ligand states in the basis set. The results are compared to calculations done with maximally localized Wannier functions, and the physical features appearing in the orbitally resolved spectral functions are discussed.

  1. Simulation of chain diffusion in diblock copolymer microstructures using dynamical self-consistent mean-field theory

    NASA Astrophysics Data System (ADS)

    Grzetic, Douglas; Wickham, Robert

    We simulate chain diffusion in ordered phases of a diblock copolymer melt, using our recently-developed dynamical self-consistent mean-field theory [J. Chem. Phys. 140, 244907 (2014)]. This theory enables us to study large length and time scales in these dense systems, while remaining connected, in a self-consistent manner, to the microscopic physics of Brownian chains whose beads interact via a species-dependent modified Lennard-Jones potential. In the LAM and HEX phases, chain diffusion perpendicular to the microdomain interface is exponentially suppressed with increasing segregation, while parallel diffusion is unaffected. In the BCC phase, diffusion is isotropic and is gradually suppressed with increasing segregation. Chain diffusion is also isotropic in the gyroid phase, but does not vanish with increasing segregation. Instead, the diffusion constant asymptotes to a value consistent with chain diffusion being restricted to the interface of the three-dimensional gyroid network of struts, characterized by a network tortuosity value of 1 . 72 . Finally, we measure the out-of-equilibrium evolution of the anisotropy in the chain diffusion as metastable LAM transforms to stable HEX over long times.

  2. Lanczos-based Low-Rank Correction Method for Solving the Dyson Equation in Inhomogenous Dynamical Mean-Field Theory

    NASA Astrophysics Data System (ADS)

    Carrier, Pierre; Tang, Jok M.; Saad, Yousef; Freericks, James K.

    Inhomogeneous dynamical mean-field theory has been employed to solve many interesting strongly interacting problems from transport in multilayered devices to the properties of ultracold atoms in a trap. The main computational step, especially for large systems, is the problem of calculating the inverse of a large sparse matrix to solve Dyson's equation and determine the local Green's function at each lattice site from the corresponding local self-energy. We present a new e_cient algorithm, the Lanczos-based low-rank algorithm, for the calculation of the inverse of a large sparse matrix which yields this local (imaginary time) Green's function. The Lanczos-based low-rank algorithm is based on a domain decomposition viewpoint, but avoids explicit calculation of Schur complements and relies instead on low-rank matrix approximations derived from the Lanczos algorithm, for solving the Dyson equation. We report at least a 25-fold improvement of performance compared to explicit decomposition (such as sparse LU) of the matrix inverse. We also report that scaling relative to matrix sizes, of the low-rank correction method on the one hand and domain decomposition methods on the other, are comparable.

  3. Combined local-density and dynamical mean field theory calculations for the compressed lanthanides Ce, Pr, and Nd

    SciTech Connect

    McMahan, A K

    2005-03-30

    This paper reports calculations for compressed Ce (4f{sup 1}), Pr (4f{sup 2}), and Nd (4f{sup 3}) using a combination of the local-density approximation (LDA) and dynamical mean field theory (DMFT), or LDA+DMFT. The 4f moment, spectra, and the total energy among other properties are examined as functions of volume and atomic number for an assumed face-centered cubic (fcc) structure. These materials are seen to be strongly localized at ambient pressure and for compressions up through the experimentally observed fcc phases ({gamma} phase for Ce), in the sense of having fully formed Hund's rules moments and little 4f spectral weight at the Fermi level. Subsequent compression for all three lanthanides brings about significant deviation of the moments from their Hund's rules values, a growing Kondo resonance at the fermi level, an associated softening in the total energy, and quenching of the spin orbit since the Kondo resonance is of mixed spin-orbit character while the lower Hubbard band is predominantly j = 5/2. while the most dramatic changes for Ce occur within the two-phase region of the {gamma}-{alpha} volume collapse transition, as found in earlier work, those for Pr and Nd occur within the volume range of the experimentally observed distorted fcc (dfcc) phase, which is therefore seen here as transitional and not part of the localized trivalent lanthanide sequence. The experimentally observed collapse to the {alpha}-U structure in Pr occurs only on further compression, and no such collapse is found in Nd. These lanthanides start closer to the localized limit for increasing atomic number, and so the theoretical signatures noted above are also offset to smaller volume as well, which is possibly related to the measured systematics of the size of the volume collapse being 15%, 9%, and none for Ce, Pr, and Nd, respectively.

  4. Pressure-driven metal-insulator transition in BiFeO3 from dynamical mean-field theory

    NASA Astrophysics Data System (ADS)

    Shorikov, A. O.; Lukoyanov, A. V.; Anisimov, V. I.; Savrasov, S. Y.

    2015-07-01

    A metal-insulator transition (MIT) in BiFeO3 under pressure was investigated by a method combining generalized gradient corrected local density approximation with dynamical mean-field theory (GGA+DMFT). Our paramagnetic calculations are found to be in agreement with the experimental phase diagram: Magnetic and spectral properties of BiFeO3 at ambient and high pressures were calculated for three experimental crystal structures R 3 c , P b n m , and P m 3 ¯m . At ambient pressure in the R 3 c phase, an insulating gap of 1.2 eV was obtained in good agreement with its experimental value. Both R 3 c and P b n m phases have a metal-insulator transition that occurs simultaneously with a high-spin (HS) to low-spin (LS) transition. The critical pressure for the P b n m phase is 25-33 GPa, which agrees well with the experimental observations. The high-pressure and -temperature P m 3 ¯m phase exhibits a metallic behavior observed experimentally as well as in our calculations in the whole range of considered pressures and undergoes the LS state at 33 GPa, where a P b n m to P m 3 ¯m transition is experimentally observed. The antiferromagnetic GGA+DMFT calculations carried out for the P b n m structure result in simultaneous MIT and HS-LS transitions at a critical pressure of 43 GPa in agreement with the experimental data.

  5. Tetragonal and collapsed-tetragonal phases of CaFe2As2 : A view from angle-resolved photoemission and dynamical mean-field theory

    NASA Astrophysics Data System (ADS)

    van Roekeghem, Ambroise; Richard, Pierre; Shi, Xun; Wu, Shangfei; Zeng, Lingkun; Saparov, Bayrammurad; Ohtsubo, Yoshiyuki; Qian, Tian; Sefat, Athena S.; Biermann, Silke; Ding, Hong

    2016-06-01

    We present a study of the tetragonal to collapsed-tetragonal transition of CaFe2As2 using angle-resolved photoemission spectroscopy and dynamical mean field theory-based electronic structure calculations. We observe that the collapsed-tetragonal phase exhibits reduced correlations and a higher coherence temperature due to the stronger Fe-As hybridization. Furthermore, a comparison of measured photoemission spectra and theoretical spectral functions shows that momentum-dependent corrections to the density functional band structure are essential for the description of low-energy quasiparticle dispersions. We introduce those using the recently proposed combined "screened exchange + dynamical mean field theory" scheme.

  6. Meta-Orbital Transition in Heavy-Fermion Systems: Analysis by Dynamical Mean Field Theory and Self-Consistent Renormalization Theory of Orbital Fluctuations

    NASA Astrophysics Data System (ADS)

    Hattori, Kazumasa

    2010-11-01

    We investigate a two-orbital Anderson lattice model with Ising orbital intersite exchange interactions on the basis of a dynamical mean field theory combined with the static mean field approximation of intersite orbital interactions. Focusing on Ce-based heavy-fermion compounds, we examine the orbital crossover between two orbital states, when the total f-electron number per site nf is ˜1. We show that a “meta-orbital” transition, at which the occupancy of two orbitals changes steeply, occurs when the hybridization between the ground-state f-electron orbital and conduction electrons is smaller than that between the excited f-electron orbital and conduction electrons at low pressures. Near the meta-orbital critical end point, orbital fluctuations are enhanced and couple with charge fluctuations. A critical theory of meta-orbital fluctuations is also developed by applying the self-consistent renormalization theory of itinerant electron magnetism to orbital fluctuations. The critical end point, first-order transition, and crossover are described within Gaussian approximations of orbital fluctuations. We discuss the relevance of our results to CeAl2, CeCu2Si2, CeCu2Ge2, and related compounds, which all have low-lying crystalline-electric-field excited states.

  7. Tensor effects in shell evolution at Z, N=8, 20, and 28 using nonrelativistic and relativistic mean-field theory

    SciTech Connect

    Moreno-Torres, M.; Anguiano, M.; Grasso, M.; Van Giai, N.; Liang, H.; De Donno, V.

    2010-06-15

    Tensor effects in shell evolution are studied within the mean-field approach. Particular attention is paid to the analysis of the magic gaps in different regions of the nuclear chart, namely, Z,N=8, 20, and 28. Hartree-Fock calculations with Skyrme and Gogny interactions are performed where the tensor term has a zero and finite range, respectively. Results obtained with and without the tensor component are compared between them and with the experimental data, when available. To complete this analysis, the tensor effect is also investigated within the relativistic Hartree-Fock model, where the exchange of rho mesons and pions is taken into account. It turns out that the tensor effect in the evolution of the magic gaps can be more easily identified in the cases Z,N=8 and 20, whereas the interpretation of the effect is more complicated for Z or N= 28. Consequently, we indicate the regions defined by the magic numbers 8 and 20 as suitable for fitting the tensor parameters in a mean-field approach: We suggest to include explicitly the data associated to these gap evolutions in the fitting procedures. In general, with the parametrizations used in this work (which have not been fitted on these data), the mean-field results obtained with the tensor contribution do not reproduce the experimental trend, that is, the reduction of the gaps at 8 and 20 that is observed when going toward the drip lines. Since some of the considered nuclei have N=Z, a discussion will be devoted to the interpretation of the experimental data concerning these nuclei and to the Wigner-energy correction.

  8. What is a particle-conserving Topological Superfluid? The fate of Majorana modes beyond mean-field theory

    NASA Astrophysics Data System (ADS)

    Ortiz, Gerardo; Cobanera, Emilio

    2016-09-01

    We investigate Majorana modes of number-conserving fermionic superfluids from both basic physics principles, and concrete models perspectives. After reviewing a criterion for establishing topological superfluidity in interacting systems, based on many-body fermionic parity switches, we reveal the emergence of zero-energy modes anticommuting with fermionic parity. Those many-body Majorana modes are constructed as coherent superpositions of states with different number of fermions. While realization of Majorana modes beyond mean field is plausible, we show that the challenge to quantum-control them is compounded by particle-conservation, and more realistic protocols will have to balance engineering needs with astringent constraints coming from superselection rules. Majorana modes in number-conserving systems are the result of a peculiar interplay between quantum statistics, fermionic parity, and an unusual form of spontaneous symmetry breaking. We test these ideas on the Richardson-Gaudin-Kitaev chain, a number-conserving model solvable by way of the algebraic Bethe ansatz, and equivalent in mean field to a long-range Kitaev chain.

  9. Mean-field theory of baryonic matter for QCD in the large Nc and heavy quark mass limits

    NASA Astrophysics Data System (ADS)

    Adhikari, Prabal; Cohen, Thomas D.

    2013-11-01

    We discuss theoretical issues pertaining to baryonic matter in the combined heavy-quark and large Nc limits of QCD. Witten's classic argument that baryons and interacting systems of baryons can be described in a mean-field approximation with each of the quarks moving in an average potential due to the remaining quarks is heuristic. It is important to justify this heuristic description for the case of baryonic matter since systems of interacting baryons are intrinsically more complicated than single baryons due to the possibility of hidden color states—states in which the subsystems making up the entire baryon crystal are not color-singlet nucleons but rather colorful states coupled together to make a color-singlet state. In this work, we provide a formal justification of this heuristic prescription. In order to do this, we start by taking the heavy quark limit, thus effectively reducing the problem to a many-body quantum mechanical system. This problem can be formulated in terms of integrals over coherent states, which for this problem are simple Slater determinants. We show that for the many-body problem, the support region for these integrals becomes narrow at large Nc, yielding an energy which is well approximated by a single coherent state—that is a mean-field description. Corrections to the energy are of relative order 1/Nc. While hidden color states are present in the exact state of the heavy quark system, they only influence the interaction energy below leading order in 1/Nc.

  10. Mean-Field Theories for Terrace-Width Distributions of Vicinal Surfaces: Beyond the Generalized Wigner Distribution

    NASA Astrophysics Data System (ADS)

    Richards, Howard L.; Einstein, T. L.

    2000-03-01

    The so-called generalized Wigner distribution (GWD) has been shown to provide an excellent description of terrace width distributions (TWDs) on vicinal surfaces for which there are repulsive interactions between steps that are proportional to the inverse square of the step separation.(T. L. Einstein and O. Pierre-Louis, Surface Sci. 424), L299 (1999). (S. D. Cohen, H. L. Richards, and T. L. Einstein, preprint.) Until recently, however, there was no plausible physical explanation for the excellent agreement between the GWD and the TWDs observed in Monte Carlo simulations^3 or derived from a few integrable models.^2 Here we show that the GWD can be derived from a mean-field approximation similar in spirit to the Gruber-Mullins approximation.(E. E. Gruber and W. W. Mullins, J. Phys. Chem. Solids 28), 875 (1967) This mean-field treatment can be generalized to other forms of step-step repulsions; the resulting predictions are in good agreement with Monte Carlo simulations. Finally, the process can be inverted to allow nontrivial step-step interactions to be extracted from experimental TWDs.

  11. Dynamic mean field theory for lattice gas models of fluids confined in porous materials: Higher order theory based on the Bethe-Peierls and path probability method approximations

    SciTech Connect

    Edison, John R.; Monson, Peter A.

    2014-07-14

    Recently we have developed a dynamic mean field theory (DMFT) for lattice gas models of fluids in porous materials [P. A. Monson, J. Chem. Phys. 128(8), 084701 (2008)]. The theory can be used to describe the relaxation processes in the approach to equilibrium or metastable states for fluids in pores and is especially useful for studying system exhibiting adsorption/desorption hysteresis. In this paper we discuss the extension of the theory to higher order by means of the path probability method (PPM) of Kikuchi and co-workers. We show that this leads to a treatment of the dynamics that is consistent with thermodynamics coming from the Bethe-Peierls or Quasi-Chemical approximation for the equilibrium or metastable equilibrium states of the lattice model. We compare the results from the PPM with those from DMFT and from dynamic Monte Carlo simulations. We find that the predictions from PPM are qualitatively similar to those from DMFT but give somewhat improved quantitative accuracy, in part due to the superior treatment of the underlying thermodynamics. This comes at the cost of greater computational expense associated with the larger number of equations that must be solved.

  12. Schwinger boson mean field theories of spin liquid states on a honeycomb lattice: Projective symmetry group analysis and critical field theory

    NASA Astrophysics Data System (ADS)

    Wang, Fa

    2010-07-01

    Motivated by the recent numerical evidence [Z. Meng, T. Lang, S. Wessel, F. Assaad, and A. Muramatsu, Nature (London) 464, 847 (2010)10.1038/nature08942] of a short-range resonating valence bond state in the honeycomb lattice Hubbard model, we consider Schwinger boson mean field theories of possible spin liquid states on honeycomb lattice. From general stability considerations the possible spin liquids will have gapped spinons coupled to Z2 gauge field. We apply the projective symmetry group method to classify possible Z2 spin liquid states within this formalism on honeycomb lattice. It is found that there are only two relevant Z2 states, differed by the value of gauge flux, zero or π , in the elementary hexagon. The zero-flux state is a promising candidate for the observed spin liquid and continuous phase transition into commensurate Néel order. We also derive the critical field theory for this transition, which is the well-studied O(4) invariant theory [A. V. Chubukov, T. Senthil, and S. Sachdev, Phys. Rev. Lett. 72, 2089 (1994)10.1103/PhysRevLett.72.2089; A. V. Chubukov, S. Sachdev, and T. Senthil, Nucl. Phys. B 426, 601 (1994)10.1016/0550-3213(94)90023-X; S. V. Isakov, T. Senthil, and Y. B. Kim, Phys. Rev. B 72, 174417 (2005)10.1103/PhysRevB.72.174417], and has an irrelevant coupling between Higgs and boson fields with cubic power of spatial derivatives as required by lattice symmetry. This is in sharp contrast to the conventional theory [S. Sachdev and N. Read, Int. J. Mod. Phys. B 5, 219 (1991)10.1142/S0217979291000158], where such transition generically leads to incommensurate magnetic order. In this scenario the Z2 spin liquid could be close to a tricritical point. Soft boson modes will exist at seven different wave vectors. This will show up as low-frequency dynamical spin susceptibility peaks not only at the Γ point (the Néel order wave vector) but also at Brillouin-zone-edge center M points and twelve other points. Some simple properties of the

  13. Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles

    SciTech Connect

    Speck, Thomas; Menzel, Andreas M.; Bialké, Julian; Löwen, Hartmut

    2015-06-14

    Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.

  14. Mass action law versus local contagion dynamics. A mean-field statistical approach with application to the theory of epidemics

    NASA Astrophysics Data System (ADS)

    Ovidiu Vlad, Marcel; Schönfisch, Birgitt

    1996-08-01

    A mean-field approach for epidemic processes with high migration is suggested by analogy with non-equilibrium statistical mechanics. For large systems a limit of the thermodynamic type is introduced for which both the total size of the system and the total number of individuals tend to infinity but the population density remains constant. In the thermodynamic limit the infection rate is proportional to the product of the proportion of individuals susceptible to infection and the average probability of infection. The limit form of the average probability of infection is insensitive to the detailed behaviour of the fluctuations of the number of infectious individuals and may belong to two universality classes: (1) if the fluctuation of the number of infectives is non-intermittent it increases with the increase of the partial density of infectives and approaches exponentially the asymptotic value one for large densities; (2) for intermittent fluctuations obeying a power-law scaling the average probability of infection also displays a saturation effect for large densities of infectives but the asymptotic value one is approached according to a power law rather than exponentially. For low densities of infectives both expressions for the average probability of infection are linear functions of the proportion of infectives and the infection rate is given by the mass-action law.

  15. Screening and nonlocal correlations in the extended Hubbard model from self-consistent combined GW and dynamical mean field theory

    NASA Astrophysics Data System (ADS)

    Ayral, Thomas; Biermann, Silke; Werner, Philipp

    2013-03-01

    We describe a recent implementation of the combined GW and dynamical mean field method (GW+DMFT) for the two-dimensional Hubbard model with onsite and nearest-neighbor repulsion. We clarify the relation of the GW+DMFT scheme to alternative approaches in the literature, and discuss the corresponding approximations to the free-energy functional of the model. Furthermore, we describe a numerically exact technique for the solution of the GW+DMFT equations, namely, the hybridization expansion continuous-time algorithm for impurity models with retarded interactions. We compute the low-temperature phase diagram of the half-filled extended Hubbard model, addressing the metal-insulator transition at small intersite interactions and the transition to a charge-ordered state for stronger intersite repulsions. GW+DMFT introduces a nontrivial momentum dependence into the many-body self-energy and polarization. We find that the charge fluctuations included in the present approach have a larger impact on the latter than on the former. Finally, within the GW+DMFT framework, as in extended DMFT, the intersite repulsion translates into a frequency dependence of the local effective interaction. We analyze this dependence and show how it affects the local spectral function.

  16. Spin-orbit and orbit-orbit strengths for the radioactive neutron-rich doubly magic nucleus {sup 132}Sn in relativistic mean-field theory

    SciTech Connect

    Liang Haozhao; Zhao Pengwei; Li Lulu; Meng Jie

    2011-01-15

    Relativistic mean-field (RMF) theory is applied to investigate the properties of the radioactive neutron-rich doubly magic nucleus {sup 132}Sn and the corresponding isotopes and isotones. The two-neutron and two-proton separation energies are well reproduced by the RMF theory. In particular, the RMF results agree with the experimental single-particle spectrum in {sup 132}Sn as well as the Nilsson spin-orbit parameter C and orbit-orbit parameter D thus extracted, but remarkably differ from the traditional Nilsson parameters. Furthermore, the present results provide a guideline for the isospin dependence of the Nilsson parameters.

  17. STM sub-gap structure in cuprates is a consequence of density waves, according to Mean-Field Theory and CDMFT

    NASA Astrophysics Data System (ADS)

    Verret, Simon; Roy, Jyotirmoy; Sénéchal, David; Tremblay, A.-M. S.

    Much work has been done to find how the pseudogap is related to charge density waves in cuprates. In scanning tunneling microscopy (STM) measurements, the superconducting gap and pseudogap of cuprates are sometimes accompanied by a small sub-gap structure at very low energy. This was documented early in vortex cores studies, and has now been reported at zero field for YBCO.(1) Here, we show that this can be caused by density waves, first through a standard mean-field approach, and then with Cellular Dynamical Mean-Field Theory for the Hubbard model using an exact diagonalization solver. We comment on the implication of these results for the relation between pseudogap and charge order. (1) Jens Bruér et al. arXiv:1507.06775 Supported by NSERC, CIFAR and the Tier I Canada Research Chair Program.

  18. Comparison of the order of magnetic phase transitions in several magnetocaloric materials using the rescaled universal curve, Banerjee and mean field theory criteria

    SciTech Connect

    Burrola-Gándara, L. A. Santillan-Rodriguez, C. R.; Rivera-Gomez, F. J.; Saenz-Hernandez, R. J.; Botello-Zubiate, M. E.; Matutes-Aquino, J. A.

    2015-05-07

    Magnetocaloric materials with second order phase transition near the Curie temperature can be described by critical phenomena theory. In this theory, scaling, universality, and renormalization are key concepts from which several phase transition order criteria are derived. In this work, the rescaled universal curve, Banerjee and mean field theory criteria were used to make a comparison for several magnetocaloric materials including pure Gd, SmCo{sub 1.8}Fe{sub 0.2}, MnFeP{sub 0.46}As{sub 0.54}, and La{sub 0.7}Ca{sub 0.15}Sr{sub 0.15}MnO{sub 3}. Pure Gd, SmCo{sub 1.8}Fe{sub 0.2}, and La{sub 0.7}Ca{sub 0.15}Sr{sub 0.15}MnO{sub 3} present a collapse of the rescaled magnetic entropy change curves into a universal curve, which indicates a second order phase transition; applying Banerjee criterion to H/σ vs σ{sup 2} Arrot plots and the mean field theory relation |ΔS{sub M}| ∝ (μ{sub 0}H/T{sub c}){sup 2/3} for the same materials also determines a second order phase transition. However, in the MnFeP{sub 0.46}As{sub 0.54} sample, the Banerjee criterion applied to the H/σ vs σ{sup 2} Arrot plot indicates a first order magnetic phase transition, while the mean field theory prediction for a second order phase transition, |ΔS{sub M}| ∝ (μ{sub 0}H/T{sub c}){sup 2/3}, describes a second order behavior. Also, a mixture of first and second order behavior was indicated by the rescaled universal curve criterion. The diverse results obtained for each criterion in MnFeP{sub 0.46}As{sub 0.54} are apparently related to the magnetoelastic effect and to the simultaneous presence of weak and strong magnetism in Fe (3f) and Mn (3g) alternate atomic layers, respectively. The simultaneous application of the universal curve, the Banerjee and the mean field theory criteria has allowed a better understanding about the nature of the order of the phase transitions in different magnetocaloric materials.

  19. Impurity-induced magnetic moments on the graphene-lattice Hubbard model: An inhomogeneous cluster dynamical mean-field theory study

    NASA Astrophysics Data System (ADS)

    Charlebois, M.; Sénéchal, D.; Gagnon, A.-M.; Tremblay, A.-M. S.

    2015-01-01

    Defect-induced magnetic moments are at the center of the research effort on spintronic applications of graphene. Here, we study the problem of a nonmagnetic impurity in graphene with a new theoretical method, inhomogeneous cluster dynamical mean-field theory (I-CDMFT), which takes into account interaction-induced short-range correlations while allowing long-range inhomogeneities. The system is described by a Hubbard model on the honeycomb lattice. The impurity is modeled by a local potential. For a large enough potential, interactions induce local antiferromagnetic correlations around the impurity and a net total spin 1/2 appears, in agreement with Lieb's theorem. Bound states caused by the impurity are visible in the local density of states (LDOS) and have their energies shifted by interactions in a spin-dependent way, leading to the antiferromagnetic correlations. Our results take into account dynamical correlations; nevertheless they qualitatively agree with previous mean-field and density functional theory (DFT) studies. Moreover, they provide a relation between impurity potential and on-site repulsion U that could in principle be used to determine experimentally the value of U .

  20. Mean-field density functional theory of a nanoconfined classical, three-dimensional Heisenberg fluid. I. The role of molecular anchoring.

    PubMed

    Cattes, Stefanie M; Gubbins, Keith E; Schoen, Martin

    2016-05-21

    In this work, we employ classical density functional theory (DFT) to investigate for the first time equilibrium properties of a Heisenberg fluid confined to nanoscopic slit pores of variable width. Within DFT pair correlations are treated at modified mean-field level. We consider three types of walls: hard ones, where the fluid-wall potential becomes infinite upon molecular contact but vanishes otherwise, and hard walls with superimposed short-range attraction with and without explicit orientation dependence. To model the distance dependence of the attractions, we employ a Yukawa potential. The orientation dependence is realized through anchoring of molecules at the substrates, i.e., an energetic discrimination of specific molecular orientations. If the walls are hard or attractive without specific anchoring, the results are "quasi-bulk"-like in that they can be linked to a confinement-induced reduction of the bulk mean field. In these cases, the precise nature of the walls is completely irrelevant at coexistence. Only for specific anchoring nontrivial features arise, because then the fluid-wall interaction potential affects the orientation distribution function in a nontrivial way and thus appears explicitly in the Euler-Lagrange equations to be solved for minima of the grand potential of coexisting phases. PMID:27208962

  1. Dynamical screening effects in correlated electron materials-a progress report on combined many-body perturbation and dynamical mean field theory: 'GW + DMFT'.

    PubMed

    Biermann, Silke

    2014-04-30

    We give a summary of recent progress in the field of electronic structure calculations for materials with strong electronic Coulomb correlations. The discussion focuses on developments beyond the by now well established combination of density functional and dynamical mean field theory dubbed 'LDA + DMFT'. It is organized around the description of dynamical screening effects in the solid. Indeed, screening in the solid gives rise to dynamical local Coulomb interactions U(ω) (Aryasetiawan et al 2004 Phys. Rev. B 70 195104), and this frequency dependence leads to effects that cannot be neglected in a truly first principles description. We review the recently introduced extension of LDA + DMFT to dynamical local Coulomb interactions 'LDA + U(ω) + DMFT' (Casula et al 2012 Phys. Rev. B 85 035115, Werner et al 2012 Nature Phys. 1745-2481). A reliable description of dynamical screening effects is also a central ingredient of the 'GW + DMFT' scheme (Biermann et al 2003 Phys. Rev. Lett. 90 086402), a combination of many-body perturbation theory in Hedin's GW approximation and dynamical mean field theory. Recently, the first GW + DMFT calculations including dynamical screening effects for real materials have been achieved, with applications to SrV O3 (Tomczak et al 2012 Europhys. Lett. 100 67001, Tomczak et al Phys. Rev. B submitted (available electronically as arXiv:1312.7546)) and adatom systems on surfaces (Hansmann et al 2013 Phys. Rev. Lett. 110 166401). We review these and comment on further perspectives in the field. This review is an attempt to put elements of the original works into the broad perspective of the development of truly first principles techniques for correlated electron materials. PMID:24722486

  2. Functional renormalization-group approaches, one-particle (irreducible) reducible with respect to local Green’s functions, with dynamical mean-field theory as a starting point

    SciTech Connect

    Katanin, A. A.

    2015-06-15

    We consider formulations of the functional renormalization-group (fRG) flow for correlated electronic systems with the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those neglecting one-particle irreducible six-point vertices (with respect to the local Green’s functions) and neglecting one-particle reducible six-point vertices. The former class is represented by the recently introduced DMF{sup 2}RG approach [31], but also by the scale-dependent generalization of the one-particle irreducible representation (with respect to local Green’s functions, 1PI-LGF) of the generating functional [20]. The second class is represented by the fRG flow within the dual fermion approach [16, 32]. We compare formulations of the fRG approach in each of these cases and suggest their further application to study 2D systems within the Hubbard model.

  3. Successively thresholded domain boundary roughening driven by pinning centers and missing bonds: Hard-spin mean-field theory applied to d=3 Ising magnets.

    PubMed

    Çağlar, Tolga; Berker, A Nihat

    2015-12-01

    Hard-spin mean-field theory has recently been applied to Ising magnets, correctly yielding the absence and presence of an interface roughening transition respectively in d=2 and d=3 dimensions and producing the ordering-roughening phase diagram for isotropic and anisotropic systems. The approach has now been extended to the effects of quenched random pinning centers and missing bonds on the interface of isotropic and anisotropic Ising models in d=3. We find that these frozen impurities cause domain boundary roughening that exhibits consecutive thresholding transitions as a function of interaction anisotropy. For both missing-bond and pinning-center impurities, for moderately large values of the anisotropy, the systems saturate to the "solid-on-solid" limit, exhibiting a single universal curve for the domain boundary width as a function of impurity concentration. PMID:26764656

  4. Dynamical Mean-Field Theory Plus Numerical Renormalization-Group Study of Spin-Orbital Separation in a Three-Band Hund Metal.

    PubMed

    Stadler, K M; Yin, Z P; von Delft, J; Kotliar, G; Weichselbaum, A

    2015-09-25

    We show that the numerical renormalization group is a viable multi-band impurity solver for dynamical mean-field theory (DMFT), offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund metal problem for a three-band model on a Bethe lattice at 1/3 filling. The ground state is a Fermi liquid. The one-particle spectral function undergoes a coherence-incoherence crossover with increasing temperature, with spectral weight being transferred from low to high energies. Further, it exhibits a strong particle-hole asymmetry. In the incoherent regime, the self-energy displays approximate power-law behavior for positive frequencies only. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales. PMID:26451570

  5. Dynamical Mean-Field Theory Plus Numerical Renormalization-Group Study of Spin-Orbital Separation in a Three-Band Hund Metal

    NASA Astrophysics Data System (ADS)

    Stadler, K. M.; Yin, Z. P.; von Delft, J.; Kotliar, G.; Weichselbaum, A.

    2015-09-01

    We show that the numerical renormalization group is a viable multi-band impurity solver for dynamical mean-field theory (DMFT), offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund metal problem for a three-band model on a Bethe lattice at 1 /3 filling. The ground state is a Fermi liquid. The one-particle spectral function undergoes a coherence-incoherence crossover with increasing temperature, with spectral weight being transferred from low to high energies. Further, it exhibits a strong particle-hole asymmetry. In the incoherent regime, the self-energy displays approximate power-law behavior for positive frequencies only. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales.

  6. Systematic study of nuclear matrix elements in neutrinoless double-β decay with a beyond-mean-field covariant density functional theory

    NASA Astrophysics Data System (ADS)

    Yao, J. M.; Song, L. S.; Hagino, K.; Ring, P.; Meng, J.

    2015-02-01

    We report a systematic study of nuclear matrix elements (NMEs) in neutrinoless double-β decays with a state-of-the-art beyond-mean-field covariant density functional theory. The dynamic effects of particle-number and angular-momentum conservations as well as quadrupole shape fluctuations are taken into account with projections and generator coordinate method for both initial and final nuclei. The full relativistic transition operator is adopted to calculate the NMEs. The present systematic studies show that in most of the cases there is a much better agreement with the previous nonrelativistic calculation based on the Gogny force than in the case of the nucleus 150Nd found by Song et al. [Phys. Rev. C 90, 054309 (2014), 10.1103/PhysRevC.90.054309]. In particular, we find that the total NMEs can be well approximated by the pure axial-vector coupling term with a considerable reduction of the computational effort.

  7. Composition and temperature dependent electronic structures of NiS2 -xSex alloys: First-principles dynamical mean-field theory approach

    NASA Astrophysics Data System (ADS)

    Moon, Chang-Youn; Kang, Hanhim; Jang, Bo Gyu; Shim, Ji Hoon

    2015-12-01

    We investigate the evolution of the electronic structure of NiS2 -xSex alloys with varying temperature and composition x by using the combined approach of density-functional theory and dynamical mean-field theory. Adopting realistic alloy structures containing S and Se dimers, we map their electronic correlation strength on the phase diagram and observe the metal-insulator transition (MIT) at the composition x =0.5 , which is consistent with the experimental measurements. The temperature dependence of the local magnetic susceptibility is found to show a typical Curie-Weiss-like behavior in the insulating phase while it shows a constant Pauli-like behavior in the metallic phase. A comparison of the electronic structures for NiS2 and NiSe2 in different lattice structures suggests that the MIT in this alloy system can be classified as of bandwidth-control type, where the change in the hybridization strength between Ni d and chalcogen p orbitals is the most important parameter.

  8. Cluster dynamical mean field theory study of antiferromagnetic transition in the square-lattice Hubbard model: Optical conductivity and electronic structure

    NASA Astrophysics Data System (ADS)

    Sato, Toshihiro; Tsunetsugu, Hirokazu

    2016-08-01

    We numerically study optical conductivity σ (ω ) near the "antiferromagnetic" phase transition in the square-lattice Hubbard model at half filling. We use a cluster dynamical mean field theory and calculate conductivity including vertex corrections and, to this end, we have reformulated the vertex corrections in the antiferromagnetic phase. We find that the vertex corrections change various important details in temperature and ω dependencies of conductivity in the square lattice, and this contrasts sharply the case of the Mott transition in the frustrated triangular lattice. Generally, the vertex corrections enhance variations in the ω dependence, and sharpen the Drude peak and a high-ω incoherent peak in the paramagnetic phase. They also enhance the dip in σ (ω ) at ω =0 in the antiferromagnetic phase. Therefore, the dc conductivity is enhanced in the paramagnetic phase and suppressed in the antiferromagnetic phase, but this change occurs slightly below the transition temperature. We also find a temperature region above the transition temperature in which the dc conductivity shows an insulating behavior but σ (ω ) retains the Drude peak, and this region is stabilized by the vertex corrections. We also investigate which fluctuations are important in the vertex corrections and analyze momentum dependence of the vertex function in detail.

  9. Numerical analysis of kinetic boundary conditions at net evaporation/condensation interfaces in various liquid temperatures based on mean-field kinetic theory

    NASA Astrophysics Data System (ADS)

    Kon, Misaki; Kobayashi, Kazumichi; Watanabe, Masao

    2014-12-01

    This study aims to investigate the liquid temperature dependency of the kinetic boundary condition at a vapor-liquid interface in net evaporation/condensation. The numerical simulations based on the mean-field kinetic theory and the molecular gas dynamics in the cases of various liquid temperatures were carried out. We focused on two important issues for the kinetic boundary condition; one is to investigate the applicable limit of the kinetic boundary condition which is assumed to be the isotropic velocity distribution at the liquid temperature and the other is to estimate the value of the condensation coefficient included in the kinetic boundary condition. The simulation results showed that the applicable limit of the isotropic velocity distribution in net evaporation/condensation practically independent from the liquid temperature. Furthermore, the condensation coefficients in net evaporation/condensation depend significantly on the liquid temperature; the condensation coefficient is constant and equal to the evaporation coefficient in net evaporation, while, in net condensation, the condensation coefficient increases with the increase of the degree of nonequilibrium.

  10. Electric-field-driven Mott metal-insulator transition in correlated thin films: An inhomogeneous dynamical mean-field theory approach

    NASA Astrophysics Data System (ADS)

    Bakalov, P.; Nasr Esfahani, D.; Covaci, L.; Peeters, F. M.; Tempere, J.; Locquet, J.-P.

    2016-04-01

    Simulations are carried out based on the dynamical mean-field theory (DMFT) in order to investigate the properties of correlated thin films for various values of the chemical potential, temperature, interaction strength, and applied transverse electric field. Application of a sufficiently strong field to a thin film at half filling leads to the appearance of conducting regions near the surfaces of the film, whereas in doped slabs the application of a field leads to a conductivity enhancement on one side of the film and a gradual transition to the insulating state on the opposite side. In addition to the inhomogeneous DMFT, a local density approximation (LDA) is considered in which the particle density n , quasiparticle residue Z , and spectral weight at the Fermi level A (ω =0 ) of each layer are approximated by a homogeneous bulk environment. A systematic comparison between the two approaches reveals that the less expensive LDA results are in good agreement with the DMFT approach, except close to the metal-to-insulator transition points and in the layers immediately at the film surfaces. LDA values for n are overall more reliable than those for Z and A (ω =0 ) . The hysteretic behavior (memory effect) characteristic of the bulk doping driven Mott transition persists in the slab.

  11. {alpha}-decay properties of superheavy elements Z=113-125 in the relativistic mean-field theory with vector self-coupling of {omega} meson

    SciTech Connect

    Sharma, M.M.; Farhan, A.R.; Muenzenberg, G.

    2005-05-01

    We have investigated properties of {alpha}-decay chains of recently produced superheavy elements Z=115 and Z=113 using the new Lagrangian model NL-SV1 with inclusion of the vector self-coupling of the {omega} meson in the framework of relativistic mean-field theory. It is shown that the experimentally observed {alpha}-decay energies and half-lives are reproduced well by this Lagrangian model. Further calculations for the heavier elements with Z=117-125 show that these nuclei are superdeformed with a prolate shape in the ground state. A superdeformed shell closure at Z=118 lends an additional binding and an extra stability to nuclei in this region. Consequently, it is predicted that the corresponding Q{sub {alpha}} values provide {alpha}-decay half-lives for heavier superheavy nuclei within experimentally feasible conditions. The results are compared with those of macroscopic-microscopic approaches. A perspective of the difference in shell effects among various approaches is presented and its consequences for superheavy nuclei are discussed.

  12. Spins and parities of the odd-A P isotopes within a relativistic mean-field model and elastic magnetic electron-scattering theory

    NASA Astrophysics Data System (ADS)

    Wang, Zaijun; Ren, Zhongzhou; Dong, Tiekuang; Xu, Chang

    2014-08-01

    The ground-state spins and parities of the odd-A phosphorus isotopes 25-47P are studied with the relativistic mean-field (RMF) model and relativistic elastic magnetic electron-scattering theory (REMES). Results of the RMF model with the NL-SH, TM2, and NL3 parameters show that the 2s1/2 and 1d3/2 proton level inversion may occur for the neutron-rich isotopes 37-47P, and, consequently, the possible spin-parity values of 37-47P may be 3/2+, which, except for P47, differs from those given by the NUBASE2012 nuclear data table by Audi et al. Calculations of the elastic magnetic electron scattering of 37-47P with the single valence proton in the 2s1/2 and 1d3/2 state show that the form factors have significant differences. The results imply that elastic magnetic electron scattering can be a possible way to study the 2s1/2 and 1d3/2 level inversion and the spin-parity values of 37-47P. The results can also provide new tests as to what extent the RMF model, along with its various parameter sets, is valid for describing the nuclear structures. In addition, the contributions of the upper and lower components of the Dirac four-spinors to the form factors and the isotopic shifts of the magnetic form factors are discussed.

  13. Information geometry of mean-field approximation.

    PubMed

    Tanaka, T

    2000-08-01

    I present a general theory of mean-field approximation based on information geometry and applicable not only to Boltzmann machines but also to wider classes of statistical models. Using perturbation expansion of the Kullback divergence (or Plefka expansion in statistical physics), a formulation of mean-field approximation of general orders is derived. It includes in a natural way the "naive" mean-field approximation and is consistent with the Thouless-Anderson-Palmer (TAP) approach and the linear response theorem in statistical physics. PMID:10953246

  14. Universality in bipartite mean field spin glasses

    NASA Astrophysics Data System (ADS)

    Genovese, Giuseppe

    2012-12-01

    In this work, we give a proof of universality with respect to the choice of the statistical distribution of the quenched noise, for mean field bipartite spin glasses. We use mainly techniques of spin glasses theory, as Guerra's interpolation and the cavity approach.

  15. A mean field approach to watershed hydrology

    NASA Astrophysics Data System (ADS)

    Bartlett, Mark; Porporato, Amilcare

    2016-04-01

    Mean field theory (also known as self-consistent field theory) is commonly used in statistical physics when modeling the space-time behavior of complex systems. The mean field theory approximates a complex multi-component system by considering a lumped (or average) effect for all individual components acting on a single component. Thus, the many body problem is reduced to a one body problem. For watershed hydrology, a mean field theory reduces the numerous point component effects to more tractable watershed averages, resulting in a consistent method for linking the average watershed fluxes to the local fluxes at each point. We apply this approach to the spatial distribution of soil moisture, and as a result, the numerous local interactions related to lateral fluxes of soil water are parameterized in terms of the average soil moisture. The mean field approach provides a basis for unifying and extending common event-based models (e.g. Soil Conservation Service curve number (SCS-CN) method) with more modern semi-distributed models (e.g. Variable Infiltration Capacity (VIC) model, the Probability Distributed (PDM) model, and TOPMODEL). We obtain simple equations for the fractions of the different source areas of runoff, the spatial variability of runoff, and the average runoff value (i.e., the so-called runoff curve). The resulting space time distribution of soil moisture offers a concise description of the variability of watershed fluxes.

  16. Stochastic kinetic mean field model

    NASA Astrophysics Data System (ADS)

    Erdélyi, Zoltán; Pasichnyy, Mykola; Bezpalchuk, Volodymyr; Tomán, János J.; Gajdics, Bence; Gusak, Andriy M.

    2016-07-01

    This paper introduces a new model for calculating the change in time of three-dimensional atomic configurations. The model is based on the kinetic mean field (KMF) approach, however we have transformed that model into a stochastic approach by introducing dynamic Langevin noise. The result is a stochastic kinetic mean field model (SKMF) which produces results similar to the lattice kinetic Monte Carlo (KMC). SKMF is, however, far more cost-effective and easier to implement the algorithm (open source program code is provided on

  17. Spatial Correlations and the Insulating Phase of the High-Tc Cuprates: Insights from a Configuration-Interaction-Based Solver for Dynamical Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Go, Ara; Millis, Andrew J.

    2015-01-01

    A recently proposed configuration-interaction-based impurity solver is used in combination with the single-site and four-site cluster dynamical mean field approximations to investigate the three-band copper oxide model believed to describe the electronic structure of high transition temperature copper-oxide superconductors. Use of the configuration interaction solver enables verification of the convergence of results with respect to the number of bath orbitals. The spatial correlations included in the cluster approximation substantially shift the metal-insulator phase boundary relative to the prediction of the single-site approximation and increase the predicted energy gap of the insulating phase by about 1 eV above the single-site result. Vertex corrections occurring in the four-site approximation act to dramatically increase the value of the optical conductivity near the gap edge, resulting in better agreement with the data. The calculations reveal two distinct correlated insulating states: the "magnetically correlated insulator," in which nontrivial intersite correlations play an essential role in stabilizing the insulating state, and the strongly correlated insulator, in which local physics suffices. Comparison of the calculations to the data places the cuprates in the magnetically correlated Mott insulator regime.

  18. Co-non-solvency: Mean-field polymer theory does not describe polymer collapse transition in a mixture of two competing good solvents

    SciTech Connect

    Mukherji, Debashish; Stuehn, Torsten; Kremer, Kurt; Marques, Carlos M.

    2015-03-21

    Smart polymers are a modern class of polymeric materials that often exhibit unpredictable behavior in mixtures of solvents. One such phenomenon is co-non-solvency. Co-non-solvency occurs when two (perfectly) miscible and competing good solvents, for a given polymer, are mixed together. As a result, the same polymer collapses into a compact globule within intermediate mixing ratios. More interestingly, polymer collapses when the solvent quality remains good and even gets increasingly better by the addition of the better cosolvent. This is a puzzling phenomenon that is driven by strong local concentration fluctuations. Because of the discrete particle based nature of the interactions, Flory-Huggins type mean field arguments become unsuitable. In this work, we extend the analysis of the co-non-solvency effect presented earlier [D. Mukherji et al., Nat. Commun. 5, 4882 (2014)]. We explain why co-non-solvency is a generic phenomenon, which can only be understood by the thermodynamic treatment of the competitive displacement of (co)solvent components. This competition can result in a polymer collapse upon improvement of the solvent quality. Specific chemical details are not required to understand these complex conformational transitions. Therefore, a broad range of polymers are expected to exhibit similar reentrant coil-globule-coil transitions in competing good solvents.

  19. Field theory for size- and charge-asymmetric primitive model of ionic systems: mean-field stability analysis and pretransitional effects.

    PubMed

    Ciach, A; Góźdź, W T; Stell, G

    2007-05-01

    The primitive model of ionic systems is investigated within a field-theoretic description for the whole range of diameter-, lambda , and charge, Z ratios of the two ionic species. Two order parameters (OP) are identified. The relation of the OP's to physically relevant quantities is nontrivial. Each OP is a linear combination of the charge density and the number-density waves. Instabilities of the disordered phase associated with the two OP's are determined in the mean-field approximation (MF). In MF a gas-liquid separation occurs for any Z and lambda is not equal to 1 . In addition, an instability with respect to various types of periodic ordering of the two kinds of ions is found. Depending on lambda and Z , one or the other transition is metastable in different thermodynamic states. For sufficiently large size disparity we find a sequence of fluid-crystal-fluid transitions for the increasing volume fraction of ions, in agreement with experimental observations. The instabilities found in MF represent weak ordering of the most probable instantaneous states, and are identified with structural loci associated with pretransitional effects. PMID:17677071

  20. The Brownian mean field model

    NASA Astrophysics Data System (ADS)

    Chavanis, Pierre-Henri

    2014-05-01

    We discuss the dynamics and thermodynamics of the Brownian mean field (BMF) model which is a system of N Brownian particles moving on a circle and interacting via a cosine potential. It can be viewed as the canonical version of the Hamiltonian mean field (HMF) model. The BMF model displays a second order phase transition from a homogeneous phase to an inhomogeneous phase below a critical temperature T c = 1 / 2. We first complete the description of this model in the mean field approximation valid for N → +∞. In the strong friction limit, the evolution of the density towards the mean field Boltzmann distribution is governed by the mean field Smoluchowski equation. For T < T c , this equation describes a process of self-organization from a non-magnetized (homogeneous) phase to a magnetized (inhomogeneous) phase. We obtain an analytical expression for the temporal evolution of the magnetization close to T c . Then, we take fluctuations (finite N effects) into account. The evolution of the density is governed by the stochastic Smoluchowski equation. From this equation, we derive a stochastic equation for the magnetization and study its properties both in the homogenous and inhomogeneous phase. We show that the fluctuations diverge at the critical point so that the mean field approximation ceases to be valid. Actually, the limits N → +∞ and T → T c do not commute. The validity of the mean field approximation requires N( T - T c ) → +∞ so that N must be larger and larger as T approaches T c . We show that the direction of the magnetization changes rapidly close to T c while its amplitude takes a long time to relax. We also indicate that, for systems with long-range interactions, the lifetime of metastable states scales as e N except close to a critical point. The BMF model shares many analogies with other systems of Brownian particles with long-range interactions such as self-gravitating Brownian particles, the Keller-Segel model describing the chemotaxis

  1. Non-mean-field critical exponent in a mean-field model: dynamics versus statistical mechanics.

    PubMed

    Ogawa, Shun; Patelli, Aurelio; Yamaguchi, Yoshiyuki Y

    2014-03-01

    Mean-field theory tells us that the classical critical exponent of susceptibility is twice that of magnetization. However, linear response theory based on the Vlasov equation, which is naturally introduced by the mean-field nature, makes the former exponent half of the latter for families of quasistationary states having second order phase transitions in the Hamiltonian mean-field model and its variances, in the low-energy phase. We clarify that this strange exponent is due to the existence of Casimir invariants which trap the system in a quasistationary state for a time scale diverging with the system size. The theoretical prediction is numerically confirmed by N-body simulations for the equilibrium states and a family of quasistationary states. PMID:24730814

  2. Mean-field sparse optimal control

    PubMed Central

    Fornasier, Massimo; Piccoli, Benedetto; Rossi, Francesco

    2014-01-01

    We introduce the rigorous limit process connecting finite dimensional sparse optimal control problems with ODE constraints, modelling parsimonious interventions on the dynamics of a moving population divided into leaders and followers, to an infinite dimensional optimal control problem with a constraint given by a system of ODE for the leaders coupled with a PDE of Vlasov-type, governing the dynamics of the probability distribution of the followers. In the classical mean-field theory, one studies the behaviour of a large number of small individuals freely interacting with each other, by simplifying the effect of all the other individuals on any given individual by a single averaged effect. In this paper, we address instead the situation where the leaders are actually influenced also by an external policy maker, and we propagate its effect for the number N of followers going to infinity. The technical derivation of the sparse mean-field optimal control is realized by the simultaneous development of the mean-field limit of the equations governing the followers dynamics together with the Γ-limit of the finite dimensional sparse optimal control problems. PMID:25288818

  3. Momentum dependence of the nuclear mean field

    SciTech Connect

    Baldo, M.; Bombaci, I.; Giansiracusa, G.; Lombardo, U. Dipartimento di Fisica, Universita di Catania, Corso Italia 57, 95129 Catania, Italy)

    1989-08-01

    The dependence on the momentum of the nuclear mean field is studied in the framework of the self-consistent Bethe-Brueckner theory. It is pointed out that the rearrangement term, coming from the variation of the {ital G} matrix, gives a substantial contribution at the lowest momenta. The resulting single particle potential exhibits a good rate of convergence. Its momentum dependence appears to be negligible up to 2 fm{sup {minus}1}, in contrast with potentials used in calculations of heavy-ion collisions at intermediate energies.

  4. Optical weights and waterfalls in doped charge-transfer insulators: A local density approximation and dynamical mean-field theory study of La2-xSrxCuO4

    NASA Astrophysics Data System (ADS)

    Weber, Cédric; Haule, Kristjan; Kotliar, Gabriel

    2008-10-01

    We use the local density approximation in combination with the dynamical mean-field theory to investigate intermediate energy properties of the copper oxides. We identify coherent and incoherent spectral features that result from doping a charge-transfer insulator, namely quasiparticles, Zhang-Rice singlet band, and the upper and lower Hubbard bands. Angle resolving these features, we identify a waterfall-like feature between the quasiparticle part and the incoherent part of the Zhang-Rice band. We investigate the asymmetry between particle and hole doping. On the hole-doped side, there is a very rapid transfer of spectral weight upon doping in the one particle spectra. The optical spectral weight increases superlinearly on the hole-doped side in agreement with experiments.

  5. Electronic localization and bad-metallicity in pure and electron-doped troilite: A local-density-approximation plus dynamical-mean-field-theory study of FeS for lithium-ion batteries

    NASA Astrophysics Data System (ADS)

    Craco, L.; Faria, J. L. B.

    2016-02-01

    Iron sulfides are promising candidates for the next generation of rechargeable lithium-ion battery materials. Motivated thereby, we present a detailed study of correlation- and doping-induced electronic reconstruction in troilite. Based on local-density-approximation plus dynamical-mean-field-theory, we stress the importance of multi-orbital Coulomb interactions in concert with first-principles band structure calculations for a consistent understanding of intrinsic Mott-Hubbard insulating state in FeS. We explore the anomalous nature of electron doping-induced insulator-bad metal transition, showing that it is driven by orbital-selective dynamical spectral weight transfer. Our results are relevant for understanding charge dynamics upon electrochemical lithiation of iron monosulfides electrode materials for lithium-ion batteries.

  6. Chemical potential beyond the quasiparticle mean field

    SciTech Connect

    Dinh Dang, N.; Hung, N. Quang

    2010-03-15

    The effects of quantal and thermal fluctuations beyond the BCS quasiparticle mean field on the chemical potential are studied within a model, which consists of N particles distributed amongst {Omega} doubly folded equidistant levels interacting via a pairing force with parameter G. The results obtained at zero and finite temperatures T within several approaches, which include the fluctuations beyond the BCS theory, are compared with the exact results. The chemical potential, defined as the Lagrangian multiplier to preserve the average number of particles, is compared with the corresponding quantity, which includes the effect from fluctuations of particle and quasiparticle numbers beyond the BCS quasiparticle mean field. The analysis of the results shows that the latter differs significantly from the former as functions of G and T. The chemical potential loses its physical meaning in the system with a fixed number of particles or after eliminating quantal fluctuations of particle (quasiparticle) numbers by means of particle number projection. The validity of the criterion for the signature of the transition to Bose-Einstein condensation, which occurs in infinite systems when the chemical potential hits the bottom of the energy spectrum, is reexamined for the finite multilevel model.

  7. Continuous Time Finite State Mean Field Games

    SciTech Connect

    Gomes, Diogo A.; Mohr, Joana Souza, Rafael Rigao

    2013-08-01

    In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N{yields}{infinity} of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games.

  8. Deterministic Mean-Field Ensemble Kalman Filtering

    DOE PAGESBeta

    Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul

    2016-05-03

    The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d theory.« less

  9. Parametrization of light clusters within relativistic mean field models

    SciTech Connect

    Ferreira, Marcio; Providencia, Constanca

    2013-06-10

    Light clusters are included in the equation of state of nuclearmatter within the relativistic mean field theory. The effect of the cluster-meson coupling constants on the dissolution density is discussed. Theoretical and experimental constraints are used to fix the cluster-meson couplings at T Almost-Equal-To 5 MeV.

  10. Microscopically constrained mean-field models from chiral nuclear thermodynamics

    NASA Astrophysics Data System (ADS)

    Rrapaj, Ermal; Roggero, Alessandro; Holt, Jeremy W.

    2016-06-01

    We explore the use of mean-field models to approximate microscopic nuclear equations of state derived from chiral effective field theory across the densities and temperatures relevant for simulating astrophysical phenomena such as core-collapse supernovae and binary neutron star mergers. We consider both relativistic mean-field theory with scalar and vector meson exchange as well as energy density functionals based on Skyrme phenomenology and compare to thermodynamic equations of state derived from chiral two- and three-nucleon forces in many-body perturbation theory. Quantum Monte Carlo simulations of symmetric nuclear matter and pure neutron matter are used to determine the density regimes in which perturbation theory with chiral nuclear forces is valid. Within the theoretical uncertainties associated with the many-body methods, we find that select mean-field models describe well microscopic nuclear thermodynamics. As an additional consistency requirement, we study as well the single-particle properties of nucleons in a hot/dense environment, which affect e.g., charged-current weak reactions in neutron-rich matter. The identified mean-field models can be used across a larger range of densities and temperatures in astrophysical simulations than more computationally expensive microscopic models.

  11. Mean-Field Games for Marriage

    PubMed Central

    Bauso, Dario; Dia, Ben Mansour; Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul

    2014-01-01

    This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple’s network on their feeling states and their well-being. PMID:24804835

  12. Degenerate approach to the mean field Bose-Hubbard Hamiltonian

    NASA Astrophysics Data System (ADS)

    Belemuk, Alexander M.; Ryzhov, Valentin N.

    2016-04-01

    A degenerate variant of mean field perturbation theory for the on-site Bose-Hubbard Hamiltonian is presented. We split the perturbation into two terms and perform exact diagonalization in the two-dimensional subspace corresponding to the degenerate states. The final relations for the second order ground state energy and first order wave function do not contain singularities at integer values of the chemical potentials. The resulting equation for the phase boundary between superfluid and Mott states coincides with the prediction from the conventional mean field perturbation approach.

  13. "Phase diagram" of a mean field game

    NASA Astrophysics Data System (ADS)

    Swiecicki, Igor; Gobron, Thierry; Ullmo, Denis

    2016-01-01

    Mean field games were introduced by J-M. Lasry and P-L. Lions in the mathematical community, and independently by M. Huang and co-workers in the engineering community, to deal with optimization problems when the number of agents becomes very large. In this article we study in detail a particular example called the "seminar problem" introduced by O. Guéant, J-M. Lasry, and P-L. Lions in 2010. This model contains the main ingredients of any mean field game but has the particular feature that all agents are coupled only through a simple random event (the seminar starting time) that they all contribute to form. In the mean field limit, this event becomes deterministic and its value can be fixed through a self consistent procedure. This allows for a rather thorough understanding of the solutions of the problem, through both exact results and a detailed analysis of various limiting regimes. For a sensible class of initial configurations, distinct behaviors can be associated to different domains in the parameter space. For this reason, the "seminar problem" appears to be an interesting toy model on which both intuition and technical approaches can be tested as a preliminary study toward more complex mean field game models.

  14. Shell corrections, magic numbers, and mean field

    SciTech Connect

    Denisov, V. Yu.

    2007-02-15

    It is shown that the positions of deep local minima of shell corrections associated with magic numbers in the region of superheavy nuclei depend on the parameters of the central and spin-orbit mean-field potentials. The accuracy of nuclear-mass predictions made within various models for superheavy nuclei is analyzed.

  15. Instabilities in the Mean Field Limit

    NASA Astrophysics Data System (ADS)

    Han-Kwan, Daniel; Nguyen, Toan T.

    2016-03-01

    Consider a system of N particles interacting through Newton's second law with Coulomb interaction potential in one spatial dimension or a {C}^2 smooth potential in any dimension. We prove that in the mean field limit N → + ∞, the N particles system displays instabilities in times of order log N, for some configurations approximately distributed according to unstable homogeneous equilibria.

  16. Unstable infinite nuclear matter in stochastic mean field approach

    SciTech Connect

    Colonna, M.; Chomaz, P. Laboratorio Nazionale del Sud, Viale Andrea Doria, Catania )

    1994-04-01

    In this article, we consider a semiclassical stochastic mean-field approach. In the case of unstable infinite nuclear matter, we calculate the characteristic time of the exponential growing of fluctuations and the diffusion coefficients associated to the unstable modes, in the framework of the Boltzmann-Langevin theory. These two quantities are essential to describe the dynamics of fluctuations and instabilities since, in the unstable regions, the evolution of the system will be dominated by the amplification of fluctuations. In order to make realistic 3D calculations feasible, we suggest to replace the complicated Boltzmann-Langevin theory by a simpler stochastic mean-field approach corresponding to a standard Boltzmann evolution, complemented by a simple noise chosen to reproduce the dynamics of the most unstable modes. Finally we explain how to approximately implement this method by simply tuning the noise associated to the use of a finite number of test particles in Boltzman-like calculations.

  17. Robust mean field games for coupled Markov jump linear systems

    NASA Astrophysics Data System (ADS)

    Moon, Jun; Başar, Tamer

    2016-07-01

    We consider robust stochastic large population games for coupled Markov jump linear systems (MJLSs). The N agents' individual MJLSs are governed by different infinitesimal generators, and are affected not only by the control input but also by an individual disturbance (or adversarial) input. The mean field term, representing the average behaviour of N agents, is included in the individual worst-case cost function to capture coupling effects among agents. To circumvent the computational complexity and analyse the worst-case effect of the disturbance, we use robust mean field game theory to design low-complexity robust decentralised controllers and to characterise the associated worst-case disturbance. We show that with the individual robust decentralised controller and the corresponding worst-case disturbance, which constitute a saddle-point solution to a generic stochastic differential game for MJLSs, the actual mean field behaviour can be approximated by a deterministic function which is a fixed-point solution to the constructed mean field system. We further show that the closed-loop system is uniformly stable independent of N, and an approximate optimality can be obtained in the sense of ε-Nash equilibrium, where ε can be taken to be arbitrarily close to zero as N becomes sufficiently large. A numerical example is included to illustrate the results.

  18. On Mean Field Limits for Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Boers, Niklas; Pickl, Peter

    2016-07-01

    We present a purely probabilistic proof of propagation of molecular chaos for N-particle systems in dimension 3 with interaction forces scaling like 1/\\vert q\\vert ^{3λ - 1} with λ smaller but close to one and cut-off at q = N^{-1/3}. The proof yields a Gronwall estimate for the maximal distance between exact microscopic and approximate mean-field dynamics. This can be used to show weak convergence of the one-particle marginals to solutions of the respective mean-field equation without cut-off in a quantitative way. Our results thus lead to a derivation of the Vlasov equation from the microscopic N-particle dynamics with force term arbitrarily close to the physically relevant Coulomb- and gravitational forces.

  19. Mean-Field Evolution of Fermionic Systems

    NASA Astrophysics Data System (ADS)

    Benedikter, Niels; Porta, Marcello; Schlein, Benjamin

    2014-11-01

    The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems. In this paper, we study the dynamics of initial data close to a Slater determinant, whose reduced one-particle density is an orthogonal projection ω N with the appropriate semiclassical structure. Assuming some regularity of the interaction potential, we show that the evolution of such an initial data remains close to a Slater determinant, with reduced one-particle density given by the solution of the Hartree-Fock equation with initial data ω N . Our result holds for all (semiclassical) times, and gives effective bounds on the rate of the convergence towards the Hartree-Fock dynamics.

  20. Mean-Field Dynamical Semigroups on C*-ALGEBRAS

    NASA Astrophysics Data System (ADS)

    Duffield, N. G.; Werner, R. F.

    We study a notion of the mean-field limit of a sequence of dynamical semigroups on the n-fold tensor products of a C*-algebra { A} with itself. In analogy with the theory of semigroups on Banach spaces we give abstract conditions for the existence of these limits. These conditions are verified in the case of semigroups whose generators are determined by the successive resymmetrizations of a fixed operator, as well as generators which can be approximated by generators of this type. This includes the time evolutions of the mean-field versions of quantum lattice systems. In these cases the limiting dynamical semigroup is given by a continuous flow on the state space of { A}. For a class of such flows we show stability by constructing a Liapunov function. We also give examples where the limiting evolution is given by a diffusion, rather than a flow on the state space of { A}.

  1. Relativistic Mean Field description of exotic nuclei

    NASA Astrophysics Data System (ADS)

    Gambhir, Y. K.

    1994-03-01

    The Relativistic Mean Field (RMF) approach which essentially is an extension of the original σ — ω model of Walecka, has been applied to exotic nuclei as an illustration. We consider nuclei near Z = 34 in the very interesting 2p-1f region. The calculated binding energies, root mean square radii, deformations and other observables are very satisfactory and are in accordance with the experiment (where available) and also with the available empirical studies. Large deformations and shape co-existence are obtained for several cases.

  2. A minimax approach to mean field games

    NASA Astrophysics Data System (ADS)

    Averboukh, Yu V.

    2015-07-01

    An initial boundary value problem for the system of equations of a determined mean field game is considered. The proposed definition of a generalized solution is based on the minimax approach to the Hamilton-Jacobi equation. We prove the existence of the generalized (minimax) solution using the Nash equilibrium in the auxiliary differential game with infinitely many identical players. We show that the minimax solution of the original system provides the \\varepsilon-Nash equilibrium in the differential game with a finite number of players. Bibliography: 34 titles.

  3. Extended Chiral ({sigma},{pi},{omega}) Mean-Field Model with Vacuum Fluctuation Corrections

    SciTech Connect

    Uechi, Schun T.; Uechi, Hiroshi

    2011-10-21

    Density-dependent relations among saturation properties of symmetric nuclear matter and properties of hadronic stars are discussed by applying the conserving chiral nonlinear ({sigma},{pi},{omega}) mean-field theory. The chiral nonlinear ({sigma},{pi},{omega}) mean-field theory is an extension of the conserving nonlinear (nonchiral){sigma}-{omega} mean-field theory, which is thermodynamically consistent, relativistic and Lorentz-covariant. In the extended chiral ({sigma},{pi},{omega}) mean-field model, all the masses of hadrons are produced by the spontaneous chiral symmetry breaking, which is different from conventional chiral partner models. By comparing both nonchiral and chiral mean-field approximations, the effects of the chiral symmetry breaking mechanism on the mass of {sigma}-meson, coefficients of nonlinear interactions and Fermi-liquid properties are investigated in nuclear matter and neutron stars.

  4. Coulomb Glass: a Mean Field Study

    NASA Astrophysics Data System (ADS)

    Mandra, Salvatore; Palassini, Matteo

    2012-02-01

    We study the Coulomb glass model of disordered localized electrons with long-range Coulomb interaction, which describes systems such as disordered insulators, granular metals, amorphous semiconductors, or doped crystalline semiconductors. Long ago Efros and Shklovskii showed that the long-range repulsion induces a soft Coulomb gap in the single particle density of states at low temperatures. Recent works suggested that this gap is associated to a transition to a glass phase, similar to the Almeida-Thouless transition in spin glasses. In this work, we use a mean field approach to characterize several physical properties of the Coulomb glass. In particular, following a seminal work of Bray and Moore, we show that the Edward-Anderson parameter qEA and the spin glass susceptibility χSG are directly related to spectrum distribution of the Hessian matrix around free energy minima. Using this result, we show that no glass transition is associated to the gap formation.

  5. Invisible dynamo in mean-field models

    NASA Astrophysics Data System (ADS)

    Reshetnyak, M. Yu.

    2016-07-01

    The inverse problem in a spherical shell to find the two-dimensional spatial distributions of the α-effect and differential rotation in a mean-field dynamo model has been solved. The derived distributions lead to the generation of a magnetic field concentrated inside the convection zone. The magnetic field is shown to have no time to rise from the region of maximum generation located in the lower layers to the surface in the polarity reversal time due to magnetic diffusion. The ratio of the maximum magnetic energy in the convection zone to its value at the outer boundary reaches two orders of magnitude or more. This result is important in interpreting the observed stellar and planetary magnetic fields. The proposed method of solving the inverse nonlinear dynamo problem is easily adapted for a wide class of mathematical-physics problems.

  6. Neural Population Dynamics Modeled by Mean-Field Graphs

    NASA Astrophysics Data System (ADS)

    Kozma, Robert; Puljic, Marko

    2011-09-01

    In this work we apply random graph theory approach to describe neural population dynamics. There are important advantages of using random graph theory approach in addition to ordinary and partial differential equations. The mathematical theory of large-scale random graphs provides an efficient tool to describe transitions between high- and low-dimensional spaces. Recent advances in studying neural correlates of higher cognition indicate the significance of sudden changes in space-time neurodynamics, which can be efficiently described as phase transitions in the neuropil medium. Phase transitions are rigorously defined mathematically on random graph sequences and they can be naturally generalized to a class of percolation processes called neuropercolation. In this work we employ mean-field graphs with given vertex degree distribution and edge strength distribution. We demonstrate the emergence of collective oscillations in the style of brains.

  7. Stochastic mean-field polycrystal plasticity methods

    NASA Astrophysics Data System (ADS)

    Tonks, Michael R.

    To accommodate multiple length scales, mean-field polycrystal plasticity models treat each material point as an aggregate of N crystals. The crystal velocity gradients Lc are approximated and then used to evaluate the crystal stresses T c. The Tc are averaged to determine the material point stress T. Commonly, the Lc are approximated with the fully constrained model (FCM) based on the Taylor hypothesis which equates Lc to the macro-scale velocity gradient L. Herein, we present two stochastic models that relax the FCM constraint. Through various applications we show that these computationally efficient stochastic models provide realistic response predictions. We first investigate the texture evolution in a planar polycrystal with our stochastic Taylor model (STM), in which we define L c as a realization of a normal distribution with mean equal to L. Our STM predictions agree with crystal plasticity finite element method (CPFEM) predictions, demonstrating the development of a steady-state texture that is not predicted by the FCM. The computational cost of the STM is comparable to the FCM, i.e. substantially less than the CPFEM. We develop the STM for 3-D polycrystals based on CPFEM analysis results which show that Lc follows a normal distribution. In addition to the STM, we develop the stochastic no-constraints model (SNCM), which differs from the STM in the manner with which the Lc distribution means are determined. Calibration and validation of the models are performed using tantalum compression experiment data. Both models predict the compression textures more accurately than the FCM, and the SNCM predicts them more accurately than the STM. The STM is slightly more computationally expensive than the FCM, while the SNCM is three times more expensive. Finally, we incorporate the STM in a finite element simulation of the Taylor impact of two tantalum specimens. Our simulation predictions mimic the texture and deformation data measured from a powder metallurgy

  8. Benchmarking mean-field approximations to level densities

    NASA Astrophysics Data System (ADS)

    Alhassid, Y.; Bertsch, G. F.; Gilbreth, C. N.; Nakada, H.

    2016-04-01

    We assess the accuracy of finite-temperature mean-field theory using as a standard the Hamiltonian and model space of the shell model Monte Carlo calculations. Two examples are considered: the nucleus 162Dy, representing a heavy deformed nucleus, and 148Sm, representing a nearby heavy spherical nucleus with strong pairing correlations. The errors inherent in the finite-temperature Hartree-Fock and Hartree-Fock-Bogoliubov approximations are analyzed by comparing the entropies of the grand canonical and canonical ensembles, as well as the level density at the neutron resonance threshold, with shell model Monte Carlo calculations, which are accurate up to well-controlled statistical errors. The main weak points in the mean-field treatments are found to be: (i) the extraction of number-projected densities from the grand canonical ensembles, and (ii) the symmetry breaking by deformation or by the pairing condensate. In the absence of a pairing condensate, we confirm that the usual saddle-point approximation to extract the number-projected densities is not a significant source of error compared to other errors inherent to the mean-field theory. We also present an alternative formulation of the saddle-point approximation that makes direct use of an approximate particle-number projection and avoids computing the usual three-dimensional Jacobian of the saddle-point integration. We find that the pairing condensate is less amenable to approximate particle-number projection methods because of the explicit violation of particle-number conservation in the pairing condensate. Nevertheless, the Hartree-Fock-Bogoliubov theory is accurate to less than one unit of entropy for 148Sm at the neutron threshold energy, which is above the pairing phase transition. This result provides support for the commonly used "back-shift" approximation, treating pairing as only affecting the excitation energy scale. When the ground state is strongly deformed, the Hartree-Fock entropy is significantly

  9. Mean Field Analysis of Quantum Annealing Correction

    NASA Astrophysics Data System (ADS)

    Matsuura, Shunji; Nishimori, Hidetoshi; Albash, Tameem; Lidar, Daniel A.

    2016-06-01

    Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the p -body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for p =2 , where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p ≥3 , where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder.

  10. Mean Field Analysis of Quantum Annealing Correction.

    PubMed

    Matsuura, Shunji; Nishimori, Hidetoshi; Albash, Tameem; Lidar, Daniel A

    2016-06-01

    Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the p-body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for p=2, where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p≥3, where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder. PMID:27314705

  11. Mean field approach to fluctuations of surface line defects

    NASA Astrophysics Data System (ADS)

    Margetis, Dionisios

    2011-03-01

    Below the roughening transition temperature, the dynamics of crystal surfaces are driven by the motion of line defects (steps) of atomic size. According to the celebrated Burton Cabrera-Frank (BCF) model, the steps move by mass conservation, as adsorbed atoms (adatoms) diffuse on terraces and attach/detach at step edges. The resulting deterministic equations of motion incorporate nonlinear couplings due to entropic and elastic-dipole step-step interactions. In this talk, I will discuss a formal theory for stochastic aspects of step motion by adding noise to the BCF model in 1+1 dimensions. I will define systematically a ``mean field'' that enables the conversion of the coupled, nonlinear stochastic equations for the distance between neighboring steps (terrace widths) to a single Langevin-type equation for an effective terrace width. In the course of my study, I invoke the Bogoliubov-Born-Green Kirkwood-Yvon (BBGKY) hierarchy for joint terrace-width probability densities and a decorrelation ansatz for terrace widths. By using an example drawn from epitaxial growth (with material deposition from above), I will compare the mean field approach to an exact result from a linearized growth model. [D. Margetis, J. Phys A: Math. Theor. 43, 065003 (2010).] This work was supported by NSF under Grant DMS-0847587.

  12. Dispersion-Corrected Mean-Field Electronic Structure Methods.

    PubMed

    Grimme, Stefan; Hansen, Andreas; Brandenburg, Jan Gerit; Bannwarth, Christoph

    2016-05-11

    Mean-field electronic structure methods like Hartree-Fock, semilocal density functional approximations, or semiempirical molecular orbital (MO) theories do not account for long-range electron correlation (London dispersion interaction). Inclusion of these effects is mandatory for realistic calculations on large or condensed chemical systems and for various intramolecular phenomena (thermochemistry). This Review describes the recent developments (including some historical aspects) of dispersion corrections with an emphasis on methods that can be employed routinely with reasonable accuracy in large-scale applications. The most prominent correction schemes are classified into three groups: (i) nonlocal, density-based functionals, (ii) semiclassical C6-based, and (iii) one-electron effective potentials. The properties as well as pros and cons of these methods are critically discussed, and typical examples and benchmarks on molecular complexes and crystals are provided. Although there are some areas for further improvement (robustness, many-body and short-range effects), the situation regarding the overall accuracy is clear. Various approaches yield long-range dispersion energies with a typical relative error of 5%. For many chemical problems, this accuracy is higher compared to that of the underlying mean-field method (i.e., a typical semilocal (hybrid) functional like B3LYP). PMID:27077966

  13. Mean field bipartite spin models treated with mechanical techniques

    NASA Astrophysics Data System (ADS)

    Barra, Adriano; Galluzzi, Andrea; Guerra, Francesco; Pizzoferrato, Andrea; Tantari, Daniele

    2014-03-01

    Inspired by a continuously increasing interest in modeling and framing complex systems in a thermodynamic rationale, in this paper we continue our investigation in adapting well-known techniques (originally stemmed in fields of physics and mathematics far from the present) for solving for the free energy of mean field spin models in a statistical mechanics scenario. Focusing on the test cases of bipartite spin systems embedded with all the possible interactions (self and reciprocal), we show that both the fully interacting bipartite ferromagnet, as well as the spin glass counterpart, at least at the replica symmetric level, can be solved via the fundamental theorem of calculus, trough an analogy with the Hamilton-Jacobi theory and lastly with a mapping to a Fourier diffusion problem. All these technologies are shown symmetrically for ferromagnets and spin-glasses in full details and contribute as powerful tools in the investigation of complex systems.

  14. Phase transitions of nuclear matter beyond mean field theory

    SciTech Connect

    Tran Huu Phat; Nguyen Tuan Anh; Nguyen Van Long; Le Viet Hoa

    2007-10-15

    The Cornwall-Jackiw-Tomboulis (CJT) effective action approach is applied to study the phase transition of nuclear matter modeled by the four-nucleon interaction. It is shown that in the Hartree-Fock approximation (HFA) a first-order phase transition takes place at low temperature, whereas the phase transition is of second order at higher temperature.

  15. Dynamic scaling in entangled mean-field gelation polymers.

    PubMed

    Das, Chinmay; Read, Daniel J; Kelmanson, Mark A; McLeish, Tom C B

    2006-07-01

    We present a simple reaction kinetics model to describe the polymer synthesis used by Lusignan et al. [Phys. Rev. E 60, 5657 (1999)] to produce randomly branched polymers in the vulcanization class. Numerical solution of the rate equations gives probabilities for different connections in the final product, which we use to generate a numerical ensemble of representative molecules. All structural quantities probed in the experiments are in quantitative agreement with our results for the entire range of molecular weights considered. However, with detailed topological information available in our calculations, our estimate of the "rheologically relevant" linear segment length is smaller than that estimated from the experimental results. We use a numerical method based on a tube model of polymer melts to calculate the rheological properties of such molecules. Results are in good agreement with experiment, except that in the case of the largest molecular weight samples our estimate of the zero-shear viscosity is significantly lower than the experimental findings. Using acid concentration as an indicator for closeness to the gelation transition, we show that the high-molecular-weight polymers considered are at the limit of mean-field behavior--which possibly is the reason for this disagreement. For a truly mean-field gelation class of model polymers, we numerically calculate the rheological properties for a range of segment lengths. Our calculations show that the tube theory with dynamical dilation predicts that, very close to the gelation limit, the contribution to viscosity for this class of polymers is dominated by the contribution from constraint-release Rouse motion and the final viscosity exponent approaches a Rouse-like value. PMID:16907093

  16. Relativistic mean field model based on realistic nuclear forces

    SciTech Connect

    Hirose, S.; Serra, M.; Ring, P.; Otsuka, T.; Akaishi, Y.

    2007-02-15

    In order to predict properties of asymmetric nuclear matter, we construct a relativistic mean field (RMF) model consisting of one-meson exchange (OME) terms and point coupling (PC) terms. In order to determine the density dependent parameters of this model, we use properties of isospin symmetric nuclear matter in combination with the information on nucleon-nucleon scattering data, which are given in the form of the density dependent G-matrix derived from Brueckner calculations based on the Tamagaki potential. We show that the medium- and long-range components of this G-matrix can be described reasonably well by our effective OME interaction. In order to take into account the short-range part of the nucleon-nucleon interaction, which cannot be described well in this manner, a point coupling term is added. Its analytical form is taken from a model based on chiral perturbation theory. It contains only one additional parameter, which does not depend on the density. It is, together with the parameters of the OME potentials adjusted to the equation of state of symmetric nuclear matter. We apply this model for the investigation of asymmetric nuclear matter and find that the results for the symmetry energy as well as for the equation of state of pure neutron matter are in good agreement with either experimental data or with presently adopted theoretical predictions. In order to test the model at higher density, we use its equation of state for an investigation of properties of neutron stars.

  17. Mean-field dynamos: The old concept and some recent developments. Karl Schwarzschild Award Lecture 2013

    NASA Astrophysics Data System (ADS)

    Rädler, K.-H.

    This article elucidates the basic ideas of electrodynamics and magnetohydrodynamics of mean fields in turbulently moving conducting fluids. It is stressed that the connection of the mean electromotive force with the mean magnetic field and its first spatial derivatives is in general neither local nor instantaneous and that quite a few claims concerning pretended failures of the mean-field concept result from ignoring this aspect. In addition to the mean-field dynamo mechanisms of α2 and α Ω type several others are considered. Much progress in mean-field electrodynamics and magnetohydrodynamics results from the test-field method for calculating the coefficients that determine the connection of the mean electromotive force with the mean magnetic field. As an important example the memory effect in homogeneous isotropic turbulence is explained. In magnetohydrodynamic turbulence there is the possibility of a mean electromotive force that is primarily independent of the mean magnetic field and labeled as Yoshizawa effect. Despite of many efforts there is so far no convincing comprehensive theory of α quenching, that is, the reduction of the α effect with growing mean magnetic field, and of the saturation of mean-field dynamos. Steps toward such a theory are explained. Finally, some remarks on laboratory experiments with dynamos are made.

  18. Quark mean field approach with derivative coupling for nuclear matter

    SciTech Connect

    Kawabata, M.; Akiyama, S.; Futami, Y.; Nakasone, T.; Yukino, T.

    2008-05-15

    We propose the quark mean field model including derivative coupling between quarks and scalar mesons in nuclear matter. This model concisely interprets an increasing size of the nucleon as well as a modification of coupling constant in the nuclear environment.

  19. Mean field limit for bosons and propagation of Wigner measures

    NASA Astrophysics Data System (ADS)

    Ammari, Z.; Nier, F.

    2009-04-01

    We consider the N-body Schrödinger dynamics of bosons in the mean field limit with a bounded pair-interaction potential. According to the previous work [Ammari, Z. and Nier, F., "Mean field limit for bosons and infinite dimensional phase-space analysis," Ann. Henri Poincare 9, 1503 (2008)], the mean field limit is translated into a semiclassical problem with a small parameter ɛ →0, after introducing an ɛ-dependent bosonic quantization. The limits of quantum correlation functions are expressed as a push forward by a nonlinear flow (e.g., Hartree) of the associated Wigner measures. These object and their basic properties were introduced by Ammari and Nier in the infinite dimensional setting. The additional result presented here states that the transport by the nonlinear flow holds for a rather general class of quantum states in their mean field limit.

  20. Mean field limit for bosons and propagation of Wigner measures

    SciTech Connect

    Ammari, Z.; Nier, F.

    2009-04-15

    We consider the N-body Schroedinger dynamics of bosons in the mean field limit with a bounded pair-interaction potential. According to the previous work [Ammari, Z. and Nier, F., 'Mean field limit for bosons and infinite dimensional phase-space analysis', Ann. Henri Poincare 9, 1503 (2008)], the mean field limit is translated into a semiclassical problem with a small parameter {epsilon}{yields}0, after introducing an {epsilon}-dependent bosonic quantization. The limits of quantum correlation functions are expressed as a push forward by a nonlinear flow (e.g., Hartree) of the associated Wigner measures. These object and their basic properties were introduced by Ammari and Nier in the infinite dimensional setting. The additional result presented here states that the transport by the nonlinear flow holds for a rather general class of quantum states in their mean field limit.

  1. Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows

    NASA Astrophysics Data System (ADS)

    Rädler, Karl-Heinz; Brandenburg, Axel; Del Sordo, Fabio; Rheinhardt, Matthias

    2011-10-01

    Certain aspects of the mean-field theory of turbulent passive scalar transport and of mean-field electrodynamics are considered with particular emphasis on aspects of compressible fluids. It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible flow may well be smaller than the molecular diffusivity. This is in full analogy to an old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid. These phenomena occur if the irrotational part of the motion dominates the vortical part, the Péclet or magnetic Reynolds number is not too large, and, in addition, the variation of the flow pattern is slow. For both the passive scalar and the magnetic cases several further analytical results on mean-field diffusivities and related quantities found within the second-order correlation approximation are presented, as well as numerical results obtained by the test-field method, which applies independently of this approximation. Particular attention is paid to nonlocal and noninstantaneous connections between the turbulence-caused terms and the mean fields. Two examples of irrotational flows, in which interesting phenomena in the above sense occur, are investigated in detail. In particular, it is demonstrated that the decay of a mean scalar in a compressible fluid under the influence of these flows can be much slower than without any flow, and can be strongly influenced by the so-called memory effect, that is, the fact that the relevant mean-field coefficients depend on the decay rates themselves.

  2. Mean-field Ohm's law and coaxial helicity injection in force-free plasmas

    SciTech Connect

    Weening, R. H.

    2011-12-15

    A theoretical analysis of steady-state coaxial helicity injection (CHI) in force-free plasmas is presented using a parallel mean-field Ohm's law that includes resistivity {eta} and hyper-resistivity {Lambda} terms. Using Boozer coordinates, a partial differential equation is derived for the time evolution of the mean-field poloidal magnetic flux, or magnetic Hamiltonian function, from the parallel mean-field Ohm's law. A general expression is obtained from the mean-field theory for the efficiency of CHI current drive in force-free plasmas. Inductances of internal energy, magnetic helicity, and poloidal magnetic flux are used to characterize axisymmetric plasma equilibria that have a model current profile. Using the model current profile, a method is suggested to determine the level of magnetohydrodynamic activity at the magnetic axis and the consequent deviation from the completely relaxed Taylor state. The mean-field Ohm's law model suggests that steady-state CHI can be viewed most simply as a boundary layer problem.

  3. Mean-field cluster model for the critical behaviour of ferromagnets

    NASA Astrophysics Data System (ADS)

    Chamberlin, Ralph V.

    2000-11-01

    Two separate theories are often used to characterize the paramagnetic properties of ferromagnetic materials. At temperatures T well above the Curie temperature, TC (where the transition from paramagnetic to ferromagnetic behaviour occurs), classical mean-field theory yields the Curie-Weiss law for the magnetic susceptibility: χ( T) ~ 1/(T - Θ), where Θ is the Weiss constant. Close to TC, however, the standard mean-field approach breaks down so that better agreement with experimental data is provided by critical scaling theory: χ(T) ~ 1/(T - TC)γ , where γ is a scaling exponent. But there is no known model capable of predicting the measured values of γ nor its variation among different substances. Here I use a mean-field cluster model based on finite-size thermostatistics to extend the range of mean-field theory, thereby eliminating the need for a separate scaling regime. The mean-field approximation is justified by using a kinetic-energy term to maintain the microcanonical ensemble. The model reproduces the Curie-Weiss law at high temperatures, but the classical Weiss transition at TC = Θ is suppressed by finite-size effects. Instead, the fraction of clusters with a specific amount of order diverges at T C, yielding a transition that is mathematically similar to Bose-Einstein condensation. At all temperatures above T C, the model matches the measured magnetic susceptibilities of crystalline EuO, Gd, Co and Ni, thus providing a unified picture for both the critical-scaling and Curie-Weiss regimes.

  4. Local excitations in mean-field spin glasses

    NASA Astrophysics Data System (ADS)

    Krzakala, F.; Parisi, G.

    2004-06-01

    We address the question of geometrical as well as energetic properties of local excitations in mean-field Ising spin glasses. We study analytically the Random Energy Model and numerically a dilute mean-field model, first on tree-like graphs, equivalent to a replica-symmetric computation, and then directly on finite-connectivity random lattices. In the first model, characterized by a discontinuous replica symmetry breaking, we found that the energy of finite-volume excitation is infinite, whereas in the dilute mean-field model, described by a continuous replica symmetry breaking, it slowly decreases with sizes and saturates at a finite value, in contrast with what would be naively expected. The geometrical properties of these excitations are similar to those of lattice animals or branched polymers. We discuss the meaning of these results in terms of replica symmetry breaking and also possible relevance in finite-dimensional systems.

  5. MEAN FIELD AND MONTE CARLO MODELING OF MULTIBLOCK COPOLYMERS

    SciTech Connect

    K. RASMUSSEN; ET AL

    2001-01-01

    The authors discuss and apply extensions needed to treat multiblock copolymers within the mean field theoretical framework for microphase separation in diblock copolymer metals, originally due to Leibler. The mean field calculations are complemented by lattice Monte Carlo realizations using the bond fluctuation model. They find that the microphase separation transition occurs at larger {sub {chi}}N as the number of blocks in increased beyond two (i.e., beyond diblock), and that the characteristic length scale of the emerging morphology decreases as the number of blocks increases. The latter prediction is in qualitative agreement with published experimental results due to Sontak and co-workers for model multiblock poly(styrene-isoprene) systems and recent results due to Hjelm and co-workers for a segmented poly(ester-urethane) relevant to Los Alamos interests. Additionally, the mean field predictions and bond fluctuation realizations yield consistent results.

  6. Mean-field description of topological charge 4e superconductors

    NASA Astrophysics Data System (ADS)

    Gabriele, Victoria; Luo, Jing; Teo, Jeffrey C. Y.

    BCS superconductors can be understood by a mean-field approximation of two-body interacting Hamiltonians, whose ground states break charge conservation spontaneously by allowing non-vanishing expectation values of charge 2e Cooper pairs. Topological superconductors, such as one-dimensional p-wave wires, have non-trivial ground states that support robust gapless boundary excitations. We construct a four-body Hamiltonian in one dimension and perform a mean-field analysis. The mean-field Hamiltonian is now quartic in fermions but is still exactly solvable. The ground state exhibits 4-fermion expectation values instead of Cooper pair ones. There also exists a topological phase, where the charge 4e superconductor carries exotic zero energy boundary excitations.

  7. Incorporating spatial correlations into multispecies mean-field models

    NASA Astrophysics Data System (ADS)

    Markham, Deborah C.; Simpson, Matthew J.; Maini, Philip K.; Gaffney, Eamonn A.; Baker, Ruth E.

    2013-11-01

    In biology, we frequently observe different species existing within the same environment. For example, there are many cell types in a tumour, or different animal species may occupy a given habitat. In modeling interactions between such species, we often make use of the mean-field approximation, whereby spatial correlations between the locations of individuals are neglected. Whilst this approximation holds in certain situations, this is not always the case, and care must be taken to ensure the mean-field approximation is only used in appropriate settings. In circumstances where the mean-field approximation is unsuitable, we need to include information on the spatial distributions of individuals, which is not a simple task. In this paper, we provide a method that overcomes many of the failures of the mean-field approximation for an on-lattice volume-excluding birth-death-movement process with multiple species. We explicitly take into account spatial information on the distribution of individuals by including partial differential equation descriptions of lattice site occupancy correlations. We demonstrate how to derive these equations for the multispecies case and show results specific to a two-species problem. We compare averaged discrete results to both the mean-field approximation and our improved method, which incorporates spatial correlations. We note that the mean-field approximation fails dramatically in some cases, predicting very different behavior from that seen upon averaging multiple realizations of the discrete system. In contrast, our improved method provides excellent agreement with the averaged discrete behavior in all cases, thus providing a more reliable modeling framework. Furthermore, our method is tractable as the resulting partial differential equations can be solved efficiently using standard numerical techniques.

  8. Many-Body Mean-Field Equations: Parallel implementation

    SciTech Connect

    Vallieres, M.; Umar, S.; Chinn, C.; Strayer, M.

    1993-12-31

    We describe the implementation of Hartree-Fock Many-Body Mean-Field Equations on a Parallel Intel iPSC/860 hypercube. We first discuss the Nuclear Mean-Field approach in physical terms. Then we describe our parallel implementation of this approach on the Intel iPSC/860 hypercube. We discuss and compare the advantages and disadvantages of the domain partition versus the Hilbert space partition for this problem. We conclude by discussing some timing experiments on various computing platforms.

  9. Density-Dependent Properties of Hadronic Matter in the self-consistent Chiral ({sigma},{pi},{omega}) Mean-Field Model

    SciTech Connect

    Uechi, Schun T.; Uechi, Hiroshi

    2011-05-06

    Density-dependent relations among saturation properties of symmetric nuclear matter and properties of hadronic stars are discussed by applying the conserving chiral nonlinear ({sigma},{pi},{omega}) hadronic mean-field theory. The chiral nonlinear ({sigma},{pi},{omega}) mean-field theory is an extension of the conserving nonlinear (nonchiral) {sigma}-{omega} hadronic mean-field theory which is thermodynamically consistent, relativistic and is a Lorentz-covariant mean-field theory of hadrons. In the extended chiral ({sigma},{pi},{omega}) mean-field model, all the masses of hadrons are produced by the breaking of chiral symmetry, which is different from other conventional chiral partner models. By comparing both nonchiral and chiral mean-field approximations, the effects of the chiral symmetry breaking mechanism on the mass of {sigma}-meson, coefficients of nonlinear interactions and Fermi-liquid properties are investigated in nuclear matter and neutron stars.

  10. Numerical accuracy of mean-field calculations in coordinate space

    NASA Astrophysics Data System (ADS)

    Ryssens, W.; Heenen, P.-H.; Bender, M.

    2015-12-01

    Background: Mean-field methods based on an energy density functional (EDF) are powerful tools used to describe many properties of nuclei in the entirety of the nuclear chart. The accuracy required of energies for nuclear physics and astrophysics applications is of the order of 500 keV and much effort is undertaken to build EDFs that meet this requirement. Purpose: Mean-field calculations have to be accurate enough to preserve the accuracy of the EDF. We study this numerical accuracy in detail for a specific numerical choice of representation for mean-field equations that can accommodate any kind of symmetry breaking. Method: The method that we use is a particular implementation of three-dimensional mesh calculations. Its numerical accuracy is governed by three main factors: the size of the box in which the nucleus is confined, the way numerical derivatives are calculated, and the distance between the points on the mesh. Results: We examine the dependence of the results on these three factors for spherical doubly magic nuclei, neutron-rich 34Ne , the fission barrier of 240Pu , and isotopic chains around Z =50 . Conclusions: Mesh calculations offer the user extensive control over the numerical accuracy of the solution scheme. When appropriate choices for the numerical scheme are made the achievable accuracy is well below the model uncertainties of mean-field methods.

  11. On the Mean Field and Classical Limits of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Golse, François; Mouhot, Clément; Paul, Thierry

    2016-04-01

    The main result in this paper is a new inequality bearing on solutions of the N-body linear Schrödinger equation and of the mean field Hartree equation. This inequality implies that the mean field limit of the quantum mechanics of N identical particles is uniform in the classical limit and provides a quantitative estimate of the quality of the approximation. This result applies to the case of C 1,1 interaction potentials. The quantity measuring the approximation of the N-body quantum dynamics by its mean field limit is analogous to the Monge-Kantorovich (or Wasserstein) distance with exponent 2. The inequality satisfied by this quantity is reminiscent of the work of Dobrushin on the mean field limit in classical mechanics [Func. Anal. Appl. 13, 115-123, (1979)]. Our approach to this problem is based on a direct analysis of the N-particle Liouville equation, and avoids using techniques based on the BBGKY hierarchy or on second quantization.

  12. Deviations from the mean-field predictions for the phase behaviour of random copolymers melts

    NASA Astrophysics Data System (ADS)

    Houdayer, J.; Müller, M.

    2002-06-01

    We investigate the phase behaviour of random copolymers melts via large-scale Monte Carlo simulations. We observe macrophase separation into A- and B-rich phases as predicted by the mean-field theory only for systems with a very large correlation λ of blocks along the polymer chains, far away from the Lifshitz point. For smaller values of λ, we find that a locally segregated, disordered microemulsion-like structure gradually forms as the temperature decreases. As we increase the number of blocks in the polymers, the region of macrophase separation further shrinks. The results of our Monte Carlo simulation are in agreement with a Ginzburg criterium, which suggests that the mean-field theory becomes worse as the number of blocks in polymers increases.

  13. Schrödinger Approach to Mean Field Games

    NASA Astrophysics Data System (ADS)

    Swiecicki, Igor; Gobron, Thierry; Ullmo, Denis

    2016-03-01

    Mean field games (MFG) provide a theoretical frame to model socioeconomic systems. In this Letter, we study a particular class of MFG that shows strong analogies with the nonlinear Schrödinger and Gross-Pitaevskii equations introduced in physics to describe a variety of physical phenomena. Using this bridge, many results and techniques developed along the years in the latter context can be transferred to the former, which provides both a new domain of application for the nonlinear Schrödinger equation and a new and fruitful approach in the study of mean field games. Utilizing this approach, we analyze in detail a population dynamics model in which the "players" are under a strong incentive to coordinate themselves.

  14. Disorder Chaos in the Spherical Mean-Field Model

    NASA Astrophysics Data System (ADS)

    Chen, Wei-Kuo; Hsieh, Hsi-Wei; Hwang, Chii-Ruey; Sheu, Yuan-Chung

    2015-07-01

    We study the problem of disorder chaos in the spherical mean-field model. It concerns the behavior of the overlap between two independently sampled spin configurations from two Gibbs measures with the same external parameters. The prediction states that if the disorders in the Hamiltonians are slightly decoupled, then the overlap will be concentrated near a constant value. Following Guerra's replica symmetry breaking scheme, we establish this at the levels of the free energy and the Gibbs measure.

  15. Neutron star cooling: A challenge to the nuclear mean field

    SciTech Connect

    Hoang Sy Than; Nguyen Van Giai

    2009-12-15

    The two recent density-dependent versions of the finite-range M3Y interaction (CDM3Yn and M3Y-Pn) have been probed against the bulk properties of asymmetric nuclear matter (NM) in the nonrelativistic Hartree-Fock (HF) formalism. The same HF study has also been done with the famous Skyrme (SLy4) and Gogny (D1S and D1N) interactions that were well tested in the nuclear structure calculations. Our HF results are compared with those given by other many-body calculations like the Dirac-Brueckner Hartree-Fock approach or ab initio variational calculations using free nucleon-nucleon interaction and by both the nonrelativistic and relativistic mean-field studies using different model parameters. Although the two considered density-dependent versions of the M3Y interaction were proven to be quite realistic in the nuclear structure or reaction studies, they give two distinct behaviors of the NM symmetry energy at high densities, like the Asy-soft and Asy-stiff scenarios found earlier with other mean-field interactions. As a consequence, we obtain two different behaviors of the proton fraction in the {beta}-equilibrium that in turn can imply two drastically different mechanisms for the neutron star cooling. While some preference of the Asy-stiff scenario was found based on predictions of the latest microscopic many-body calculations or empirical NM pressure and isospin diffusion data deduced from heavy-ion collisions, a consistent mean-field description of nuclear structure database is more often given by some Asy-soft type interaction like the Gogny or M3Y-Pn ones. Such a dilemma poses an interesting challenge to the modern mean-field approaches.

  16. Mean field dynamo saturation: toward understanding conflicting results

    NASA Astrophysics Data System (ADS)

    Blackman, Eric G.; Field, George B.

    Mean field dynamos may explain the origin of large scale magnetic fields of galaxies, but controversy arises over the extent of dynamo quenching by the growing field. Here we explain how apparently conflicting results may be mutually consistent, by showing the role of magnetic helicity conservation and boundary terms usually neglected. We estimate the associated magnetic energy flowing out of the Galaxy but emphasize that the mechanism of field escape needs to be addressed.

  17. Stochastic Mean-Field Dynamics For Nuclear Collisions

    SciTech Connect

    Ayik, Sakir

    2008-11-11

    We discuss a stochastic approach to improve description of nuclear dynamics beyond the mean-field approximation at low energies. For small amplitude fluctuations, this approach gives a result for the dispersion of a one-body observable that is identical to the result obtained previously through a variational approach. Furthermore, it incorporates one-body dissipation and fluctuation mechanisms in accordance with quantal fluctuation-dissipation relation.

  18. Absorbing boundaries in the mean-field approximation

    SciTech Connect

    Jhala, Chirag; Dreissigacker, Ingo; Lein, Manfred

    2010-12-15

    Absorbing boundaries in the mean-field approximation are investigated and applied to small systems interacting with strong laser fields. Two types of calculations are considered: (i) a variational approach with a complex absorbing potential included in the full Hamiltonian and (ii) the inclusion of a complex absorbing potential in the single-particle equations. It is elucidated that the second approach outperforms the variational approach for small grids.

  19. Mean-field description of plastic flow in amorphous solids

    NASA Astrophysics Data System (ADS)

    Lin, Jie; Wyart, Matthieu

    Failure and flow of amorphous materials are central to various phenomena including earthquakes and landslides. There is accumulating evidence that the yielding transition between a flowing and an arrested phase is a critical phenomenon, but the associated exponents are not understood, even at a mean-field level where the validity of popular models is debated. Here we solve a mean-field model that captures the broad distribution of the mechanical noise generated by plasticity, whose behavior is related to biased Lévy flights near an absorbing boundary. We compute the exponent θ characterizing the density of shear transformation P (x) ~xθ , where x is the stress increment beyond which they yield. We find that after an isotropic thermal quench, θ = 1 / 2 . However, θ depends continuously on the applied shear stress, this dependence is not monotonic, and its value at the yield stress is not universal. The model rationalizes previously unexplained observations, and captures reasonably well the value of exponents in three dimensions. These results support that it is the true mean-field model that applies in large dimension, and raise fundamental questions on the nature of the yielding transition.

  20. Mean-Field Description of Plastic Flow in Amorphous Solids

    NASA Astrophysics Data System (ADS)

    Lin, Jie; Wyart, Matthieu

    2016-01-01

    Failure and flow of amorphous materials are central to various phenomena including earthquakes and landslides. There is accumulating evidence that the yielding transition between a flowing and an arrested phase is a critical phenomenon, but the associated exponents are not understood, even at a mean-field level where the validity of popular models is debated. Here, we solve a mean-field model that captures the broad distribution of the mechanical noise generated by plasticity, whose behavior is related to biased Lévy flights near an absorbing boundary. We compute the exponent θ characterizing the density of shear transformation P (x )˜xθ, where x is the stress increment beyond which they yield. We find that after an isotropic thermal quench, θ =1 /2 . However, θ depends continuously on the applied shear stress; this dependence is not monotonic, and its value at the yield stress is not universal. The model rationalizes previously unexplained observations and captures reasonably well the value of exponents in three dimensions. Values of exponents in four dimensions are accurately predicted. These results support the fact that it is the true mean-field model that applies in large dimensions, and they raise fundamental questions about the nature of the yielding transition.

  1. The glass crossover from mean-field Spin-Glasses to supercooled liquids

    NASA Astrophysics Data System (ADS)

    Rizzo, Tommaso

    2016-03-01

    Stochastic-Beta-Relaxation provides a characterisation of the glass crossover in discontinuous Spin-Glasses and supercoooled liquid. Notably it can be derived through a rigorous computation from a dynamical Landau theory. In this paper, I will discuss the precise meaning of this connection in a language that does not require familiarity with statistical field theory. I will discuss finite-size corrections in mean-field Spin-Glass models and loop corrections in finite-dimensional models that are both described by the dynamical Landau theory considered. Then I will argue that the same Landau theory can be associated to supercooled liquid described by Mode-Coupling Theory invoking a physical principle of time-scale invariance.

  2. An assessment of mean-field mixed semiclassical approaches: Equilibrium populations and algorithm stability

    NASA Astrophysics Data System (ADS)

    Bellonzi, Nicole; Jain, Amber; Subotnik, Joseph E.

    2016-04-01

    We study several recent mean-field semiclassical dynamics methods, focusing on the ability to recover detailed balance for long time (equilibrium) populations. We focus especially on Miller and Cotton's [J. Phys. Chem. A 117, 7190 (2013)] suggestion to include both zero point electronic energy and windowing on top of Ehrenfest dynamics. We investigate three regimes: harmonic surfaces with weak electronic coupling, harmonic surfaces with strong electronic coupling, and anharmonic surfaces with weak electronic coupling. In most cases, recent additions to Ehrenfest dynamics are a strong improvement upon mean-field theory. However, for methods that include zero point electronic energy, we show that anharmonic potential energy surfaces often lead to numerical instabilities, as caused by negative populations and forces. We also show that, though the effect of negative forces can appear hidden in harmonic systems, the resulting equilibrium limits do remain dependent on any windowing and zero point energy parameters.

  3. Ehrenfest breakdown of the mean-field dynamics of Bose gases

    NASA Astrophysics Data System (ADS)

    Han, Xizhi; Wu, Biao

    2016-02-01

    The unstable mean-field dynamics of a Bose gas is shown to break down at time τh=(c1/γ ) lnN , where γ is the Lyapunov exponent of the mean-field theory, N is the number of bosons, and c1 is a system-dependent constant. The breakdown time τh is essentially the Ehrenfest time that characterizes the breakdown of the correspondence between classical and quantum dynamics. This breakdown can be well described by a quantum fidelity defined for one-particle reduced density matrices. Our results are obtained with the formalism in particle-number phase space and are illustrated with a triple-well model. The logarithmic quantum-classical correspondence time may be verified experimentally with Bose-Einstein condensates.

  4. Modeling asset price processes based on mean-field framework

    NASA Astrophysics Data System (ADS)

    Ieda, Masashi; Shiino, Masatoshi

    2011-12-01

    We propose a model of the dynamics of financial assets based on the mean-field framework. This framework allows us to construct a model which includes the interaction among the financial assets reflecting the market structure. Our study is on the cutting edge in the sense of a microscopic approach to modeling the financial market. To demonstrate the effectiveness of our model concretely, we provide a case study, which is the pricing problem of the European call option with short-time memory noise.

  5. A mechanical approach to mean field spin models

    NASA Astrophysics Data System (ADS)

    Genovese, Giuseppe; Barra, Adriano

    2009-05-01

    Inspired by the bridge pioneered by Guerra among statistical mechanics on lattice and analytical mechanics on 1+1 continuous Euclidean space time, we built a self-consistent method to solve for the thermodynamics of mean field models defined on lattice, whose order parameters self-average. We show the whole procedure by analyzing in full detail the simplest test case, namely, the Curie-Weiss model. Further, we report some applications also to models whose order parameters do not self-average by using the Sherrington-Kirkpatrick spin glass as a guide.

  6. Thermal entanglement of spins in mean-field clusters

    SciTech Connect

    Asoudeh, M.; Karimipour, V.

    2006-06-15

    We determine thermal entanglement in mean-field clusters of N spin one-half particles interacting via the anisotropic Heisenberg interaction, with and without external magnetic field. For the xxx cluster in the absence of magnetic field we prove that only the N=2 ferromagnetic cluster shows entanglement. An external magnetic field B can only entangle xxx antiferromagnetic clusters in certain regions of the B-T plane. On the other hand, the xxz clusters of size N>2 are entangled only when the interaction is ferromagnetic. Detailed dependence of the entanglement on various parameters is investigated in each case.

  7. Relativistic mean field calculations in neutron-rich nuclei

    SciTech Connect

    Gangopadhyay, G.; Bhattacharya, Madhubrata; Roy, Subinit

    2014-08-14

    Relativistic mean field calculations have been employed to study neutron rich nuclei. The Lagrange's equations have been solved in the co-ordinate space. The effect of the continuum has been effectively taken into account through the method of resonant continuum. It is found that BCS approximation performs as well as a more involved Relativistic Continuum Hartree Bogoliubov approach. Calculations reveal the possibility of modification of magic numbers in neutron rich nuclei. Calculation for low energy proton scattering cross sections shows that the present approach reproduces the density in very light neutron rich nuclei.

  8. Isomeric state in {sup 53}Co: A mean field analysis

    SciTech Connect

    Patra, S. K.; Bhat, F. H.; Panda, R. N.; Arumugam, P.; Gupta, Raj K.

    2009-04-15

    We study the ground and the first excited intrinsic states of {sup 53}Co and its mirror nucleus {sup 53}Fe, within the frameworks of the relativistic and nonrelativistic mean field formalisms. The analysis of the single-particle energy spectra of these nuclei show a competition of spins 1/2{sup -} and 3/2{sup -} in a low-lying excited state, which agrees well with the recent experimental observation [D. Rudolph et al., Eur. Phys. J. A 36, 131 (2008)] of spin and parity J{sup {pi}}=3/2{sup -} for the isomeric configuration in {sup 53}Co.

  9. Mean-field approach for diffusion of interacting particles.

    PubMed

    Suárez, G; Hoyuelos, M; Mártin, H

    2015-12-01

    A nonlinear Fokker-Planck equation is obtained in the continuous limit of a one-dimensional lattice with an energy landscape of wells and barriers. Interaction is possible among particles in the same energy well. A parameter γ, related to the barrier's heights, is introduced. Its value is determinant for the functional dependence of the mobility and diffusion coefficient on particle concentration, but has no influence on the equilibrium solution. A relation between the mean-field potential and the microscopic interaction energy is derived. The results are illustrated with classical particles with interactions that reproduce fermion and boson statistics. PMID:26764643

  10. A mean field Ohm's law for collisionless plasmas

    SciTech Connect

    Biglari, H. ); Diamond, P.H. )

    1993-11-01

    A mean field Ohm's law valid for collisionless plasmas is derived kinetically. It is shown that contrary to conventional thinking, the resulting hyperresistivity is significantly smaller than its fluid counterpart due to the fact that the turbulent decorrelation rate is linked to the rapid electron ballistic motion rather than the slower nonlinear mixing time. Moreover, the off-diagonal contributions to the parallel electron momentum flux are shown to result in Ohm's law renormalizations that dwarf the current diffusivity and break radial parity symmetry.

  11. Systematic study of bubble nuclei in relativistic mean field model

    NASA Astrophysics Data System (ADS)

    Shukla, A.; Åberg, S.; Bajpeyi, A.

    2016-01-01

    We have theoretically studied potential bubble nuclei (20,22O, 34,36Si, and 46Ar), which are experimentally accessible and have attracted several studies in the recent past. Relativistic mean field is employed in conjunction with the NL-SH parameter set. Our results show that among the possible candidates, 22Oand 34Si may be the most prominent candidates, showing significant depletion of density at the center, which could be verified experimentally in the near future with some of the experiments underway.

  12. Simulated Tempering and Swapping on Mean-Field Models

    NASA Astrophysics Data System (ADS)

    Bhatnagar, Nayantara; Randall, Dana

    2016-08-01

    Simulated and parallel tempering are families of Markov Chain Monte Carlo algorithms where a temperature parameter is varied during the simulation to overcome bottlenecks to convergence due to multimodality. In this work we introduce and analyze the convergence for a set of new tempering distributions which we call entropy dampening. For asymmetric exponential distributions and the mean field Ising model with an external field simulated tempering is known to converge slowly. We show that tempering with entropy dampening distributions mixes in polynomial time for these models. Examining slow mixing times of tempering more closely, we show that for the mean-field 3-state ferromagnetic Potts model, tempering converges slowly regardless of the temperature schedule chosen. On the other hand, tempering with entropy dampening distributions converges in polynomial time to stationarity. Finally we show that the slow mixing can be very expensive practically. In particular, the mixing time of simulated tempering is an exponential factor longer than the mixing time at the fixed temperature.

  13. Mean-field limit of systems with multiplicative noise.

    PubMed

    Muñoz, Miguel A; Colaiori, Francesca; Castellano, Claudio

    2005-11-01

    A detailed study of the mean-field solution of Langevin equations with multiplicative noise is presented. Three different regimes depending on noise intensity (weak, intermediate, and strong noise) are identified by performing a self-consistent calculation on a fully connected lattice. The most interesting, strong-noise, regime is shown to be intrinsically unstable with respect to the inclusion of fluctuations, as a Ginzburg criterion shows. On the other hand, the self-consistent approach is shown to be valid only in the thermodynamic limit, while for finite systems the critical behavior is found to be different. In this last case, the self-consistent field itself is broadly distributed rather than taking a well defined mean value; its fluctuations, described by an effective zero-dimensional multiplicative noise equation, govern the critical properties. These findings are obtained analytically for a fully connected graph, and verified numerically both on fully connected graphs and on random regular networks. The results presented here shed some doubt on what is the validity and meaning of a standard mean-field approach in systems with multiplicative noise in finite dimensions, where each site does not see an infinite number of neighbors, but a finite one. The implications of all this on the existence of a finite upper critical dimension for multiplicative noise and Kardar-Parisi-Zhang problems are briefly discussed. PMID:16383683

  14. Beyond mean-field calculations for odd-mass nuclei.

    PubMed

    Bally, B; Avez, B; Bender, M; Heenen, P-H

    2014-10-17

    Beyond mean-field methods are very successful tools for the description of large-amplitude collective motion for even-even atomic nuclei. The state-of-the-art framework of these methods consists in a generator coordinate method based on angular-momentum and particle-number projected triaxially deformed Hartree-Fock-Bogoliubov (HFB) states. The extension of this scheme to odd-mass nuclei is a long-standing challenge. We present for the first time such an extension, where the generator coordinate space is built from self-consistently blocked one-quasiparticle HFB states. One of the key points for this success is that the same Skyrme interaction is used for the mean-field and the pairing channels, thus avoiding problems related to the violation of the Pauli principle. An application to ^{25}Mg illustrates the power of our method, as agreement with experiment is obtained for the spectrum, electromagnetic moments, and transition strengths, for both positive and negative parity states and without the necessity for effective charges or effective moments. Although the effective interaction still requires improvement, our study opens the way to systematically describe odd-A nuclei throughout the nuclear chart. PMID:25361253

  15. Beyond Mean-Field Calculations for Odd-Mass Nuclei

    NASA Astrophysics Data System (ADS)

    Bally, B.; Avez, B.; Bender, M.; Heenen, P.-H.

    2014-10-01

    Beyond mean-field methods are very successful tools for the description of large-amplitude collective motion for even-even atomic nuclei. The state-of-the-art framework of these methods consists in a generator coordinate method based on angular-momentum and particle-number projected triaxially deformed Hartree-Fock-Bogoliubov (HFB) states. The extension of this scheme to odd-mass nuclei is a long-standing challenge. We present for the first time such an extension, where the generator coordinate space is built from self-consistently blocked one-quasiparticle HFB states. One of the key points for this success is that the same Skyrme interaction is used for the mean-field and the pairing channels, thus avoiding problems related to the violation of the Pauli principle. An application to Mg25 illustrates the power of our method, as agreement with experiment is obtained for the spectrum, electromagnetic moments, and transition strengths, for both positive and negative parity states and without the necessity for effective charges or effective moments. Although the effective interaction still requires improvement, our study opens the way to systematically describe odd-A nuclei throughout the nuclear chart.

  16. Mean field game theoretic approach for security in mobile ad-hoc networks

    NASA Astrophysics Data System (ADS)

    Wang, Yanwei; Tang, Helen; Yu, F. Richard; Huang, Minyi

    2013-05-01

    Game theory can provide a useful tool to study the security problem in mobile ad hoc networks (MANETs). Most existing work on applying game theories to security only considers two players in the security game model: an attacker and a defender. While this assumption is valid for a network with centralized administration, it may not be realistic in MANETs, where centralized administration is not available. Consequently, each individual node in a MANET should be treated separately in the security game model. In this paper, using recent advances in mean field game theory, we propose a novel game theoretic approach for security in MANETs. Mean field game theory provides a powerful mathematical tool for problems with a large number of players. Since security defence mechanisms consume precious system resources (e.g., energy), the proposed scheme considers not only the security requirement of MANETs but also the system resources. In addition, each node only needs to know its own state information and the aggregate effect of the other nodes in the MANET. Therefore, the proposed scheme is a fully distributed scheme. Simulation results are presented to illustrate the effectiveness of the proposed scheme.

  17. Antimagnetic rotation in 108,110In with tilted axis cranking relativistic mean-field approach

    NASA Astrophysics Data System (ADS)

    Sun, Wu-Ji; Xu, Hai-Dan; Li, Jian; Liu, Yong-Hao; Ma, Ke-Yan; Yang, Dong; Lu, Jing-Bing; Ma, Ying-Jun

    2016-08-01

    Based on tilted axis cranking relativistic mean-field theory within point-coupling interaction PC-PK1, the rotational structure and the characteristic features of antimagnetic rotation for ΔI = 2 bands in 108,110In are studied. Tilted axis cranking relativistic mean-field calculations reproduce the experimental energy spectrum well and are in agreement with the experimental I ∼ ω plot, although the calculated spin overestimates the experimental values. In addition, the two-shears-like mechanism in candidate antimagnetic rotation bands is clearly illustrated and the contributions from two-shears-like orbits, neutron (gd) orbits above Z = 50 shell and Z = 50, N = 50 core are investigated microscopically. The predicted B(E2), dynamic moment of inertia ℑ(2), deformation parameters β and γ, and ℑ(2)/B(E2) ratios in tilted axis cranking relativistic mean-field calculations are discussed and the characteristic features of antimagnetic rotation for the bands before and after alignment are shown. Supported by National Natural Science Foundation of China (11205068, 11205069, 11405072, 11475072, 11547308) and China Postdoctoral Science Foundation (2012M520667)

  18. Mean-Field Approximation to the Hydrophobic Hydration in the Liquid-Vapor Interface of Water.

    PubMed

    Abe, Kiharu; Sumi, Tomonari; Koga, Kenichiro

    2016-03-01

    A mean-field approximation to the solvation of nonpolar solutes in the liquid-vapor interface of aqueous solutions is proposed. It is first remarked with a numerical illustration that the solvation of a methane-like solute in bulk liquid water is accurately described by the mean-field theory of liquids, the main idea of which is that the probability (Pcav) of finding a cavity in the solvent that can accommodate the solute molecule and the attractive interaction energy (uatt) that the solute would feel if it is inserted in such a cavity are both functions of the solvent density alone. It is then assumed that the basic idea is still valid in the liquid-vapor interface, but Pcav and uatt are separately functions of different coarse-grained local densities, not functions of a common local density. Validity of the assumptions is confirmed for the solvation of the methane-like particle in the interface of model water at temperatures between 253 and 613 K. With the mean-field approximation extended to the inhomogeneous system the local solubility profiles across the interface at various temperatures are calculated from Pcav and uatt obtained at a single temperature. The predicted profiles are in excellent agreement with those obtained by the direct calculation of the excess chemical potential over an interfacial region where the solvent local density varies most rapidly. PMID:26595441

  19. Driven-dissipative Ising model: Mean-field solution

    NASA Astrophysics Data System (ADS)

    Goldstein, G.; Aron, C.; Chamon, C.

    2015-11-01

    We study the fate of the Ising model and its universal properties when driven by a rapid periodic drive and weakly coupled to a bath at equilibrium. The far-from-equilibrium steady-state regime is accessed by means of a Floquet mean-field approach. We show that, depending on the details of the bath, the drive can strongly renormalize the critical temperature to higher temperatures, modify the critical exponents, or even change the nature of the phase transition from second to first order after the emergence of a tricritical point. Moreover, by judiciously selecting the frequency of the field and by engineering the spectrum of the bath, one can drive a ferromagnetic Hamiltonian to an antiferromagnetically ordered phase and vice versa.

  20. Double binding energy differences: Mean-field or pairing effect?

    NASA Astrophysics Data System (ADS)

    Qi, Chong

    2012-10-01

    In this Letter we present a systematic analysis on the average interaction between the last protons and neutrons in atomic nuclei, which can be extracted from the double differences of nuclear binding energies. The empirical average proton-neutron interaction Vpn thus derived from experimental data can be described in a very simple form as the interplay of the nuclear mean field and the pairing interaction. It is found that the smooth behavior as well as the local fluctuations of the Vpn in even-even nuclei with N ≠ Z are dominated by the contribution from the proton-neutron monopole interactions. A strong additional contribution from the isoscalar monopole interaction and isovector proton-neutron pairing interaction is seen in the Vpn for even-even N = Z nuclei and for the adjacent odd-A nuclei with one neutron or proton being subtracted.

  1. Scattering bright solitons: Quantum versus mean-field behavior

    NASA Astrophysics Data System (ADS)

    Gertjerenken, Bettina; Billam, Thomas P.; Khaykovich, Lev; Weiss, Christoph

    2012-09-01

    We investigate scattering bright solitons off a potential using both analytical and numerical methods. Our paper focuses on low kinetic energies for which differences between the mean-field description via the Gross-Pitaevskii equation (GPE) and the quantum behavior are particularly large. On the N-particle quantum level, adding an additional harmonic confinement leads to a simple signature to distinguish quantum superpositions from statistical mixtures. While the nonlinear character of the GPE does not allow quantum superpositions, the splitting of GPE solitons takes place only partially. When the potential strength is increased, the fraction of the soliton which is transmitted or reflected jumps noncontinuously. We explain these jumps via energy conservation and interpret them as indications for quantum superpositions on the N-particle level. On the GPE level, we also investigate the transition from this stepwise behavior to the continuous case.

  2. Lifting mean field degeneracies in anisotropic spin systems

    NASA Astrophysics Data System (ADS)

    Sizyuk, Yuriy; Perkins, Natalia; Wolfle, Peter

    We propose a method for calculating the fluctuation contribution to the free energy of anisotropic spin systems with generic bilinear superexchange magnetic Hamiltonian based on the Hubbard-Stratonovich transformation. We show that this contribution splits the set of mean field degenerate states with rotational symmetry, and chooses states with the order parameter directed along lattice symmetric directions as the true ground states. We consider the simple example of Heisenberg-compass model on cubic lattice to show that depending on the relative strength of the compass and Heisenberg interactions the spontaneous magnetization is pinned to either one of the cubic directions or one of the cubic body diagonals with a intermediate phase in between where the minima and maxima of the free energy interchange. DMR-1005932, DMR-1511768, and NSF PHY11-25915.

  3. Finite- to zero-range relativistic mean-field interactions

    SciTech Connect

    Niksic, T.; Vretenar, D.; Lalazissis, G. A.; Ring, P.

    2008-03-15

    We study the relation between the finite-range (meson-exchange) and zero-range (point-coupling) representations of effective nuclear interactions in the relativistic mean-field framework. Starting from the phenomenological interaction DD-ME2 with density-dependent meson-nucleon couplings, we construct a family of point-coupling effective interactions for different values of the strength parameter of the isoscalar-scalar derivative term. In the meson-exchange picture this corresponds to different values of the {sigma}-meson mass. The parameters of the isoscalar-scalar and isovector-vector channels of the point-coupling interactions are adjusted to nuclear matter and ground-state properties of finite nuclei. By comparing results for infinite and semi-infinite nuclear matter, ground-state masses, charge radii, and collective excitations, we discuss constraints on the parameters of phenomenological point-coupling relativistic effective interaction.

  4. Two stochastic mean-field polycrystal plasticity methods

    SciTech Connect

    Tonks, Michael

    2008-01-01

    In this work, we develop two mean-field polycrystal plasticity models in which the L{sup c} are approximated stochastically. Through comprehensive CPFEM analyses of an idealized tantalum polycrystal, we verify that the L{sup c} tend to follow a normal distribution and surmise that this is due to the crystal interactions. We draw on these results to develop the STM and the stochastic no-constraints model (SNCM), which differ in the manner in which the crystal strain rates D{sup c} are prescribed. Calibration and validation of the models are performed using data from tantalum compression experiments. Both models predict the compression textures more accurately than the FCM, and the SNCM predicts them more accurately than the STM. The STM is extremely computationally efficient, only slightly more expensive than the FCM, while the SNCM is three times more computationally expensive than the STM.

  5. Superfluidity and mean-field energy loops: Hysteretic behavior in Bose-Einstein condensates

    SciTech Connect

    Mueller, Erich J.

    2002-12-01

    We present a theory of hysteretic phenomena in Bose gases, using superfluidity in one-dimensional rings and in optical lattices as primary examples. Through this study we are able to give a physical interpretation of swallow-tail loops recently found by many authors in the mean-field energy structure of trapped atomic gases. These loops are a generic sign of hysteresis, and in the present context are an indication of superfluidity. We have also calculated the rate of decay of metastable current-carrying states due to quantum fluctuations.

  6. Stochastic mean-field dynamics for fermions in the weak-coupling limit

    SciTech Connect

    Lacroix, Denis

    2006-04-15

    Assuming that the effect of the residual interaction beyond the mean field is weak and has a short memory time, two approximate treatments of correlation in fermionic systems by means of the Markovian quantum jump are presented. A simplified scenario for the introduction of fluctuations beyond the mean field is presented first. In this theory, part of the quantum correlations between the residual interaction and the one-body density matrix are neglected and jumps occur between many-body densities formed of pairs of states D={phi}{sub a}><{phi}{sub b}/<{phi}{sub b}{phi}{sub a}>, where {phi}{sub a}> and {phi}{sub b}> are antisymmetrized products of single-particle states. The underlying stochastic mean-field theory is discussed and is applied to the monopole vibration of a spherical {sup 40}Ca nucleus under the influence of a statistical ensemble of two-body contact interactions. This framework is however too simplistic to account for both fluctuation and dissipation. In the second part of this work, an alternative quantum jump method is obtained without making the approximation on quantum correlations. By restricting to two-particle-two-hole residual interactions, the evolution of the one-body density matrix of a correlated system is transformed into a Lindblad equation. The associated dissipative dynamics can be simulated by quantum jumps between densities written as D=|{phi}><{phi}|, where |{phi}> is a normalized Slater determinant. The associated stochastic Schroedinger equation for single-particle wave functions is given.

  7. Individual based and mean-field modeling of direct aggregation

    PubMed Central

    Burger, Martin; Haškovec, Jan; Wolfram, Marie-Therese

    2013-01-01

    We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighborhood. In the first-order model the location of each individual is subject to a density-dependent random walk, while in the second-order model the density-dependent random walk acts on the velocity variable, together with a density-dependent damping term. The main novelty of our models is that we do not assume any explicit aggregative force acting on the individuals; instead, aggregation is obtained exclusively by reducing the individual stochasticity in response to higher perceived density. We formally derive the corresponding mean-field limits, leading to nonlocal degenerate diffusions. Then, we carry out the mathematical analysis of the first-order model, in particular, we prove the existence of weak solutions and show that it allows for measure-valued steady states. We also perform linear stability analysis and identify conditions for pattern formation. Moreover, we discuss the role of the nonlocality for well-posedness of the first-order model. Finally, we present results of numerical simulations for both the first- and second-order model on the individual-based and continuum levels of description. PMID:24926113

  8. Mean-field-diffusion-induced chimera death state

    NASA Astrophysics Data System (ADS)

    Banerjee, Tanmoy

    2015-06-01

    Recently a novel dynamical state, called the chimera death, has been discovered in a network of nonlocally coupled identical oscillators (Zakharova A., Kapeller M. and Schöll E., Phys. Rev. Lett., 112 (2014) 154101), which is defined as the coexistence of spatially coherent and incoherent oscillation death state. This state arises due to the interplay of nonlocality and symmetry breaking and thus it bridges the gap between two important dynamical states, namely the chimera and oscillation death. In this paper we show that the chimera death can be induced in a network of generic identical oscillators with mean-field diffusive coupling and thus we establish that a nonlocal coupling is not essential to obtain chimera death. We identify a new transition route to the chimera death state, namely the transition from in-phase synchronized oscillation to chimera death via global amplitude death state. We ascribe the occurrence of chimera death to the bifurcation structure of the network in the limiting condition and show that multi-cluster chimera death states can be achieved by a proper choice of initial conditions.

  9. Relativistic mean-field models and nuclear matter constraints

    SciTech Connect

    Dutra, M.; Lourenco, O.; Carlson, B. V.; Delfino, A.; Menezes, D. P.; Avancini, S. S.; Stone, J. R.; Providencia, C.; Typel, S.

    2013-05-06

    This work presents a preliminary study of 147 relativistic mean-field (RMF) hadronic models used in the literature, regarding their behavior in the nuclear matter regime. We analyze here different kinds of such models, namely: (i) linear models, (ii) nonlinear {sigma}{sup 3}+{sigma}{sup 4} models, (iii) {sigma}{sup 3}+{sigma}{sup 4}+{omega}{sup 4} models, (iv) models containing mixing terms in the fields {sigma} and {omega}, (v) density dependent models, and (vi) point-coupling ones. In the finite range models, the attractive (repulsive) interaction is described in the Lagrangian density by the {sigma} ({omega}) field. The isospin dependence of the interaction is modeled by the {rho} meson field. We submit these sets of RMF models to eleven macroscopic (experimental and empirical) constraints, used in a recent study in which 240 Skyrme parametrizations were analyzed. Such constraints cover a wide range of properties related to symmetric nuclear matter (SNM), pure neutron matter (PNM), and both SNM and PNM.

  10. First principles based mean field model for oxygen reduction reaction.

    PubMed

    Jinnouchi, Ryosuke; Kodama, Kensaku; Hatanaka, Tatsuya; Morimoto, Yu

    2011-12-21

    A first principles-based mean field model was developed for the oxygen reduction reaction (ORR) taking account of the coverage- and material-dependent reversible potentials of the elementary steps. This model was applied to the simulation of single crystal surfaces of Pt, Pt alloy and Pt core-shell catalysts under Ar and O(2) atmospheres. The results are consistent with those shown by past experimental and theoretical studies on surface coverages under Ar atmosphere, the shape of the current-voltage curve for the ORR on Pt(111) and the material-dependence of the ORR activity. This model suggests that the oxygen associative pathway including HO(2)(ads) formation is the main pathway on Pt(111), and that the rate determining step (RDS) is the removal step of O(ads) on Pt(111). This RDS is accelerated on several highly active Pt alloys and core-shell surfaces, and this acceleration decreases the reaction intermediate O(ads). The increase in the partial pressure of O(2)(g) increases the surface coverage with O(ads) and OH(ads), and this coverage increase reduces the apparent reaction order with respect to the partial pressure to less than unity. This model shows details on how the reaction pathway, RDS, surface coverages, Tafel slope, reaction order and material-dependent activity are interrelated. PMID:22064886

  11. Mean-field inference of Hawkes point processes

    NASA Astrophysics Data System (ADS)

    Bacry, Emmanuel; Gaïffas, Stéphane; Mastromatteo, Iacopo; Muzy, Jean-François

    2016-04-01

    We propose a fast and efficient estimation method that is able to accurately recover the parameters of a d-dimensional Hawkes point-process from a set of observations. We exploit a mean-field approximation that is valid when the fluctuations of the stochastic intensity are small. We show that this is notably the case in situations when interactions are sufficiently weak, when the dimension of the system is high or when the fluctuations are self-averaging due to the large number of past events they involve. In such a regime the estimation of a Hawkes process can be mapped on a least-squares problem for which we provide an analytic solution. Though this estimator is biased, we show that its precision can be comparable to the one of the maximum likelihood estimator while its computation speed is shown to be improved considerably. We give a theoretical control on the accuracy of our new approach and illustrate its efficiency using synthetic datasets, in order to assess the statistical estimation error of the parameters.

  12. HELICITY CONSERVATION IN NONLINEAR MEAN-FIELD SOLAR DYNAMO

    SciTech Connect

    Pipin, V. V.; Sokoloff, D. D.; Zhang, H.; Kuzanyan, K. M.

    2013-05-01

    It is believed that magnetic helicity conservation is an important constraint on large-scale astrophysical dynamos. In this paper, we study a mean-field solar dynamo model that employs two different formulations of the magnetic helicity conservation. In the first approach, the evolution of the averaged small-scale magnetic helicity is largely determined by the local induction effects due to the large-scale magnetic field, turbulent motions, and the turbulent diffusive loss of helicity. In this case, the dynamo model shows that the typical strength of the large-scale magnetic field generated by the dynamo is much smaller than the equipartition value for the magnetic Reynolds number 10{sup 6}. This is the so-called catastrophic quenching (CQ) phenomenon. In the literature, this is considered to be typical for various kinds of solar dynamo models, including the distributed-type and the Babcock-Leighton-type dynamos. The problem can be resolved by the second formulation, which is derived from the integral conservation of the total magnetic helicity. In this case, the dynamo model shows that magnetic helicity propagates with the dynamo wave from the bottom of the convection zone to the surface. This prevents CQ because of the local balance between the large-scale and small-scale magnetic helicities. Thus, the solar dynamo can operate in a wide range of magnetic Reynolds numbers up to 10{sup 6}.

  13. Antiferromagnetic and topological states in silicene: A mean field study

    NASA Astrophysics Data System (ADS)

    Liu, Feng; Liu, Cheng-Cheng; Yao, Yu-Gui

    2015-08-01

    It has been widely accepted that silicene is a topological insulator, and its gap closes first and then opens again with increasing electric field, which indicates a topological phase transition from the quantum spin Hall state to the band insulator state. However, due to the relatively large atomic spacing of silicene, which reduces the bandwidth, the electron-electron interaction in this system is considerably strong and cannot be ignored. The Hubbard interaction, intrinsic spin orbital coupling (SOC), and electric field are taken into consideration in our tight-binding model, with which the phase diagram of silicene is carefully investigated on the mean field level. We have found that when the magnitudes of the two mass terms produced by the Hubbard interaction and electric potential are close to each other, the intrinsic SOC flips the sign of the mass term at either K or K‧ for one spin and leads to the emergence of the spin-polarized quantum anomalous Hall state. Project supported by the National Key Basic Research Program of China (Grant Nos. 2014CB920903, 2013CB921903, 2011CBA00108, and 2012CB937500), the National Natural Science Foundation of China (Grant Nos. 11021262, 11172303, 11404022, 11225418, and 11174337), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20121101110046), the Excellent Young Scholars Research Fund of Beijing Institute of Technology (Grant No. 2014CX04028), and the Basic Research Funds of Beijing Institute of Technology (Grant No. 20141842001).

  14. Modeling distributed axonal delays in mean-field brain dynamics

    NASA Astrophysics Data System (ADS)

    Roberts, J. A.; Robinson, P. A.

    2008-11-01

    The range of conduction delays between connected neuronal populations is often modeled as a single discrete delay, assumed to be an effective value averaging over all fiber velocities. This paper shows the effects of distributed delays on signal propagation. A distribution acts as a linear filter, imposing an upper frequency cutoff that is inversely proportional to the delay width. Distributed thalamocortical and corticothalamic delays are incorporated into a physiologically based mean-field model of the cortex and thalamus to illustrate their effects on the electroencephalogram (EEG). The power spectrum is acutely sensitive to the width of the thalamocortical delay distribution, and more so than the corticothalamic distribution, because all input signals must travel along the thalamocortical pathway. This imposes a cutoff frequency above which the spectrum is overly damped. The positions of spectral peaks in the resting EEG depend primarily on the distribution mean, with only weak dependences on distribution width. Increasing distribution width increases the stability of fixed point solutions. A single discrete delay successfully approximates a distribution for frequencies below a cutoff that is inversely proportional to the delay width, provided that other model parameters are moderately adjusted. A pair of discrete delays together having the same mean, variance, and skewness as the distribution approximates the distribution over the same frequency range without needing parameter adjustment. Delay distributions with large fractional widths are well approximated by low-order differential equations.

  15. Spectral Synthesis via Mean Field approach to Independent Component Analysis

    NASA Astrophysics Data System (ADS)

    Hu, Ning; Su, Shan-Shan; Kong, Xu

    2016-03-01

    We apply a new statistical analysis technique, the Mean Field approach to Independent Component Analysis (MF-ICA) in a Bayseian framework, to galaxy spectral analysis. This algorithm can compress a stellar spectral library into a few Independent Components (ICs), and the galaxy spectrum can be reconstructed by these ICs. Compared to other algorithms which decompose a galaxy spectrum into a combination of several simple stellar populations, the MF-ICA approach offers a large improvement in efficiency. To check the reliability of this spectral analysis method, three different methods are used: (1) parameter recovery for simulated galaxies, (2) comparison with parameters estimated by other methods, and (3) consistency test of parameters derived with galaxies from the Sloan Digital Sky Survey. We find that our MF-ICA method can not only fit the observed galaxy spectra efficiently, but can also accurately recover the physical parameters of galaxies. We also apply our spectral analysis method to the DEEP2 spectroscopic data, and find it can provide excellent fitting results for low signal-to-noise spectra.

  16. Classical mutual information in mean-field spin glass models

    NASA Astrophysics Data System (ADS)

    Alba, Vincenzo; Inglis, Stephen; Pollet, Lode

    2016-03-01

    We investigate the classical Rényi entropy Sn and the associated mutual information In in the Sherrington-Kirkpatrick (S-K) model, which is the paradigm model of mean-field spin glasses. Using classical Monte Carlo simulations and analytical tools we investigate the S-K model in the n -sheet booklet. This is achieved by gluing together n independent copies of the model, and it is the main ingredient for constructing the Rényi entanglement-related quantities. We find a glassy phase at low temperatures, whereas at high temperatures the model exhibits paramagnetic behavior, consistent with the regular S-K model. The temperature of the paramagnetic-glassy transition depends nontrivially on the geometry of the booklet. At high temperatures we provide the exact solution of the model by exploiting the replica symmetry. This is the permutation symmetry among the fictitious replicas that are used to perform disorder averages (via the replica trick). In the glassy phase the replica symmetry has to be broken. Using a generalization of the Parisi solution, we provide analytical results for Sn and In and for standard thermodynamic quantities. Both Sn and In exhibit a volume law in the whole phase diagram. We characterize the behavior of the corresponding densities, Sn/N and In/N , in the thermodynamic limit. Interestingly, at the critical point the mutual information does not exhibit any crossing for different system sizes, in contrast with local spin models.

  17. Beyond the mean field in the particle-vibration coupling scheme

    NASA Astrophysics Data System (ADS)

    Baldo, M.; Bortignon, P. F.; Colò, G.; Rizzo, D.; Sciacchitano, L.

    2015-08-01

    The energy density functional theory is one of the most used methods developed in nuclear structure. It is based on the assumption that the energy of the ground state is a functional only of the density profile. The method is extremely successful within the effective force approach, noticeably the Skyrme or Gogny forces, in reproducing the nuclear binding energies and other bulk properties along the whole mass table. Although the density functional is in this case represented formally as the Hartree-Fock mean field of an effective force, the corresponding single particle (s.p.) states in general do not reproduce the phenomenology particularly well. To overcome this difficulty, a strategy has been developed where the effective force is adjusted to reproduce directly the s.p. energies, trying to keep the ground state energy sufficiently well reproduced. An alternative route, that has been developed over several years, for solving this problem is to introduce the mean field fluctuations, as represented by the collective vibrations of the nuclear system, and their influence on the s.p. dynamics and structure. This is the basis of the particle-vibration coupling (PVC) model. In this paper we present a formal theory of the PVC model based on Green's function method. The theory extends to realistic effective forces the macroscopic PVC models and the (microscopic) nuclear field theory. It is formalized within the functional derivative approach to many-body theory. An expansion in diagrams is devised for the s.p. self-energy and the phonon propagator. Critical aspects of the PVC model are analysed in general. Applications at the lowest order of the expansion are presented and discussed.

  18. Resonating Valence Bonds and Mean-Field d-Wave Superconductivity in Graphite

    SciTech Connect

    Black-Schaffer, Annica M.

    2010-04-27

    We investigate the possibility of inducing superconductivity in a graphite layer by electronic correlation effects. We use a phenomenological microscopic Hamiltonian which includes nearest neighbor hopping and an interaction term which explicitly favors nearest neighbor spin-singlets through the well-known resonance valence bond (RVB) character of planar organic molecules. Treating this Hamiltonian in mean-field theory, allowing for bond-dependent variation of the RVB order parameter, we show that both s- and d-wave superconducting states are possible. The d-wave solution belongs to a two-dimensional representation and breaks time reversal symmetry. At zero doping there exists a quantum critical point at the dimensionless coupling J/t = 1.91 and the s- and d-wave solutions are degenerate for low temperatures. At finite doping the d-wave solution has a significantly higher T{sub c} than the s-wave solution. By using density functional theory we show that the doping induced from sulfur absorption on a graphite layer is enough to cause an electronically driven d-wave superconductivity at graphite-sulfur interfaces. We also discuss applying our results to the case of the intercalated graphites as well as the validity of a mean-field approach.

  19. Metabifurcation analysis of a mean field model of the cortex

    NASA Astrophysics Data System (ADS)

    Frascoli, Federico; van Veen, Lennaert; Bojak, Ingo; Liley, David T. J.

    2011-05-01

    Mean field models (MFMs) of cortical tissue incorporate salient, average features of neural masses in order to model activity at the population level, thereby linking microscopic physiology to macroscopic observations, e.g., with the electroencephalogram (EEG). One of the common aspects of MFM descriptions is the presence of a high-dimensional parameter space capturing neurobiological attributes deemed relevant to the brain dynamics of interest. We study the physiological parameter space of a MFM of electrocortical activity and discover robust correlations between physiological attributes of the model cortex and its dynamical features. These correlations are revealed by the study of bifurcation plots, which show that the model responses to changes in inhibition belong to two archetypal categories or “families”. After investigating and characterizing them in depth, we discuss their essential differences in terms of four important aspects: power responses with respect to the modeled action of anesthetics, reaction to exogenous stimuli such as thalamic input, and distributions of model parameters and oscillatory repertoires when inhibition is enhanced. Furthermore, while the complexity of sustained periodic orbits differs significantly between families, we are able to show how metamorphoses between the families can be brought about by exogenous stimuli. We here unveil links between measurable physiological attributes of the brain and dynamical patterns that are not accessible by linear methods. They instead emerge when the nonlinear structure of parameter space is partitioned according to bifurcation responses. We call this general method “metabifurcation analysis”. The partitioning cannot be achieved by the investigation of only a small number of parameter sets and is instead the result of an automated bifurcation analysis of a representative sample of 73,454 physiologically admissible parameter sets. Our approach generalizes straightforwardly and is well

  20. Magnetic material in mean-field dynamos driven by small scale helical flows

    NASA Astrophysics Data System (ADS)

    Giesecke, A.; Stefani, F.; Gerbeth, G.

    2014-07-01

    We perform kinematic simulations of dynamo action driven by a helical small scale flow of a conducting fluid in order to deduce mean-field properties of the combined induction action of small scale eddies. We examine two different flow patterns in the style of the G O Roberts flow but with a mean vertical component and with internal fixtures that are modelled by regions with vanishing flow. These fixtures represent either rods that lie in the center of individual eddies, or internal dividing walls that provide a separation of the eddies from each other. The fixtures can be made of magnetic material with a relative permeability larger than one which can alter the dynamo behavior. The investigations are motivated by the widely unknown induction effects of the forced helical flow that is used in the core of liquid sodium cooled fast reactors, and from the key role of soft iron impellers in the von-Kármán-sodium dynamo. For both examined flow configurations the consideration of magnetic material within the fluid flow causes a reduction of the critical magnetic Reynolds number of up to 25%. The development of the growth-rate in the limit of the largest achievable permeabilities suggests no further significant reduction for even larger values of the permeability. In order to study the dynamo behavior of systems that consist of tens of thousands of helical cells we resort to the mean-field dynamo theory (Krause and Rädler 1980 Mean-field Magnetohydrodynamics and Dynamo Theory (Oxford: Pergamon)) in which the action of the small scale flow is parameterized in terms of an α- and β-effect. We compute the relevant elements of the α- and the β-tensor using the so called testfield method. We find a reasonable agreement between the fully resolved models and the corresponding mean-field models for wall or rod materials in the considered range 1\\leqslant {{\\mu }_{r}}\\leqslant 20. Our results may be used for the development of global large scale models with recirculation

  1. Magnetization and compensation temperature in transition metal -- rare earth multilayers: a mean-field approach

    NASA Astrophysics Data System (ADS)

    Tornau, E. E.; Šmakov, J.; Lapinskas, S.; Rosengren, A.

    1998-03-01

    Mean-field theory is used to explain the magnetization as a function of layer thickness in transition metal -- rare earth multilayers. Long-range dipole interactions are included along with FM nearest neighbor interactions within the layers and AF nearest neighbor interactions at the interface. The obtained dependencies of saturation magnetization and compensation temperature on layer thickness agree with experimental data on Tb/Co multilayers( L. Ertl, G. Endl, and H. Hoffmann, J. Magn. Magn. Mater. 113, 227 (1992).). The saturation magnetization is constant for very thin films (the behavior characteristic to Tb - Co alloys) but it decreases with increase of layer thickness. At thick enough films the magnetization starts to increase again confirming the importance of the long - range forces. The compensation temperature also decreases with layer thickness. The proposed theory is extended to calculate the magnetization of FM/AFM layers with a spacer layer in between.

  2. Two-particle photoemission from strongly correlated systems: A dynamical mean-field approach

    SciTech Connect

    Napitu, B. D.; Berakdar, J.

    2010-05-15

    We study theoretically the simultaneous photoinduced two-particle excitations of strongly correlated systems on the basis of the Hubbard model. Under certain conditions specified in this work, the corresponding transition probability is related to the two-particle spectral function which we calculate using three different methods: the dynamical mean-field theory combined with quantum Monte Carlo technique, the first-order perturbation theory and the ladder approximations. The results are analyzed and compared for systems at the verge of the metal-insulator transitions. The dependencies on the electronic correlation strength and on doping are explored. In addition, the account for the orbital degeneracy allows an insight into the influence of interband correlations on the two-particle excitations. A suitable experimental realization is discussed.

  3. Magnetic Field Line Random Walk in Isotropic Turbulence with Varying Mean Field

    NASA Astrophysics Data System (ADS)

    Sonsrettee, W.; Subedi, P.; Ruffolo, D.; Matthaeus, W. H.; Snodin, A. P.; Wongpan, P.; Chuychai, P.; Rowlands, G.; Vyas, S.

    2016-08-01

    In astrophysical plasmas, the magnetic field line random walk (FLRW) plays an important role in guiding particle transport. The FLRW behavior is scaled by the Kubo number R=(b/{B}0)({{\\ell }}\\parallel /{{\\ell }}\\perp ) for rms magnetic fluctuation b, large-scale mean field {{\\boldsymbol{B}}}0, and coherence scales parallel ({{\\ell }}\\parallel ) and perpendicular ({{\\ell }}\\perp ) to {{\\boldsymbol{B}}}0. Here we use a nonperturbative analytic framework based on Corrsin’s hypothesis, together with direct computer simulations, to examine the R-scaling of the FLRW for varying B 0 with finite b and isotropic fluctuations with {{\\ell }}\\parallel /{{\\ell }}\\perp =1, instead of the well-studied route of varying {{\\ell }}\\parallel /{{\\ell }}\\perp for b \\ll {B}0. The FLRW for isotropic magnetic fluctuations is also of astrophysical interest regarding transport processes in the interstellar medium. With a mean field, fluctuations may have variance anisotropy, so we consider limiting cases of isotropic variance and transverse variance (with b z = 0). We obtain analytic theories, and closed-form solutions for extreme cases. Padé approximants are provided to interpolate all versions of theory and simulations to any B 0. We demonstrate that, for isotropic turbulence, Corrsin-based theories generally work well, and with increasing R there is a transition from quasilinear to Bohm diffusion. This holds even with b z = 0, when different routes to R\\to ∞ are mathematically equivalent; in contrast with previous studies, we find that a Corrsin-based theory with random ballistic decorrelation works well even up to R = 400, where the effects of trapping are barely perceptible in simulation results.

  4. Hartree-Fock Mean-Field Models Using Separable Interactions

    SciTech Connect

    Stevenson, P.; Stone, J.R.; Strayer, M.R.

    1999-06-28

    An effective two-body nuclear interaction is presented which is a sum of terms separable in coordinate space. Calculations are made using this interaction of some doubly closed-shell spherical nuclei using many-body perturbation theory with the Hartree-Fock state as a reference state. It is demonstrated that the interaction gives good bulk properties in finite nuclei.

  5. An exactly solvable spherical mean-field plus extended monopole pairing model

    NASA Astrophysics Data System (ADS)

    Pan, Feng; Ding, Xiaoxue; Launey, Kristina D.; Li, Hui; Xu, Xinxin; Draayer, Jerry P.

    2016-03-01

    An extended pairing Hamiltonian that describes pairing interactions among monopole nucleon pairs up to an infinite order in a spherical mean field, such as the spherical shell model, is proposed based on the local E˜2 algebraic structure, which includes the extended pairing interaction within a deformed mean-field theory (Pan et al., 2004) [19] as a special case. The advantage of the model lies in the fact that numerical solutions of the model can be obtained more easily and with less computational time than the solutions to the standard pairing model. Thus, open-shell large-scale calculations within the model become feasible. As an example of the application, pairing contribution to the binding energy of 12-28O is estimated in the present model with neutron pairs allowed to occupy a no-core shell model space of 11 j-orbits up to the fifth major harmonic oscillator shell including excitations up to 14 ħω for 12O and up to 40 ħω for 28O. The results for 12O are also compared and found to be in agreement with those of ab initio calculations. It is shown that the pairing energy per particle in 12-28O ranges from 0.4 to 1.8 MeV/A with the strongest one observed for a small number of pairs.

  6. Mean-field diffusion-limited aggregation: a "density" model for viscous fingering phenomena.

    PubMed

    Bogoyavlenskiy, V A

    2001-12-01

    We explore a universal "density" formalism to describe nonequilibrium growth processes, specifically, the immiscible viscous fingering in Hele-Shaw cells (usually referred to as the Saffman-Taylor problem). For that we develop an alternative approach to the viscous fingering phenomena, whose basic concepts have been recently published in a Rapid Communication [Phys. Rev. E 63, 045305(R) (2001)]. This approach uses the diffusion-limited aggregation (DLA) paradigm as a core: we introduce a mean-field DLA generalization in stochastic and deterministic formulations. The stochastic model, a quasicontinuum DLA, simulates Monte Carlo patterns, which demonstrate a striking resemblance to natural Hele-Shaw fingers and, for steady-state growth regimes, follow precisely the Saffman-Taylor analytical solutions in channel and sector configurations. The relevant deterministic theory, a complete set of differential equations for a time development of density fields, is derived from that stochastic model. As a principal conclusion, we prove an asymptotic equivalency of both the stochastic and deterministic mean-field DLA formulations to the classic Saffman-Taylor hydrodynamics in terms of an interface evolution. PMID:11736272

  7. Relativistic mean-field hadronic models under nuclear matter constraints

    NASA Astrophysics Data System (ADS)

    Dutra, M.; Lourenço, O.; Avancini, S. S.; Carlson, B. V.; Delfino, A.; Menezes, D. P.; Providência, C.; Typel, S.; Stone, J. R.

    2014-11-01

    Background: The microscopic composition and properties of infinite hadronic matter at a wide range of densities and temperatures have been subjects of intense investigation for decades. The equation of state (EoS) relating pressure, energy density, and temperature at a given particle number density is essential for modeling compact astrophysical objects such as neutron stars, core-collapse supernovae, and related phenomena, including the creation of chemical elements in the universe. The EoS depends not only on the particles present in the matter, but, more importantly, also on the forces acting among them. Because a realistic and quantitative description of infinite hadronic matter and nuclei from first principles in not available at present, a large variety of phenomenological models has been developed in the past several decades, but the scarcity of experimental and observational data does not allow a unique determination of the adjustable parameters. Purpose: It is essential for further development of the field to determine the most realistic parameter sets and to use them consistently. Recently, a set of constraints on properties of nuclear matter was formed and the performance of 240 nonrelativistic Skyrme parametrizations was assessed [M. Dutra et al., Phys. Rev. C 85, 035201 (2012), 10.1103/PhysRevC.85.035201] in describing nuclear matter up to about three times nuclear saturation density. In the present work we examine 263 relativistic-mean-field (RMF) models in a comparable approach. These models have been widely used because of several important aspects not always present in nonrelativistic models, such as intrinsic Lorentz covariance, automatic inclusion of spin, appropriate saturation mechanism for nuclear matter, causality, and, therefore, no problems related to superluminal speed of sound in medium. Method: Three different sets of constraints related to symmetric nuclear matter, pure neutron matter, symmetry energy, and its derivatives were used. The

  8. Orbital magnetism of ultracold fermionic gases in a lattice: Dynamical mean-field approach

    NASA Astrophysics Data System (ADS)

    Cichy, Agnieszka; Sotnikov, Andrii

    2016-05-01

    We study finite-temperature properties of ultracold four-component mixtures of alkaline-earth-metal-like atoms in optical lattices that can be effectively described by the two-band spin-1 /2 Hubbard model including Hund's exchange coupling term. Our main goal is to investigate the effect of exchange interactions on finite-temperature magnetic phases for a wide range of lattice fillings. We use the dynamical mean-field theory approach and its real-space generalization to obtain finite-temperature phase diagrams including transitions to magnetically ordered phases. It allows to determine optimal experimental regimes for approaching long-range ferromagnetic ordering in ultracold gases. We also calculate the entropy in the vicinity of magnetically ordered phases, which provides quantitative predictions for ongoing and future experiments aiming at approaching and studying long-range ordered states in optical lattices.

  9. Critical temperature enhancement of topological superconductors: A dynamical mean-field study

    NASA Astrophysics Data System (ADS)

    Nagai, Yuki; Hoshino, Shintaro; Ota, Yukihiro

    2016-06-01

    We show that a critical temperature Tc for spin-singlet two-dimensional superconductivity is enhanced by a cooperation between the Zeeman magnetic field and the Rashba spin-orbit coupling, where a superconductivity becomes topologically nontrivial below Tc. The dynamical mean-field theory with the segment-based hybridization-expansion continuous-time quantum Monte Carlo impurity solver is used for accurately evaluating a critical temperature, without any fermion sign problem. A strong-coupling approach shows that spin-flip-driven local pair hopping leads to part of this enhancement, especially effects of the magnetic field. We propose physical settings suitable for verifying the present calculations, a one-atom-layer system on Si(111) and ionic-liquid-based electric double-layer transistors.

  10. Nuclear reaction cross sections of exotic nuclei in the Glauber model for relativistic mean field densities

    SciTech Connect

    Patra, S. K.; Panda, R. N.; Arumugam, P.; Gupta, Raj K.

    2009-12-15

    We have calculated the total nuclear reaction cross sections of exotic nuclei in the framework of the Glauber model, using as inputs the standard relativistic mean field (RMF) densities and the densities obtained from the more recently developed effective-field-theory-motivated RMF (the E-RMF). Both light and heavy nuclei are taken as the representative targets, and the light neutron-rich nuclei as projectiles. We found the total nuclear reaction cross section to increase as a function of the mass number, for both the target and projectile nuclei. The differential nuclear elastic scattering cross sections are evaluated for some selected systems at various incident energies. We found a large dependence of the differential elastic scattering cross section on incident energy. Finally, we have applied the same formalism to calculate both the total nuclear reaction cross section and the differential nuclear elastic scattering cross section for the recently discussed superheavy nucleus with atomic number Z=122.

  11. Relativistic mean-field model with energy dependent self-energies

    SciTech Connect

    Antic, S.; Typel, S.

    2015-02-24

    Conventional relativistic mean-field theory is extended with the introduction of higher-order derivative couplings of nucleons with the meson fields. The Euler-Lagrange equations follow from the principle of stationary action. From invariance principles of the Lagrangian density the most general expressions for the conserved current and energy-momentum tensor are derived. The nucleon self-energies show the explicit dependence on the meson fields. They contain additional regulator functions which describe the energy dependence. The density dependence of meson-nucleon couplings causes the apperance of additional rearrangement contributions in the self-energies. The equation of state of infinite nuclear matter is obtained and the thermodynamical consistency of the model is demonstrated. This model is applied to the description of spherical, non-rotating stars in β-equilibrium. Stellar structure is calculated by solving the Tolman-Oppenheimer-Volkov (TOV) equations. The results for neutron stars are shown in terms of mass-radius relations.

  12. Nonequilibrium inhomogeneous steady state distribution in disordered, mean-field rotator systems

    NASA Astrophysics Data System (ADS)

    Campa, Alessandro; Gupta, Shamik; Ruffo, Stefano

    2015-05-01

    We present a novel method to compute the phase space distribution in the nonequilibrium stationary state of a wide class of mean-field systems involving rotators subject to quenched disordered external drive and dissipation. The method involves a series expansion of the stationary distribution in inverse of the damping coefficient; the expansion coefficients satisfy recursion relations whose solution requires computing a matrix where about three quarters of the elements vanish, making numerical evaluation simple and efficient. We illustrate our method for the paradigmatic Kuramoto model of spontaneous collective synchronization and for its two mode generalization, in the presence of noise and inertia, and demonstrate an excellent agreement between simulations and theory for the phase space distribution.

  13. Beyond-mean-field boson-fermion model for odd-mass nuclei

    NASA Astrophysics Data System (ADS)

    Nomura, K.; Nikšić, T.; Vretenar, D.

    2016-05-01

    A novel method for calculating spectroscopic properties of medium-mass and heavy atomic nuclei with an odd number of nucleons is introduced, based on the framework of nuclear energy density functional theory and the particle-core coupling scheme. The deformation energy surface of the even-even core, as well as the spherical single-particle energies and occupation probabilities of the odd particle(s), are obtained in a self-consistent mean-field calculation determined by the choice of the energy density functional and pairing interaction. This method uniquely determines the parameters of the Hamiltonian of the boson core, and only the strength of the particle-core coupling is specifically adjusted to selected data for a particular nucleus. The approach is illustrated in a systematic study of low-energy excitation spectra and transition rates of axially deformed odd-mass Eu isotopes.

  14. Beyond Mean Field Study of Properties of Single-Particle States

    NASA Astrophysics Data System (ADS)

    Cao, Li-Gang; Sagawa, H.; Colò, G.; Bortignon, P. F.

    The properties of single-particle states in magic nucleus 208Pb, such as the energies, spectroscopic factors and the effective mass, have been studied with beyond mean field theory. All selected phonons are obtained by the random phase approximation (RPA) and the same Skyrme interaction is also used in the Particle-vibration coupling (PVC) vertex. We have paid more attention to the effect of the two-body spin-orbit and tensor interactions on the single-particle properties. We find that the contributions of those terms are important to improve the results. The calculated results are compared to available experimental data. The single-particle level density around the Fermi surface is significantly increased due to the effect of PVC.

  15. Mean-field magnetohydrodynamics associated with random Alfven waves in a plasma with weak magnetic diffusion

    NASA Astrophysics Data System (ADS)

    Hamabata, Hiromitsu; Namikawa, Tomikazu

    1988-02-01

    Using first-order smoothing theory, Fourier analysis and perturbation methods, a new equation is derived governing the evolution of the spectrum tensor (including the energy and helicity spectrum functions) of the random velocity field as well as the ponderomotive and mean electromotive forces generated by random Alfven waves in a plasma with weak magnetic diffusion. The ponderomotive and mean electromotive forces are expressed as series involving spatial derivatives of mean magnetic and velocity fields whose coefficients are associated with the helicity spectrum function of the random velocity field. The effect of microscale random Alfven waves, through ponderomotive and mean electromotive forces generated by them, on the propagation of large-scale Alfven waves is also investigated by solving the mean-field equations, including the transport equation of the helicity spectrum function.

  16. Mean-field dynamic criticality and geometric transition in the Gaussian core model

    NASA Astrophysics Data System (ADS)

    Coslovich, Daniele; Ikeda, Atsushi; Miyazaki, Kunimasa

    2016-04-01

    We use molecular dynamics simulations to investigate dynamic heterogeneities and the potential energy landscape of the Gaussian core model (GCM). Despite the nearly Gaussian statistics of particles' displacements, the GCM exhibits giant dynamic heterogeneities close to the dynamic transition temperature. The divergence of the four-point susceptibility is quantitatively well described by the inhomogeneous version of the mode-coupling theory. Furthermore, the potential energy landscape of the GCM is characterized by large energy barriers, as expected from the lack of activated, hopping dynamics, and display features compatible with a geometric transition. These observations demonstrate that all major features of mean-field dynamic criticality can be observed in a physically sound, three-dimensional model.

  17. Mean-field dynamic criticality and geometric transition in the Gaussian core model.

    PubMed

    Coslovich, Daniele; Ikeda, Atsushi; Miyazaki, Kunimasa

    2016-04-01

    We use molecular dynamics simulations to investigate dynamic heterogeneities and the potential energy landscape of the Gaussian core model (GCM). Despite the nearly Gaussian statistics of particles' displacements, the GCM exhibits giant dynamic heterogeneities close to the dynamic transition temperature. The divergence of the four-point susceptibility is quantitatively well described by the inhomogeneous version of the mode-coupling theory. Furthermore, the potential energy landscape of the GCM is characterized by large energy barriers, as expected from the lack of activated, hopping dynamics, and display features compatible with a geometric transition. These observations demonstrate that all major features of mean-field dynamic criticality can be observed in a physically sound, three-dimensional model. PMID:27176347

  18. Mean field spin glasses treated with PDE techniques

    NASA Astrophysics Data System (ADS)

    Barra, Adriano; Del Ferraro, Gino; Tantari, Daniele

    2013-07-01

    Following an original idea of Guerra, in these notes we analyze the Sherrington-Kirkpatrick model from different perspectives, all sharing the underlying approach which consists in linking the resolution of the statistical mechanics of the model (e.g. solving for the free energy) to well-known partial differential equation (PDE) problems (in suitable spaces). The plan is then to solve the related PDE using techniques involved in their native field and lastly bringing back the solution in the proper statistical mechanics framework. Within this strand, after a streamlined test-case on the Curie-Weiss model to highlight the methods more than the physics behind, we solve the SK both at the replica symmetric and at the 1-RSB level, obtaining the correct expression for the free energy via an analogy to a Fourier equation and for the self-consistencies with an analogy to a Burger equation, whose shock wave develops exactly at critical noise level (triggering the phase transition). Our approach, beyond acting as a new alternative method (with respect to the standard routes) for tackling the complexity of spin glasses, links symmetries in PDE theory with constraints in statistical mechanics and, as a novel result from the theoretical physics perspective, we obtain a new class of polynomial identities (namely of Aizenman-Contucci type, but merged within the Guerra's broken replica measures), whose interest lies in understanding, via the recent Panchenko breakthroughs, how to force the overlap organization to the ultrametric tree predicted by Parisi.

  19. Clusters and Fluctuations at Mean-Field Critical Points and Spinodals

    SciTech Connect

    Klein, W.; CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 ; Gould, Harvey; Tobochnik, J.; Alexander, F. J.; Anghel, M.; Johnson, Gregory

    2000-08-07

    We show that the structure of the fluctuations close to spinodals and mean-field critical points is qualitatively different from the structure close to non-mean-field critical points. This difference has important implications for many areas including the formation of glasses in supercooled liquids. In particular, the divergence of the measured static structure function in near-mean-field systems close to the glass transition is suppressed relative to the mean-field prediction in systems for which a spatial symmetry is broken. (c) 2000 The American Physical Society.

  20. T-->0 mean-field population dynamics approach for the random 3-satisfiability problem.

    PubMed

    Zhou, Haijun

    2008-06-01

    During the past decade, phase-transition phenomena in the random 3-satisfiability ( 3 -SAT) problem has been intensively studied by statistical physics methods. In this work, we study the random 3 -SAT problem by the mean-field first-step replica-symmetry-broken cavity theory at the limit of temperature T-->0 . The reweighting parameter y of the cavity theory is allowed to approach infinity together with the inverse temperature beta with fixed ratio r=ybeta . Focusing on the system's space of satisfiable configurations, we carry out extensive population dynamics simulations using the technique of importance sampling, and we obtain the entropy density s(r) and complexity Sigma(r) of zero-energy clusters at different r values. We demonstrate that the population dynamics may reach different fixed points with different types of initial conditions. By knowing the trends of s(r) and Sigma(r) with r , we can judge whether a certain type of initial condition is appropriate at a given r value. This work complements and confirms the results of several other very recent theoretical studies. PMID:18643331

  1. Chain architecture and micellization: A mean-field coarse-grained model for poly(ethylene oxide) alkyl ether surfactants

    SciTech Connect

    García Daza, Fabián A.; Mackie, Allan D.; Colville, Alexander J.

    2015-03-21

    Microscopic modeling of surfactant systems is expected to be an important tool to describe, understand, and take full advantage of the micellization process for different molecular architectures. Here, we implement a single chain mean field theory to study the relevant equilibrium properties such as the critical micelle concentration (CMC) and aggregation number for three sets of surfactants with different geometries maintaining constant the number of hydrophobic and hydrophilic monomers. The results demonstrate the direct effect of the block organization for the surfactants under study by means of an analysis of the excess energy and entropy which can be accurately determined from the mean-field scheme. Our analysis reveals that the CMC values are sensitive to branching in the hydrophilic head part of the surfactant and can be observed in the entropy-enthalpy balance, while aggregation numbers are also affected by splitting the hydrophobic tail of the surfactant and are manifested by slight changes in the packing entropy.

  2. MAGNETIC FIELD LINE RANDOM WALK IN ISOTROPIC TURBULENCE WITH ZERO MEAN FIELD

    SciTech Connect

    Sonsrettee, W.; Ruffolo, D.; Snodin, A. P.; Wongpan, P.; Subedi, P.; Matthaeus, W. H.; Chuychai, P. E-mail: david.ruf@mahidol.ac.th E-mail: pat.wongpan@postgrad.otago.ac.nz E-mail: prasub@udel.edu

    2015-01-01

    In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B {sub 0})(ℓ{sub ∥}/ℓ ) for rms magnetic fluctuation b, large-scale mean field B {sub 0}, and parallel and perpendicular coherence scales ℓ{sub ∥} and ℓ , respectively. Here we examine the FLRW when R → ∞ by taking B {sub 0} → 0 for finite b{sub z} (fluctuation component along B {sub 0}), which differs from the well-studied route with b{sub z} = 0 or b{sub z} << B {sub 0} as the turbulence becomes quasi-two-dimensional (quasi-2D). Fluctuations with B {sub 0} = 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k {sup –1} or k {sup –2} moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B {sub 0} → 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality.

  3. Magnetic Field Line Random Walk in Isotropic Turbulence with Zero Mean Field

    NASA Astrophysics Data System (ADS)

    Sonsrettee, W.; Subedi, P.; Ruffolo, D.; Matthaeus, W. H.; Snodin, A. P.; Wongpan, P.; Chuychai, P.

    2015-01-01

    In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B 0)(l∥/l) for rms magnetic fluctuation b, large-scale mean field B 0, and parallel and perpendicular coherence scales l∥ and l, respectively. Here we examine the FLRW when R → ∞ by taking B 0 → 0 for finite bz (fluctuation component along B 0), which differs from the well-studied route with bz = 0 or bz Lt B 0 as the turbulence becomes quasi-two-dimensional (quasi-2D). Fluctuations with B 0 = 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k -1 or k -2 moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B 0 → 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality.

  4. Perturbative Calculation of Quasi-Potential in Non-equilibrium Diffusions: A Mean-Field Example

    NASA Astrophysics Data System (ADS)

    Bouchet, Freddy; Gawȩdzki, Krzysztof; Nardini, Cesare

    2016-06-01

    In stochastic systems with weak noise, the logarithm of the stationary distribution becomes proportional to a large deviation rate function called the quasi-potential. The quasi-potential, and its characterization through a variational problem, lies at the core of the Freidlin-Wentzell large deviations theory (Freidlin and Wentzell, Random perturbations of dynamical systems, 2012). In many interacting particle systems, the particle density is described by fluctuating hydrodynamics governed by Macroscopic Fluctuation Theory (Bertini et al., arXiv:1404.6466 , 2014), which formally fits within Freidlin-Wentzell's framework with a weak noise proportional to 1/√{N}, where N is the number of particles. The quasi-potential then appears as a natural generalization of the equilibrium free energy to non-equilibrium particle systems. A key physical and practical issue is to actually compute quasi-potentials from their variational characterization for non-equilibrium systems for which detailed balance does not hold. We discuss how to perform such a computation perturbatively in an external parameter λ , starting from a known quasi-potential for λ =0. In a general setup, explicit iterative formulae for all terms of the power-series expansion of the quasi-potential are given for the first time. The key point is a proof of solvability conditions that assure the existence of the perturbation expansion to all orders. We apply the perturbative approach to diffusive particles interacting through a mean-field potential. For such systems, the variational characterization of the quasi-potential was proven by Dawson and Gartner (Stochastics 20:247-308, 1987; Stochastic differential systems, vol 96, pp 1-10, 1987). Our perturbative analysis provides new explicit results about the quasi-potential and about fluctuations of one-particle observables in a simple example

  5. Perturbative Calculation of Quasi-Potential in Non-equilibrium Diffusions: A Mean-Field Example

    NASA Astrophysics Data System (ADS)

    Bouchet, Freddy; Gawȩdzki, Krzysztof; Nardini, Cesare

    2016-04-01

    In stochastic systems with weak noise, the logarithm of the stationary distribution becomes proportional to a large deviation rate function called the quasi-potential. The quasi-potential, and its characterization through a variational problem, lies at the core of the Freidlin-Wentzell large deviations theory (Freidlin and Wentzell, Random perturbations of dynamical systems, 2012). In many interacting particle systems, the particle density is described by fluctuating hydrodynamics governed by Macroscopic Fluctuation Theory (Bertini et al., arXiv:1404.6466, 2014), which formally fits within Freidlin-Wentzell's framework with a weak noise proportional to 1/√{N} , where N is the number of particles. The quasi-potential then appears as a natural generalization of the equilibrium free energy to non-equilibrium particle systems. A key physical and practical issue is to actually compute quasi-potentials from their variational characterization for non-equilibrium systems for which detailed balance does not hold. We discuss how to perform such a computation perturbatively in an external parameter λ , starting from a known quasi-potential for λ =0 . In a general setup, explicit iterative formulae for all terms of the power-series expansion of the quasi-potential are given for the first time. The key point is a proof of solvability conditions that assure the existence of the perturbation expansion to all orders. We apply the perturbative approach to diffusive particles interacting through a mean-field potential. For such systems, the variational characterization of the quasi-potential was proven by Dawson and Gartner (Stochastics 20:247-308, 1987; Stochastic differential systems, vol 96, pp 1-10, 1987). Our perturbative analysis provides new explicit results about the quasi-potential and about fluctuations of one-particle observables in a simple example of mean field diffusions: the Shinomoto-Kuramoto model of coupled rotators (Prog Theoret Phys 75:1105-1110, [74]). This

  6. Deviation from mean-field behavior in a low molecular weight critical polymer blend

    NASA Astrophysics Data System (ADS)

    Hair, D. W.; Hobbie, E. K.; Nakatani, A. I.; Han, C. C.

    1992-06-01

    A deviation from mean-field behavior is observed in the static susceptibility and correlation length measured with small angle neutron scattering as a function of temperature near the phase boundary of a relatively low molecular weight critical polymer mixture. The possibility of a fluctuation influenced crossover from mean-field to nonmean-field behavior is considered.

  7. Study of the tensor correlation in a neutron-rich sd-shell region with mean-field and beyond-mean-field methods

    SciTech Connect

    Sugimoto, Satoru; Toki, Hiroshi; Ikeda, Kiyomi

    2008-04-29

    We study the effect of the tensor force on nuclear structure with mean-field and beyond-mean-field methods. An important correlation induced by the tensor force is a two-particle-two-hole (2p2h) correlation, which cannot be treated with a standard mean-field method. To treat the 2p2h tensor correlation, we develop a new framework [charge- and parity-projected Hartree-Fock (CPPHF) method], which is a beyond-mean-field method. In the CPPHF method, we introduce single-particle states with parity and charge mixing. The parity and charge projections are performed on a total wave function before variation. We apply the CPPHF method to oxygen isotopes including neutron-rich ones. The potential energy from the tensor force has the same order of magnitude as that from the LS force and becomes smaller with neutron number, which indicates that excess neutrons do not contribute to the 2p2h tensor correlation significantly. We also study the effect of the tensor force on spin-orbit-splitting (ls-splitting) in a neutron-rich fluorine isotope {sup 23}F. The tensor force reduces the ls-splitting for the proton d-orbits by about 3 MeV. This effect is important to reproduce the experimental value.

  8. Thermal conduction in polymeric nanofluids under mean field approximation: role of interfacial adsorption layers

    NASA Astrophysics Data System (ADS)

    Nisha, M. R.; Philip, J.

    2013-07-01

    Polymeric nanofluids of TiO2/PVA (polyvinyl alcohol) and Cu/PVA have been prepared by dispersing nanoparticles of TiO2 or metallic copper in PVA. The thermal diffusivities and thermal conductivities of these nanofluids have been measured as a function of particle loading following a thermal wave interference technique in a thermal wave resonant cavity. It is found that in both cases thermal conductivity increases with particle concentration, with Cu/PVA nanofluids showing a much larger increase. The results have been compared with the corresponding values calculated following different theoretical models. Comparison of the results with model-based calculations shows that the thermal conductivity variations in these nanofluids are within the framework of the classical mean field theory including the formation of thin interfacial adsorption layers around nanoparticles. Although the molecular weight of PVA is very high, it is found that the adsorption layer thickness is limited by the hydrodynamic radius of the nanoparticles. It is found that particle clustering followed by interfacial layering accounts for the larger increase in thermal conductivity found for Cu/PVA compared to TiO2/PVA.

  9. Mean-field description of odd-frequency superconductivity with staggered ordering vector

    NASA Astrophysics Data System (ADS)

    Hoshino, Shintaro

    2014-09-01

    A low-energy fixed-point Hamiltonian is constructed for the s-wave odd-frequency pairing state with staggered ordering vector in the two-channel Kondo lattice. The effective model is justified because it reproduces low-energy behaviors of self-energy obtained by the dynamical mean-field theory. The retardation effect is essential for the odd-frequency pairing, which comes from the hybridization process between conduction electrons and pseudofermions originating from localized spins at low energies. Using the effective Hamiltonian, the electromagnetic response functions are microscopically calculated. The present system shows a "weak" Meissner effect, where both paramagnetic and diamagnetic parts contribute to the Meissner kernel to give a small total diamagnetic response in the superconducting state. This feature is in contrast to the ordinary s-wave BCS pairing where only the diamagnetic kernel is finite in the ground state. The staggered nature of the odd-frequency order parameter plays an important role for the sign of the Meissner kernel.

  10. Kaon Condensation and Lambda-Nucleon Loop in the Relativistic Mean-Field Approach

    SciTech Connect

    Tomoyuki Maruyama; Takumi Muto; Toshitaka Tatsumi; Kazuo Tsushima; Anthony W. Thomas

    2005-02-24

    The possibility of kaon condensation in high-density symmetric nuclear matter is investigated including both s- and p-wave kaon-baryon interactions within the relativistic mean-field (RMF) theory. Above a certain density, we have a collective K{sub s} state carrying the same quantum numbers as the antikaon. The appearance of the K{sub s} state is caused by the time component of the axial-vector interaction between kaons and baryons. It is shown that the system becomes unstable with respect to condensation of K-Kbar{sub s} pairs. We consider how the effective baryon masses affect the kaon self-energy coming from the time component of the axial-vector interaction. Also, the role of the spatial component of the axial-vector interaction on the possible existence of the collective kaonic states is discussed in connection with Lambda-mixing effects in the ground state of high-density matter. Implications of K-Kbar{sub s} condensation for high-energy heavy-ion collisions are briefly mentioned.

  11. Beyond-mean-field corrections within the second random-phase approximation

    NASA Astrophysics Data System (ADS)

    Grasso, M.; Gambacurta, D.; Engel, J.

    2016-06-01

    A subtraction procedure, introduced to overcome double-counting problems in beyond-mean-field theories, is used in the second random-phase approximation (SRPA). Doublecounting problems arise in the energy-density functional framework in all cases where effective interactions tailored at leading order are used for higher-order calculations, such as those done in the SRPA model. It was recently shown that this subtraction procedure also guarantees that the stability condition related to the Thouless theorem is verified in extended RPA models. We discuss applications of the subtraction procedure, introduced within the SRPA model, to the nucleus 16O. The application of the subtraction procedure leads to: (i) stable results that are weakly cutoff dependent; (ii) a considerable upwards correction of the SRPA spectra (which were systematically shifted downwards by several MeV with respect to RPA spectra, in all previous calculations). With this important implementation of the model, many applications may be foreseen to analyze the genuine impact of 2 particle-2 hole configurations (without any cutoff dependences and anomalous shifts) on the excitation spectra of medium-mass and heavy nuclei.

  12. Relativistic self-consistent mean-field description of Sm isotopes

    NASA Astrophysics Data System (ADS)

    Karim, Afaque; Ahmad, Shakeb

    2015-12-01

    The evolution of the shape from the spherical to the axially deformed shapes of the neutron-rich, even-even Sm-164144 transitional nuclei is investigated. The investigations are performed with explicit density-dependent meson-nucleon and point-coupling models within the framework of the covariant density functional theory. A nonlinear meson-nucleon coupling model represented by the NL3* parametrization of the relativistic mean-field Lagrangian has also been used. The bulk and the microscopic properties of these nuclei have been investigated to analyze the phase-transition region and the critical-point behavior. The microscopic and self-consistent quadrupole deformation-constrained calculations show a clear shape change for even-even Sm isotopes with N =82 -102 . The potential energy surfaces for 148Sm,150Sm , and 152Sm obtained using different interactions are found to be relatively flat, which may be the possible critical-point nuclei. By examining the single-particle spectra, it is found that these nuclei distribute more uniformly as compared to other isotopes. Investigations also support the proposed shell-closure properties of 162Sm. Overall good agreement is found within the different models used and between the calculated and experimental results wherever available.

  13. Quantum Dynamics of Dark and Dark-Bright Solitons beyond the Mean-Field Approximation

    NASA Astrophysics Data System (ADS)

    Krönke, Sven; Schmelcher, Peter

    2014-05-01

    Dark solitons are well-known excitations in one-dimensional repulsively interacting Bose-Einstein condensates, which feature a characteristical phase-jump across a density dip and form stability in the course of their dynamics. While these objects are stable within the celebrated Gross-Pitaevskii mean-field theory, the situation changes dramatically in the full many-body description: The condensate being initially in a dark soliton state dynamically depletes and the density notch fills up with depleted atoms. We analyze this process in detail with a particular focus on two-body correlations and the fate of grey solitons (dark solitons with finite density in the notch) and thereby complement the existing results in the literature. Moreover, we extend these studies to mixtures of two repulsively interacting bosonic species with a dark-bright soliton (dark soliton in one component filled with localized atoms of the other component) as the initial state. All these many-body quantum dynamics simulations are carried out with the recently developed multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB).

  14. Corrected mean-field models for spatially dependent advection-diffusion-reaction phenomena

    NASA Astrophysics Data System (ADS)

    Simpson, Matthew J.; Baker, Ruth E.

    2011-05-01

    In the exclusion-process literature, mean-field models are often derived by assuming that the occupancy status of lattice sites is independent. Although this assumption is questionable, it is the foundation of many mean-field models. In this work we develop methods to relax the independence assumption for a range of discrete exclusion-process-based mechanisms motivated by applications from cell biology. Previous investigations that focused on relaxing the independence assumption have been limited to studying initially uniform populations and ignored any spatial variations. By ignoring spatial variations these previous studies were greatly simplified due to translational invariance of the lattice. These previous corrected mean-field models could not be applied to many important problems in cell biology such as invasion waves of cells that are characterized by moving fronts. Here we propose generalized methods that relax the independence assumption for spatially inhomogeneous problems, leading to corrected mean-field descriptions of a range of exclusion-process-based models that incorporate (i) unbiased motility, (ii) biased motility, and (iii) unbiased motility with agent birth and death processes. The corrected mean-field models derived here are applicable to spatially variable processes including invasion wave-type problems. We show that there can be large deviations between simulation data and traditional mean-field models based on invoking the independence assumption. Furthermore, we show that the corrected mean-field models give an improved match to the simulation data in all cases considered.

  15. Static and Dynamic Chain Structures in the Mean-Field Theory

    NASA Astrophysics Data System (ADS)

    Ichikawa, T.; Itagaki, N.; Loebl, N.; Maruhn, J. A.; Oberacker, V. E.; Ohkubo, S.; Schuetrumpf, B.; Umar, A. S.

    2011-10-01

    We give a brief overview of recent work examining the presence of α-clusters in light nuclei within the Skyrme-force Hartree-Fock model. Of special signif cance are investigations into α-chain structures in carbon isotopes and 16O. Their stability and possible role in fusion reactions are examined in static and time-dependent Hartree-Fock calculations. We f nd a new type of shape transition in collisions and a centrifugal stabilization of the 4α chain state in a limited range of angular momenta. No stabilization is found for the 3α chain.

  16. Light propagation beyond the mean-field theory of standard optics.

    PubMed

    Javanainen, Juha; Ruostekoski, Janne

    2016-01-25

    With ready access to massive computer clusters we may now study light propagation in a dense cold atomic gas by means of basically exact numerical simulations. We report on a direct comparison between traditional optics, that is, electrodynamics of a polarizable medium, and numerical simulations in an elementary problem of light propagating through a slab of matter. The standard optics fails already at quite low atom densities, and the failure becomes dramatic when the average interatomic separation is reduced to around k(-1), where k is the wave number of resonant light. The difference between the two solutions originates from correlations between the atoms induced by light-mediated dipole-dipole interactions. PMID:26832481

  17. Monogamy of entanglement and improved mean-field ansatz for spin lattices

    NASA Astrophysics Data System (ADS)

    Osterloh, Andreas; Schützhold, Ralf

    2015-03-01

    We consider rather general spin-1 /2 lattices with large coordination numbers Z . Based on the monogamy of entanglement and other properties of the concurrence C , we derive rigorous bounds for the entanglement between neighboring spins, such as C ≤1 /√{Z } , which show that C decreases for large Z . In addition, we demonstrate that the concurrence C measures the deviation from mean-field behavior and can only vanish if the mean-field ansatz yields an exact ground state of the Hamiltonian. Motivated by these findings, we propose an improved mean-field ansatz by adding entanglement.

  18. Statistics of Dislocation Slip Avalanches in Nanosized Single Crystals Show Tuned Critical Behavior Predicted by a Simple Mean Field Model

    NASA Astrophysics Data System (ADS)

    Friedman, Nir; Jennings, Andrew T.; Tsekenis, Georgios; Kim, Ju-Young; Tao, Molei; Uhl, Jonathan T.; Greer, Julia R.; Dahmen, Karin A.

    2012-08-01

    We show that slowly sheared metallic nanocrystals deform via discrete strain bursts (slips), whose size distributions follow power laws with stress-dependent cutoffs. We show for the first time that plasticity reflects tuned criticality, by collapsing the stress-dependent slip-size distributions onto a predicted scaling function. Both power-law exponents and scaling function agree with mean-field theory predictions. Our study of 7 materials and 2 crystal structures, at various deformation rates, stresses, and crystal sizes down to 75 nm, attests to the universal characteristics of plasticity.

  19. Self-consistent Green's function embedding for advanced electronic structure methods based on a dynamical mean-field concept

    NASA Astrophysics Data System (ADS)

    Chibani, Wael; Ren, Xinguo; Scheffler, Matthias; Rinke, Patrick

    2016-04-01

    We present an embedding scheme for periodic systems that facilitates the treatment of the physically important part (here a unit cell or a supercell) with advanced electronic structure methods, that are computationally too expensive for periodic systems. The rest of the periodic system is treated with computationally less demanding approaches, e.g., Kohn-Sham density-functional theory, in a self-consistent manner. Our scheme is based on the concept of dynamical mean-field theory formulated in terms of Green's functions. Our real-space dynamical mean-field embedding scheme features two nested Dyson equations, one for the embedded cluster and another for the periodic surrounding. The total energy is computed from the resulting Green's functions. The performance of our scheme is demonstrated by treating the embedded region with hybrid functionals and many-body perturbation theory in the GW approach for simple bulk systems. The total energy and the density of states converge rapidly with respect to the computational parameters and approach their bulk limit with increasing cluster (i.e., computational supercell) size.

  20. Can realistic interaction be useful for nuclear mean-field approaches?

    NASA Astrophysics Data System (ADS)

    Nakada, H.; Sugiura, K.; Inakura, T.; Margueron, J.

    2016-07-01

    Recent applications of the M3Y-type semi-realistic interaction to the nuclear mean-field approaches are presented: i) Prediction of magic numbers and ii) isotope shifts of nuclei with magic proton numbers. The results exemplify that the realistic interaction, which is derived from the bare 2 N and 3 N interaction, furnishes a new theoretical instrument for advancing nuclear mean-field approaches.

  1. Beyond mean-field ground-state energies and correlation properties of a trapped Bose-Einstein condensate

    NASA Astrophysics Data System (ADS)

    Sofianos, S. A.; Das, T. K.; Chakrabarti, B.; Lekala, M. L.; Adam, R. M.; Rampho, G. J.

    2013-01-01

    A two-body correlated basis set is used to develop a many-body theory which is valid for any number of bosons in the trap. The formalism incorporates the van der Waals interaction and two-body correlations in an exact way. The theory has successfully been applied to Bose-Einstein condensates—dilute weakly interacting and also dilute but having a large scattering length. Even in the extreme dilute condition, we observe the breakdown of the shape-independent approximation and the interatomic correlation plays an important role in the large particle-number limit. This correlated many-body calculation can handle, within the two-body correlation approximation, the entire range of atom number of experimentally achieved condensates. Next we successfully push the basis function for large scattering lengths where the mean-field results are manifestly bad. The sharp increase in correlation energy clearly shows the beyond-mean-field effect. We also calculate one-particle densities for various scattering lengths and particle numbers. Our many-body calculation exhibits the finite-size effect in the one-body density.

  2. Improved quasiparticle wave functions and mean field for G0W0 calculations: Initialization with the COHSEX operator

    NASA Astrophysics Data System (ADS)

    Jain, Manish; Deslippe, Jack; Samsonidze, Georgy; Cohen, Marvin L.; Chelikowsky, James R.; Louie, Steven G.

    2014-09-01

    The GW approximation to the electron self-energy has become a standard method for ab initio calculation of excited-state properties of condensed-matter systems. In many calculations, the GW self-energy operator, Σ, is taken to be diagonal in the density functional theory (DFT) Kohn-Sham basis within the G0W0 scheme. However, there are known situations in which this diagonal G0W0 approximation starting from DFT is inadequate. We present two schemes to resolve such problems. The first, which we called sc -COHSEX+GW, involves construction of an improved mean field using the static limit of GW, known as COHSEX (Coulomb hole and screened exchange), which is significantly simpler to treat than GW. In this scheme, frequency-dependent self energy Σ (ω), is constructed and taken to be diagonal in the COHSEX orbitals after the system is solved self-consistently within this formalism. The second method is called off diagonal-COHSEX GW (od -COHSEX+GW). In this method, one does not self-consistently change the mean-field starting point but diagonalizes the COHSEX Hamiltonian within the Kohn-Sham basis to obtain quasiparticle wave functions and uses the resulting orbitals to construct the GW Σ in the diagonal form. We apply both methods to a molecular system, silane, and to two bulk systems, Si and Ge under pressure. For silane, both methods give good quasiparticle wave functions and energies. Both methods give good band gaps for bulk silicon and maintain good agreement with experiment. Further, the sc -COHSEX+GW method solves the qualitatively incorrect DFT mean-field starting point (having a band overlap) in bulk Ge under pressure.

  3. Ultrafast dynamics of finite Hubbard clusters: A stochastic mean-field approach

    NASA Astrophysics Data System (ADS)

    Lacroix, Denis; Hermanns, S.; Hinz, C. M.; Bonitz, M.

    2014-09-01

    Finite lattice models are a prototype for interacting quantum systems and capture essential properties of condensed matter systems. With the dramatic progress in ultracold atoms in optical lattices, finite fermionic Hubbard systems have become directly accessible in experiments, including their ultrafast dynamics far from equilibrium. Here, we present a theoretical approach that is able to treat these dynamics in any dimension and fully includes inhomogeneity effects. The method consists in stochastic sampling of mean-field trajectories and is—for not too large two-body interaction strength—found to be much more accurate than time-dependent mean-field at the same order of numerical costs. Furthermore, it can well compete with recent nonequilibrium Green function approaches using second-order Born approximation, which are of substantially larger complexity. The performance of the stochastic mean-field approach is demonstrated for Hubbard clusters with up to 512 particles in one, two, and three dimensions.

  4. Carbon diffusion in supersaturated ferrite: a comparison of mean-field and atomistic predictions

    NASA Astrophysics Data System (ADS)

    Lawrence, B.; Sinclair, C. W.; Perez, M.

    2014-09-01

    Hillert's mean-field elastic prediction of the diffusivity of carbon in ferrite is regularly used to explain the experimental observation of slow diffusion of carbon in supersaturated ferrite. With increasing carbon supersaturation, the appropriateness of assuming that many-body carbon interactions can be ignored needs to be re-examined. In this work, we have sought to evaluate the limits of such mean-field predictions for activation barrier prediction by comparing such models with molecular dynamics simulations. The results of this analysis show that even at extremely high levels of supersaturation (up to 8 at% C), mean-field elasticity models can be used with confidence when the effects of carbon concentration on the energy of carbon at octahedral and tetrahedral sites are considered. The reasons for this finding and its consequences are discussed.

  5. Mean-field approximation for a Bose-Hubbard dimer with complex interaction strength

    NASA Astrophysics Data System (ADS)

    Graefe, Eva-Maria; Liverani, Chiara

    2013-11-01

    In the limit of large particle numbers and low densities systems of cold atoms can be effectively described as macroscopic single-particle systems in a mean-field approximation. In the case of a Bose-Hubbard system, modelling bosons on a discrete lattice with on-site interactions, this yields a discrete nonlinear Schrödinger equation of Gross-Pitaevskii type. It has been recently shown that the correspondence between the Gross-Pitaevskii equation and the Bose-Hubbard system breaks down for complex extensions. In particular, for a Bose-Hubbard dimer with complex on-site energy the mean-field approximation yields a generalized complex nonlinear Schrödinger equation. Conversely, a Gross-Pitaevskii equation with complex on-site energies arises as the mean-field approximation of many-particle Lindblad dynamics rather than a complex extension of the Bose-Hubbard system. Here we address the question of how the mean-field description is modified in the presence of a complex-valued particle interaction term for a Bose-Hubbard dimer. We derive the mean-field equations of motion leading to nonlinear dissipative Bloch dynamics, related to a nontrivial complex generalization of the nonlinear Schrödinger equation. The resulting dynamics are analysed in detail. It is shown that depending on the parameter values there can be up to six stationary states, and for small values of the interaction strength there are limit cycles. Furthermore, we show how a Gross-Pitaevskii equation with a complex interaction term can be derived as the mean-field approximation of a Bose-Hubbard dimer with an additional Lindblad term modelling two-particle losses.

  6. Streamlined mean field variational Bayes for longitudinal and multilevel data analysis.

    PubMed

    Lee, Cathy Yuen Yi; Wand, Matt P

    2016-07-01

    Streamlined mean field variational Bayes algorithms for efficient fitting and inference in large models for longitudinal and multilevel data analysis are obtained. The number of operations is linear in the number of groups at each level, which represents a two orders of magnitude improvement over the naïve approach. Storage requirements are also lessened considerably. We treat models for the Gaussian and binary response situations. Our algorithms allow the fastest ever approximate Bayesian analyses of arbitrarily large longitudinal and multilevel datasets, with little degradation in accuracy compared with Markov chain Monte Carlo. The modularity of mean field variational Bayes allows relatively simple extension to more complicated scenarios. PMID:27214238

  7. Beyond mean-field dynamics in open Bose-Hubbard chains

    NASA Astrophysics Data System (ADS)

    Witthaut, D.; Trimborn, F.; Hennig, H.; Kordas, G.; Geisel, T.; Wimberger, S.

    2011-06-01

    We investigate the effects of phase noise and particle loss on the dynamics of a Bose-Einstein condensate in an optical lattice. Starting from the many-body master equation, we discuss the applicability of generalized mean-field approximations in the presence of dissipation as well as methods to simulate quantum effects beyond mean field by including higher-order correlation functions. It is shown that localized particle dissipation leads to surprising dynamics, as it can suppress decay and restore the coherence of a Bose-Einstein condensate. These effects can be applied to engineer coherent structures such as stable discrete breathers and dark solitons.

  8. Beyond-mean-field study of a binary bosonic mixture in a state-dependent honeycomb lattice

    NASA Astrophysics Data System (ADS)

    Cao, Lushuai; Krönke, Sven; Stockhofe, Jan; Simonet, Juliette; Sengstock, Klaus; Lühmann, Dirk-Sören; Schmelcher, Peter

    2015-04-01

    We investigate a binary mixture of bosonic atoms loaded into a state-dependent honeycomb lattice. For this system, the emergence of a so-called twisted-superfluid ground state was experimentally observed in Soltan-Panahi et al. [Nat. Phys. 8, 71 (2012), 10.1038/nphys2128]. Theoretically, the origin of this effect is not understood. We perform numerical simulations of an extended single-band Bose-Hubbard model adapted to the experimental parameters employing the multilayer multiconfiguration time-dependent Hartree method for Bosons. Our results confirm the overall applicability of mean-field theory in the relevant parameter range, within the extended single-band Bose-Hubbard model. Beyond this, we provide a detailed analysis of correlation effects correcting the mean-field result. These have the potential to induce asymmetries in single shot time-of-flight measurements, but we find no indication of the patterns characteristic of the twisted superfluid. We comment on the restrictions of our model and possible extensions.

  9. Mott transitions in a three-component Falicov-Kimball model: A slave boson mean-field study

    NASA Astrophysics Data System (ADS)

    Le, Duc-Anh; Tran, Minh-Tien

    2015-05-01

    Metal-insulator transitions in a three-component Falicov-Kimball model are investigated within the Kotliar-Ruckenstein slave boson mean-field approach. The model describes a mixture of two interacting fermion atom species loaded into an optical lattice at ultralow temperature. One species is two-component atoms, which can hop in the optical lattice, and the other is single-component atoms, which are localized. Different correlation-driven metal-insulator transitions are observed depending on the atom filling conditions and local interactions. These metal-insulator transitions are classified by the band renormalization factors and the double occupancies of the atom species. The filling conditions and the critical value of the local interactions for these metal-insulator transitions are also analytically established. The obtained results not only are in good agreement with the dynamical mean-field theory for the three-component Falicov-Kimball model but also clarify the nature and properties of the metal-insulator transitions in a simple physics picture.

  10. Multidimensionally constrained relativistic mean-field study of triple-humped barriers in actinides

    NASA Astrophysics Data System (ADS)

    Zhao, Jie; Lu, Bing-Nan; Vretenar, Dario; Zhao, En-Guang; Zhou, Shan-Gui

    2015-01-01

    Background: Potential energy surfaces (PES's) of actinide nuclei are characterized by a two-humped barrier structure. At large deformations beyond the second barrier, the occurrence of a third barrier was predicted by macroscopic-microscopic model calculations in the 1970s, but contradictory results were later reported by a number of studies that used different methods. Purpose: Triple-humped barriers in actinide nuclei are investigated in the framework of covariant density functional theory (CDFT). Methods: Calculations are performed using the multidimensionally constrained relativistic mean field (MDC-RMF) model, with the nonlinear point-coupling functional PC-PK1 and the density-dependent meson exchange functional DD-ME2 in the particle-hole channel. Pairing correlations are treated in the BCS approximation with a separable pairing force of finite range. Results: Two-dimensional PES's of 226,228,230,232Th and 232,235,236,238U are mapped and the third minima on these surfaces are located. Then one-dimensional potential energy curves along the fission path are analyzed in detail and the energies of the second barrier, the third minimum, and the third barrier are determined. The functional DD-ME2 predicts the occurrence of a third barrier in all Th nuclei and 238U . The third minima in 230 ,232Th are very shallow, whereas those in 226 ,228Th and 238U are quite prominent. With the functional PC-PK1 a third barrier is found only in 226 ,228 ,230Th . Single-nucleon levels around the Fermi surface are analyzed in 226Th, and it is found that the formation of the third minimum is mainly due to the Z =90 proton energy gap at β20≈1.5 and β30≈0.7 . Conclusions: The possible occurrence of a third barrier on the PES's of actinide nuclei depends on the effective interaction used in multidimensional CDFT calculations. More pronounced minima are predicted by the DD-ME2 functional, as compared to the functional PC-PK1. The depth of the third well in Th isotopes decreases

  11. Mean field limit for bosons with compact kernels interactions by Wigner measures transportation

    SciTech Connect

    Liard, Quentin Pawilowski, Boris

    2014-09-15

    We consider a class of many-body Hamiltonians composed of a free (kinetic) part and a multi-particle (potential) interaction with a compactness assumption on the latter part. We investigate the mean field limit of such quantum systems following the Wigner measures approach. We prove in particular the propagation of these measures along the flow of a nonlinear (Hartree) field equation. This enhances and complements some previous results of the same type shown in Z. Ammari and F. Nier and Fröhlich et al. [“Mean field limit for bosons and propagation of Wigner measures,” J. Math. Phys. 50(4), 042107 (2009); Z. Ammari and F. Nier and Fröhlich et al., “Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states,” J. Math. Pures Appl. 95(6), 585–626 (2011); Z. Ammari and F. Nier and Fröhlich et al., “Mean-field- and classical limit of many-body Schrödinger dynamics for bosons,” Commun. Math. Phys. 271(3), 681–697 (2007)].

  12. Gluon condensate in a pion superfluid beyond the mean-field approximation

    SciTech Connect

    Jiang Yin; Zhuang Pengfei

    2011-03-15

    We study gluon condensate in a pion superfluid by calculating the equation of state of the system in the Nambu-Jona-Lasinio model. While in mean-field approximation the growing pion condensate leads to an increasing gluon condensate, meson fluctuations reduce the gluon condensate, and the broken scalar symmetry can be smoothly restored at finite isospin density.

  13. A simplified BBGKY hierarchy for correlated fermions from a stochastic mean-field approach

    NASA Astrophysics Data System (ADS)

    Lacroix, Denis; Tanimura, Yusuke; Ayik, Sakir; Yilmaz, Bulent

    2016-04-01

    The stochastic mean-field (SMF) approach allows to treat correlations beyond mean-field using a set of independent mean-field trajectories with appropriate choice of fluctuating initial conditions. We show here that this approach is equivalent to a simplified version of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy between one-, two-, ..., N -body degrees of freedom. In this simplified version, one-body degrees of freedom are coupled to fluctuations to all orders while retaining only specific terms of the general BBGKY hierarchy. The use of the simplified BBGKY is illustrated with the Lipkin-Meshkov-Glick (LMG) model. We show that a truncated version of this hierarchy can be useful, as an alternative to the SMF, especially in the weak coupling regime to get physical insight in the effect beyond mean-field. In particular, it leads to approximate analytical expressions for the quantum fluctuations both in the weak and strong coupling regime. In the strong coupling regime, it can only be used for short time evolution. In that case, it gives information on the evolution time-scale close to a saddle point associated to a quantum phase-transition. For long time evolution and strong coupling, we observed that the simplified BBGKY hierarchy cannot be truncated and only the full SMF with initial sampling leads to reasonable results.

  14. Mean-field models for heterogeneous networks of two-dimensional integrate and fire neurons

    PubMed Central

    Nicola, Wilten; Campbell, Sue Ann

    2013-01-01

    We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential and quartic integrate and fire models. The heterogeneity in the parameters leads to different moment closure assumptions that can be made in the derivation of the mean-field model from the population density equation for the large network. Three different moment closure assumptions lead to three different mean-field systems. These systems can be used for distinct purposes such as bifurcation analysis of the large networks, prediction of steady state firing rate distributions, parameter estimation for actual neurons and faster exploration of the parameter space. We use the mean-field systems to analyze adaptation induced bursting under realistic sources of heterogeneity in multiple parameters. Our analysis demonstrates that the presence of heterogeneity causes the Hopf bifurcation associated with the emergence of bursting to change from sub-critical to super-critical. This is confirmed with numerical simulations of the full network for biologically reasonable parameter values. This change decreases the plausibility of adaptation being the cause of bursting in hippocampal area CA3, an area with a sizable population of heavily coupled, strongly adapting neurons. PMID:24416013

  15. MAGNETOHYDRODYNAMIC SIMULATION-DRIVEN KINEMATIC MEAN FIELD MODEL OF THE SOLAR CYCLE

    SciTech Connect

    Simard, Corinne; Charbonneau, Paul; Bouchat, Amelie E-mail: paulchar@astro.umontreal.ca

    2013-05-01

    We construct a series of kinematic axisymmetric mean-field dynamo models operating in the {alpha}{Omega}, {alpha}{sup 2}{Omega} and {alpha}{sup 2} regimes, all using the full {alpha}-tensor extracted from a global magnetohydrodynamical simulation of solar convection producing large-scale magnetic fields undergoing solar-like cyclic polarity reversals. We also include an internal differential rotation profile produced in a purely hydrodynamical parent simulation of solar convection, and a simple meridional flow profile described by a single cell per meridional quadrant. An {alpha}{sup 2}{Omega} mean-field model, presumably closest to the mode of dynamo action characterizing the MHD simulation, produces a spatiotemporal evolution of magnetic fields that share some striking similarities with the zonally-averaged toroidal component extracted from the simulation. Comparison with {alpha}{sup 2} and {alpha}{Omega} mean-field models operating in the same parameter regimes indicates that much of the complexity observed in the spatiotemporal evolution of the large-scale magnetic field in the simulation can be traced to the turbulent electromotive force. Oscillating {alpha}{sup 2} solutions are readily produced, and show some similarities with the observed solar cycle, including a deep-seated toroidal component concentrated at low latitudes and migrating equatorward in the course of the solar cycle. Various numerical experiments performed using the mean-field models reveal that turbulent pumping plays an important role in setting the global characteristics of the magnetic cycles.

  16. Self-consistent chaos in a mean-field Hamiltonian model of fluids and plasmas

    NASA Astrophysics Data System (ADS)

    del-Castillo-Negrete, D.; Firpo, Marie-Christine

    2002-11-01

    We present a mean-field Hamiltonian model that describes the collective dynamics of marginally stable fluids and plasmas. In plasmas, the model describes the self-consistent evolution of electron holes and clumps in phase space. In fluids, the model describes the dynamics of vortices with negative and positive circulation in shear flows. The mean-field nature of the system makes it a tractable model to study the dynamics of large degrees-of-freedom, coupled Hamiltonian systems. Here we focus in the role of self-consistent chaos in the formation and destruction of phase space coherent structures. Numerical simulations in the finite N and in the Narrow kinetic limit (where N is the number of particles) show the existence of coherent, rotating dipole states. We approximate the dipole as two macroparticles, and show that the N = 2 limit has a family of rotating integrable solutions described by a one degree-of-freedom nontwist Hamiltonian. The coherence of the dipole is explained in terms of a parametric resonance between the rotation frequency of the macroparticles and the oscillation frequency of the self-consistent mean field. For a class of initial conditions, the mean field exhibits a self-consistent, elliptic-hyperbolic bifurcation that leads to the destruction of the dipole and violent mixing of the phase space.

  17. Magnetohydrodynamic Simulation-driven Kinematic Mean Field Model of the Solar Cycle

    NASA Astrophysics Data System (ADS)

    Simard, Corinne; Charbonneau, Paul; Bouchat, Amélie

    2013-05-01

    We construct a series of kinematic axisymmetric mean-field dynamo models operating in the αΩ, α2Ω and α2 regimes, all using the full α-tensor extracted from a global magnetohydrodynamical simulation of solar convection producing large-scale magnetic fields undergoing solar-like cyclic polarity reversals. We also include an internal differential rotation profile produced in a purely hydrodynamical parent simulation of solar convection, and a simple meridional flow profile described by a single cell per meridional quadrant. An α2Ω mean-field model, presumably closest to the mode of dynamo action characterizing the MHD simulation, produces a spatiotemporal evolution of magnetic fields that share some striking similarities with the zonally-averaged toroidal component extracted from the simulation. Comparison with α2 and αΩ mean-field models operating in the same parameter regimes indicates that much of the complexity observed in the spatiotemporal evolution of the large-scale magnetic field in the simulation can be traced to the turbulent electromotive force. Oscillating α2 solutions are readily produced, and show some similarities with the observed solar cycle, including a deep-seated toroidal component concentrated at low latitudes and migrating equatorward in the course of the solar cycle. Various numerical experiments performed using the mean-field models reveal that turbulent pumping plays an important role in setting the global characteristics of the magnetic cycles.

  18. a Mean-Field Version of the Ssb Model for X-Chromosome Inactivation

    NASA Astrophysics Data System (ADS)

    Gaeta, Giuseppe

    Nicodemi and Prisco recently proposed a model for X-chromosome inactivation in mammals, explaining this phenomenon in terms of a spontaneous symmetry-breaking mechanism [{\\it Phys. Rev. Lett.} 99 (2007), 108104]. Here we provide a mean-field version of their model.

  19. A Note on the Guerra and Talagrand Theorems for Mean Field Spin Glasses: The Simple Case of Spherical Models

    NASA Astrophysics Data System (ADS)

    Franz, Silvio; Tria, Francesca

    2006-01-01

    The aim of this paper is to discuss the main ideas of the Talagrand proof of the Parisi Ansatz for the free-energy of Mean Field Spin Glasses with a physicist's approach. We consider the case of the spherical p-spin model, which has the following advantages: (1) the Parisi Ansatz takes the simple "one step replica symmetry breaking form," (2) the replica free-energy as a function of the order parameters is simple enough to allow for numerical maximization with arbitrary precision. We present the essential ideas of the proof, we stress its connections with the theory of effective potentials for glassy systems, and we reduce the technically more difficult part of the Talagrand's analysis to an explicit evaluation of the solution of a variational problem.

  20. Electronic and magnetic properties of TbNi4Si: Ab initio calculations, mean field approximation and Monte Carlo simulation

    NASA Astrophysics Data System (ADS)

    Bensadiq, A.; Zaari, H.; Benyoussef, A.; El Kenz, A.

    2016-09-01

    Using the density functional theory, the electronic structure; density of states, band structure and exchange couplings of Tb Ni4 Si compound have been investigated. Magnetic and magnetocaloric properties of this material have been studied using Monte Carlo Simulation (MCS) and Mean Field Approximation (MFA) within a three dimensional Ising model. We calculated the isothermal magnetic entropy change, adiabatic temperature change and relative cooling power (RCP) for different external magnetic field and temperature. The highest obtained isothermal magnetic entropy change is of -14.52 J kg-1 K-1 for a magnetic field of H=4 T. The adiabatic temperature reaches a maximum value equal to 3.7 K and the RCP maximum value is found to be 125.12 J kg-1 for a field magnetic of 14 T.

  1. Computer program for the relativistic mean field description of the ground state properties of even-even axially deformed nuclei

    NASA Astrophysics Data System (ADS)

    Ring, P.; Gambhir, Y. K.; Lalazissis, G. A.

    1997-09-01

    We present a Fortran program for the calculation of the ground state properties of axially deformed even-even nuclei in the framework of Relativistic Mean Field Theory (RMF). In this approach a set of coupled partial differentials has to be solved self-consistently: the Dirac equation for the nucleons moving in self-consistent fields and the Klein-Gordon equations for the meson fields and the electromagnetic field, whose sources are scalar and vector densities determined of the nucleons. For this purpose the Dirac spinors as well as the meson fields are expanded in terms of anisotropic oscillator wave functions in cylindrical coordinates. This requires a matrix diagonalization for the solution of the Dirac equations and the solution of an inhomogeneous matrix equation for the meson fields. For the determination of the Coulomb field the Greens function method is used.

  2. Avalanche-size distributions in mean-field plastic yielding models.

    PubMed

    Jagla, E A

    2015-10-01

    We discuss the size distribution N(S) of avalanches occurring at the yielding transition of mean-field (i.e., Hebraud-Lequeux) models of amorphous solids. The size distribution follows a power law dependence of the form N(S)∼S(-τ). However (contrary to what is found in its depinning counterpart), the value of τ depends on details of the dynamic protocol used. For random triggering of avalanches we recover the τ=3/2 exponent typical of mean-field models, which, in particular, is valid for the depinning case. However, for the physically relevant case of external loading through a quasistatic increase of applied strain, a smaller exponent (close to 1) is obtained. This result is rationalized by mapping the problem to an effective random walk in the presence of a moving absorbing boundary. PMID:26565196

  3. Mean-field regime of trapped dipolar Bose-Einstein condensates in one and two dimensions

    NASA Astrophysics Data System (ADS)

    Cai, Yongyong; Rosenkranz, Matthias; Lei, Zhen; Bao, Weizhu

    2010-10-01

    We derive rigorous one- and two-dimensional mean-field equations for cigar- and pancake-shaped dipolar Bose-Einstein condensates with arbitrary polarization angle. We show how the dipolar interaction modifies the contact interaction of the strongly confined atoms. In addition, our equations introduce a nonlocal potential, which is anisotropic for pancake-shaped condensates. We propose to observe this anisotropy via measurement of the condensate aspect ratio. We also derive analytically approximate density profiles from our equations. Both the numerical solutions of our reduced mean-field equations and the analytical density profiles agree well with numerical solutions of the full Gross-Pitaevskii equation while being more efficient to compute.

  4. Mean-Field Dynamics and Fisher Information in Matter Wave Interferometry.

    PubMed

    Haine, Simon A

    2016-06-10

    There has been considerable recent interest in the mean-field dynamics of various atom-interferometry schemes designed for precision sensing. In the field of quantum metrology, the standard tools for evaluating metrological sensitivity are the classical and quantum Fisher information. In this Letter, we show how these tools can be adapted to evaluate the sensitivity when the behavior is dominated by mean-field dynamics. As an example, we compare the behavior of four recent theoretical proposals for gyroscopes based on matter-wave interference in toroidally trapped geometries. We show that while the quantum Fisher information increases at different rates for the various schemes considered, in all cases it is consistent with the well-known Sagnac phase shift after the matter waves have traversed a closed path. However, we argue that the relevant metric for quantifying interferometric sensitivity is the classical Fisher information, which can vary considerably between the schemes. PMID:27341216

  5. Mean-Field Dynamics and Fisher Information in Matter Wave Interferometry

    NASA Astrophysics Data System (ADS)

    Haine, Simon A.

    2016-06-01

    There has been considerable recent interest in the mean-field dynamics of various atom-interferometry schemes designed for precision sensing. In the field of quantum metrology, the standard tools for evaluating metrological sensitivity are the classical and quantum Fisher information. In this Letter, we show how these tools can be adapted to evaluate the sensitivity when the behavior is dominated by mean-field dynamics. As an example, we compare the behavior of four recent theoretical proposals for gyroscopes based on matter-wave interference in toroidally trapped geometries. We show that while the quantum Fisher information increases at different rates for the various schemes considered, in all cases it is consistent with the well-known Sagnac phase shift after the matter waves have traversed a closed path. However, we argue that the relevant metric for quantifying interferometric sensitivity is the classical Fisher information, which can vary considerably between the schemes.

  6. Neutron-skin thickness of finite nuclei in relativistic mean-field models with chiral limits

    SciTech Connect

    Jiang Weizhou; Li Baoan; Chen Liewen

    2007-11-15

    We study several structure properties of finite nuclei using relativistic mean-field Lagrangians constructed according to the Brown-Rho scaling due to the chiral symmetry restoration at high densities. The models are consistent with current experimental constraints for the equations of state of symmetric matter at both normal and supranormal densities and of asymmetric matter at subsaturation densities. It is shown that these models can successfully describe the binding energies and charge radii of finite nuclei. Compared to calculations with usual relativistic mean-field models, these models give a reduced thickness of neutron skin in {sup 208}Pb between 0.17 fm and 0.21 fm. The reduction of the predicted neutron skin thickness is found to be due to not only the softening of the symmetry energy but also the scaling property of {rho} meson required by the partial restoration of chiral symmetry.

  7. Core-halo quasi-stationary states in the Hamiltonian mean-field model

    NASA Astrophysics Data System (ADS)

    Konishi, Eiji

    2016-04-01

    A characteristic feature of long-range interacting systems is that they become trapped in a non-equilibrium and long-lived quasi-stationary state (QSS) during the early stages of their development. We present a comprehensive review of recent studies of the core-halo structure of QSSs, in the Hamiltonian mean-field model (HMF), which is a mean-field model of mutually coupled ferromagnetic XY spins located at a point, obtained by starting from various unsteady rectangular water-bag type initial phase-space distributions. The main result exposed in this review is that the core-halo structure can be described by the superposition of two independent Lynden-Bell distributions. We discuss the completeness of collisionless relaxation of this double Lynden-Bell distribution by using both of Lynden-Bell entropy and double Lynden-Bell entropy for the systems at low energies per particle.

  8. Statistical physics approach to dendritic computation: The excitable-wave mean-field approximation

    NASA Astrophysics Data System (ADS)

    Gollo, Leonardo L.; Kinouchi, Osame; Copelli, Mauro

    2012-01-01

    We analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly predict a nonequilibrium phase transition which is not allowed in the model. We propose an excitable-wave mean-field approximation which shows good agreement with previously published simulation results [Gollo , PLoS Comput. Biol.NERNET1553-734X10.1371/journal.pcbi.1000402 5, e1000402 (2009)] and accounts for finite-size effects. We also discuss the relevance of our results to experiments in neuroscience, emphasizing the role of active dendrites in the enhancement of dynamic range and in gain control modulation.

  9. Real-time estimation of mean field bias in radar rainfall data

    NASA Astrophysics Data System (ADS)

    Seo, D.-J.; Breidenbach, J. P.; Johnson, E. R.

    1999-10-01

    To reduce systematic errors in radar rainfall data used for operational hydrologic forecasting, the precipitation estimation stream in the National Weather Service (NWS) uses procedures that estimate mean field bias in real time. Being a multiplicative correction over a very large area, bias adjustment has a huge impact, particularly on volumetric estimation of rainwater, and hence performance of the procedure is extremely important to quantitative hydrologic forecasting using radar rainfall data. In this paper, we describe a new procedure for real-time estimation of mean field bias in WSR-88D (Weather Surveillance Radar—1988 Doppler version) rainfall products. Based largely on operational experience of the existing procedures in NWS, the proposed procedure is intended to be unbiased, parsimonious, and intuitive. To evaluate the procedure, true validation is performed using hourly rain gage and WSR-88D rainfall data from Tulsa and Twin Lakes, Oklahoma.

  10. Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis.

    PubMed

    Szabó-Solticzky, András; Berthouze, Luc; Kiss, Istvan Z; Simon, Péter L

    2016-04-01

    An adaptive network model using SIS epidemic propagation with link-type-dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out, showing that three typical behaviours may occur; namely, oscillations can be observed besides disease-free or endemic steady states. The oscillatory behaviour in the stochastic simulations is studied using Fourier analysis, as well as through analysing the exact master equations of the stochastic model. By going beyond simply comparing simulation results to mean-field models, our approach yields deeper insights into the observed phenomena and help better understand and map out the limitations of mean-field models. PMID:26063525

  11. Solving the eigenvalue problem of the nuclear Yukawa-folded mean-field Hamiltonian

    NASA Astrophysics Data System (ADS)

    Dobrowolski, A.; Pomorski, K.; Bartel, J.

    2016-02-01

    The nuclear Hamiltonian with a Yukawa-folded mean-field potential is diagonalized within the basis of a deformed harmonic-oscillator in Cartesian coordinates. The nuclear shape is characterized by the equivalent sharp surface described either by the well known Funny-Hills or the Trentalange-Koonin-Sierk parametrizations. They are both able to describe a very vast variety of nuclear deformations, including necked-in shapes, left-right asymmetry and non-axiality. The only imposed limitation on the nuclear shape is the z-signature symmetry, which corresponds to a symmetry of the shape with respect to a rotation by an angle π around the z-axis. On output, the computer code produces for a given nucleus with mass number A and charge number Z the energy eigenvalues and eigenfunctions of the mean-field Hamiltonian at chosen deformation.

  12. Toward relativistic mean-field description of Nbar-nucleus reactions

    NASA Astrophysics Data System (ADS)

    Gaitanos, T.; Kaskulov, M.

    2015-08-01

    In this work we study the antinucleon-nucleus optical potential in the framework of the non-linear derivative (NLD) model with momentum dependent mean-fields. We apply the NLD model to interaction of antinucleons (Nbar) in nuclear matter and, in particular, to antiproton scattering on nuclei. In nuclear matter a strong suppression of the Nbar-optical potential at rest and at high kinetic energies is found and caused by the momentum dependence of relativistic mean-fields. The NLD results are consistent with known empirical Nbar-nucleus observations and agree well with antiproton-nucleus scattering data. This makes the NLD approach compatible with both, nucleon and antinucleon Dirac phenomenologies. Furthermore, in nuclear matter an effective mass splitting between nucleons and antinucleons is predicted.

  13. The ground states of Perovskite nickelates: A dynamical mean field approach

    NASA Astrophysics Data System (ADS)

    Misra, D.; Taraphder, A.

    2014-04-01

    The Perovskite Nickelates (RNiO3,R=Rare-earth) exhibit a strong connection between their structural, transport and magnetic properties. All the members of Nickelate series have orthorhombic structure except LaNiO3 which has a rhombohedral symmetry. While the ground states of most of the Nickelates are antiferromagnetic insulators, and they undergo a sharp, temperature driven metal-Insulator transition, LaNiO3 is a paramagnetic metal irrespective of the temperature and does not undergo any metal-insulator transition. Whether the AFM insulating ground state of Nickelates (R≠La) is due to charge or orbital ordering or both, is a matter of current dispute. Here we give a theoretical account of the metallic property of LaNiO3 and insulating ground states of other Nickelates, using LCAO and static mean field calculation, followed by a dynamical mean field analysis.

  14. Synchronization and Spin-Flop Transitions for a Mean-Field XY Model in Random Field

    NASA Astrophysics Data System (ADS)

    Collet, Francesca; Ruszel, Wioletta

    2016-08-01

    We characterize the phase space for the infinite volume limit of a ferromagnetic mean-field XY model in a random field pointing in one direction with two symmetric values. We determine the stationary solutions and detect possible phase transitions in the interaction strength for fixed random field intensity. We show that at low temperature magnetic ordering appears perpendicularly to the field. The latter situation corresponds to a spin-flop transition.

  15. Cooperative Localization for Mobile Networks: A Distributed Belief Propagation–Mean Field Message Passing Algorithm

    NASA Astrophysics Data System (ADS)

    Cakmak, Burak; Urup, Daniel N.; Meyer, Florian; Pedersen, Troels; Fleury, Bernard H.; Hlawatsch, Franz

    2016-06-01

    We propose a hybrid message passing method for distributed cooperative localization and tracking of mobile agents. Belief propagation and mean field message passing are employed for, respectively, the motion-related and measurement-related part of the factor graph. Using a Gaussian belief approximation, only three real values per message passing iteration have to be broadcast to neighboring agents. Despite these very low communication requirements, the estimation accuracy can be comparable to that of particle-based belief propagation.

  16. Inverse magnetic catalysis in Nambu-Jona-Lasinio model beyond mean field

    NASA Astrophysics Data System (ADS)

    Mao, Shijun

    2016-07-01

    We study inverse magnetic catalysis in the Nambu-Jona-Lasinio model beyond mean field approximation. The feed-down from mesons to quarks is embedded in an effective coupling constant at finite temperature and magnetic field. While the magnetic catalysis is still the dominant effect at low temperature, the meson dressed quark mass drops down with increasing magnetic field at high temperature due to the dimension reduction of the Goldstone mode in the Pauli-Villars regularization scheme.

  17. Multiple chiral doublet candidate nucleus {sup 105}Rh in a relativistic mean-field approach

    SciTech Connect

    Li Jian; Zhang, S. Q.; Meng, J.

    2011-03-15

    Following the reports of two pairs of chiral doublet bands observed in {sup 105}Rh, the adiabatic and configuration-fixed constrained triaxial relativistic mean-field calculations are performed to investigate their triaxial deformations with the corresponding configuration and the possible multiple chiral doublet (M{chi}D) phenomenon. The existence of the M{chi}D phenomenon in {sup 105}Rh is highly expected.

  18. {alpha}-decay calculations of heavy and superheavy nuclei using effective mean-field potentials

    SciTech Connect

    Pei, J. C.; Lin, Z. J.; Xu, F. R.; Zhao, E. G.

    2007-10-15

    Using an effective potential that is based on the Skyrme-Hartree-Fock mean-field model, systematic {alpha}-decay properties of even-even heavy and superheavy nuclei have been investigated. Calculations do not raise any adjustable parameter. The obtained {alpha}-decay half-lives agree reasonably well with experimental data. The characteristics of the effective potential and the deformation effect on the {alpha} decay are discussed.

  19. A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type

    SciTech Connect

    Hosking, John Joseph Absalom

    2012-12-15

    We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966-979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197-216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.

  20. Nonperturbative heterogeneous mean-field approach to epidemic spreading in complex networks

    NASA Astrophysics Data System (ADS)

    Gómez, Sergio; Gómez-Gardeñes, Jesús; Moreno, Yamir; Arenas, Alex

    2011-09-01

    Since roughly a decade ago, network science has focused among others on the problem of how the spreading of diseases depends on structural patterns. Here, we contribute to further advance our understanding of epidemic spreading processes by proposing a nonperturbative formulation of the heterogeneous mean-field approach that has been commonly used in the physics literature to deal with this kind of spreading phenomena. The nonperturbative equations we propose have no assumption about the proximity of the system to the epidemic threshold, nor any linear approximation of the dynamics. In particular, we first develop a probabilistic description at the node level of the epidemic propagation for the so-called susceptible-infected-susceptible family of models, and after we derive the corresponding heterogeneous mean-field approach. We propose to use the full extension of the approach instead of pruning the expansion to first order, which leads to a nonperturbative formulation that can be solved by fixed-point iteration, and used with reliability far away from the epidemic threshold to assess the prevalence of the epidemics. Our results are in close agreement with Monte Carlo simulations, thus enhancing the predictive power of the classical heterogeneous mean-field approach, while providing a more effective framework in terms of computational time.

  1. Nonperturbative heterogeneous mean-field approach to epidemic spreading in complex networks.

    PubMed

    Gómez, Sergio; Gómez-Gardeñes, Jesús; Moreno, Yamir; Arenas, Alex

    2011-09-01

    Since roughly a decade ago, network science has focused among others on the problem of how the spreading of diseases depends on structural patterns. Here, we contribute to further advance our understanding of epidemic spreading processes by proposing a nonperturbative formulation of the heterogeneous mean-field approach that has been commonly used in the physics literature to deal with this kind of spreading phenomena. The nonperturbative equations we propose have no assumption about the proximity of the system to the epidemic threshold, nor any linear approximation of the dynamics. In particular, we first develop a probabilistic description at the node level of the epidemic propagation for the so-called susceptible-infected-susceptible family of models, and after we derive the corresponding heterogeneous mean-field approach. We propose to use the full extension of the approach instead of pruning the expansion to first order, which leads to a nonperturbative formulation that can be solved by fixed-point iteration, and used with reliability far away from the epidemic threshold to assess the prevalence of the epidemics. Our results are in close agreement with Monte Carlo simulations, thus enhancing the predictive power of the classical heterogeneous mean-field approach, while providing a more effective framework in terms of computational time. PMID:22060454

  2. TURBULENT CONVECTION IN STELLAR INTERIORS. III. MEAN-FIELD ANALYSIS AND STRATIFICATION EFFECTS

    SciTech Connect

    Viallet, Maxime; Meakin, Casey; Mocak, Miroslav; Arnett, David

    2013-05-20

    We present three-dimensional implicit large eddy simulations of the turbulent convection in the envelope of a 5 M{sub Sun} red giant star and in the oxygen-burning shell of a 23 M{sub Sun} supernova progenitor. The numerical models are analyzed in the framework of one-dimensional Reynolds-Averaged Navier-Stokes equations. The effects of pressure fluctuations are more important in the red giant model, owing to larger stratification of the convective zone. We show how this impacts different terms in the mean-field equations. We clarify the driving sources of kinetic energy, and show that the rate of turbulent dissipation is comparable to the convective luminosity. Although our flows have low Mach numbers and are nearly adiabatic, our analysis is general and can be applied to photospheric convection as well. The robustness of our analysis of turbulent convection is supported by the insensitivity of the mean-field balances to linear mesh resolution. We find robust results for the turbulent convection zone and the stable layers in the oxygen-burning shell model, and robust results everywhere in the red giant model, but the mean fields are not well converged in the narrow boundary regions (which contain steep gradients) in the oxygen-burning shell model. This last result illustrates the importance of unresolved physics at the convective boundary, which governs the mixing there.

  3. Construction of traveling clusters in the Hamiltonian mean-field model by nonequilibrium statistical mechanics and Bernstein-Greene-Kruskal waves.

    PubMed

    Yamaguchi, Yoshiyuki Y

    2011-07-01

    Traveling clusters are ubiquitously observed in the Hamiltonian mean-field model for a wide class of initial states, which are not predicted to become spatially inhomogeneous states by nonequilibrium statistical mechanics and by nonlinear Landau damping. To predict such a cluster state from a given initial state, we combine nonequilibrium statistical mechanics and a construction method of Bernstein-Greene-Kruskal (BGK) waves with the aid of phenomenological assumptions. The phenomenological theory is partially successful, and the theoretically constructed cluster states are in good agreement with N-body simulations. Robustness of the theory is also discussed for unsuccessful initial states. PMID:21867277

  4. Antiferromagnetic spintronics of Mn2Au: An experiment, first principle, mean field and series expansions calculations study

    NASA Astrophysics Data System (ADS)

    Masrour, R.; Hlil, E. K.; Hamedoun, M.; Benyoussef, A.; Boutahar, A.; Lassri, H.

    2015-11-01

    The self-consistent ab initio calculations, based on DFT (Density Functional Theory) approach and using FLAPW (Full potential Linear Augmented Plane Wave) method, are performed to investigate both electronic and magnetic properties of the Mn2Au. Polarized spin and spin-orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Mn plans. Magnetic moment considered to lie along (110) axes are computed. Obtained data from ab initio calculations are used as input for the high temperature series expansions (HTSEs) calculations to compute other magnetic parameters. The exchange interactions between the magnetic atoms Mn-Mn in Mn2Au are given by using the experiment results and the mean field theory. The High Temperature Series Expansions (HTSEs) of the magnetic susceptibility with the magnetic moments in Mn2Au (mMn) is given up to tenth order series in, 1/kBT. The Néel temperature TN is obtained by HTSEs combined with the Padé approximant method. The critical exponent associated with the magnetic susceptibility is deduced as well.

  5. Hot and dense hadronic matter in an effective mean-field approach

    SciTech Connect

    Lavagno, A.

    2010-04-15

    We investigate the equation of state of hadronic matter at finite values of baryon density and temperature reachable in high-energy heavy-ion collisions. The analysis is performed by requiring the Gibbs conditions on the global conservation of baryon number, electric charge fraction, and zero net strangeness. We consider an effective relativistic mean-field model with the inclusion of DELTA isobars, hyperons, and the lightest pseudoscalar and vector meson degrees of freedom. In this context, we study the influence of the DELTA-isobar degrees of freedom in the hadronic equation of state and, in connection, the behavior of different particle-antiparticle ratios and strangeness production.

  6. Critical temperature for {alpha}-particle condensation within a momentum-projected mean-field approach

    SciTech Connect

    Sogo, T.; Roepke, G.; Lazauskas, R.

    2009-05-15

    {alpha}-particle (quartet) condensation in homogeneous spin-isospin symmetric nuclear matter is investigated. The usual Thouless criterion for the critical temperature is extended to the quartet case. The in-medium four-body problem is strongly simplified by the use of a momentum-projected mean-field ansatz for the quartet. The self-consistent single-particle wave functions are shown and discussed for various values of the density at the critical temperature. Excellent agreement of the critical temperature with a numerical solution of the Faddeev-Yakubovsky equation is obtained.

  7. Density Functional Plus Dynamical Mean Field Study of Spin Crossover Molecule

    NASA Astrophysics Data System (ADS)

    Chen, Jia; Millis, Andrew; Marianetti, Chris

    2015-03-01

    We report a density functional plus dynamical mean field study of spin crossover molecule Fe(phen)2(NCS)2. The temperature dependent magnetic susceptibility, Fe-d spectral and total energy were calculated and compared with experimental magnetization, metal L-edge x-ray adsorption spectroscopy. The importance of dynamic effect on energetics is demonstrated by comparison with density functional plus U method, and the role of full charge self-consistency is identified. Moreover, the local spin density plus U (LSDA+U) method with exchange interaction explicitly included is shown to dramatically overemphasize magnetic interaction.

  8. Asymmetric neutrino production in magnetized proto-neutron stars in fully relativistic mean-field approach

    SciTech Connect

    Maruyama, Tomoyuki; Kajino, Toshitaka; Hidaka, Jun; Takiwaki, Tomoya; Yasutake, Nobutoshi; Kuroda, Takami; Cheoun, Myung-Ki; Ryu, Chung-Yeol; Mathews, Grant J.

    2014-05-02

    We calculate the neutrino production cross-section in the proto-neutron-star matter under a strong magnetic field in the relativistic mean-field approach. We introduce a new parameter-set which can reproduce the 1.96 solar mass neutron star. We find that the production process increases emitted neutrinos along the direction parallel to the magnetic field and decrease those along its opposite direction. It means that resultant asymmetry due to the neutrino absorption and scattering process in the magnetic field becomes larger by the addition of the neutrino production process.

  9. Mean-field equations, bifurcation map and route to chaos in discrete time neural networks

    NASA Astrophysics Data System (ADS)

    Cessac, B.; Doyon, B.; Quoy, M.; Samuelides, M.

    1994-07-01

    We investigate the dynamical behaviour of neural networks with asymmetric synaptic weights, in the presence of random thresholds. We inspect low gain dynamics before using mean-field equations to study the bifurcations of the fixed points and the change of regime that occurs when varying control parameters. We infer different areas with various regimes summarized by a bifurcation map in the parameter space. We numerically show the occurence of chaos that arises generically by a quasi-periodicity route. We then discuss some features of our system in relation with biological observations such as low firing rates and refractory periods.

  10. Lagrangian approach to the semirelativistic electron dynamics in the mean-field approximation

    NASA Astrophysics Data System (ADS)

    Dixit, Anant; Hinschberger, Yannick; Zamanian, Jens; Manfredi, Giovanni; Hervieux, Paul-Antoine

    2013-09-01

    We derive a mean-field model that is based on a two-component Pauli-like equation and incorporates quantum, spin, and relativistic effects up to second order in 1/c. Using a Lagrangian approach, we obtain the self-consistent charge and current densities that act as sources in the Maxwell equations. A physical interpretation is provided for the second-order corrections to the sources. The Maxwell equations are also expanded to the same order. The resulting self-consistent model constitutes a suitable semirelativistic approximation to the full Dirac-Maxwell equations.

  11. Study of shape transitions in N{approx}90 isotopes with beyond mean field calculations

    SciTech Connect

    Rodriguez, Tomas R.; Egido, J. L.

    2009-01-28

    We study the spherical to prolate-deformed shape transition in {sup 144-158}Sm and {sup 146-160}Gd isotopes with modern calculations beyond the mean field with the Gogny D1S force. We compare the results with the shape-phase transition predicted by the collective Hamiltonian model and with the experimental data. Our calculations do not support the existence of a first order phase transition in these isotopic chains in the viewpoint of the Bohr Hamiltonian neither the interpretation of the nuclei N = 90 as critical points.

  12. Mean-field microrheology of a very soft colloidal suspension: Inertia induces shear thickening.

    PubMed

    Démery, Vincent

    2015-06-01

    Colloidal suspensions have a rich rheology and can exhibit shear thinning as well as shear thickening. Numerical simulations recently suggested that shear-thickening may be attributed to the inertia of the colloids, besides the hydrodynamic interactions between them. Here, we consider the ideal limit of a dense bath of soft colloids following an underdamped Langevin dynamics. We use a mean-field equation for the colloidal density to get an analytical expression of the drag force felt by a probe pulled at constant velocity through the suspension. Our results show that inertia can indeed induce shear thickening by allowing density waves to propagate through the suspension. PMID:26172713

  13. Systematic study of Bh isotopes in a relativistic mean field formalism

    NASA Astrophysics Data System (ADS)

    Mehta, M. S.; Raj, B. K.; Patra, S. K.; Gupta, Raj K.

    2002-10-01

    The binding energy, charge radius, and quadrupole deformation parameter for the isotopic chain of the superheavy element bohrium (107Bh), from proton to neutron drip line, are calculated by using an axially deformed relativistic mean field model. The potential energy surfaces for some of the selected nuclei are plotted and the various possible shapes are investigated. The rms radii, density distributions, and two-neutron separation energies are also evaluated and the single-particle energies for some illustrative cases are analyzed to see the magic structures. Furthermore, the α-decay rates are calculated and compared with the available experimental data for the recently observed new isotopes 266,267Bh.

  14. Mean-field approximation for a limit order driven market model.

    PubMed

    Slanina, F

    2001-11-01

    A mean-field variant of the model of limit order driven market introduced recently by Maslov is formulated and solved. The agents do not have any strategies and the memory of the system is kept within the order book. We show that the evolution of the order book is governed by a matrix multiplicative process. The resulting stationary distribution of step-to-step price changes is calculated. It exhibits a power-law tail with exponent 2. We obtain also the price autocorrelation function, which agrees qualitatively with the experimentally observed negative autocorrelation for short times. PMID:11736043

  15. Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral

    NASA Astrophysics Data System (ADS)

    Tanizaki, Yuya; Nishimura, Hiromichi; Kashiwa, Kouji

    2015-05-01

    The fermion sign problem appearing in the mean-field approximation is considered, and the systematic computational scheme of the free energy is devised by using the Lefschetz-thimble method. We show that the Lefschetz-thimble method respects the reflection symmetry, which makes physical quantities manifestly real at any order of approximations using complex saddle points. The formula is demonstrated through the Airy integral as an example, and its application to the Polyakov-loop effective model of dense QCD is discussed in detail.

  16. Mean-field analysis of quantum annealing with XX-type terms

    NASA Astrophysics Data System (ADS)

    Nishimori, Hidetoshi

    I analyze the role of XX-type terms in quantum annealing for a few mean-field systems including the Ising ferromagnet and the Hopfield model, both with many-body interactions. The XX-type terms are shown to be effective to remove first-order quantum phase transitions, which exist in the conventional implementation of quantum annealing using only transverse fields. This means an exponential increase in efficiency, and is suggestive for the design of quantum annealers. I will discuss how and why this phenomenon emerges and what may happen on realistic finite-dimensional lattices.

  17. Collective aspects of microscopic mean-field evolution along the fission path

    NASA Astrophysics Data System (ADS)

    Tanimura, Yusuke; Lacroix, Denis; Scamps, Guillaume

    2016-01-01

    We propose a new method to extract the collective masses and momenta associated with a given set of collective coordinates, along a dynamical microscopic mean-field evolution. We apply our method to the symmetric fission of 258Fm nucleus, and analyze the dynamical evolution of the system in the collective space. We compare, between the dynamical and the adiabatic paths, the force acting on the quadrupole degree of freedom, which is closely related to the relative distance between fragments. It is shown that dynamical effects beyond the adiabatic limit are important for formation and scission of the neck between emitted fragments.

  18. Mean-field approximation for the Sznajd model in complex networks

    NASA Astrophysics Data System (ADS)

    Araújo, Maycon S.; Vannucchi, Fabio S.; Timpanaro, André M.; Prado, Carmen P. C.

    2015-02-01

    This paper studies the Sznajd model for opinion formation in a population connected through a general network. A master equation describing the time evolution of opinions is presented and solved in a mean-field approximation. Although quite simple, this approximation allows us to capture the most important features regarding the steady states of the model. When spontaneous opinion changes are included, a discontinuous transition from consensus to polarization can be found as the rate of spontaneous change is increased. In this case we show that a hybrid mean-field approach including interactions between second nearest neighbors is necessary to estimate correctly the critical point of the transition. The analytical prediction of the critical point is also compared with numerical simulations in a wide variety of networks, in particular Barabási-Albert networks, finding reasonable agreement despite the strong approximations involved. The same hybrid approach that made it possible to deal with second-order neighbors could just as well be adapted to treat other problems such as epidemic spreading or predator-prey systems.

  19. Mean Field Approximation for Biased Diffusion on Japanese Inter-Firm Trading Network

    PubMed Central

    Watanabe, Hayafumi

    2014-01-01

    By analysing the financial data of firms across Japan, a nonlinear power law with an exponent of 1.3 was observed between the number of business partners (i.e. the degree of the inter-firm trading network) and sales. In a previous study using numerical simulations, we found that this scaling can be explained by both the money-transport model, where a firm (i.e. customer) distributes money to its out-edges (suppliers) in proportion to the in-degree of destinations, and by the correlations among the Japanese inter-firm trading network. However, in this previous study, we could not specifically identify what types of structure properties (or correlations) of the network determine the 1.3 exponent. In the present study, we more clearly elucidate the relationship between this nonlinear scaling and the network structure by applying mean-field approximation of the diffusion in a complex network to this money-transport model. Using theoretical analysis, we obtained the mean-field solution of the model and found that, in the case of the Japanese firms, the scaling exponent of 1.3 can be determined from the power law of the average degree of the nearest neighbours of the network with an exponent of −0.7. PMID:24626149

  20. Cluster Mean-Field Approach to the Steady-State Phase Diagram of Dissipative Spin Systems

    NASA Astrophysics Data System (ADS)

    Jin, Jiasen; Biella, Alberto; Viyuela, Oscar; Mazza, Leonardo; Keeling, Jonathan; Fazio, Rosario; Rossini, Davide

    2016-07-01

    We show that short-range correlations have a dramatic impact on the steady-state phase diagram of quantum driven-dissipative systems. This effect, never observed in equilibrium, follows from the fact that ordering in the steady state is of dynamical origin, and is established only at very long times, whereas in thermodynamic equilibrium it arises from the properties of the (free) energy. To this end, by combining the cluster methods extensively used in equilibrium phase transitions to quantum trajectories and tensor-network techniques, we extend them to nonequilibrium phase transitions in dissipative many-body systems. We analyze in detail a model of spin-1 /2 on a lattice interacting through an X Y Z Hamiltonian, each of them coupled to an independent environment that induces incoherent spin flips. In the steady-state phase diagram derived from our cluster approach, the location of the phase boundaries and even its topology radically change, introducing reentrance of the paramagnetic phase as compared to the single-site mean field where correlations are neglected. Furthermore, a stability analysis of the cluster mean field indicates a susceptibility towards a possible incommensurate ordering, not present if short-range correlations are ignored.

  1. A mean-field thermodynamic description of the kinetics of overdriven interfaces

    NASA Astrophysics Data System (ADS)

    Haxhimali, Tomorr; Belof, Jonathan; Sadigh, Babak

    A key aspect of an accurate description of shock-induced structural phase transitions is the rigorous computation of the dynamics of the interfaces between coexisting phases. In the wake of the shock, the system will be exposed to strong gradient fields that give rise to overdriven interfaces during the induced phase transformation. In this work we take a mean-field approach using a time-dependent Ginzburg-Landau formalism to describe the dynamics of such overdriven interfaces. We make a connection of the mean-field result to a quasi-Langevin description, the Kardar-Parisi-Zhang (KPZ) equation, of the kinetics of the interface. Further, larger coarse-grained descriptions of the phase transition such as the Kolmogorov-Johnson-Mehl-Avrami (KJMA) model, which are commonly coupled to hydrodynamic equations that describe the evolution of the temperature and pressure during the shock propagation, ignore the details of the dynamics and structure of the interfacial regions. Overlaying the KPZ description of the interface evolution to these coarse-grained methods will result in physically more accurate multiscale models for shock propagation. We will present results from our efforts in this regard. This work is performed under the auspices of the U. S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

  2. Mean-field study of the role of lateral cracks in microtubule dynamics

    NASA Astrophysics Data System (ADS)

    Margolin, Gennady; Goodson, Holly V.; Alber, Mark S.

    2011-04-01

    A link between dimer-scale processes and microtubule (MT) dynamics at macroscale is studied by comparing simulations obtained using computational dimer-scale model with its mean-field approximation. The novelty of the mean-field model (MFM) is in its explicit representation of inter-protofilament cracks, as well as in the direct incorporation of the dimer-level kinetics. Due to inclusion of both longitudinal and lateral dimer interactions, the MFM is two dimensional, in contrast to previous theoretical models of MTs. It is the first analytical model that predicts and quantifies crucial features of MT dynamics such as (i) existence of a minimal soluble tubulin concentration needed for the polymerization (with concentration represented as a function of model parameters), (ii) existence of steady-state growth and shortening phases (given with their respective velocities), and (iii) existence of an unstable pause state near zero velocity. In addition, the size of the GTP cap of a growing MT is estimated. Theoretical predictions are shown to be in good agreement with the numerical simulations.

  3. Dynamical Aspects of Mean Field Plane Rotators and the Kuramoto Model

    NASA Astrophysics Data System (ADS)

    Bertini, Lorenzo; Giacomin, Giambattista; Pakdaman, Khashayar

    2010-02-01

    The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc. We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N oscillators, each driven by an independent Brownian motion with a constant drift, that is each oscillator has its own frequency, which, in general, changes from one oscillator to another (these frequencies are usually taken to be random and they may be viewed as a quenched disorder). The interactions between oscillators are of long range type (mean field). We review some results on the Kuramoto model from a statistical mechanics standpoint: we give in particular necessary and sufficient conditions for reversibility and we point out a formal analogy, in the N→∞ limit, with local mean field models with conservative dynamics (an analogy that is exploited to identify in particular a Lyapunov functional in the reversible set-up). We then focus on the reversible Kuramoto model with sinusoidal interactions in the N→∞ limit and analyze the stability of the non-trivial stationary profiles arising when the interaction parameter K is larger than its critical value K c . We provide an analysis of the linear operator describing the time evolution in a neighborhood of the synchronized profile: we exhibit a Hilbert space in which this operator has a self-adjoint extension and we establish, as our main result, a spectral gap inequality for every K> K c .

  4. Comparative study of nuclear masses in the relativistic mean-field model

    NASA Astrophysics Data System (ADS)

    Hua, XueMin; Heng, TaiHua; Niu, ZhongMing; Sun, BaoHua; Guo, JianYou

    2012-12-01

    With experimental masses updated from AME11, the predictive power of relativistic mean-field (RMF) mass model is carefully examined and compared with HFB-17, FRDM, WS*, and DZ28 mass models. In the relativistic mean-field model, the calculation with the PC-PK1 has improved significantly in describing masses compared to the TMA, especially for the neutron-deficient nuclei. The corresponding rms deviation with respect to the known masses falls to 1.4 MeV. Furthermore, it is found that the RMF mass model better describes the nuclei with large deformations. The rms deviation for nuclei with the absolute value of quadrupole deformation parameter greater than 0.25 falls to 0.93, crossing the 1 MeV accuracy threshold for the PC-PK1, which may indicate the new model is more suitable for those largely-deformed nuclei. In addition, the necessity of new high-precision experimental data to evaluate and develop the nuclear mass models is emphasized as well.

  5. Mean field approximation for biased diffusion on Japanese inter-firm trading network.

    PubMed

    Watanabe, Hayafumi

    2014-01-01

    By analysing the financial data of firms across Japan, a nonlinear power law with an exponent of 1.3 was observed between the number of business partners (i.e. the degree of the inter-firm trading network) and sales. In a previous study using numerical simulations, we found that this scaling can be explained by both the money-transport model, where a firm (i.e. customer) distributes money to its out-edges (suppliers) in proportion to the in-degree of destinations, and by the correlations among the Japanese inter-firm trading network. However, in this previous study, we could not specifically identify what types of structure properties (or correlations) of the network determine the 1.3 exponent. In the present study, we more clearly elucidate the relationship between this nonlinear scaling and the network structure by applying mean-field approximation of the diffusion in a complex network to this money-transport model. Using theoretical analysis, we obtained the mean-field solution of the model and found that, in the case of the Japanese firms, the scaling exponent of 1.3 can be determined from the power law of the average degree of the nearest neighbours of the network with an exponent of -0.7. PMID:24626149

  6. Modeling and computation of mean field equilibria in producers' game with emission permits trading

    NASA Astrophysics Data System (ADS)

    Zhang, Shuhua; Wang, Xinyu; Shanain, Aleksandr

    2016-08-01

    In this paper, we present a mean field game to model the production behaviors of a very large number of producers, whose carbon emissions are regulated by government. Especially, an emission permits trading scheme is considered in our model, in which each enterprise can trade its own permits flexibly. By means of the mean field equilibrium, we obtain a Hamilton-Jacobi-Bellman (HJB) equation coupled with a Kolmogorov equation, which are satisfied by the adjoint state and the density of producers (agents), respectively. Then, we propose a so-called fitted finite volume method to solve the HJB equation and the Kolmogorov equation. The efficiency and the usefulness of this method are illustrated by the numerical experiments. Under different conditions, the equilibrium states as well as the effects of the emission permits price are examined, which demonstrates that the emission permits trading scheme influences the producers' behaviors, that is, more populations would like to choose a lower rather than a higher emission level when the emission permits are expensive.

  7. Amplitude death and synchronized states in nonlinear time-delay systems coupled through mean-field diffusion

    NASA Astrophysics Data System (ADS)

    Banerjee, Tanmoy; Biswas, Debabrata

    2013-12-01

    We explore and experimentally demonstrate the phenomena of amplitude death (AD) and the corresponding transitions through synchronized states that lead to AD in coupled intrinsic time-delayed hyperchaotic oscillators interacting through mean-field diffusion. We identify a novel synchronization transition scenario leading to AD, namely transitions among AD, generalized anticipatory synchronization (GAS), complete synchronization (CS), and generalized lag synchronization (GLS). This transition is mediated by variation of the difference of intrinsic time-delays associated with the individual systems and has no analogue in non-delayed systems or coupled oscillators with coupling time-delay. We further show that, for equal intrinsic time-delays, increasing coupling strength results in a transition from the unsynchronized state to AD state via in-phase (complete) synchronized states. Using Krasovskii-Lyapunov theory, we derive the stability conditions that predict the parametric region of occurrence of GAS, GLS, and CS; also, using a linear stability analysis, we derive the condition of occurrence of AD. We use the error function of proper synchronization manifold and a modified form of the similarity function to provide the quantitative support to GLS and GAS. We demonstrate all the scenarios in an electronic circuit experiment; the experimental time-series, phase-plane plots, and generalized autocorrelation function computed from the experimental time series data are used to confirm the occurrence of all the phenomena in the coupled oscillators.

  8. Exact chiral spin liquids and mean-field perturbations of gamma matrix models on the ruby lattice

    NASA Astrophysics Data System (ADS)

    Whitsitt, Seth; Chua, Victor; Fiete, Gregory A.

    2012-11-01

    We theoretically studied an exactly solvable gamma matrix generalization of the Kitaev spin model on the ruby lattice, which is a honeycomb lattice with ‘expanded’ vertices and links. We find that this model displays an exceptionally rich phase diagram that includes (i) gapless phases with stable spin Fermi surfaces, (ii) gapless phases with low-energy Dirac cones and quadratic band touching points and (iii) gapped phases with finite Chern numbers possessing the values ±4,±3,±2 and ±1. The model is then generalized to include Ising-like interactions that break the exact solvability of the model in a controlled manner. When these terms are dominant, they lead to a trivial Ising ordered phase which is shown to be adiabatically connected to a large coupling limit of the exactly solvable phase. In the limit where these interactions are weak, we treat them within mean-field theory and present the resulting phase diagrams. We discuss the nature of the transitions between various phases. Our results show the richness of possible ground states in closely related magnetic systems.

  9. Core-level Photoemission Study for Cuprates with a Dynamical Mean-Field Approach Considering Realistic Crystal Structure

    NASA Astrophysics Data System (ADS)

    Hariki, Atsushi; Uozumi, Takayuki

    2013-03-01

    Recently, remarkable experimental progress reveals some characteristic spectral features in the 2p3/2main line of Cu 2p core-level X-ray photoemission spectra (XPS). The structures show strong material dependence and drastic changes for electron or hole doping. Van Veenendaal et al., pointed out that the main line shape is strongly affected by the so-called nonlocal screening which is accompanied by a formation of a Zhang-Rice singlet (ZRS) in the XPS final state. On the other hand, Taguchi et al., shows these features are reproduced by introducing an phenomenological extended impurity model. We consider that this topic on 2pXPS of cuprates still remain controversial. In this study, we propose another approach based on the dynamical mean field theory(DMFT) considering the realistic crystal structure. Many-particle effects including the ZRS is appropriately embedded in the hybridization function of a single impurity Anderson model through the DMFT self-consistent cycle. Our approach reproduces experimental results and shows that the Cu 2p3/2 main line is closely related with the quasi-particle structure near the Fermi energy.

  10. Spin-correlation functions in ultracold paired atomic-fermion systems: Sum rules, self-consistent approximations, and mean fields

    NASA Astrophysics Data System (ADS)

    Yu, Z.; Baym, G.

    2006-06-01

    The spin response functions measured in multicomponent fermion gases by means of rf transitions between hyperfine states are strongly constrained by the symmetry of the interatomic interactions. Such constraints are reflected in the spin f -sum rule that the response functions must obey. In particular, only if the effective interactions are not fully invariant in SU(2) spin space, are the response functions sensitive to mean field and pairing effects. We demonstrate, via a self-consistent calculation of the spin-spin correlation function within the framework of Hartree-Fock-BCS theory, how one can derive a correlation function explicitly obeying the f -sum rule. By contrast, simple one-loop approximations to the spin response functions do not satisfy the sum rule, except in special cases. As we show, the emergence of a second peak at higher frequency in the rf spectrum, as observed in a recent experiment in trapped Li6 , can be understood as the contribution from the paired fermions, with a shift of the peak from the normal particle response proportional to the square of the BCS pairing gap.

  11. A multiscale variational approach to the kinetics of viscous classical liquids: The coarse-grained mean field approximation

    SciTech Connect

    Sereda, Yuriy V.; Ortoleva, Peter J.

    2014-04-07

    A closed kinetic equation for the single-particle density of a viscous simple liquid is derived using a variational method for the Liouville equation and a coarse-grained mean-field (CGMF) ansatz. The CGMF ansatz is based on the notion that during the characteristic time of deformation a given particle interacts with many others so that it experiences an average interaction. A trial function for the N-particle probability density is constructed using a multiscale perturbation method and the CGMF ansatz is applied to it. The multiscale perturbation scheme is based on the ratio of the average nearest-neighbor atom distance to the total size of the assembly. A constraint on the initial condition is discovered which guarantees that the kinetic equation is mass-conserving and closed in the single-particle density. The kinetic equation has much of the character of the Vlasov equation except that true viscous, and not Landau, damping is accounted for. The theory captures condensation kinetics and takes much of the character of the Gross-Pitaevskii equation in the weak-gradient short-range force limit.

  12. Structural Properties of the Disordered Spherical and Other Mean Field Spin Models

    NASA Astrophysics Data System (ADS)

    Sanctis, Luca De

    2007-03-01

    We extend the approach of Aizenman, Sims and Starr for the SK-type models to their spherical versions. Such an extension has already been performed for diluted spin glasses. The factorization property of the optimal structures found by Guerra for the SK model, which holds for diluted models as well, is verified also in the case of spherical systems, with the due modifications. Hence we show that there are some common structural features in various mean field spin models. These similarities seem to be quite paradigmatic, and we summarize the various techniques typically used to prove the structural analogies and to tackle the computation of the free energy per spin in the thermodynamic limit.

  13. Modeling of coherent ultrafast magneto-optical experiments: Light-induced molecular mean-field model

    SciTech Connect

    Hinschberger, Y.; Hervieux, P.-A.

    2015-12-28

    We present calculations which aim to describe coherent ultrafast magneto-optical effects observed in time-resolved pump-probe experiments. Our approach is based on a nonlinear semi-classical Drude-Voigt model and is used to interpret experiments performed on nickel ferromagnetic thin film. Within this framework, a phenomenological light-induced coherent molecular mean-field depending on the polarizations of the pump and probe pulses is proposed whose microscopic origin is related to a spin-orbit coupling involving the electron spins of the material sample and the electric field of the laser pulses. Theoretical predictions are compared to available experimental data. The model successfully reproduces the observed experimental trends and gives meaningful insight into the understanding of magneto-optical rotation behavior in the ultrafast regime. Theoretical predictions for further experimental studies are also proposed.

  14. Ground state phase transition in the Nilsson mean-field plus standard pairing model

    NASA Astrophysics Data System (ADS)

    Guan, Xin; Xu, Haocheng; Zhang, Yu; Pan, Feng; Draayer, Jerry P.

    2016-08-01

    The ground state phase transition in Nd, Sm, and Gd isotopes is investigated by using the Nilsson mean-field plus standard pairing model based on the exact solutions obtained from the extended Heine-Stieltjes correspondence. The results of the model calculations successfully reproduce the critical phenomena observed experimentally in the odd-even mass differences, odd-even differences of two-neutron separation energy, and the α -decay and double β--decay energies of these isotopes. Since the odd-even effects are the most important signatures of pairing interactions in nuclei, the model calculations yield microscopic insight into the nature of the ground state phase transition manifested by the standard pairing interaction.

  15. Metastates in Mean-Field Models with Random External Fields Generated by Markov Chains

    NASA Astrophysics Data System (ADS)

    Formentin, M.; Külske, C.; Reichenbachs, A.

    2012-01-01

    We extend the construction by Külske and Iacobelli of metastates in finite-state mean-field models in independent disorder to situations where the local disorder terms are a sample of an external ergodic Markov chain in equilibrium. We show that for non-degenerate Markov chains, the structure of the theorems is analogous to the case of i.i.d. variables when the limiting weights in the metastate are expressed with the aid of a CLT for the occupation time measure of the chain. As a new phenomenon we also show in a Potts example that for a degenerate non-reversible chain this CLT approximation is not enough, and that the metastate can have less symmetry than the symmetry of the interaction and a Gaussian approximation of disorder fluctuations would suggest.

  16. β-decay of magic nuclei: Beyond mean-field description

    SciTech Connect

    Niu, Yifei; Niu, Zhongming; Colò, Gianluca; Vigezzi, Enrico

    2015-10-15

    Nuclear β-decay plays an important role not only in nuclear physics but also in astrophysics. The widely used self-consistent Random Phase Approximation (RPA) models tend to overestimate the half-lives of magic nuclei. To overcome this problem, we go beyond the mean-field description and include the effects of particle-vibration coupling (PVC) on top of the RPA model. The β-decay half-lives of {sup 34}Si, {sup 68}Ni, {sup 78}Ni, and {sup 132}Sn are studied within this approach in the case of the Skyrme interaction SkM*. It is found that the low-lying Gamow-Teller (GT) strength is shifted downwards with the inclusion of the PVC effect, and as a consequence, the half-lives are reduced due to the increase of the phase space available for β-decay, which leads to a good agreement between theoretical and experimental lifetimes.

  17. Occupation numbers of spherical orbits in self-consistent beyond-mean-field methods

    NASA Astrophysics Data System (ADS)

    Rodríguez, Tomás R.; Poves, Alfredo; Nowacki, Frédéric

    2016-05-01

    We present a method to compute the number of particles occupying spherical single-particle (SSP) levels within the energy density functional (EDF) framework. These SSP levels are defined for each nucleus by performing self-consistent mean-field calculations. The nuclear many-body states, in which the occupation numbers are evaluated, are obtained with a symmetry conserving configuration mixing (SCCM) method based on the Gogny EDF. The method allows a closer comparison between EDF and shell model with configuration mixing in large valence spaces (SM-CI) results, and can serve as a guidance to define physically sound valence spaces for SM-CI calculations. As a first application of the method, we analyze the onset of deformation in neutron-rich N =40 isotones and the role of the SSP levels around this harmonic oscillator magic number, with particular emphasis in the structure of 64Cr.

  18. Mean-field approach for the B phase of (La,Ca)MnO{sub 3}

    SciTech Connect

    Schlottmann, P.

    2001-06-01

    I consider a simple cubic lattice of mixed valent Mn ions (Mn{sup 4+} and Mn{sup 3+}) and calculate the ground state energy for the ferromagnetic B phase using a slave-boson mean-field approach. Each Mn ion has three localized t{sub 2g} electrons with their spins ferromagnetically coupled to form a spin S=3/2. Ions in the Mn{sup 3+} configuration have an additional e{sub g} electron to form a total spin of (S+1/2). The e{sub g} electrons are allowed to hop between the Mn sites (giving rise to the double exchange), but the multiple occupancy of the e{sub g} levels is excluded at each site. Five slave bosons per site are introduced to take into account the correlations between the e{sub g} electrons. {copyright} 2001 American Institute of Physics.

  19. Improving Solar Cycle Prediction Using Variational Data Assimilation in a Mean-Field Dynamo Model

    NASA Astrophysics Data System (ADS)

    Fournier, A.; Hung, C. P.; Jouve, L.; Brun, S.

    2014-12-01

    We present our recent effort to implement modern variational data assimilation techniques into a mean field solar dynamo code. This work extends the work of (Jouve et al. 2011, ApJ) to take into account the correct spherical geometry and meridional circulation into so-called Babcock-Leigthon flux transport dynamo models. Based on twin-experiments, in which we observe our dynamo simulations, and on a well defined cost function using toroidal and poloidal field observations we are able to recover the main attributes of the dynamo solution used to test our data assimilation algorithm. By assimilating solar data (such as Wolf number or butterfly diagram) we are starting to deduce the profile and temporal variations of key ingredients of the solar dynamo. We find that the data sampling and the temporal window are key to get reliable results. We show how such a powerful technique can be used to improve our ability to predict the solar magnetic activity.

  20. Critical wetting of a class of nonequilibrium interfaces: a mean-field picture.

    PubMed

    de Los Santos, Francisco; Romera, Elvira; Al Hammal, Omar; Muñoz, Miguel Angel

    2007-03-01

    A self-consistent mean-field method is used to study critical wetting transitions under nonequilibrium conditions by analyzing Kardar-Parisi-Zhang (KPZ) interfaces in the presence of a bounding substrate. In the case of positive KPZ nonlinearity a single (Gaussian) regime is found. On the contrary, interfaces corresponding to negative nonlinearities lead to three different regimes of critical behavior for the surface order parameter: (i) a trivial Gaussian regime, (ii) a weak-fluctuation regime with a trivially located critical point and nontrivial exponents, and (iii) a highly nontrivial strong-fluctuation regime, for which we provide a full solution by finding the zeros of parabolic-cylinder functions. These analytical results are also verified by solving numerically the self-consistent equation in each case. Analogies with and differences from equilibrium critical wetting as well as nonequilibrium complete wetting are also discussed. PMID:17500666

  1. Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations

    NASA Astrophysics Data System (ADS)

    Vrettas, Michail D.; Opper, Manfred; Cornford, Dan

    2015-01-01

    This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.

  2. The Mean-Field Limit for a Regularized Vlasov-Maxwell Dynamics

    NASA Astrophysics Data System (ADS)

    Golse, François

    2012-03-01

    The present work establishes the mean-field limit of a N-particle system towards a regularized variant of the relativistic Vlasov-Maxwell system, following the work of Braun-Hepp [Commun Math Phys 56:101-113, 1977] and Dobrushin [Func Anal Appl 13:115-123, 1979] for the Vlasov-Poisson system. The main ingredients in the analysis of this system are (a) a kinetic formulation of the Maxwell equations in terms of a distribution of electromagnetic potential in the momentum variable, (b) a regularization procedure for which an analogue of the total energy—i.e. the kinetic energy of the particles plus the energy of the electromagnetic field—is conserved and (c) an analogue of Dobrushin's stability estimate for the Monge-Kantorovich-Rubinstein distance between two solutions of the regularized Vlasov-Poisson dynamics adapted to retarded potentials.

  3. Application of Gaussian expansion method to nuclear mean-field calculations with deformation

    NASA Astrophysics Data System (ADS)

    Nakada, H.

    2008-08-01

    We extensively develop a method of implementing mean-field calculations for deformed nuclei, using the Gaussian expansion method (GEM). This GEM algorithm has the following advantages: (i) it can efficiently describe the energy-dependent asymptotics of the wave functions at large r, (ii) it is applicable to various effective interactions including those with finite ranges, and (iii) the basis parameters are insensitive to nuclide, thereby many nuclei in wide mass range can be handled by a single set of bases. Superposing the spherical GEM bases with feasible truncation for the orbital angular momentum, we obtain deformed single-particle wave-functions to reasonable precision. We apply the new algorithm to the Hartree-Fock and the Hartree-Fock-Bogolyubov calculations of Mg nuclei with the Gogny interaction, by which neck structure of a deformed neutron halo is suggested for 40Mg.

  4. Thermodynamics of the one-dimensional parallel Kawasaki model: Exact solution and mean-field approximations

    NASA Astrophysics Data System (ADS)

    Pazzona, Federico G.; Demontis, Pierfranco; Suffritti, Giuseppe B.

    2014-08-01

    The adsorption isotherm for the recently proposed parallel Kawasaki (PK) lattice-gas model [Phys. Rev. E 88, 062144 (2013), 10.1103/PhysRevE.88.062144] is calculated exactly in one dimension. To do so, a third-order difference equation for the grand-canonical partition function is derived and solved analytically. In the present version of the PK model, the attraction and repulsion effects between two neighboring particles and between a particle and a neighboring empty site are ruled, respectively, by the dimensionless parameters ϕ and θ. We discuss the inflections induced in the isotherms by situations of high repulsion, the role played by finite lattice sizes in the emergence of substeps, and the adequacy of the two most widely used mean-field approximations in lattice gases, namely, the Bragg-Williams and the Bethe-Peierls approximations.

  5. Mean field study of the topological Haldane-Hubbard model of spin-1/2 fermions

    NASA Astrophysics Data System (ADS)

    Arun, V. S.; Sohal, R.; Hickey, C.; Paramekanti, A.

    2016-03-01

    Motivated by exploring the effect of interactions on Chern insulators, and by recent experiments realizing topological bands for ultracold atoms in synthetic gauge fields, we study the honeycomb lattice Haldane-Hubbard model of spin-1/2 fermions. Using an unrestricted mean field approach, we map out the instability of the topological band insulator towards magnetically ordered insulators which emerge with increasing Hubbard repulsion. In addition to the topological Néel phase, we recover various chiral noncoplanar magnetic orders previously identified within a strong-coupling approach. We compute the band structure of these ordered phases, showing that the triple-Q tetrahedral phase harbors topological Chern bands with large Chern numbers.

  6. Angular momentum projection for a Nilsson mean-field plus pairing model

    NASA Astrophysics Data System (ADS)

    Wang, Yin; Pan, Feng; Launey, Kristina D.; Luo, Yan-An; Draayer, J. P.

    2016-06-01

    The angular momentum projection for the axially deformed Nilsson mean-field plus a modified standard pairing (MSP) or the nearest-level pairing (NLP) model is proposed. Both the exact projection, in which all intrinsic states are taken into consideration, and the approximate projection, in which only intrinsic states with K = 0 are taken in the projection, are considered. The analysis shows that the approximate projection with only K = 0 intrinsic states seems reasonable, of which the configuration subspace considered is greatly reduced. As simple examples for the model application, low-lying spectra and electromagnetic properties of 18O and 18Ne are described by using both the exact and approximate angular momentum projection of the MSP or the NLP, while those of 20Ne and 24Mg are described by using the approximate angular momentum projection of the MSP or NLP.

  7. Mean-field model for the growth and coarsening of stoichiometric precipitates at grain boundaries

    NASA Astrophysics Data System (ADS)

    Kozeschnik, E.; Svoboda, J.; Radis, R.; Fischer, F. D.

    2010-01-01

    In this paper, a model for growth and coarsening of precipitates at grain boundaries is developed. The concept takes into account that the evolution of grain boundary precipitates involves fast short-circuit diffusion along grain boundaries as well as slow bulk diffusion of atoms from the grain interior to the grain boundaries. The mathematical formalism is based on a mean-field approximation, utilizing the thermodynamic extremal principle. The model is applied to the precipitation of aluminum nitrides in microalloyed steel in austenite, where precipitation occurs predominately at the austenite grain boundaries. It is shown that the kinetics of precipitation predicted by the proposed model differs significantly from that calculated for randomly distributed precipitates with spherical diffusion fields. Good agreement of the numerical solution is found with experimental observations as well as theoretical treatment of precipitate coarsening.

  8. β-decay of magic nuclei: Beyond mean-field description

    NASA Astrophysics Data System (ADS)

    Niu, Yifei; Niu, Zhongming; Colò, Gianluca; Vigezzi, Enrico

    2015-10-01

    Nuclear β-decay plays an important role not only in nuclear physics but also in astrophysics. The widely used self-consistent Random Phase Approximation (RPA) models tend to overestimate the half-lives of magic nuclei. To overcome this problem, we go beyond the mean-field description and include the effects of particle-vibration coupling (PVC) on top of the RPA model. The β-decay half-lives of 34Si, 68Ni, 78Ni, and 132Sn are studied within this approach in the case of the Skyrme interaction SkM*. It is found that the low-lying Gamow-Teller (GT) strength is shifted downwards with the inclusion of the PVC effect, and as a consequence, the half-lives are reduced due to the increase of the phase space available for β-decay, which leads to a good agreement between theoretical and experimental lifetimes.

  9. Isospin-symmetry-breaking effects in A∼70 nuclei within beyond-mean-field approach

    SciTech Connect

    Petrovici, A.; Andrei, O.

    2015-02-24

    Particular isospin-symmetry-breaking probes including Coulomb energy differences (CED), mirror energy differences (MED), and triplet energy differences (TED) manifest anomalies in the A∼70 isovector triplets of nuclei. The structure of proton-rich nuclei in the A∼70 mass region suggests shape coexistence and competition between pairing correlations in different channels. Recent results concerning the interplay between isospin-mixing and shape-coexistence effects on exotic phenomena in A∼70 nuclei obtained within the beyond-mean-field complex Excited Vampir variational model with symmetry projection before variation using a realistic effective interaction in a relatively large model space are presented. Excited Vampir predictions concerning the Gamow-Teller β decay to the odd-odd N=Z {sup 66}As and {sup 70}Br nuclei correlated with the pair structure analysis in the T=1 and T=0 channel of the involved wave functions are discussed.

  10. Mean-field dynamics of a random neural network with noise

    NASA Astrophysics Data System (ADS)

    Klinshov, Vladimir; Franović, Igor

    2015-12-01

    We consider a network of randomly coupled rate-based neurons influenced by external and internal noise. We derive a second-order stochastic mean-field model for the network dynamics and use it to analyze the stability and bifurcations in the thermodynamic limit, as well as to study the fluctuations due to the finite-size effect. It is demonstrated that the two types of noise have substantially different impact on the network dynamics. While both sources of noise give rise to stochastic fluctuations in the case of the finite-size network, only the external noise affects the stationary activity levels of the network in the thermodynamic limit. We compare the theoretical predictions with the direct simulation results and show that they agree for large enough network sizes and for parameter domains sufficiently away from bifurcations.

  11. Bayesian Learning in Sparse Graphical Factor Models via Variational Mean-Field Annealing

    PubMed Central

    Yoshida, Ryo; West, Mike

    2010-01-01

    We describe a class of sparse latent factor models, called graphical factor models (GFMs), and relevant sparse learning algorithms for posterior mode estimation. Linear, Gaussian GFMs have sparse, orthogonal factor loadings matrices, that, in addition to sparsity of the implied covariance matrices, also induce conditional independence structures via zeros in the implied precision matrices. We describe the models and their use for robust estimation of sparse latent factor structure and data/signal reconstruction. We develop computational algorithms for model exploration and posterior mode search, addressing the hard combinatorial optimization involved in the search over a huge space of potential sparse configurations. A mean-field variational technique coupled with annealing is developed to successively generate “artificial” posterior distributions that, at the limiting temperature in the annealing schedule, define required posterior modes in the GFM parameter space. Several detailed empirical studies and comparisons to related approaches are discussed, including analyses of handwritten digit image and cancer gene expression data. PMID:20890391

  12. Dynamics and Self-consistent Chaos in a Mean Field Hamiltonian Model

    NASA Astrophysics Data System (ADS)

    del-Castillo-Negrete, Diego

    We study a mean field Hamiltonian model that describes the collective dynamics of marginally stable fluids and plasmas in the finite N and N-> infty kinetic limit (where N is the number of particles). The linear stability of equilibria in the kinetic model is studied as well as the initial value problem including Landau damping . Numerical simulations show the existence of coherent, rotating dipole states. We approximate the dipole as two macroparticles and show that the N=2 limit has a family of rotating integrable solutions that provide an accurate description of the dynamics. We discuss the role of self-consistent Hamiltonian chaos in the formation of coherent structures, and discuss a mechanism of "violent" mixing caused by a self-consistent elliptic-hyperbolic bifurcation in phase space.

  13. Economic dynamics with financial fragility and mean-field interaction: A model

    NASA Astrophysics Data System (ADS)

    Di Guilmi, C.; Gallegati, M.; Landini, S.

    2008-06-01

    Following Aoki’s statistical mechanics methodology [Masanao Aoki, New Approaches to Macroeconomic Modeling, Cambridge University Press, 1996; Masanao Aoki, Modeling Aggregate Behaviour and Fluctuations in Economics, Cambridge University Press, 2002; Masanao Aoki, and Hiroshi Yoshikawa, Reconstructing Macroeconomics, Cambridge University Press, 2006], we provide some insights into the well-known works of [Bruce Greenwald, Joseph Stiglitz, Macroeconomic models with equity and credit rationing, in: R. Hubbard (Ed.), Information, Capital Markets and Investment, Chicago University Press, Chicago, 1990; Bruce Greenwald, Joseph Stiglitz, Financial markets imperfections and business cycles, Quarterly journal of Economics (1993)]. Specifically, we reach analytically a closed form solution of their models overcoming the aggregation problem. The key idea is to represent the economy as an evolving complex system, composed by heterogeneous interacting agents, that can be partitioned into a space of macroscopic states. This meso level of aggregation permits to adopt mean-field interaction modeling and master equation techniques.

  14. Mean-field behavior of the negative-weight percolation model on random regular graphs.

    PubMed

    Melchert, Oliver; Hartmann, Alexander K; Mézard, Marc

    2011-10-01

    We investigate both analytically and numerically the ensemble of minimum-weight loops in the negative-weight percolation model on random graphs with fixed connectivity and bimodal weight distribution. This allows us to study the mean-field behavior of this model. The analytical study is based on a conjectured equivalence with the problem of self-avoiding walks in a random medium. The numerical study is based on a mapping to a standard minimum-weight matching problem for which fast algorithms exist. Both approaches yield results that are in agreement on the location of the phase transition, on the value of critical exponents, and on the absence of any sizable indications of a glass phase. By these results, the previously conjectured upper critical dimension of d(u)=6 is confirmed. PMID:22181086

  15. Effects of anisotropies in turbulent magnetic diffusion in mean-field solar dynamo models

    SciTech Connect

    Pipin, V. V.; Kosovichev, A. G.

    2014-04-10

    We study how anisotropies of turbulent diffusion affect the evolution of large-scale magnetic fields and the dynamo process on the Sun. The effect of anisotropy is calculated in a mean-field magnetohydrodynamics framework assuming that triple correlations provide relaxation to the turbulent electromotive force (so-called the 'minimal τ-approximation'). We examine two types of mean-field dynamo models: the well-known benchmark flux-transport model and a distributed-dynamo model with a subsurface rotational shear layer. For both models, we investigate effects of the double- and triple-cell meridional circulation, recently suggested by helioseismology and numerical simulations. To characterize the anisotropy effects, we introduce a parameter of anisotropy as a ratio of the radial and horizontal intensities of turbulent mixing. It is found that the anisotropy affects the distribution of magnetic fields inside the convection zone. The concentration of the magnetic flux near the bottom and top boundaries of the convection zone is greater when the anisotropy is stronger. It is shown that the critical dynamo number and the dynamo period approach to constant values for large values of the anisotropy parameter. The anisotropy reduces the overlap of toroidal magnetic fields generated in subsequent dynamo cycles, in the time-latitude 'butterfly' diagram. If we assume that sunspots are formed in the vicinity of the subsurface shear layer, then the distributed dynamo model with the anisotropic diffusivity satisfies the observational constraints from helioseismology and is consistent with the value of effective turbulent diffusion estimated from the dynamics of surface magnetic fields.

  16. Origin of the neutron skin thickness of {sup 208}Pb in nuclear mean-field models

    SciTech Connect

    Centelles, M.; Roca-Maza, X.; Vinas, X.; Warda, M.

    2010-11-15

    We study whether the neutron skin thickness {Delta}r{sub np} of {sup 208}Pb originates from the bulk or from the surface of the nucleon density distributions, according to the mean-field models of nuclear structure, and find that it depends on the stiffness of the nuclear symmetry energy. The bulk contribution to {Delta}r{sub np} arises from an extended sharp radius of neutrons, whereas the surface contribution arises from different widths of the neutron and proton surfaces. Nuclear models where the symmetry energy is stiff, as typical of relativistic models, predict a bulk contribution in {Delta}r{sub np} of {sup 208}Pb about twice as large as the surface contribution. In contrast, models with a soft symmetry energy like common nonrelativistic models predict that {Delta}r{sub np} of {sup 208}Pb is divided similarly into bulk and surface parts. Indeed, if the symmetry energy is supersoft, the surface contribution becomes dominant. We note that the linear correlation of {Delta}r{sub np} of {sup 208}Pb with the density derivative of the nuclear symmetry energy arises from the bulk part of {Delta}r{sub np}. We also note that most models predict a mixed-type (between halo and skin) neutron distribution for {sup 208}Pb. Although the halo-type limit is actually found in the models with a supersoft symmetry energy, the skin-type limit is not supported by any mean-field model. Finally, we compute parity-violating electron scattering in the conditions of the {sup 208}Pb parity radius experiment (PREX) and obtain a pocket formula for the parity-violating asymmetry in terms of the parameters that characterize the shape of the {sup 208}Pb nucleon densities.

  17. Mean-field analysis of an inductive reasoning game: Application to influenza vaccination

    NASA Astrophysics Data System (ADS)

    Breban, Romulus; Vardavas, Raffaele; Blower, Sally

    2007-09-01

    Recently we have introduced an inductive reasoning game of voluntary yearly vaccination to establish whether or not a population of individuals acting in their own self-interest would be able to prevent influenza epidemics. Here, we analyze our model to describe the dynamics of the collective yearly vaccination uptake. We discuss the mean-field equations of our model and first order effects of fluctuations. We explain why our model predicts that severe epidemics are periodically expected even without the introduction of pandemic strains. We find that fluctuations in the collective yearly vaccination uptake induce severe epidemics with an expected periodicity that depends on the number of independent decision makers in the population. The mean-field dynamics also reveal that there are conditions for which the dynamics become robust to the fluctuations. However, the transition between fluctuation-sensitive and fluctuation-robust dynamics occurs for biologically implausible parameters. We also analyze our model when incentive-based vaccination programs are offered. When a family-based incentive is offered, the expected periodicity of severe epidemics is increased. This results from the fact that the number of independent decision makers is reduced, increasing the effect of the fluctuations. However, incentives based on the number of years of prepayment of vaccination may yield fluctuation-robust dynamics where severe epidemics are prevented. In this case, depending on prepayment, the transition between fluctuation-sensitive and fluctuation-robust dynamics may occur for biologically plausible parameters. Our analysis provides a practical method for identifying how many years of free vaccination should be provided in order to successfully ameliorate influenza epidemics.

  18. Chiral and magnetic rotation in atomic nuclei studied within self-consistent mean-field methods

    NASA Astrophysics Data System (ADS)

    Olbratowski, P.

    2004-07-01

    Currently, one application of the mean-field methods in nuclear physics is the investigation of exotic nuclear symmetries. This is related, in particular, to the study of nuclear rotation about an axis tilted with respect to the principal axes of the mass distribution in the Tilted-Axis Cranking (TAC) model. The present work presents one of the first TAC calculations performed within fully self-consistent methods. The Hartree-Fock method with the Skyrme effective two-body interaction has been used. A computer code has been developed that allows for the breaking of all spatial symmetries of the solution. As a first application, calculations for the magnetic bands in 142Gd and for the chiral bands in 130Cs, 132La, 134Pr, and 136Pm have been carried out. The appearance of those bands is due to a new mechanism of breaking the spherical symmetry and to the spontaneous breaking of the chiral symmetry, respectively. The self-consistent solutions for 142Gd confirm the important role of the shears mechanism in generating the total angular momentum. However, the agreement with experimental data is not satisfactory, probably due to the lack of the pairing correlations in the calculations or to the possibly overestimated deformation. The results obtained for 132La constitute the first fully self-consistent proof that the nuclear rotation can attain a chiral character. It has been shown that the chiral rotation can only exist above a certain critical angular frequency. It has also been checked that the terms of the Skyrme mean field odd under the time reversal have no qualitative influence on the results.

  19. Mean-field thalamocortical modeling of longitudinal EEG acquired during intensive meditation training.

    PubMed

    Saggar, Manish; Zanesco, Anthony P; King, Brandon G; Bridwell, David A; MacLean, Katherine A; Aichele, Stephen R; Jacobs, Tonya L; Wallace, B Alan; Saron, Clifford D; Miikkulainen, Risto

    2015-07-01

    Meditation training has been shown to enhance attention and improve emotion regulation. However, the brain processes associated with such training are poorly understood and a computational modeling framework is lacking. Modeling approaches that can realistically simulate neurophysiological data while conforming to basic anatomical and physiological constraints can provide a unique opportunity to generate concrete and testable hypotheses about the mechanisms supporting complex cognitive tasks such as meditation. Here we applied the mean-field computational modeling approach using the scalp-recorded electroencephalogram (EEG) collected at three assessment points from meditating participants during two separate 3-month-long shamatha meditation retreats. We modeled cortical, corticothalamic, and intrathalamic interactions to generate a simulation of EEG signals recorded across the scalp. We also present two novel extensions to the mean-field approach that allow for: (a) non-parametric analysis of changes in model parameter values across all channels and assessments; and (b) examination of variation in modeled thalamic reticular nucleus (TRN) connectivity over the retreat period. After successfully fitting whole-brain EEG data across three assessment points within each retreat, two model parameters were found to replicably change across both meditation retreats. First, after training, we observed an increased temporal delay between modeled cortical and thalamic cells. This increase provides a putative neural mechanism for a previously observed reduction in individual alpha frequency in these same participants. Second, we found decreased inhibitory connection strength between the TRN and secondary relay nuclei (SRN) of the modeled thalamus after training. This reduction in inhibitory strength was found to be associated with increased dynamical stability of the model. Altogether, this paper presents the first computational approach, taking core aspects of physiology and

  20. Biopolymers under large external forces and mean-field RNA virus evolutionary dynamics

    NASA Astrophysics Data System (ADS)

    Ahsan, Syed Amir

    The modeling of the mechanical response of single-molecules of DNA and RNA under large external forces through statistical mechanical methods is central to this thesis with a small portion devoted to modeling the evolutionary dynamics of positive-sense single-stranded RNA viruses. In order to develop and test models of biopolymer mechanics and illuminate the mechanisms underlying biological processes where biopolymers undergo changes in energy on the order of the thermal energy, , entails measuring forces and lengths on the scale of piconewtons (pN) and nanometers (nm), respectively. A capacity achieved in the past two decades at the single-molecule level through the development of micromanipulation techniques such as magnetic and optical tweezers, atomic force microscopy, coupled with advances in micro- and nanofabrication. The statistical mechanical models of biopolymers developed in this dissertation are dependent upon and the outcome of these advancements and resulting experiments. The dissertation begins in chapter 1 with an introduction to the structure and thermodynamics of DNA and RNA, highlighting the importance and effectiveness of simple, two-state models in their description as a prelude to the emergence of two-state models in the research manuscripts. In chapter 2 the standard models of the elasticity of polymers and of a polymer gel are reviewed, characterizing the continuum and mean-field models, including the scaling behavior of DNA in confined spaces. The research manuscript presented in the last section of chapter 2 (section 2.5), subsequent to a review of a Flory gel and in contrast to it, is a model of the elasticity of RNA as a gel, with viral RNA illustrating an instance of such a network, and shown to exhibit anomalous elastic behavior, a negative Poisson ratio, and capable of facilitating viral RNA encapsidation with further context provided in section 5.1. In chapter 3 the experimental methods and behavior of DNA and RNA under mechanical

  1. Mean-field and direct numerical simulations of magnetic flux concentrations from vertical field

    NASA Astrophysics Data System (ADS)

    Brandenburg, A.; Gressel, O.; Jabbari, S.; Kleeorin, N.; Rogachevskii, I.

    2014-02-01

    Context. Strongly stratified hydromagnetic turbulence has previously been found to produce magnetic flux concentrations if the domain is large enough compared with the size of turbulent eddies. Mean-field simulations (MFS) using parameterizations of the Reynolds and Maxwell stresses show a large-scale negative effective magnetic pressure instability and have been able to reproduce many aspects of direct numerical simulations (DNS) regarding growth rate, shape of the resulting magnetic structures, and their height as a function of magnetic field strength. Unlike the case of an imposed horizontal field, for a vertical one, magnetic flux concentrations of equipartition strength with the turbulence can be reached, resulting in magnetic spots that are reminiscent of sunspots. Aims: We determine under what conditions magnetic flux concentrations with vertical field occur and what their internal structure is. Methods: We use a combination of MFS, DNS, and implicit large-eddy simulations (ILES) to characterize the resulting magnetic flux concentrations in forced isothermal turbulence with an imposed vertical magnetic field. Results: Using DNS, we confirm earlier results that in the kinematic stage of the large-scale instability the horizontal wavelength of structures is about 10 times the density scale height. At later times, even larger structures are being produced in a fashion similar to inverse spectral transfer in helically driven turbulence. Using ILES, we find that magnetic flux concentrations occur for Mach numbers between 0.1 and 0.7. They occur also for weaker stratification and larger turbulent eddies if the domain is wide enough. Using MFS, the size and aspect ratio of magnetic structures are determined as functions of two input parameters characterizing the parameterization of the effective magnetic pressure. DNS, ILES, and MFS show magnetic flux tubes with mean-field energies comparable to the turbulent kinetic energy. These tubes can reach a length of about

  2. Structural versus dynamical origins of mean-field behavior in a self-organized critical model of neuronal avalanches.

    PubMed

    Moosavi, S Amin; Montakhab, Afshin

    2015-11-01

    Critical dynamics of cortical neurons have been intensively studied over the past decade. Neuronal avalanches provide the main experimental as well as theoretical tools to consider criticality in such systems. Experimental studies show that critical neuronal avalanches show mean-field behavior. There are structural as well as recently proposed [Phys. Rev. E 89, 052139 (2014)] dynamical mechanisms that can lead to mean-field behavior. In this work we consider a simple model of neuronal dynamics based on threshold self-organized critical models with synaptic noise. We investigate the role of high-average connectivity, random long-range connections, as well as synaptic noise in achieving mean-field behavior. We employ finite-size scaling in order to extract critical exponents with good accuracy. We conclude that relevant structural mechanisms responsible for mean-field behavior cannot be justified in realistic models of the cortex. However, strong dynamical noise, which can have realistic justifications, always leads to mean-field behavior regardless of the underlying structure. Our work provides a different (dynamical) origin than the conventionally accepted (structural) mechanisms for mean-field behavior in neuronal avalanches. PMID:26651741

  3. Structural versus dynamical origins of mean-field behavior in a self-organized critical model of neuronal avalanches

    NASA Astrophysics Data System (ADS)

    Moosavi, S. Amin; Montakhab, Afshin

    2015-11-01

    Critical dynamics of cortical neurons have been intensively studied over the past decade. Neuronal avalanches provide the main experimental as well as theoretical tools to consider criticality in such systems. Experimental studies show that critical neuronal avalanches show mean-field behavior. There are structural as well as recently proposed [Phys. Rev. E 89, 052139 (2014), 10.1103/PhysRevE.89.052139] dynamical mechanisms that can lead to mean-field behavior. In this work we consider a simple model of neuronal dynamics based on threshold self-organized critical models with synaptic noise. We investigate the role of high-average connectivity, random long-range connections, as well as synaptic noise in achieving mean-field behavior. We employ finite-size scaling in order to extract critical exponents with good accuracy. We conclude that relevant structural mechanisms responsible for mean-field behavior cannot be justified in realistic models of the cortex. However, strong dynamical noise, which can have realistic justifications, always leads to mean-field behavior regardless of the underlying structure. Our work provides a different (dynamical) origin than the conventionally accepted (structural) mechanisms for mean-field behavior in neuronal avalanches.

  4. Self-consistent mean-field model for palmitoyloleoylphosphatidylcholine-palmitoyl sphingomyelin-cholesterol lipid bilayers

    NASA Astrophysics Data System (ADS)

    Tumaneng, Paul W.; Pandit, Sagar A.; Zhao, Guijun; Scott, H. L.

    2011-03-01

    The connection between membrane inhomogeneity and the structural basis of lipid rafts has sparked interest in the lateral organization of model lipid bilayers of two and three components. In an effort to investigate anisotropic lipid distribution in mixed bilayers, a self-consistent mean-field theoretical model is applied to palmitoyloleoylphosphatidylcholine (POPC)-palmitoyl sphingomyelin (PSM)-cholesterol mixtures. The compositional dependence of lateral organization in these mixtures is mapped onto a ternary plot. The model utilizes molecular dynamics simulations to estimate interaction parameters and to construct chain conformation libraries. We find that at some concentration ratios the bilayers separate spatially into regions of higher and lower chain order coinciding with areas enriched with PSM and POPC, respectively. To examine the effect of the asymmetric chain structure of POPC on bilayer lateral inhomogeneity, we consider POPC-lipid interactions with and without angular dependence. Results are compared with experimental data and with results from a similar model for mixtures of dioleoylphosphatidylcholine, steroyl sphingomyelin, and cholesterol.

  5. Criticality in neural ensembles: a mean field approach to expand network size from measured data

    NASA Astrophysics Data System (ADS)

    Wasnik, Vaibhav; Caracheo, Barak; Seamans, Jeremy; Emberly, Eldon

    2014-03-01

    At the point of a second order phase transition also termed as a critical point, systems display long range order and their macroscopic behaviours are independent of the microscopic details making up the system. This makes the idea of criticality interesting for studying biological systems which even though are different microscopically still have similar macroscopic behaviours. Recent high-throughput methods in neuroscience are making it possible to explore whether criticality exists in neural networks. Despite being high-throughput, many data sets are still only a minute sample of the neural system and methods towards expanding these data sets have to be considered in order to study the existence of criticality. Using measurements of firing neurons from the pre-frontal cortex (PFC) of rats, we map the data to a system of Ising spins and calculate the specific heat as a function of the measured network size, looking for the existence of critical points. In order to go to the thermodynamic limit, we propose a mean field approach for expanding such data. Our preliminary results show that such an approach can capture the statistical properties of much larger neuronal populations even when only a smaller subset is measured.

  6. Effects of Large-scale Non-axisymmetric Perturbations in the Mean-field Solar Dynamo.

    NASA Astrophysics Data System (ADS)

    Pipin, V. V.; Kosovichev, A. G.

    2015-11-01

    We explore the response of a nonlinear non-axisymmetric mean-field solar dynamo model to shallow non-axisymmetric perturbations. After a relaxation period, the amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, and the depth of perturbation. It is found that a perturbation that is anchored at 0.9 R⊙ has a profound effect on the dynamo process, producing a transient magnetic cycle of the axisymmetric magnetic field, if it is initiated at the growing phase of the cycle. The non-symmetric, with respect to the equator, perturbation results in a hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric fields depends on the turbulent magnetic Reynolds number Rm. In the range of Rm = 104-106 the evolution returns to the normal course in the next cycle, in which the non-axisymmetric field is generated due to a nonlinear α-effect and magnetic buoyancy. In the stationary state, the large-scale magnetic field demonstrates a phenomenon of “active longitudes” with cyclic 180° “flip-flop” changes of the large-scale magnetic field orientation. The flip-flop effect is known from observations of solar and stellar magnetic cycles. However, this effect disappears in the model, which includes the meridional circulation pattern determined by helioseismology. The rotation rate of the non-axisymmetric field components varies during the relaxation period and carries important information about the dynamo process.

  7. Self-consistent inhomogeneous steady states in Hamiltonian mean-field dynamics

    NASA Astrophysics Data System (ADS)

    de Buyl, Pierre; Mukamel, David; Ruffo, Stefano

    2011-12-01

    Long-lived quasistationary states, associated with stationary stable solutions of the Vlasov equation, are found in systems with long-range interactions. Studies of the relaxation time in a model of N globally coupled particles moving on a ring, the Hamiltonian mean-field model (HMF), have shown that it diverges as Nγ for large N, with γ≃1.7 for some initial conditions with homogeneously distributed particles. We propose a method for identifying exact inhomogeneous steady states in the thermodynamic limit, based on analyzing models of uncoupled particles moving in an external field. For the HMF model, we show numerically that the relaxation time of these states diverges with N with the exponent γ≃1. The method, applicable to other models with globally coupled particles, also allows an exact evaluation of the stability limit of homogeneous steady states. In some cases, it provides a good approximation for the correspondence between the initial condition and the final steady state.

  8. TURBULENT CROSS-HELICITY IN THE MEAN-FIELD SOLAR DYNAMO PROBLEM

    SciTech Connect

    Pipin, V. V.; Kuzanyan, K. M.; Zhang, H.; Kosovichev, A. G.

    2011-12-20

    We study the dynamical and statistical properties of turbulent cross-helicity (correlation of the aligned fluctuating velocity and magnetic field components). We derive an equation governing generation and evolution of the turbulent cross-helicity and discuss its meaning for the dynamo. Using the symmetry properties of the problem we suggest a general expression for the turbulent cross-helicity. Effects of the density stratification, large-scale magnetic fields, differential rotation, and turbulent convection are taken into account. We investigate the relative contribution of these effects to the cross-helicity evolution for two kinds of dynamo models of the solar cycle: a distributed mean-field model and a flux-transport dynamo model. We show that the contribution from the density stratification follows the evolution of the radial magnetic field, while large-scale electric currents produce a more complicated pattern of the cross-helicity of comparable magnitude. The pattern of the cross-helicity evolution strongly depends on details of the dynamo mechanism. Thus, we anticipate that direct observations of the cross-helicity on the Sun may serve for the diagnostic purpose of the solar dynamo process.

  9. A stochastic mean field model for an excitatory and inhibitory synaptic drive cortical neuronal network.

    PubMed

    Hui, Qing; Haddad, Wassim M; Bailey, James M; Hayakawa, Tomohisa

    2014-04-01

    With the advances in biochemistry, molecular biology, and neurochemistry there has been impressive progress in understanding the molecular properties of anesthetic agents. However, there has been little focus on how the molecular properties of anesthetic agents lead to the observed macroscopic property that defines the anesthetic state, that is, lack of responsiveness to noxious stimuli. In this paper, we develop a mean field synaptic drive firing rate cortical neuronal model and demonstrate how the induction of general anesthesia can be explained using multistability; the property whereby the solutions of a dynamical system exhibit multiple attracting equilibria under asymptotically slowly changing inputs or system parameters. In particular, we demonstrate multistability in the mean when the system initial conditions or the system coefficients of the neuronal connectivity matrix are random variables. Uncertainty in the system coefficients is captured by representing system uncertain parameters by a multiplicative white noise model wherein stochastic integration is interpreted in the sense of Itô. Modeling a priori system parameter uncertainty using a multiplicative white noise model is motivated by means of the maximum entropy principle of Jaynes and statistical analysis. PMID:24807952

  10. Generalized mean-field description of entanglement in dimerized spin systems

    NASA Astrophysics Data System (ADS)

    Boette, A.; Rossignoli, R.; Canosa, N.; Matera, J. M.

    2015-02-01

    We discuss a generalized self-consistent mean-field (MF) treatment, based on the selection of an arbitrary subset of operators for representing the system density matrix, and its application to the problem of entanglement evaluation in composite quantum systems. As a specific example, we examine in detail a pair MF approach to the ground state (GS) of dimerized spin-1 /2 systems with anisotropic ferromagnetic-type X Y and X Y Z couplings in a transverse field, including chains and arrays with first neighbor and also longer range couplings. The approach is fully analytic and able to capture the main features of the GS of these systems, in contrast with the conventional single-spin MF. Its phase diagram differs significantly from that of the latter, exhibiting (Sz) parity breaking just in a finite field window if the coupling between pairs is sufficiently weak, together with a fully dimerized phase below this window and a partially aligned phase above it. It is then shown that through symmetry restoration, the approach is able to correctly predict not only the concurrence of a pair, but also its entanglement with the rest of the chain, which shows a pronounced peak in the parity breaking window. Perturbative corrections allow to reproduce more subtle observables like the entanglement between weakly coupled spins and the low lying energy spectrum. All predictions are tested against exact results for finite systems.

  11. Hydration in discrete water. A mean field, cellular automata based approach to calculating hydration free energies.

    PubMed

    Setny, Piotr; Zacharias, Martin

    2010-07-01

    A simple, semiheuristic solvation model based on a discrete, BCC grid of solvent cells has been presented. The model utilizes a mean field approach for the calculation of solute-solvent and solvent-solvent interaction energies and a cellular automata based algorithm for the prediction of solvent distribution in the presence of solute. The construction of the effective Hamiltonian for a solvent cell provides an explicit coupling between orientation-dependent water-solute electrostatic interactions and water-water hydrogen bonding. The water-solute dispersion interaction is also explicitly taken into account. The model does not depend on any arbitrary definition of the solute-solvent interface nor does it use a microscopic surface tension for the calculation of nonpolar contributions to the hydration free energies. It is demonstrated that the model provides satisfactory predictions of hydration free energies for drug-like molecules and is able to reproduce the distribution of buried water molecules within protein structures. The model is computationally efficient and is applicable to arbitrary molecules described by atomistic force field. PMID:20552986

  12. Novel dynamics and thermodynamics of a new Hamiltonian mean field model

    NASA Astrophysics Data System (ADS)

    Curilef, Sergio; Atenas, Boris

    Statistical systems are idealized by the hypothesis that the particles do not interact among them, or the range of interactions is short enough, reaching very fast the statistical state that we know as equilibrium. However, systems with long-range interactions are common in nature because of they are observed from the atomic scale to the astronomical scale, exhibiting some anomalies as inequivalence of ensembles, negative heat capacity, ergodicity breaking, non equilibrium phase transitions, quasi-stationarity, anomalous diffusion, etc. We present in this contribution a new Hamiltonian mean field model whose potential is inspired in the dipole-dipole interactions. The equilibrium is analytically studied in the canonical ensemble and coincides with the one obtained from molecular dynamics simulations (microcanonical ensemble). We notice, this model presents a kind of inequivalence of ensembles in long-standing states before arriving at equilibrium. However, the novelty, compared to other models presented in recent literature, is that two quasi-stationary states appear in the behavior of this system. The first quasi-stationary state decays to a second one, which is different to the first, before going to the equilibrium.We characterize them by its dynamics and thermodynamics. We acknowledge partial financial support by Anillo ACT-1204, VRIDT-UCN105/2015. We appreciate the computational assistance of A. Pluchino.

  13. Correlation patterns of NIKKEI index constituents. Towards a mean-field model

    NASA Astrophysics Data System (ADS)

    Hayashi, Katsuhiko; Kaizoji, Taisei; Pichl, Lukáš

    2007-09-01

    An analysis of minute-tick data from the Japanese stock index market is reported for a three-year period of 2000/7/4-2003/6/30. Correlation patterns and principal component distributions were determined for 180 constituents of the NIKKEI 225 index, excluding the effects of after-hours trading and constituent revisions. The first principal component describes about 30% of the total variance in constituent log returns (subject to slow decrease with the size of the correlation window), suggesting that a small number of physical parameters may describe the internal dynamics of the index, allowing for an adiabatic representation of index dynamics, and a self-consistent mean-field model of its constituents. Finally, it is shown that the introduction of a time gap into minute-tick data significantly improves the correlations of the price-weighed index with its constituents, even when such gap inserts are strictly penalized. This phenomenon corresponds to a heterogenous response time of index constituents to the adiabatic collective motion and also demonstrates the inhomogeneous nature of equidistant time ticks in financial trading.

  14. Critical behavior of a tumor growth model: directed percolation with a mean-field flavor.

    PubMed

    Lipowski, Adam; Ferreira, António Luis; Wendykier, Jacek

    2012-10-01

    We examine the critical behavior of a lattice model of tumor growth where supplied nutrients are correlated with the distribution of tumor cells. Our results support the previous report [Ferreira et al., Phys. Rev. E 85, 010901(R) (2012)], which suggested that the critical behavior of the model differs from the expected directed percolation (DP) universality class. Surprisingly, only some of the critical exponents (β, α, ν([perpendicular]), and z) take non-DP values while some others (β', ν(||), and spreading-dynamics exponents Θ, δ, z') remain very close to their DP counterparts. The obtained exponents satisfy the scaling relations β=αν(||), β'=δν(||), and the generalized hyperscaling relation Θ+α+δ=d/z, where the dynamical exponent z is, however, used instead of the spreading exponent z'. Both in d=1 and d=2 versions of our model, the exponent β most likely takes the mean-field value β=1, and we speculate that it might be due to the roulette-wheel selection, which is used to choose the site to supply a nutrient. PMID:23214560

  15. Accuracy criterion for the mean-field approximation in susceptible-infected-susceptible epidemics on networks

    NASA Astrophysics Data System (ADS)

    Van Mieghem, P.; van de Bovenkamp, R.

    2015-03-01

    Mean-field approximations (MFAs) are frequently used in physics. When a process (such as an epidemic or a synchronization) on a network is approximated by MFA, a major hurdle is the determination of those graphs for which MFA is reasonably accurate. Here, we present an accuracy criterion for Markovian susceptible-infected-susceptible (SIS) epidemics on any network, based on the spectrum of the adjacency and SIS covariance matrix. We evaluate the MFA criterion for the complete and star graphs analytically, and numerically for connected Erdős-Rényi random graphs for small size N ≤14 . The accuracy of MFA increases with average degree and with N . Precise simulations (up to network sizes N =100 ) of the MFA accuracy criterion versus N for the complete graph, star, square lattice, and path graphs lead us to conjecture that the worst MFA accuracy decreases, for large N , proportionally to the inverse of the spectral radius of the adjacency matrix of the graph.

  16. Mean Field Analysis of Stochastic Neural Network Models with Synaptic Depression

    NASA Astrophysics Data System (ADS)

    Yasuhiko Igarashi,; Masafumi Oizumi,; Masato Okada,

    2010-08-01

    We investigated the effects of synaptic depression on the macroscopic behavior of stochastic neural networks. Dynamical mean field equations were derived for such networks by taking the average of two stochastic variables: a firing-state variable and a synaptic variable. In these equations, the average product of thesevariables is decoupled as the product of their averages because the two stochastic variables are independent. We proved the independence of these two stochastic variables assuming that the synaptic weight Jij is of the order of 1/N with respect to the number of neurons N. Using these equations, we derived macroscopic steady-state equations for a network with uniform connections and for a ring attractor network with Mexican hat type connectivity and investigated the stability of the steady-state solutions. An oscillatory uniform state was observed in the network with uniform connections owing to a Hopf instability. For the ring network, high-frequency perturbations were shown not to affect system stability. Two mechanisms destabilize the inhomogeneous steady state, leading to two oscillatory states. A Turing instability leads to a rotating bump state, while a Hopf instability leads to an oscillatory bump state, which was previously unreported. Various oscillatory states take place in a network with synaptic depression depending on the strength of the interneuron connections.

  17. Monte Carlo Mean Field Treatment of Microbunching Instability in the FERMI@Elettra First Bunch Compressor

    SciTech Connect

    Bassi, G.; Ellison, J.A.; Heinemann, K.; Warnock, R.; /SLAC

    2009-05-07

    Bunch compressors, designed to increase the peak current, can lead to a microbunching instability with detrimental effects on the beam quality. This is a major concern for free electron lasers (FELs) where very bright electron beams are required, i.e. beams with low emittance and energy spread. In this paper, we apply our self-consistent, parallel solver to study the microbunching instability in the first bunch compressor system of FERMI{at}Elettra. Our basic model is a 2D Vlasov-Maxwell system. We treat the beam evolution through a bunch compressor using our Monte Carlo mean field approximation. We randomly generate N points from an initial phase space density. We then calculate the charge density using a smooth density estimation procedure, from statistics, based on Fourier series. The electric and magnetic fields are calculated from the smooth charge/current density using a novel field formula that avoids singularities by using the retarded time as a variable of integration. The points are then moved forward in small time steps using the beam frame equations of motion, with the fields frozen during a time step, and a new charge density is determined using our density estimation procedure. We try to choose N large enough so that the charge density is a good approximation to the density that would be obtained from solving the 2D Vlasov-Maxwell system exactly. We call this method the Monte Carlo Particle (MCP) method.

  18. On the magnetic quenching of mean-field effects in supersonic interstellar turbulence

    NASA Astrophysics Data System (ADS)

    Gressel, Oliver; Bendre, Abhijit; Elstner, Detlef

    2013-02-01

    The emergence of large-scale magnetic fields observed in the diffuse interstellar medium is explained by a turbulent dynamo. The underlying transport coefficients have previously been extracted from numerical simulations. So far, this was restricted to the kinematic regime, but we aim to extend our analysis into the realm of dynamically important fields. This marks an important step on which derived mean-field models rely to explain observed equipartition-strength fields. As in previous work, we diagnose turbulent transport coefficients by means of the test-field method. We derive quenching functions for the dynamo α effect, diamagnetic pumping and turbulent diffusivity, which are compared with theoretical expectations. At late times, we observe the suppression of the vertical wind. Because this potentially affects the removal of small-scale magnetic helicity, new concerns arise about circumventing constraints imposed by the conservation of magnetic helicity at high magnetic Reynolds numbers. While present results cannot safely rule out this possibility, the issue only becomes important at late stages and is absent when the dynamo is quenched by the wind itself.

  19. The Mean-field Solar Dynamo with a Double Cell Meridional Circulation Pattern

    NASA Astrophysics Data System (ADS)

    Pipin, V. V.; Kosovichev, A. G.

    2013-10-01

    Recent helioseismology findings, as well as advances in direct numerical simulations of global dynamics of the Sun, have indicated that in each solar hemisphere meridional circulation may form more than one cell along the radius in the convection zone. In particular, recent helioseismology results revealed a double-cell structure of the meridional circulation. We investigate properties of a mean-field solar dynamo with such double-cell meridional circulation. The dynamo model also includes the realistic profile of solar differential rotation (including the tachocline and subsurface shear layer) and takes into account effects of turbulent pumping, anisotropic turbulent diffusivity, and conservation of magnetic helicity. Contrary to previous flux-transport dynamo models, we find that the dynamo model can robustly reproduce the basic properties of the solar magnetic cycles for a wide range of model parameters and circulation speeds. The best agreement with observations is achieved when the surface meridional circulation speed is about 12 m s-1. For this circulation speed, the simulated sunspot activity shows good synchronization with the polar magnetic fields. Such synchronization was indeed observed during previous sunspot Cycles 21 and 22. We compare theoretical and observed phase diagrams of the sunspot number and the polar field strength and discuss the peculiar properties of Cycle 23.

  20. Cluster Dynamical Mean Field Methods and the Momentum-selective Mott transition

    NASA Astrophysics Data System (ADS)

    Gull, Emanuel

    2011-03-01

    Innovations in methodology and computational power have enabled cluster dynamical mean field calculations of the Hubbard model with interaction strengths and band structures representative of high temperature copper oxide superconductors, for clusters large enough that the thermodyamic limit behavior may be determined. We present the methods and show how extrapolations to the thermodynamic limit work in practice. We show that the Hubbard model with next-nearest neighbor hopping at intermediate interaction strength captures much of the exotic behavior characteristic of the high temperature superconductors. An important feature of the results is a pseudogap for hole doping but not for electron doping. The pseudogap regime is characterized by a gap for momenta near Brillouin zone face and gapless behavior near the zone diagonal. for dopings outside of the pseudogap regime we find scattering rates which vary around the fermi surface in a way consistent with recent transport measurements. Using the maximum entropy method we calculate spectra, self-energies, and response functions for Raman spectroscopy and optical conductivities, finding results also in good agreement with experiment. Olivier Parcollet, Philipp Werner, Nan Lin, Michel Ferrero, Antoine Georges, Andrew J. Millis; NSF-DMR-0705847.

  1. Hamiltonian mean field model: Effect of network structure on synchronization dynamics.

    PubMed

    Virkar, Yogesh S; Restrepo, Juan G; Meiss, James D

    2015-11-01

    The Hamiltonian mean field model of coupled inertial Hamiltonian rotors is a prototype for conservative dynamics in systems with long-range interactions. We consider the case where the interactions between the rotors are governed by a network described by a weighted adjacency matrix. By studying the linear stability of the incoherent state, we find that the transition to synchrony begins when the coupling constant K is inversely proportional to the largest eigenvalue of the adjacency matrix. We derive a closed system of equations for a set of local order parameters to study the effect of network heterogeneity on the synchronization of the rotors. When K is just beyond the transition to synchronization, we find that the degree of synchronization is highly dependent on the network's heterogeneity, but that for large K the degree of synchronization is robust to changes in the degree distribution. Our results are illustrated with numerical simulations on Erdös-Renyi networks and networks with power-law degree distributions. PMID:26651739

  2. Mean-Field Analysis of Recursive Entropic Segmentation of Biological Sequences

    NASA Astrophysics Data System (ADS)

    Cheong, Siew-Ann; Stodghill, Paul; Schneider, David; Myers, Christopher

    2007-03-01

    Horizontal gene transfer in bacteria results in genomic sequences which are mosaic in nature. An important first step in the analysis of a bacterial genome would thus be to model the statistically nonstationary nucleotide or protein sequence with a collection of P stationary Markov chains, and partition the sequence of length N into M statistically stationary segments/domains. This can be done for Markov chains of order K = 0 using a recursive segmentation scheme based on the Jensen-Shannon divergence, where the unknown parameters P and M are estimated from a hypothesis testing/model selection process. In this talk, we describe how the Jensen-Shannon divergence can be generalized to Markov chains of order K > 0, as well as an algorithm optimizing the positions of a fixed number of domain walls. We then describe a mean field analysis of the generalized recursive Jensen-Shannon segmentation scheme, and show how most domain walls appear as local maxima in the divergence spectrum of the sequence, before highlighting the main problem associated with the recursive segmentation scheme, i.e. the strengths of the domain walls selected recursively do not decrease monotonically. This problem is especially severe in repetitive sequences, whose statistical signatures we will also discuss.

  3. Numerical Tests of the Quasilinear Approximation of Mean-field Electrodynamics

    NASA Astrophysics Data System (ADS)

    Zsargo, J.; Petrovay, K.

    1995-05-01

    It is widely known that a sufficient condition for the applicability of quasilinear-type approximations (e.g. the second-order correlation approximation or SOCA) in mean-field electrodynamics is that Utau << min {l, H} where l, H, U and tau are characteristic horizontal and vertical scale lengths, velocity, and time, respectively. A necessary condition for their validity is however not known. In order to check the validity of the quasilinear results in cases where the above condition is not satisfied, as well as to study qualitative and quantitative differences between the quasilinear results and the actual solutions, we numerically solve the MHD induction equation for the kinematical case in a series of simplified "toy" model flows and then compare the results with the corresponding quasilinear solutions. Our model flows are two-dimensional two-component flows with simple (exponential or linear) stratifications. For conceptual clarity, in each model only one independent physical quantity (initial magnetic field, density, or velocity amplitude, respectively) has an inhomogeneous distribution. Solutions are computed for several widely differing values of the l/H horizontal/vertical scale length ratio. In all cases we find that the computed turbulent electromotive force does not differ from the quasilinear value by more than an order-of-unity factor, as long as Utau does not greatly exceed min {l, H}.

  4. Competing orders in a dipolar Bose-Fermi mixture on a square optical lattice: mean-field perspective

    NASA Astrophysics Data System (ADS)

    Scaramazza, Jasen A.; Kain, Ben; Ling, Hong Y.

    2016-07-01

    We consider a mixture of a two-component Fermi gas and a single-component dipolar Bose gas in a square optical lattice and reduce it into an effective Fermi system where the Fermi-Fermi interaction includes the attractive interaction induced by the phonons of a uniform dipolar Bose-Einstein condensate. Focusing on this effective Fermi system in the parameter regime that preserves the symmetry of D4, the point group of a square, we explore, within the Hartree-Fock-Bogoliubov mean-field theory, the phase competition among density wave orderings and superfluid pairings. We construct the matrix representation of the linearized gap equation in the irreducible representations of D4. We show that in the weak coupling regime, each matrix element, which is a four-dimensional (4D) integral in momentum space, can be put in a separable form involving a 1D integral, which is only a function of temperature and the chemical potential, and a pairing-specific "effective" interaction, which is an analytical function of the parameters that characterize the Fermi-Fermi interactions in our system. We analyze the critical temperatures of various competing orders as functions of different system parameters in both the absence and presence of the dipolar interaction. We find that close to half filling, the dx2 - y2-wave pairing with a critical temperature in the order of a fraction of Fermi energy (at half filling) may dominate all other phases, and at a higher filling factor, the p-wave pairing with a critical temperature in the order of a hundredth of Fermi energy may emerge as a winner. We find that tuning a dipolar interaction can dramatically enhance the pairings with dxy- and g-wave symmetries but not enough for them to dominate other competing phases.

  5. Reexamination of the mean-field phase diagram of biaxial nematic liquid crystals: Insights from Monte Carlo studies

    NASA Astrophysics Data System (ADS)

    Kamala Latha, B.; Jose, Regina; Murthy, K. P. N.; Sastry, V. S. S.

    2015-07-01

    Investigations of the phase diagram of biaxial liquid-crystal systems through analyses of general Hamiltonian models within the simplifications of mean-field theory (MFT), as well as by computer simulations based on microscopic models, are directed toward an appreciation of the role of the underlying molecular-level interactions to facilitate its spontaneous condensation into a nematic phase with biaxial symmetry. Continuing experimental challenges in realizing such a system unambiguously, despite encouraging predictions from MFT, for example, are requiring more versatile simulational methodologies capable of providing insights into possible hindering barriers within the system, typically gleaned through its free-energy dependences on relevant observables as the system is driven through the transitions. The recent paper from this group [Kamala Latha et al., Phys. Rev. E 89, 050501(R) (2014), 10.1103/PhysRevE.89.050501], summarizing the outcome of detailed Monte Carlo simulations carried out employing an entropic sampling technique, suggested a qualitative modification of the MFT phase diagram as the Hamiltonian is asymptotically driven toward the so-called partly repulsive regions. It was argued that the degree of (cross) coupling between the uniaxial and biaxial tensor components of neighboring molecules plays a crucial role in facilitating a ready condensation of the biaxial phase, suggesting that this could be a plausible factor in explaining the experimental difficulties. In this paper, we elaborate this point further, providing additional evidence from curious variations of free-energy profiles with respect to the relevant orientational order parameters, at different temperatures bracketing the phase transitions.

  6. Real-space, mean-field algorithm to numerically calculate long-range interactions

    NASA Astrophysics Data System (ADS)

    Cadilhe, A.; Costa, B. V.

    2016-02-01

    Long-range interactions are known to be of difficult treatment in statistical mechanics models. There are some approaches that introduce a cutoff in the interactions or make use of reaction field approaches. However, those treatments suffer the illness of being of limited use, in particular close to phase transitions. The use of open boundary conditions allows the sum of the long-range interactions over the entire system to be done, however, this approach demands a sum over all degrees of freedom in the system, which makes a numerical treatment prohibitive. Techniques like the Ewald summation or fast multipole expansion account for the exact interactions but are still limited to a few thousands of particles. In this paper we introduce a novel mean-field approach to treat long-range interactions. The method is based in the division of the system in cells. In the inner cell, that contains the particle in sight, the 'local' interactions are computed exactly, the 'far' contributions are then computed as the average over the particles inside a given cell with the particle in sight for each of the remaining cells. Using this approach, the large and small cells limits are exact. At a fixed cell size, the method also becomes exact in the limit of large lattices. We have applied the procedure to the two-dimensional anisotropic dipolar Heisenberg model. A detailed comparison between our method, the exact calculation and the cutoff radius approximation were done. Our results show that the cutoff-cell approach outperforms any cutoff radius approach as it maintains the long-range memory present in these interactions, contrary to the cutoff radius approximation. Besides that, we calculated the critical temperature and the critical behavior of the specific heat of the anisotropic Heisenberg model using our method. The results are in excellent agreement with extensive Monte Carlo simulations using Ewald summation.

  7. Second relativistic mean field and virial equation of state for astrophysical simulations

    SciTech Connect

    Shen, G.; Horowitz, C. J.; O'Connor, E.

    2011-06-15

    We generate a second equation of state (EOS) of nuclear matter for a wide range of temperatures, densities, and proton fractions for use in supernovae, neutron star mergers, and black hole formation simulations. We employ full relativistic mean field (RMF) calculations for matter at intermediate density and high density, and the virial expansion of a nonideal gas for matter at low density. For this EOS we use the RMF effective interaction FSUGold, whereas our earlier EOS was based on the RMF effective interaction NL3. The FSUGold interaction has a lower pressure at high densities compared to the NL3 interaction. We calculate the resulting EOS at over 100 000 grid points in the temperature range T=0 to 80 MeV, the density range n{sub B}=10{sup -8} to 1.6 fm{sup -3}, and the proton fraction range Y{sub p}=0 to 0.56. We then interpolate these data points using a suitable scheme to generate a thermodynamically consistent equation of state table on a finer grid. We discuss differences between this EOS, our NL3-based EOS, and previous EOSs by Lattimer-Swesty and H. Shen et al. for the thermodynamic properties, composition, and neutron star structure. The original FSUGold interaction produces an EOS, which we call FSU1.7, that has a maximum neutron star mass of 1.7 solar masses. A modification in the high-density EOS is introduced to increase the maximum neutron star mass to 2.1 solar masses and results in a slightly different EOS that we call FSU2.1. The EOS tables for FSU1.7 and FSU2.1 are available for download.

  8. Double Dynamo Signatures in a Global MHD Simulation and Mean-field Dynamos

    NASA Astrophysics Data System (ADS)

    Beaudoin, Patrice; Simard, Corinne; Cossette, Jean-François; Charbonneau, Paul

    2016-08-01

    The 11 year solar activity cycle is the most prominent periodic manifestation of the magnetohydrodynamical (MHD) large-scale dynamo operating in the solar interior, yet longer and shorter (quasi-) periodicities are also present. The so-called “quasi-biennial” signal appearing in many proxies of solar activity has been gaining increasing attention since its detection in p-mode frequency shifts, which suggests a subphotospheric origin. A number of candidate mechanisms have been proposed, including beating between co-existing global dynamo modes, dual dynamos operating in spatially separated regions of the solar interior, and Rossby waves driving short-period oscillations in the large-scale solar magnetic field produced by the 11 year activity cycle. In this article, we analyze a global MHD simulation of solar convection producing regular large-scale magnetic cycles, and detect and characterize shorter periodicities developing therein. By constructing kinematic mean-field α 2Ω dynamo models incorporating the turbulent electromotive force (emf) extracted from that same simulation, we find that dual-dynamo behavior materializes in fairly wide regions of the model’s parameters space. This suggests that the origin of the similar behavior detected in the MHD simulation lies with the joint complexity of the turbulent emf and differential rotation profile, rather that with dynamical interactions such as those mediated by Rossby waves. Analysis of the simulation also reveals that the dual dynamo operating therein leaves a double-period signature in the temperature field, consistent with a dual-period helioseismic signature. Order-of-magnitude estimates for the magnitude of the expected frequency shifts are commensurate with helioseismic measurements. Taken together, our results support the hypothesis that the solar quasi-biennial oscillations are associated with a secondary dynamo process operating in the outer reaches of the solar convection zone.

  9. Relativistic mean field model for entrainment in general relativistic superfluid neutron stars

    NASA Astrophysics Data System (ADS)

    Comer, G. L.; Joynt, R.

    2003-07-01

    General relativistic superfluid neutron stars have a significantly more intricate dynamics than their ordinary fluid counterparts. Superfluidity allows different superfluid (and superconducting) species of particles to have independent fluid flows, a consequence of which is that the fluid equations of motion contain as many fluid element velocities as superfluid species. Whenever the particles of one superfluid interact with those of another, the momentum of each superfluid will be a linear combination of both superfluid velocities. This leads to the so-called entrainment effect whereby the motion of one superfluid will induce a momentum in the other superfluid. We have constructed a fully relativistic model for entrainment between superfluid neutrons and superconducting protons using a relativistic σ-ω mean field model for the nucleons and their interactions. In this context there are two notions of “relativistic”: relativistic motion of the individual nucleons with respect to a local region of the star (i.e. a fluid element containing, say, an Avogadro’s number of particles), and the motion of fluid elements with respect to the rest of the star. While it is the case that the fluid elements will typically maintain average speeds at a fraction of that of light, the supranuclear densities in the core of a neutron star can make the nucleons themselves have quite high average speeds within each fluid element. The formalism is applied to the problem of slowly rotating superfluid neutron star configurations, a distinguishing characteristic being that the neutrons can rotate at a rate different from that of the protons.

  10. Solving the inverse Ising problem by mean-field methods in a clustered phase space with many states

    NASA Astrophysics Data System (ADS)

    Decelle, Aurélien; Ricci-Tersenghi, Federico

    2016-07-01

    In this work we explain how to properly use mean-field methods to solve the inverse Ising problem when the phase space is clustered, that is, many states are present. The clustering of the phase space can occur for many reasons, e.g., when a system undergoes a phase transition, but also when data are collected in different regimes (e.g., quiescent and spiking regimes in neural networks). Mean-field methods for the inverse Ising problem are typically used without taking into account the eventual clustered structure of the input configurations and may lead to very poor inference (e.g., in the low-temperature phase of the Curie-Weiss model). In this work we explain how to modify mean-field approaches when the phase space is clustered and we illustrate the effectiveness of our method on different clustered structures (low-temperature phases of Curie-Weiss and Hopfield models).

  11. Solving the inverse Ising problem by mean-field methods in a clustered phase space with many states.

    PubMed

    Decelle, Aurélien; Ricci-Tersenghi, Federico

    2016-07-01

    In this work we explain how to properly use mean-field methods to solve the inverse Ising problem when the phase space is clustered, that is, many states are present. The clustering of the phase space can occur for many reasons, e.g., when a system undergoes a phase transition, but also when data are collected in different regimes (e.g., quiescent and spiking regimes in neural networks). Mean-field methods for the inverse Ising problem are typically used without taking into account the eventual clustered structure of the input configurations and may lead to very poor inference (e.g., in the low-temperature phase of the Curie-Weiss model). In this work we explain how to modify mean-field approaches when the phase space is clustered and we illustrate the effectiveness of our method on different clustered structures (low-temperature phases of Curie-Weiss and Hopfield models). PMID:27575082

  12. On the bifurcation structure of the mean-field fluctuation in the globally coupled tent map systems

    NASA Astrophysics Data System (ADS)

    Chawanya, Tsuyoshi; Morita, Satoru

    1998-05-01

    A theoretical analysis on the behavior of the globally coupled tent map systems based on the kinetics of the mean-field value is presented. We investigated the nature of the mean-field fluctuation in large system size limit, and uncovered the existence of a complicated bifurcation structure that leads the appearance of collective motion with the increase of the coupling strength. The way to the appearance of the collective motion sensitively depends on the gradient a of individual tent-maps. For a belonging to a set which is dense in ( 2, 2 ), the collective motion appears when the coupling strength exceeds a certain threshold value, while for a belonging to another dense set in ( 2, 2 ), any non-zero coupling will induce the collective motion. The dependence of the amplitude of mean-field fluctuation on the coupling strength is also obtained as a function of the parameter a and the coupling strength.

  13. Differences between Mean-Field Dynamics and N-Particle Quantum Dynamics as a Signature of Entanglement

    SciTech Connect

    Weiss, Christoph; Teichmann, Niklas

    2008-04-11

    A Bose-Einstein condensate in a tilted double-well potential under the influence of time-periodic potential differences is investigated in the regime where the mean-field (Gross-Pitaevskii) dynamics become chaotic. For some parameters near stable regions, even averaging over several condensate oscillations does not remove the differences between mean-field and N-particle results. While introducing decoherence via piecewise deterministic processes reduces those differences, they are due to the emergence of mesoscopic entangled states in the chaotic regime.

  14. Deviations from mean-field behavior in disordered nanoscale superconductor normal-metal superconductor arrays

    NASA Astrophysics Data System (ADS)

    Kouh, Taejoon; Valles, J. M.

    2003-04-01

    We have fabricated quasi-two-dimensional disordered arrays of nanoscale Pb grains coupled by an overlayer of Ag grains. Their temperature-dependent resistive transitions follow predictions for an array of mesoscopic superconductor normal-metal superconductor junctions. The decrease of their transition temperatures with Ag overlayer thickness systematically deviates from the Cooper limit theory of the proximity effect as the Pb grain size decreases. The deviations occur when the estimated number of Cooper pairs per grain is <1 and suggest the approach to a superconductor-to-metal transition.

  15. Spatial Correlation in the Three-band Copper Oxide Model: Dynamical Mean-field Study with Configuration Interaction Based Impurity Solver

    NASA Astrophysics Data System (ADS)

    Go, Ara; Millis, Andrew J.

    2014-03-01

    The three-band copper oxide model is studied using the single-site and four-site dynamical mean-field theory with configuration interaction based impurity solver. Comparison of the single and four site approximations shows that short ranged antiferromagnetic correlations are crucial to the physics. In the undoped case, they increase the gap size, shift the metal-insulator phase boundary and enhance the conductivity at the gap edge. The relation of antiferromagnetism and the pseudogap is discussed for the doped case. The new solver permits the inclusion of more bath orbitals which are crucial for accurate studies of spectral properties near the gap edge. This work was supported by the US Department of Energy under Grants No. DOE FG02-04ER46169 and DE-SC0006613.

  16. Variational principle of Bogoliubov and generalized mean fields in many-particle interacting systems

    NASA Astrophysics Data System (ADS)

    Kuzemsky, A. L.

    2015-07-01

    The approach to the theory of many-particle interacting systems from a unified standpoint, based on the variational principle for free energy is reviewed. A systematic discussion is given of the approximate free energies of complex statistical systems. The analysis is centered around the variational principle of Bogoliubov for free energy in the context of its applications to various problems of statistical mechanics. The review presents a terse discussion of selected works carried out over the past few decades on the theory of many-particle interacting systems in terms of the variational inequalities. It is the purpose of this paper to discuss some of the general principles which form the mathematical background to this approach and to establish a connection of the variational technique with other methods, such as the method of the mean (or self-consistent) field in the many-body problem. The method is illustrated by applying it to various systems of many-particle interacting systems, such as Ising, Heisenberg and Hubbard models, superconducting (SC) and superfluid systems, etc. This work proposes a new, general and pedagogical presentation, intended both for those who are interested in basic aspects and for those who are interested in concrete applications.

  17. Irreducible Free Energy Expansion and Overlaps Locking in Mean Field Spin Glasses

    NASA Astrophysics Data System (ADS)

    Barra, Adriano

    2006-05-01

    Following the works of Guerra, 1995; Aizenmar and Contucci, J. State. Phys. 92 (5-6): 765-783 (1998), we introduce a diagrammatic formulation for a cavity field expansion around the critical temperature. This approach allows us to obtain a theory for the overlap's fluctuations and, in particular, the linear part of the Ghirlanda-Guerra relationships (GG) (often called Aizenman-Contucci polynomials (AC)) in a very simple way. We show moreover how these constraints are "superimposed" by the symmetry of the model with respect to the restriction required by thermodynamic stability. Within this framework it is possible to expand the free energy in terms of these irreducible overlaps fluctuations and in a form that simply put in evidence how the complexity of the solution is related to the complexity of the entropy.

  18. Stochastic approach to correlations beyond the mean field with the Skyrme interaction

    NASA Astrophysics Data System (ADS)

    Fukuoka, Y.; Nakatsukasa, T.; Funaki, Y.; Yabana, K.

    2012-10-01

    Large-scale calculation based on the multi-configuration Skyrme density functional theory is performed for the light N = Z even-even nucleus, 12C. Stochastic procedures and the imaginary-time evolution are utilized to prepare many Slater determinants. Each state is projected on eigenstates of parity and angular momentum. Then, performing the configuration mixing calculation with the Skyrme Hamiltonian, we obtain low-lying energy-eigenstates and their explicit wave functions. The generated wave functions are completely free from any assumption and symmetry restriction. Excitation spectra and transition probabilities are well reproduced, not only for the ground-state band, but for negative-parity excited states and the Hoyle state.

  19. Dynamics and termination cost of spatially coupled mean-field models

    NASA Astrophysics Data System (ADS)

    Caltagirone, Francesco; Franz, Silvio; Morris, Richard G.; Zdeborová, Lenka

    2014-01-01

    This work is motivated by recent progress in information theory and signal processing where the so-called spatially coupled design of systems leads to considerably better performance. We address relevant open questions about spatially coupled systems through the study of a simple Ising model. In particular, we consider a chain of Curie-Weiss models that are coupled by interactions up to a certain range. Indeed, it is well known that the pure (uncoupled) Curie-Weiss model undergoes a first-order phase transition driven by the magnetic field, and furthermore in the spinodal region such systems are unable to reach equilibrium in subexponential time if initialized in the metastable state. In contrast, the spatially coupled system is instead able to reach the equilibrium even when initialized to the metastable state. The equilibrium phase propagates along the chain in the form of a traveling wave. Here we study the speed of the wave front and the so-called termination cost—i.e., the conditions necessary for the propagation to occur. We reach several interesting conclusions about optimization of the speed and the cost.

  20. Mean field linear response within the elimination of the small component formalism to evaluate relativistic effects on magnetic properties

    NASA Astrophysics Data System (ADS)

    Roura, P. G.; Melo, J. I.; Ruiz de Azúa, M. C.; Giribet, C. G.

    2006-08-01

    The linear response within the elimination of the small component formalism is aimed at obtaining the leading order relativistic corrections to magnetic molecular properties in the context of the elimination of the small component approximation. In the present work we extend the method in order to include two-body effects in the form of a mean field one-body operator. To this end we consider the four-component Dirac-Hartree-Fock operator as the starting point in the evaluation of the second order relativistic expression of magnetic properties. The approach thus obtained is the fully consistent leading order approximation of the random phase approximation four-component formalism. The mean field effect on the relativistic corrections to both the diamagnetic and paramagnetic terms of magnetic properties taking into account both the Coulomb and Breit two-body interactions is considered.

  1. MEAN-FIELD MODELING OF AN α{sup 2} DYNAMO COUPLED WITH DIRECT NUMERICAL SIMULATIONS OF RIGIDLY ROTATING CONVECTION

    SciTech Connect

    Masada, Youhei; Sano, Takayoshi E-mail: sano@ile.osaka-u.ac.jp

    2014-10-10

    The mechanism of large-scale dynamos in rigidly rotating stratified convection is explored by direct numerical simulations (DNS) in Cartesian geometry. A mean-field dynamo model is also constructed using turbulent velocity profiles consistently extracted from the corresponding DNS results. By quantitative comparison between the DNS and our mean-field model, it is demonstrated that the oscillatory α{sup 2} dynamo wave, excited and sustained in the convection zone, is responsible for large-scale magnetic activities such as cyclic polarity reversal and spatiotemporal migration. The results provide strong evidence that a nonuniformity of the α-effect, which is a natural outcome of rotating stratified convection, can be an important prerequisite for large-scale stellar dynamos, even without the Ω-effect.

  2. Neural networks with excitatory and inhibitory components: Direct and inverse problems by a mean-field approach

    NASA Astrophysics Data System (ADS)

    di Volo, Matteo; Burioni, Raffaella; Casartelli, Mario; Livi, Roberto; Vezzani, Alessandro

    2016-01-01

    We study the dynamics of networks with inhibitory and excitatory leak-integrate-and-fire neurons with short-term synaptic plasticity in the presence of depressive and facilitating mechanisms. The dynamics is analyzed by a heterogeneous mean-field approximation, which allows us to keep track of the effects of structural disorder in the network. We describe the complex behavior of different classes of excitatory and inhibitory components, which give rise to a rich dynamical phase diagram as a function of the fraction of inhibitory neurons. Using the same mean-field approach, we study and solve a global inverse problem: reconstructing the degree probability distributions of the inhibitory and excitatory components and the fraction of inhibitory neurons from the knowledge of the average synaptic activity field. This approach unveils new perspectives on the numerical study of neural network dynamics and the possibility of using these models as a test bed for the analysis of experimental data.

  3. Brownian regime of finite-N corrections to particle motion in the XY Hamiltonian mean field model

    NASA Astrophysics Data System (ADS)

    Ribeiro, Bruno V.; Amato, Marco A.; Elskens, Yves

    2016-08-01

    We study the dynamics of the N-particle system evolving in the XY Hamiltonian mean field (HMF) model for a repulsive potential, when no phase transition occurs. Starting from a homogeneous distribution, particles evolve in a mean field created by the interaction with all others. This interaction does not change the homogeneous state of the system, and particle motion is approximately ballistic with small corrections. For initial particle data approaching a waterbag, it is explicitly proved that corrections to the ballistic velocities are in the form of independent Brownian noises over a time scale diverging not slower than {N}2/5 as N\\to ∞ , which proves the propagation of molecular chaos. Molecular dynamics simulations of the XY-HMF model confirm our analytical findings.

  4. Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons

    PubMed Central

    2012-01-01

    We derive the mean-field equations arising as the limit of a network of interacting spiking neurons, as the number of neurons goes to infinity. The neurons belong to a fixed number of populations and are represented either by the Hodgkin-Huxley model or by one of its simplified version, the FitzHugh-Nagumo model. The synapses between neurons are either electrical or chemical. The network is assumed to be fully connected. The maximum conductances vary randomly. Under the condition that all neurons’ initial conditions are drawn independently from the same law that depends only on the population they belong to, we prove that a propagation of chaos phenomenon takes place, namely that in the mean-field limit, any finite number of neurons become independent and, within each population, have the same probability distribution. This probability distribution is a solution of a set of implicit equations, either nonlinear stochastic differential equations resembling the McKean-Vlasov equations or non-local partial differential equations resembling the McKean-Vlasov-Fokker-Planck equations. We prove the well-posedness of the McKean-Vlasov equations, i.e. the existence and uniqueness of a solution. We also show the results of some numerical experiments that indicate that the mean-field equations are a good representation of the mean activity of a finite size network, even for modest sizes. These experiments also indicate that the McKean-Vlasov-Fokker-Planck equations may be a good way to understand the mean-field dynamics through, e.g. a bifurcation analysis. Mathematics Subject Classification (2000): 60F99, 60B10, 92B20, 82C32, 82C80, 35Q80. PMID:22657695

  5. Sedimentation of shelf sandstones in Queen Formation, McFarland and Means fields, central basin platform of Permian basin

    SciTech Connect

    Malicse, A.; Mazzullo, J.; Holley, C.; Mazzullo, S.J.

    1988-01-01

    The Queen Formation is a sequence of carbonates, evaporites, and sandstones of Permian (Guadalupian) age that is found across the subsurface of the Central Basin platform of the Permian basin. The formation is a major hydrocarbon reservoir in this region, and its primary reservoir facies are porous shelf sandstones and dolomites. Cores and well logs from McFarland and Means fields (on the northwest margin of the Central Basin platform) were examined to determine the sedimentary history of the shelf sandstones.

  6. Short-ranged interaction effects on Z2 topological phase transitions: The perturbative mean-field method

    NASA Astrophysics Data System (ADS)

    Lai, Hsin-Hua; Hung, Hsiang-Hsuan

    2015-02-01

    Time-reversal symmetric topological insulator (TI) is a novel state of matter that a bulk-insulating state carries dissipationless spin transport along the surfaces, embedded by the Z2 topological invariant. In the noninteracting limit, this exotic state has been intensively studied and explored with realistic systems, such as HgTe/(Hg, Cd)Te quantum wells. On the other hand, electronic correlation plays a significant role in many solid-state systems, which further influences topological properties and triggers topological phase transitions. Yet an interacting TI is still an elusive subject and most related analyses rely on the mean-field approximation and numerical simulations. Among the approaches, the mean-field approximation fails to predict the topological phase transition, in particular at intermediate interaction strength without spontaneously breaking symmetry. In this paper, we develop an analytical approach based on a combined perturbative and self-consistent mean-field treatment of interactions that is capable of capturing topological phase transitions beyond either method when used independently. As an illustration of the method, we study the effects of short-ranged interactions on the Z2 TI phase, also known as the quantum spin Hall (QSH) phase, in three generalized versions of the Kane-Mele (KM) model at half-filling on the honeycomb lattice. The results are in excellent agreement with quantum Monte Carlo (QMC) calculations on the same model and cannot be reproduced by either a perturbative treatment or a self-consistent mean-field treatment of the interactions. Our analytical approach helps to clarify how the symmetries of the one-body terms of the Hamiltonian determine whether interactions tend to stabilize or destabilize a topological phase. Moreover, our method should be applicable to a wide class of models where topological transitions due to interactions are in principle possible, but are not correctly predicted by either perturbative or self

  7. Organic crystal polymorphism: a benchmark for dispersion-corrected mean-field electronic structure methods.

    PubMed

    Brandenburg, Jan Gerit; Grimme, Stefan

    2016-08-01

    We analyze the energy landscape of the sixth crystal structure prediction blind test targets with various first principles and semi-empirical quantum chemical methodologies. A new benchmark set of 59 crystal structures (termed POLY59) for testing quantum chemical methods based on the blind test target crystals is presented. We focus on different means to include London dispersion interactions within the density functional theory (DFT) framework. We show the impact of pairwise dispersion corrections like the semi-empirical D2 scheme, the Tkatchenko-Scheffler (TS) method, and the density-dependent dispersion correction dDsC. Recent methodological progress includes higher-order contributions in both the many-body and multipole expansions. We use the D3 correction with Axilrod-Teller-Muto type three-body contribution, the TS based many-body dispersion (MBD), and the nonlocal van der Waals density functional (vdW-DF2). The density functionals with D3 and MBD correction provide an energy ranking of the blind test polymorphs in excellent agreement with the experimentally found structures. As a computationally less demanding method, we test our recently presented minimal basis Hartree-Fock method (HF-3c) and a density functional tight-binding Hamiltonian (DFTB). Considering the speed-up of three to four orders of magnitudes, the energy ranking provided by the low-cost methods is very reasonable. We compare the computed geometries with the corresponding X-ray data where TPSS-D3 performs best. The importance of zero-point vibrational energy and thermal effects on crystal densities is highlighted. PMID:27484372

  8. Hierarchical mean-field approach to the J1-J2 Heisenberg model on a square lattice

    NASA Astrophysics Data System (ADS)

    Isaev, Leonid; Ortiz, Gerardo; Dukelsky, Jorge

    2009-03-01

    We study the quantum phase diagram and excitation spectrum of the frustrated J1-J2 spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field approach, at the heart of which lies the idea of identifying relevant degrees of freedom, is developed. Thus, by performing educated, manifestly symmetry preserving mean-field approximations, we unveil fundamental properties of the system. We then compare various coverings of the square lattice with plaquettes, dimers and other degrees of freedom, and show that only the symmetric plaquette covering, which reproduces the original Bravais lattice, leads to the known phase diagram. The intermediate quantum paramagnetic phase is shown to be a (singlet) plaquette crystal, connected with the neighbouring N'eel phase by a continuous phase transition. We also introduce fluctuations around the hierarchical mean-field solutions, and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap, which closes in the N'eel and columnar phases. Our results suggest that the quantum phase transition between N'eel and paramagnetic phases can be properly described within the Ginzburg-Landau-Wilson paradigm.

  9. Hierarchical mean-field approach to the J1-J2 Heisenberg model on a square lattice

    NASA Astrophysics Data System (ADS)

    Isaev, L.; Ortiz, G.; Dukelsky, J.

    2009-01-01

    We study the quantum phase diagram and excitation spectrum of the frustrated J1-J2 spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field approach, at the heart of which lies the idea of identifying relevant degrees of freedom, is developed. Thus, by performing educated, manifestly symmetry-preserving mean-field approximations, we unveil fundamental properties of the system. We then compare various coverings of the square lattice with plaquettes, dimers, and other degrees of freedom, and show that only the symmetric plaquette covering, which reproduces the original Bravais lattice, leads to the known phase diagram. The intermediate quantum paramagnetic phase is shown to be a (singlet) plaquette crystal, connected with the neighboring Néel phase by a continuous phase transition. We also introduce fluctuations around the hierarchical mean-field solutions, and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap, which closes in the Néel and columnar phases. Our results suggest that the quantum phase transition between Néel and paramagnetic phases can be properly described within the Ginzburg-Landau-Wilson paradigm.

  10. Mean-field equations for stochastic firing-rate neural fields with delays: Derivation and noise-induced transitions

    NASA Astrophysics Data System (ADS)

    Touboul, Jonathan

    2012-08-01

    In this manuscript we analyze the collective behavior of mean-field limits of large-scale, spatially extended stochastic neuronal networks with delays. Rigorously, the asymptotic regime of such systems is characterized by a very intricate stochastic delayed integro-differential McKean-Vlasov equation that remain impenetrable, leaving the stochastic collective dynamics of such networks poorly understood. In order to study these macroscopic dynamics, we analyze networks of firing-rate neurons, i.e. with linear intrinsic dynamics and sigmoidal interactions. In that case, we prove that the solution of the mean-field equation is Gaussian, hence characterized by its two first moments, and that these two quantities satisfy a set of coupled delayed integro-differential equations. These equations are similar to usual neural field equations, and incorporate noise levels as a parameter, allowing analysis of noise-induced transitions. We identify through bifurcation analysis several qualitative transitions due to noise in the mean-field limit. In particular, stabilization of spatially homogeneous solutions, synchronized oscillations, bumps, chaotic dynamics, wave or bump splitting are exhibited and arise from static or dynamic Turing-Hopf bifurcations. These surprising phenomena allow further exploring the role of noise in the nervous system.

  11. Lars Onsager Prize: The mean field solution for Hard Sphere Jamming and a new scenario for the low temperature landscape of glasses

    NASA Astrophysics Data System (ADS)

    Parisi, Giorgio

    In a hard spheres systems particles cannot overlap. Increasing the density we reach a point where most of the particles are blocked and the density cannot be increased any more: this is the jamming point. The jamming point separates the phase, where all the constraint can be satisfied, from an unsatifiable phase, where spheres do have to overlap. A scaling theory of the behavior around the jamming critical point has been formulated and a few critical exponents have been introduced. The exponents are apparently super-universal, as far as they do seem to be independent from the space dimensions. The mean field version of the model (i.e. the infinite dimensions limit) has been solved analytically using broken replica symmetry techniques and the computed critical exponents have been found in a remarkable agreement with three-dimensional and two-dimensional numerical results and experiments. The theory predicts in hard spheres (in glasses) a new transition (the Gardener transition) from the replica symmetric phase to the replica broken phase at high density (at low temperature), in agreement with simulations on hard sphere systems. I will briefly discuss the possible consequences of this new picture on the very low temperature behavior of glasses in the quantum regime.

  12. Microstructure from ferroelastic transitions using strain pseudospin clock models in two and three dimensions: A local mean-field analysis

    NASA Astrophysics Data System (ADS)

    Vasseur, Romain; Lookman, Turab; Shenoy, Subodh R.

    2010-09-01

    We show how microstructure can arise in first-order ferroelastic structural transitions, in two and three spatial dimensions, through a local mean-field approximation of their pseudospin Hamiltonians, that include anisotropic elastic interactions. Such transitions have symmetry-selected physical strains as their NOP -component order parameters, with Landau free energies that have a single zero-strain “austenite” minimum at high temperatures, and spontaneous-strain “martensite” minima of NV structural variants at low temperatures. The total free energy also has gradient terms, and power-law anisotropic effective interactions, induced by “no-dislocation” St Venant compatibility constraints. In a reduced description, the strains at Landau minima induce temperature dependent, clocklike ZNV+1 Hamiltonians, with NOP -component strain-pseudospin vectors S⃗ pointing to NV+1 discrete values (including zero). We study elastic texturing in five such first-order structural transitions through a local mean-field approximation of their pseudospin Hamiltonians, that include the power-law interactions. As a prototype, we consider the two-variant square/rectangle transition, with a one-component pseudospin taking NV+1=3 values of S=0,±1 , as in a generalized Blume-Capel model. We then consider transitions with two-component (NOP=2) pseudospins: the equilateral to centered rectangle (NV=3) ; the square to oblique polygon (NV=4) ; the triangle to oblique (NV=6) transitions; and finally the three-dimensional (3D) cubic to tetragonal transition (NV=3) . The local mean-field solutions in two-dimensional and 3D yield oriented domain-wall patterns as from continuous-variable strain dynamics, showing the discrete-variable models capture the essential ferroelastic texturings. Other related Hamiltonians illustrate that structural transitions in materials science can be the source of interesting spin models in statistical mechanics.

  13. Mean-field dispersion-induced spatial synchrony, oscillation and amplitude death, and temporal stability in an ecological model.

    PubMed

    Banerjee, Tanmoy; Dutta, Partha Sharathi; Gupta, Anubhav

    2015-05-01

    One of the most important issues in spatial ecology is to understand how spatial synchrony and dispersal-induced stability interact. In the existing studies it is shown that dispersion among identical patches results in spatial synchrony; on the other hand, the combination of spatial heterogeneity and dispersion is necessary for dispersal-induced stability (or temporal stability). Population synchrony and temporal stability are thus often thought of as conflicting outcomes of dispersion. In contrast to the general belief, in this present study we show that mean-field dispersion is conducive to both spatial synchrony and dispersal-induced stability even in identical patches. This simultaneous occurrence of rather conflicting phenomena is governed by the suppression of oscillation states, namely amplitude death (AD) and oscillation death (OD). These states emerge through spatial synchrony of the oscillating patches in the strong-coupling strength. We present an interpretation of the mean-field diffusive coupling in the context of ecology and identify that, with increasing mean-field density, an open ecosystem transforms into a closed ecosystem. We report on the occurrence of OD in an ecological model and explain its significance. Using a detailed bifurcation analysis we show that, depending on the mortality rate and carrying capacity, the system shows either AD or both AD and OD. We also show that the results remain qualitatively the same for a network of oscillators. We identify a new transition scenario between the same type of oscillation suppression states whose geneses differ. In the parameter-mismatched case, we further report on the direct transition from OD to AD through a transcritical bifurcation. We believe that this study will lead to a proper interpretation of AD and OD in ecology, which may be important for the conservation and management of several communities in ecosystems. PMID:26066241

  14. Mean-field dispersion-induced spatial synchrony, oscillation and amplitude death, and temporal stability in an ecological model

    NASA Astrophysics Data System (ADS)

    Banerjee, Tanmoy; Dutta, Partha Sharathi; Gupta, Anubhav

    2015-05-01

    One of the most important issues in spatial ecology is to understand how spatial synchrony and dispersal-induced stability interact. In the existing studies it is shown that dispersion among identical patches results in spatial synchrony; on the other hand, the combination of spatial heterogeneity and dispersion is necessary for dispersal-induced stability (or temporal stability). Population synchrony and temporal stability are thus often thought of as conflicting outcomes of dispersion. In contrast to the general belief, in this present study we show that mean-field dispersion is conducive to both spatial synchrony and dispersal-induced stability even in identical patches. This simultaneous occurrence of rather conflicting phenomena is governed by the suppression of oscillation states, namely amplitude death (AD) and oscillation death (OD). These states emerge through spatial synchrony of the oscillating patches in the strong-coupling strength. We present an interpretation of the mean-field diffusive coupling in the context of ecology and identify that, with increasing mean-field density, an open ecosystem transforms into a closed ecosystem. We report on the occurrence of OD in an ecological model and explain its significance. Using a detailed bifurcation analysis we show that, depending on the mortality rate and carrying capacity, the system shows either AD or both AD and OD. We also show that the results remain qualitatively the same for a network of oscillators. We identify a new transition scenario between the same type of oscillation suppression states whose geneses differ. In the parameter-mismatched case, we further report on the direct transition from OD to AD through a transcritical bifurcation. We believe that this study will lead to a proper interpretation of AD and OD in ecology, which may be important for the conservation and management of several communities in ecosystems.

  15. Mean-field dynamics of the superfluid-insulator phase transition in a gas of ultracold atoms

    NASA Astrophysics Data System (ADS)

    Zakrzewski, Jakub

    2005-04-01

    A large-scale dynamical simulation of the superfluid-Mott-insulator transition in a gas of ultracold atoms placed in an optical lattice is performed using the time-dependent Gutzwiller mean-field approach. This approximate treatment allows us to take into account most of the details of the recent experiment [Greiner , Nature (London) 415, 39 (2002)] where by changing the depth of the lattice potential an adiabatic transition from a superfluid to a Mott insulator state has been reported. Our simulations reveal a significant excitation of the system with a transition to insulator in restricted regions of the trap only.

  16. A Mean-Field Photoreaction Model for the Pretilt Generation of a Liquid Crystal on Photopolymer Layers upon Ultraviolet Exposure

    NASA Astrophysics Data System (ADS)

    Na, Jun-Hee; Pae, Hyungwu; Kim, Jinyool; Yu, Chang-Jae; Lee, Sin-Doo

    2011-03-01

    We present a mean-field photoreaction model for the pretilt generation of a nematic liquid crystal (NLC) on the surfaces of photopolymers upon the exposure of ultraviolet (UV) light. The angular distribution function of photopolymer side chains, calculated in the photoreaction model, is used for determining the surface anchoring energy within the Rapini-Papoular approximation. The pretilt angle transition from the homeotropic alignment to the planar alignment of the NLC is demonstrated in two photopolymers with different alkyl chain lengths as a function of the UV exposure time. The main features of the experimental results agree well with theoretical predictions.

  17. Mean-field plus various types of pairing models and an exact boson mapping of the standard pairing model

    SciTech Connect

    Pan Feng; Wang Yin; Guan Xin; Jia Lu; Chen Xiangrong; Draayer, J. P.

    2011-06-28

    Exact solutions of Nilsson mean-field with various pairing interactions are reviewed. Some even-odd mass differences and moments of inertia of low-lying states for rare earth and actinide nuclei are calculated for the nearest-orbit pairing approximation as well as for the extended pairing model and compared to available experimental data. An exact boson mapping of the standard pairing Hamiltonian is also reported. Under the mapping, fermion pair operators are mapped exactly onto corresponding bosons. The image of the mapping is a Bose-Hubbard model with orbit-dependent hopping.

  18. A Mean Field Analysis of the Exchange Coupling (J) For 2- and 3-D Structured Tetracyanoethylenide (TCNE -)-based Magnets

    SciTech Connect

    McConnell, Amber C.; Fishman, Randy Scott; Miller, Joel S.

    2012-01-01

    Mean field expressions based on the simple Heisenberg model were derived to correlate the inter- and intralayer exchange coupling to the critical temperatures, Tc, for several TCNE (tetracyanoethylene) based magnets with extended 2- and 3-D structure types. These expressions were used to estimate the exchange coupling, J, for 2-D ferrimagnetic [MII(TCNE)(NCMe)2]+ (M = Mn, Fe), 3-D antiferromagnetic MnII(TCNE)[C4(CN)8]1/2, and 3-D ferrimagnetic MnII(TCNE)3/2(I3)1/2. The sign and magnitude of the exchange coupling are in accord with previously reported magnetic data.

  19. A Mean Field Analysis of the Exchange Coupling (J) for Non-cubic Prussian Blue Analogue Magnets

    SciTech Connect

    DaSilva, Jack G.; McConnell, Amber C.; Fishman, Randy Scott; Miller, Joel S.

    2012-01-01

    Mean field expressions based on the simple Heisenberg model were derived to correlate the intra- and interlayer exchange couplings to the critical temperatures, Tc, for three metallocyanide-based magnets with extended 2- and 3-D structure types. These expressions were used to estimate the exchange coupling, J, for 2-D ferrimagnetic [NEt4]2MnII3(CN)8, 3-D antiferromagnetic [NEt4]MnII3(CN)7, and 3-D antiferromagnetic interpenetrating 3-D MnII(CN)2. The type and magnitude of the exchange coupling are in accord with the previously reported magnetic data.

  20. Mean-Field and RPA Approaches to Stable and Unstable Nuclei with Semi-Realistic NN Interaction

    SciTech Connect

    Nakada, H.

    2011-05-06

    A M3Y-type semi-realistic NN interaction has been applied to the mean-field and the RPA calculations. Explicitly including the tensor force and the central part of the one-pion exchange potential, the semi-realistic interaction is useful in studying the Z or N dependence of the nuclear shell structure. The magicity of N = 32, 40 and 58 in the neutron-rich Ca and Ni nuclei has been investigated, and the Z = 28 magicity in {sup 78}Ni has been argued. Significance of the tensor force in magnetic transitions is demonstrated by the M1 excitation of {sup 208}Pb.

  1. Solvent electronic polarization effects on a charge transfer excitation studied by the mean-field QM/MM method

    SciTech Connect

    Nakano, Hiroshi

    2015-12-31

    Electronic polarization effects of a medium can have a significant impact on a chemical reaction in condensed phases. We discuss the effects on the charge transfer excitation of a chromophore, N,N-dimethyl-4-nitroaniline, in various solvents using the mean-field QM/MM method with a polarizable force field. The results show that the explicit consideration of the solvent electronic polarization effects is important especially for a solvent with a low dielectric constant when we study the solvatochromism of the chromophore.

  2. Connection between the nuclear matter mean-field equation of state and the quark and gluon condensates at high density

    SciTech Connect

    Malheiro, M.; Dey, M.; Delfino, A.; Dey, J. |||

    1997-01-01

    It is known now that chiral symmetry restoration requires the meson-nucleon couplings to be density-dependent in nuclear-matter mean-field models. We further show that, quite generally, the quark and gluon condensates in medium are related to the trace of the energy-momentum tensor of nuclear matter and in these models the incompressibility K must be less than 3 times the chemical potential {mu}. In the critical density {rho}{sub c}, the gluon condensate is only reduced by 20{percent}, indicating a larger effective nucleon mass. {copyright} {ital 1997} {ital The American Physical Society}

  3. Mean-field studies of time reversal breaking states in super-heavy nuclei with the Gogny force

    SciTech Connect

    Robledo, L. M.

    2015-10-15

    Recent progress on the description of time reversal breaking (odd mass and multi-quasiparticle excitation) states in super-heavy nuclei within a mean field framework and using several flavors of the Gogny interaction is reported. The study includes ground and excited states in selected odd mass isotopes of nobelium and mendelevium as well as high K isomeric states in {sup 254}No. These are two and four-quasiparticle excitations that are treated in the same self-consistent HFB plus blocking framework as the odd mass states.

  4. Obtaining Arbitrary Prescribed Mean Field Dynamics for Recurrently Coupled Networks of Type-I Spiking Neurons with Analytically Determined Weights

    PubMed Central

    Nicola, Wilten; Tripp, Bryan; Scott, Matthew

    2016-01-01

    A fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF). The NEF approach requires quantities called decoders which are solved through an optimization problem requiring large matrix inversion. Here, we show how a decoder can be obtained analytically for type I and certain type II firing rates as a function of the heterogeneity of its associated neuron. These decoders generate approximants for functions that converge to the desired function in mean-squared error like 1/N, where N is the number of neurons in the network. We refer to these decoders as scale-invariant decoders due to their structure. These decoders generate weights for a network of neurons through the NEF formula for weights. These weights force the spiking network to have arbitrary and prescribed mean field dynamics. The weights generated with scale-invariant decoders all lie on low dimensional hypersurfaces asymptotically. We demonstrate the applicability of these scale-invariant decoders and weight surfaces by constructing networks of spiking theta neurons that replicate the dynamics of various well known dynamical systems such as the neural integrator, Van der Pol system and the Lorenz system. As these decoders are analytically determined and non-unique, the weights are also analytically determined and non-unique. We discuss the implications for measured weights of neuronal networks. PMID:26973503

  5. Microstructure for ferroelastic transitions from strain pseudo-spin clock models in two and three dimensions: a mean field analysis

    SciTech Connect

    Lookman, Turab; Vasseur, Romain

    2009-01-01

    We obtain the microstructure of ferroelastic transitions in two and three dimensions from the solution of their corresponding discrete pseudo-spin models. In two dimensions we consider two transitions each from the high symmetry square and triangle symmetries: square-to-rectangle (SR), square-to-oblique (SO), triangle-to-centered rectangle (TR) and triangle-to-oblique (TO). In three dimensions we study the corresponding spin model for the cubic to tetragonal transition. The Landau free energies for these transitions result in N+ I states clock models (Z{sub N}) with long range interactions and we derive mean-field self-consistency equations for the clock model Hamiltonians. The microstructures from the mean-field solutions of the models are very similar to those obtained from the original continuum models or Monte Carlo simulations on the spin models (in the SR case), illustrating that these discrete models capture the salient physics. The models, in the presence of disorder, provide the basis for the study of the strain glass phase observed in martensitic alloys.

  6. Relativistic mean-field models with scaled hadron masses and couplings: Hyperons and maximum neutron star mass

    NASA Astrophysics Data System (ADS)

    Maslov, K. A.; Kolomeitsev, E. E.; Voskresensky, D. N.

    2016-06-01

    An equation of state of cold nuclear matter with an arbitrary isotopic composition is studied within a relativistic mean-field approach with hadron masses and coupling constants depending self-consistently on the scalar mean-field. All hadron masses decrease universally with the scalar field growth, whereas meson-nucleon coupling constants can vary differently. More specifically we focus on two modifications of the KVOR model studied previously. One extension of the model (KVORcut) demonstrates that the equation of state stiffens if the increase of the scalar-field magnitude with the density is bounded from above at some value for baryon densities above the saturation nuclear density. This can be realized if the nucleon vector-meson coupling constant changes rapidly as a function of the scalar field slightly above the desired value. The other version of the model (MKVOR) utilizes a smaller value of the nucleon effective mass at the nuclear saturation density and a saturation of the scalar field in the isospin asymmetric matter induced by a strong variation of the nucleon isovector-meson coupling constant as function of the scalar field. A possibility of hyperonization of the matter in neutron star interiors is incorporated. Our equations of state fulfill majority of known empirical constraints including the pressure-density constraint from heavy-ion collisions, direct Urca constraint, gravitational-baryon mass constraint for the pulsar J0737-3039B, and the constraint on the maximum mass of the neutron stars.

  7. Supercritical Mean Field Equations on Convex Domains and the Onsager's Statistical Description of Two-Dimensional Turbulence

    NASA Astrophysics Data System (ADS)

    Bartolucci, Daniele; De Marchis, Francesca

    2015-08-01

    We are motivated by the study of the Microcanonical Variational Principle within Onsager's description of two-dimensional turbulence in the range of energies where the equivalence of statistical ensembles fails. We obtain sufficient conditions for the existence and multiplicity of solutions for the corresponding Mean Field Equation on convex and "thin" enough domains in the supercritical (with respect to the Moser-Trudinger inequality) regime. This is a brand new achievement since existence results in the supercritical region were previously known only on multiply connected domains. We then study the structure of these solutions by the analysis of their linearized problems and we also obtain a new uniqueness result for solutions of the Mean Field Equation on thin domains whose energy is uniformly bounded from above. Finally we evaluate the asymptotic expansion of those solutions with respect to the thinning parameter and, combining it with all the results obtained so far, we solve the Microcanonical Variational Principle in a small range of supercritical energies where the entropy is shown to be concave.

  8. Mean-field approach in the multi-component gas of interacting particles applied to relativistic heavy-ion collisions

    NASA Astrophysics Data System (ADS)

    Anchishkin, D.; Vovchenko, V.

    2015-10-01

    A generalized mean-field approach for the thermodynamic description of relativistic single- and multi-component gas in the grand canonical ensemble is formulated. In the framework of the proposed approach, different phenomenological excluded-volume procedures are presented and compared to the existing ones. The mean-field approach is then used to effectively include hard-core repulsion in hadron-resonance gas model for description of chemical freeze-out in heavy-ion collisions. We calculate the collision energy dependence of several quantities for different values of hard-core hadron radius and for different excluded-volume procedures such as the van der Waals and Carnahan-Starling models. It is shown that a choice of the excluded-volume model becomes important for large particle densities. For large enough values of hadron radii (r≳ 0.9 fm) there can be a sizable difference between different excluded-volume procedures used to describe the chemical freeze-out in heavy-ion collisions. At the same time, for the smaller and more commonly used values of hard-core hadron radii (r≲ 0.5 fm), the precision of the van der Waals excluded-volume procedure is shown to be sufficient.

  9. MEAN-FIELD SOLAR DYNAMO MODELS WITH A STRONG MERIDIONAL FLOW AT THE BOTTOM OF THE CONVECTION ZONE

    SciTech Connect

    Pipin, V. V.; Kosovichev, A. G.

    2011-09-01

    This paper presents a study of kinematic axisymmetric mean-field dynamo models for the case of meridional circulation with a deep-seated stagnation point and a strong return flow at the bottom of the convection zone. This kind of circulation follows from mean-field models of the angular momentum balance in the solar convection zone. The dynamo models include turbulent sources of the large-scale poloidal magnetic field production due to kinetic helicity and a combined effect due to the Coriolis force and large-scale electric current. In these models the toroidal magnetic field, which is responsible for sunspot production, is concentrated at the bottom of the convection zone and is transported to low-latitude regions by a meridional flow. The meridional component of the poloidal field is also concentrated at the bottom of the convection zone, while the radial component is concentrated in near-polar regions. We show that it is possible for this type of meridional circulation to construct kinematic dynamo models that resemble in some aspects the sunspot magnetic activity cycle. However, in the near-equatorial regions the phase relation between the toroidal and poloidal components disagrees with observations. We also show that the period of the magnetic cycle may not always monotonically decrease with the increase of the meridional flow speed. Thus, for further progress it is important to determine the structure of the meridional circulation, which is one of the critical properties, from helioseismology observations.

  10. Modeling MHD accretion-ejection: episodic ejections of jets triggered by a mean-field disk dynamo

    SciTech Connect

    Stepanovs, Deniss; Fendt, Christian; Sheikhnezami, Somayeh E-mail: fendt@mpia.de

    2014-11-20

    We present MHD simulations exploring the launching, acceleration, and collimation of jets and disk winds. The evolution of the disk structure is consistently taken into account. Extending our earlier studies, we now consider the self-generation of the magnetic field by an α{sup 2}Ω mean-field dynamo. The disk magnetization remains on a rather low level, which helps to evolve the simulations for T > 10, 000 dynamical time steps on a domain extending 1500 inner disk radii. We find the magnetic field of the inner disk to be similar to the commonly found open field structure, favoring magneto-centrifugal launching. The outer disk field is highly inclined and predominantly radial. Here, differential rotation induces a strong toroidal component, which plays a key role in outflow launching. These outflows from the outer disk are slower, denser, and less collimated. If the dynamo action is not quenched, magnetic flux is continuously generated, diffuses outward through the disk, and fills the entire disk. We have invented a toy model triggering a time-dependent mean-field dynamo. The duty cycles of this dynamo lead to episodic ejections on similar timescales. When the dynamo is suppressed as the magnetization falls below a critical value, the generation of the outflows and also accretion is inhibited. The general result is that we can steer episodic ejection and large-scale jet knots by a disk-intrinsic dynamo that is time-dependent and regenerates the jet-launching magnetic field.

  11. Generalized mean-field approach to simulate the dynamics of large open spin ensembles with long range interactions

    NASA Astrophysics Data System (ADS)

    Krämer, Sebastian; Ritsch, Helmut

    2015-12-01

    We numerically study the collective coherent and dissipative dynamics in spin lattices with long range interactions in one, two and three dimensions. For generic geometric configurations with a small spin number, which are fully solvable numerically, we show that a dynamical mean-field approach based upon a spatial factorization of the density operator often gives a surprisingly accurate representation of the collective dynamics. Including all pair correlations at any distance in the spirit of a second order cumulant expansion improves the numerical accuracy by at least one order of magnitude. We then apply this truncated expansion method to simulate large numbers of spins from about ten in the case of the full quantum model, a few thousand, if all pair correlations are included, up to several ten-thousands in the mean-field approximation. We find collective modifications of the spin dynamics in surprisingly large system sizes. In 3D, the mutual interaction strength does not converge to a desired accuracy within the maximum system sizes we can currently implement. Extensive numerical tests help in identifying interaction strengths and geometric configurations where our approximations perform well and allow us to state fairly simple error estimates. By simulating systems of increasing size we show that in one and two dimensions we can include as many spins as needed to capture the properties of infinite size systems with high accuracy. As a practical application our approach is well suited to provide error estimates for atomic clock setups or super radiant lasers using magic wavelength optical lattices.

  12. Vlasov formalism for extended relativistic mean field models: The crust-core transition and the stellar matter equation of state

    NASA Astrophysics Data System (ADS)

    Pais, Helena; Providência, Constança

    2016-07-01

    The Vlasov formalism is extended to relativistic mean field hadron models with nonlinear terms up to fourth order and applied to the calculation of the crust-core transition density. The effect of the nonlinear ω ρ and σ ρ coupling terms on the crust-core transition density and pressure and on the macroscopic properties of some families of hadronic stars is investigated. For that purpose, six families of relativistic mean field models are considered. Within each family, the members differ in the symmetry energy behavior. For all the models, the dynamical spinodals are calculated, and the crust-core transition density and pressure and the neutron star mass-radius relations are obtained. The effect on the star radius of the inclusion of a pasta calculation in the inner crust is discussed. The set of six models that best satisfy terrestrial and observational constraints predicts a radius of 13.6 ±0.3 km and a crust thickness of 1.36 ±0.06 km for a 1.4 M⊙ star.

  13. Nonrelativistic theory of heavy-ion collisions

    SciTech Connect

    Bertsch, G.

    1984-07-17

    A wide range of phenomena is observed in heavy-ion collisions, calling for a comprehensive theory based on fundamental principles of many-particle quantum mechanics. At low energies, the nuclear dynamics is controlled by the mean field, as we know from spectroscopic nuclear physics. We therefore expect the comprehensive theory of collisions to contain mean-field theory at low energies. The mean-field theory is the subject of the first lectures in this chapter. This theory can be studied quantum mechanically, in which form it is called TDHF (time-dependent Hartree-Fock), or classically, where the equation is called the Vlasov equation. 25 references, 14 figures.

  14. Gap junctions mediate large-scale Turing structures in a mean-field cortex driven by subcortical noise.

    PubMed

    Steyn-Ross, Moira L; Steyn-Ross, D A; Wilson, M T; Sleigh, J W

    2007-07-01

    One of the grand puzzles in neuroscience is establishing the link between cognition and the disparate patterns of spontaneous and task-induced brain activity that can be measured clinically using a wide range of detection modalities such as scalp electrodes and imaging tomography. High-level brain function is not a single-neuron property, yet emerges as a cooperative phenomenon of multiply-interacting populations of neurons. Therefore a fruitful modeling approach is to picture the cerebral cortex as a continuum characterized by parameters that have been averaged over a small volume of cortical tissue. Such mean-field cortical models have been used to investigate gross patterns of brain behavior such as anesthesia, the cycles of natural sleep, memory and erasure in slow-wave sleep, and epilepsy. There is persuasive and accumulating evidence that direct gap-junction connections between inhibitory neurons promote synchronous oscillatory behavior both locally and across distances of some centimeters, but, to date, continuum models have ignored gap-junction connectivity. In this paper we employ simple mean-field arguments to derive an expression for D2, the diffusive coupling strength arising from gap-junction connections between inhibitory neurons. Using recent neurophysiological measurements reported by Fukuda [J. Neurosci. 26, 3434 (2006)], we estimate an upper limit of D2 approximately 0.6cm2. We apply a linear stability analysis to a standard mean-field cortical model, augmented with gap-junction diffusion, and find this value for the diffusive coupling strength to be close to the critical value required to destabilize the homogeneous steady state. Computer simulations demonstrate that larger values of D2 cause the noise-driven model cortex to spontaneously crystalize into random mazelike Turing structures: centimeter-scale spatial patterns in which regions of high-firing activity are intermixed with regions of low-firing activity. These structures are consistent

  15. Gap junctions mediate large-scale Turing structures in a mean-field cortex driven by subcortical noise

    NASA Astrophysics Data System (ADS)

    Steyn-Ross, Moira L.; Steyn-Ross, D. A.; Wilson, M. T.; Sleigh, J. W.

    2007-07-01

    One of the grand puzzles in neuroscience is establishing the link between cognition and the disparate patterns of spontaneous and task-induced brain activity that can be measured clinically using a wide range of detection modalities such as scalp electrodes and imaging tomography. High-level brain function is not a single-neuron property, yet emerges as a cooperative phenomenon of multiply-interacting populations of neurons. Therefore a fruitful modeling approach is to picture the cerebral cortex as a continuum characterized by parameters that have been averaged over a small volume of cortical tissue. Such mean-field cortical models have been used to investigate gross patterns of brain behavior such as anesthesia, the cycles of natural sleep, memory and erasure in slow-wave sleep, and epilepsy. There is persuasive and accumulating evidence that direct gap-junction connections between inhibitory neurons promote synchronous oscillatory behavior both locally and across distances of some centimeters, but, to date, continuum models have ignored gap-junction connectivity. In this paper we employ simple mean-field arguments to derive an expression for D2 , the diffusive coupling strength arising from gap-junction connections between inhibitory neurons. Using recent neurophysiological measurements reported by Fukuda [J. Neurosci. 26, 3434 (2006)], we estimate an upper limit of D2≈0.6cm2 . We apply a linear stability analysis to a standard mean-field cortical model, augmented with gap-junction diffusion, and find this value for the diffusive coupling strength to be close to the critical value required to destabilize the homogeneous steady state. Computer simulations demonstrate that larger values of D2 cause the noise-driven model cortex to spontaneously crystalize into random mazelike Turing structures: centimeter-scale spatial patterns in which regions of high-firing activity are intermixed with regions of low-firing activity. These structures are consistent with the

  16. Periodic ordering of clusters and stripes in a two-dimensional lattice model. I. Ground state, mean-field phase diagram and structure of the disordered phases

    SciTech Connect

    Pekalski, J.; Ciach, A.; Almarza, N. G.

    2014-03-21

    The short-range attraction and long-range repulsion between nanoparticles or macromolecules can lead to spontaneous pattern formation on solid surfaces, fluid interfaces, or membranes. In order to study the self-assembly in such systems we consider a triangular lattice model with nearest-neighbor attraction and third-neighbor repulsion. At the ground state of the model (T = 0) the lattice is empty for small values of the chemical potential μ, and fully occupied for large μ. For intermediate values of μ periodically distributed clusters, bubbles, or stripes appear if the repulsion is sufficiently strong. At the phase coexistences between the vacuum and the ordered cluster phases and between the cluster and the lamellar (stripe) phases the entropy per site does not vanish. As a consequence of this ground state degeneracy, disordered fluid phases consisting of clusters or stripes are stable, and the surface tension vanishes. For T > 0 we construct the phase diagram in the mean-field approximation and calculate the correlation function in the self-consistent Brazovskii-type field theory.

  17. Quantum Switching at a Mean-Field Instability of a Bose-Einstein Condensate in an Optical Lattice

    SciTech Connect

    Shchesnovich, V. S.; Konotop, V. V.

    2009-02-06

    It is shown that bifurcation of the mean-field dynamics of a Bose-Einstein condensate can be related to the quantum phase transition of the original many-body system. As an example we explore the intraband tunneling in the two-dimensional optical lattice. Such a system allows for easy control by the lattice depth as well as for macroscopic visualization of the phase transition. The system manifests switching between two self-trapping states or from a self-trapping state to a superposition of the macroscopically populated self-trapping states with a steplike variation of the control parameter about the bifurcation point. We have also observed the magnification of the microscopic difference between the even and odd number of atoms to a macroscopically distinguishable dynamics of the system.

  18. Approximate analytical solution for nuclear matter in a mean-field Walecka model and Coester line behavior

    SciTech Connect

    Delfino, A.; Silva, J.B.; Malheiro, M.

    2006-03-15

    We study nuclear matter, at the mean-field approximation, by considering as equal the values of the scalar and the vector density in the Walecka model, which is a very reasonable approximation up to the nuclear matter saturation density. It turns out that the model has an analytical solution for the scalar and vector couplings as functions only of the nuclear matter density and binding energy. The nuclear matter properties are very close to the original version of the model. This solution allows us to show that the correlation between the binding energy and the saturation density is Coester line like. The liquid-gas phase transition is also studied and the critical and flash temperatures are again very similar to the original ones.

  19. Bare- and Dressed-Ion Impact Collisions from Neon Atoms Studied Within a Nonperturbative Mean-Field Approach

    NASA Astrophysics Data System (ADS)

    Schenk, Gerald; Kirchner, Tom

    We study electron removal processes in collisions of bare and dressed doubly charged ions with neon atoms in the 20 keV/u to 1 MeV/u impact energy regime. The many-electron problem is represented by a single mean field, which in the case of dressed-ion impact includes the projectile electrons. Moreover, the same basis is used to propagate all active orbitals thereby ensuring orthogonality at all times and allowing for a final-state analysis in terms of standard Slater determinantal wave functions. The same approach was used in a recent work for B2+ -Ne collisions [Phys. Rev. A 88 012712], in which we examined the role of the projectile electrons for target-recoil-charge-state production. The present study expands on that work by considering additional collision channels and comparing results of equicharged dressed and bare ions in order to shed more light on the role of the projectile electrons.

  20. Dynamical transitions in large systems of mean field-coupled Landau-Stuart oscillators: Extensive chaos and cluster states

    SciTech Connect

    Ku, Wai Lim; Girvan, Michelle; Ott, Edward

    2015-12-15

    In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is “extensive” in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.

  1. Importance of realistic phase-space representations of initial quantum fluctuations using the stochastic mean-field approach for fermions

    NASA Astrophysics Data System (ADS)

    Yilmaz, Bulent; Lacroix, Denis; Curebal, Resul

    2014-11-01

    In the stochastic mean-field (SMF) approach, an ensemble of initial values for a selected set of one-body observables is formed by stochastic sampling from a phase-space distribution that reproduces the initial quantum fluctuations. Independent mean-field evolutions are performed with each set of initial values followed by averaging over the resulting ensemble. This approach has been recently shown to be rather versatile and accurate in describing the correlated dynamics beyond the independent particle picture. In the original formulation of SMF, it was proposed to use a Gaussian assumption for the phase-space distribution. This assumption turns out to be rather effective when the dynamics of an initially uncorrelated state is considered, which was the case in all applications of this approach up to now. Using the Lipkin-Meshkov-Glick (LMG) model, we show that such an assumption might not be adequate if the quantum system under interest is initially correlated and presents configuration mixing between several Slater determinants. In this case, a more realistic description of the initial phase-space is necessary. We show that the SMF approach can be advantageously combined with standard methods to describe phase-space in quantum mechanics. As an illustration, the Husimi distribution function is used here to obtain a realistic representation of the phase-space of a quantum many-body system. This method greatly improves the description of initially correlated fermionic many-body states. In the LMG model, while the Gaussian approximation failed to describe these systems in all interaction strength range, the novel approach gives a perfect agreement with the exact evolution in the weak coupling regime and significantly improves the description of correlated systems in the strong coupling regime.

  2. Ab initio implementation of quantum trajectory mean-field approach and dynamical simulation of the N2CO photodissociation.

    PubMed

    Xie, Binbin; Liu, Lihong; Cui, Ganglong; Fang, Wei-Hai; Cao, Jun; Feng, Wei; Li, Xin-qi

    2015-11-21

    In this work, the recently introduced quantum trajectory mean-field (QTMF) approach is implemented and employed to explore photodissociation dynamics of diazirinone (N2CO), which are based on the high-level ab initio calculation. For comparison, the photodissociation process has been simulated as well with the fewest-switches surface hopping (FSSH) and the ab initio multiple spawning (AIMS) methods. Overall, the dynamical behavior predicted by the three methods is consistent. The N2CO photodissociation at λ > 335 nm is an ultrafast process and the two C-N bonds are broken in a stepwise way, giving birth to CO and N2 as the final products in the ground state. Meanwhile, some noticeable differences were found in the QTMF, FSSH, and AIMS simulated time constants for fission of the C-N bonds, excited-state lifetime, and nonadiabatic transition ratios in different intersection regions. These have been discussed in detail. The present study provides a clear evidence that direct ab initio QTMF approach is one of the reliable tools for simulating nonadiabatic dynamics processes. PMID:26590527

  3. Majority-vote model on spatially embedded networks: Crossover from mean-field to Ising universality classes

    NASA Astrophysics Data System (ADS)

    Sampaio Filho, C. I. N.; dos Santos, T. B.; Moreira, A. A.; Moreira, F. G. B.; Andrade, J. S.

    2016-05-01

    We study through Monte Carlo simulations and finite-size scaling analysis the nonequilibrium phase transitions of the majority-vote model taking place on spatially embedded networks. These structures are built from an underlying regular lattice over which directed long-range connections are randomly added according to the probability Pi j˜r-α , where ri j is the Manhattan distance between nodes i and j , and the exponent α is a controlling parameter [J. M. Kleinberg, Nature (London) 406, 845 (2000), 10.1038/35022643]. Our results show that the collective behavior of this system exhibits a continuous order-disorder phase transition at a critical parameter, which is a decreasing function of the exponent α . Precisely, considering the scaling functions and the critical exponents calculated, we conclude that the system undergoes a crossover among distinct universality classes. For α ≤3 the critical behavior is described by mean-field exponents, while for α ≥4 it belongs to the Ising universality class. Finally, in the region where the crossover occurs, 3 <α <4 , the critical exponents are dependent on α .

  4. Mean-field behavior as a result of noisy local dynamics in self-organized criticality: Neuroscience implications

    NASA Astrophysics Data System (ADS)

    Moosavi, S. Amin; Montakhab, Afshin

    2014-05-01

    Motivated by recent experiments in neuroscience which indicate that neuronal avalanches exhibit scale invariant behavior similar to self-organized critical systems, we study the role of noisy (nonconservative) local dynamics on the critical behavior of a sandpile model which can be taken to mimic the dynamics of neuronal avalanches. We find that despite the fact that noise breaks the strict local conservation required to attain criticality, our system exhibits true criticality for a wide range of noise in various dimensions, given that conservation is respected on the average. Although the system remains critical, exhibiting finite-size scaling, the value of critical exponents change depending on the intensity of local noise. Interestingly, for a sufficiently strong noise level, the critical exponents approach and saturate at their mean-field values, consistent with empirical measurements of neuronal avalanches. This is confirmed for both two and three dimensional models. However, the addition of noise does not affect the exponents at the upper critical dimension (D =4). In addition to an extensive finite-size scaling analysis of our systems, we also employ a useful time-series analysis method to establish true criticality of noisy systems. Finally, we discuss the implications of our work in neuroscience as well as some implications for the general phenomena of criticality in nonequilibrium systems.

  5. Mean-field model of the von Kármán sodium dynamo experiment using soft iron impellers.

    PubMed

    Nore, C; Léorat, J; Guermond, J-L; Giesecke, A

    2015-01-01

    It has been observed that dynamo action occurs in the von-Kármán-Sodium (VKS) experiment only when the rotating disks and the blades are made of soft iron. The purpose of this paper is to numerically investigate the role of soft iron in the VKS dynamo scenario. This is done by using a mean-field model based on an axisymmetric mean flow, a localized permeability distribution, and a localized α effect modeling the action of the small velocity scales between the blades. The action of the rotating blades is modeled by an axisymmetric effective permeability field. Key properties of the flow giving to the numerical magnetic field a geometric structure similar to that observed experimentally are identified. Depending on the permeability of the disks and the effective permeability of the blades, the dynamo that is obtained is either oscillatory or stationary. Our numerical results confirm the leading role played by the ferromagnetic impellers. A scenario for the VKS dynamo is proposed. PMID:25679709

  6. Flocking dynamics and mean-field limit in the Cucker-Smale-type model with topological interactions

    NASA Astrophysics Data System (ADS)

    Haskovec, Jan

    2013-10-01

    We introduce a Cucker-Smale-type model for flocking, where the strength of interaction between two agents depends on their relative separation (called “topological distance” in previous works), which is the number of intermediate individuals separating them. This makes the model scale-free and is motivated by recent extensive observations of starling flocks, suggesting that the interaction ruling animal collective behavior depends on topological rather than the metric distance. We study the conditions leading to asymptotic flocking in the topological model, defined as the convergence of the agents’ velocities to a common vector. The shift from metric to topological interactions requires development of new analytical methods, taking into account the graph-theoretical nature of the problem. Moreover, we provide a rigorous derivation of the mean-field limit of large populations, recovering kinetic and hydrodynamic descriptions. In particular, we introduce the novel concept of relative separation in continuum descriptions, which is applicable to a broad variety of models of collective behavior. As an example, we shortly discuss a topological modification of the attraction-repulsion model and illustrate with numerical simulations that the modified model produces interesting new pattern dynamics.

  7. The origin of the helicity hemispheric sign rule reversals in the mean-field solar-type dynamo

    NASA Astrophysics Data System (ADS)

    Pipin, V. V.; Zhang, H.; Sokoloff, D. D.; Kuzanyan, K. M.; Gao, Y.

    2013-11-01

    Observations of proxies of the magnetic helicity in the Sun over the past two solar cycles revealed reversals of the helicity hemispheric sign rule (negative in the North and positive in the South hemispheres). We apply the mean-field solar dynamo model to study the reversals of the magnetic helicity sign for the dynamo operating in the bulk of the solar convection zone. The evolution of the magnetic helicity is governed by the conservation law. We found that the reversal of the sign of the small-scale magnetic helicity follows the dynamo wave propagating inside the convection zone. Therefore, the spatial patterns of the magnetic helicity reversals reflect the processes which contribute to generation and evolution of the large-scale magnetic fields. At the surface, the patterns of the helicity sign reversals are determined by the magnetic helicity boundary conditions at the top of the convection zone. We demonstrate the impact of fluctuations in the dynamo parameters and variability in dynamo cycle amplitude on the reversals of the magnetic helicity sign rule. The obtained results suggest that the magnetic helicity of the large-scale axisymmetric field can be treated as an additional observational tracer for the solar dynamo and it probably can be used for the solar activity forecast as well.

  8. Atomic detail brownian dynamics simulations of concentrated protein solutions with a mean field treatment of hydrodynamic interactions.

    SciTech Connect

    Mereghetti, Paolo; Wade, Rebecca C.

    2012-07-26

    High macromolecular concentrations are a distinguishing feature of living organisms. Understanding how the high concentration of solutes affects the dynamic properties of biological macromolecules is fundamental for the comprehension of biological processes in living systems. In this paper, we describe the implementation of mean field models of translational and rotational hydrodynamic interactions into an atomically detailed many-protein brownian dynamics simulation method. Concentrated solutions (30-40% volume fraction) of myoglobin, hemoglobin A, and sickle cell hemoglobin S were simulated, and static structure factors, oligomer formation, and translational and rotational self-diffusion coefficients were computed. Good agreement of computed properties with available experimental data was obtained. The results show the importance of both solvent mediated interactions and weak protein-protein interactions for accurately describing the dynamics and the association properties of concentrated protein solutions. Specifically, they show a qualitative difference in the translational and rotational dynamics of the systems studied. Although the translational diffusion coefficient is controlled by macromolecular shape and hydrodynamic interactions, the rotational diffusion coefficient is affected by macromolecular shape, direct intermolecular interactions, and both translational and rotational hydrodynamic interactions.

  9. Mean-field model of the von Kármán sodium dynamo experiment using soft iron impellers

    NASA Astrophysics Data System (ADS)

    Nore, C.; Léorat, J.; Guermond, J.-L.; Giesecke, A.

    2015-01-01

    It has been observed that dynamo action occurs in the von-Kármán-Sodium (VKS) experiment only when the rotating disks and the blades are made of soft iron. The purpose of this paper is to numerically investigate the role of soft iron in the VKS dynamo scenario. This is done by using a mean-field model based on an axisymmetric mean flow, a localized permeability distribution, and a localized α effect modeling the action of the small velocity scales between the blades. The action of the rotating blades is modeled by an axisymmetric effective permeability field. Key properties of the flow giving to the numerical magnetic field a geometric structure similar to that observed experimentally are identified. Depending on the permeability of the disks and the effective permeability of the blades, the dynamo that is obtained is either oscillatory or stationary. Our numerical results confirm the leading role played by the ferromagnetic impellers. A scenario for the VKS dynamo is proposed.

  10. Periodic mean-field solutions and the spectra of discrete bosonic fields: Trace formula for Bose-Hubbard models.

    PubMed

    Engl, Thomas; Urbina, Juan Diego; Richter, Klaus

    2015-12-01

    We consider the many-body spectra of interacting bosonic quantum fields on a lattice in the semiclassical limit of large particle number N. We show that the many-body density of states can be expressed as a coherent sum over oscillating long-wavelength contributions given by periodic, nonperturbative solutions of the, typically nonlinear, wave equation of the classical (mean-field) limit. To this end, we construct the semiclassical approximation for both the smooth and oscillatory parts of the many-body density of states in terms of a trace formula starting from the exact path integral form of the propagator between many-body quadrature states. We therefore avoid the use of a complexified classical limit characteristic of the coherent state representation. While quantum effects such as vacuum fluctuations and gauge invariance are exactly accounted for, our semiclassical approach captures quantum interference and therefore is valid well beyond the Ehrenfest time where naive quantum-classical correspondence breaks down. Remarkably, due to a special feature of harmonic systems with incommensurable frequencies, our formulas are generically valid also in the free-field case of noninteracting bosons. PMID:26764774

  11. Dispersal-induced synchrony, temporal stability, and clustering in a mean-field coupled Rosenzweig-MacArthur model

    NASA Astrophysics Data System (ADS)

    Arumugam, Ramesh; Dutta, Partha Sharathi; Banerjee, Tanmoy

    2015-10-01

    In spatial ecology, dispersal among a set of spatially separated habitats, named as metapopulation, preserves the diversity and persistence by interconnecting the local populations. Understanding the effects of several variants of dispersion in metapopulation dynamics and to identify the factors which promote population synchrony and population stability are important in ecology. In this paper, we consider the mean-field dispersion among the habitats in a network and study the collective dynamics of the spatially extended system. Using the Rosenzweig-MacArthur model for individual patches, we show that the population synchrony and temporal stability, which are believed to be of conflicting outcomes of dispersion, can be simultaneously achieved by oscillation quenching mechanisms. Particularly, we explore the more natural coupling configuration where the rates of dispersal of different habitats are disparate. We show that asymmetry in dispersal rate plays a crucial role in determining inhomogeneity in an otherwise homogeneous metapopulation. We further identify an unusual emergent state in the network, namely, a multi-branch clustered inhomogeneous steady state, which arises due to the intrinsic parameter mismatch among the patches. We believe that the present study will shed light on the cooperative behavior of spatially structured ecosystems.

  12. Dispersal-induced synchrony, temporal stability, and clustering in a mean-field coupled Rosenzweig-MacArthur model.

    PubMed

    Arumugam, Ramesh; Dutta, Partha Sharathi; Banerjee, Tanmoy

    2015-10-01

    In spatial ecology, dispersal among a set of spatially separated habitats, named as metapopulation, preserves the diversity and persistence by interconnecting the local populations. Understanding the effects of several variants of dispersion in metapopulation dynamics and to identify the factors which promote population synchrony and population stability are important in ecology. In this paper, we consider the mean-field dispersion among the habitats in a network and study the collective dynamics of the spatially extended system. Using the Rosenzweig-MacArthur model for individual patches, we show that the population synchrony and temporal stability, which are believed to be of conflicting outcomes of dispersion, can be simultaneously achieved by oscillation quenching mechanisms. Particularly, we explore the more natural coupling configuration where the rates of dispersal of different habitats are disparate. We show that asymmetry in dispersal rate plays a crucial role in determining inhomogeneity in an otherwise homogeneous metapopulation. We further identify an unusual emergent state in the network, namely, a multi-branch clustered inhomogeneous steady state, which arises due to the intrinsic parameter mismatch among the patches. We believe that the present study will shed light on the cooperative behavior of spatially structured ecosystems. PMID:26520087

  13. Large pseudocounts and L2-norm penalties are necessary for the mean-field inference of Ising and Potts models

    NASA Astrophysics Data System (ADS)

    Barton, J. P.; Cocco, S.; De Leonardis, E.; Monasson, R.

    2014-07-01

    The mean-field (MF) approximation offers a simple, fast way to infer direct interactions between elements in a network of correlated variables, a common, computationally challenging problem with practical applications in fields ranging from physics and biology to the social sciences. However, MF methods achieve their best performance with strong regularization, well beyond Bayesian expectations, an empirical fact that is poorly understood. In this work, we study the influence of pseudocount and L2-norm regularization schemes on the quality of inferred Ising or Potts interaction networks from correlation data within the MF approximation. We argue, based on the analysis of small systems, that the optimal value of the regularization strength remains finite even if the sampling noise tends to zero, in order to correct for systematic biases introduced by the MF approximation. Our claim is corroborated by extensive numerical studies of diverse model systems and by the analytical study of the m-component spin model for large but finite m. Additionally, we find that pseudocount regularization is robust against sampling noise and often outperforms L2-norm regularization, particularly when the underlying network of interactions is strongly heterogeneous. Much better performances are generally obtained for the Ising model than for the Potts model, for which only couplings incoming onto medium-frequency symbols are reliably inferred.

  14. Core-Level Photoemission Study for Undoped Cuprates with a Dynamical Mean-Field Approach Considering Realistic Crystal Structure

    NASA Astrophysics Data System (ADS)

    Hariki, Atsushi; Ichinozuka, Yoshiyuki; Uozumi, Takayuki

    2013-02-01

    The 2p3/2 main-line shape of Cu 2p X-ray photoemission spectra for undoped cuprates is studied by means of a dp model within a dynamical mean-field approximation. In order to consider the realistic CuO2 planar structure, we developed a framework combining an impurity Anderson model with a tight-binding calculation for the CuO2 plane. A characteristic partial density of states is obtained for a diagonally ordered antiferromagnetic phase. The calculated 2p3/2 main line shows a broad-band feature formed by screened final states with a hole in the O 2p band and by those accompanied by Zhang--Rice singlet formation. The strong relevance is emphasized between spectral shape and hybridization function which is self-consistently determined within the present framework. Qualitative agreement is also found with hard X-ray photoemission spectra observed for La2CuO4 and Nd2CuO4.

  15. An incremental-secant mean-field homogenization method with second statistical moments for elasto-plastic composite materials

    NASA Astrophysics Data System (ADS)

    Wu, L.; Doghri, I.; Noels, L.

    2015-10-01

    In this paper, the incremental-secant mean-field homogenization (MFH) scheme recently developed by the authors is extended to account for second statistical moments. The incremental-secant MFH method possesses several advantages compared to other MFH methods. Indeed the method can handle non-proportional and non-monotonic loadings, while the instantaneous stiffness operators used in the Eshelby tensor are naturally isotropic, avoiding the isotropization approximation required by the affine and incremental-tangent methods. Moreover, the incremental-secant MFH formalism was shown to be able to account for material softening when extended to include a non-local damage model in the matrix phase, thus enabling an accurate simulation of the onset and evolution of damage across the scales. In this work, by accounting for a second statistical moment estimation of the current yield stress in the composite phases, the plastic flow computation allows capturing with a better accuracy the plastic yield in the composite material phases, which in turn improves the accuracy of the predictions, mainly in the case of short fibre composite materials. The incremental-secant MFH can thus be used to model a wide variety of composite material systems with a good accuracy.

  16. Improving solar 11yr magnetic cycle prediction by using variational data assimilation in a mean field dynamo model

    NASA Astrophysics Data System (ADS)

    Hung, Ching Pui; Jouve, Laurène; Brun, Allan-Sacha; Fournier, Alexandre; Talagrand, Olivier

    2015-04-01

    We present our recent effort to implement modern variational data assimilation techniques into a 2.5 D mean field solar dynamo code. This work extend the work of (Jouve et al. 2011, ApJ) to take into account the correct spherical geometry and meridional circulation into so-called Babccok-Leigthon flux transport dynamo models. Based on twin-experiments, in which we observe our dynamo simulations, and on a well defined cost function using toroidal and poloidal field observations we are able to recover the main attributes of the dynamo solution used to test our data assimilation algorithm. By assimilating solar data (such as Wolf number or butterfly diagram) we are starting to deduce the profile and temporal variations of key ingredients of the solar dynamo. We find that the data sampling and the temporal window are key to get reliable results. We show how such powerful technique can be used to improve our ability to predict the solar magnetic activity. This work is supported by Idex Sorbonne Paris Cite via the DAMSE project.

  17. Influence of memory in deterministic walks in random media: analytical calculation within a mean-field approximation.

    PubMed

    Terçariol, César Augusto Sangaletti; Martinez, Alexandre Souto

    2008-09-01

    Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2 , as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N1) is just n=e=2.72... while in the mu=2 case, the mean number n of visited points grows proportionally to N;{12} . Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones. PMID:18850997

  18. Multiple ionization of neon atoms in collisions with bare and dressed ions: A mean-field description considering target response

    NASA Astrophysics Data System (ADS)

    Schenk, Gerald; Kirchner, Tom

    2015-05-01

    We investigate projectile-charge-state-differential electron removal from neon atoms by impact of He2+, Li3+, B2+, and C3+ ions at intermediate projectile energies (25 keV/u to 1 MeV/u ). The many-electron problem is described with an independent electron model in which active electrons at both collision centers are propagated in a common mean-field potential. Response to electron removal is taken into account in terms of a time-dependent screening potential, and a Slater-determinant-based method is used for the final-state analysis. Total cross sections for net recoil ion production, multiple ionization, and capture channels are mostly in good agreement with published experimental data. Results from equicharged bare and dressed ions are compared and the net recoil ion production cross section is broken down into contributions associated with different final projectile charge states in order to shed light on the role of the projectile electrons.

  19. Multidimensionally-constrained relativistic mean-field study of spontaneous fission: Coupling between shape and pairing degrees of freedom

    NASA Astrophysics Data System (ADS)

    Zhao, Jie; Lu, Bing-Nan; Nikšić, Tamara; Vretenar, Dario; Zhou, Shan-Gui

    2016-04-01

    Background: Studies of fission dynamics, based on nuclear energy density functionals, have shown that the coupling between shape and pairing degrees of freedom has a pronounced effect on the nonperturbative collective inertia and, therefore, on dynamic (least-action) spontaneous fission paths and half-lives. Purpose: The aim is to analyze the effects of particle-number fluctuation degrees of freedom on symmetric and asymmetric spontaneous fission (SF) dynamics, and to compare the findings with the results of recent studies based on the self-consistent Hartree-Fock-Bogoliubov (HFB) method. Methods: Collective potentials and nonperturbative cranking collective inertia tensors are calculated using the multidimensionally-constrained relativistic-mean-field (MDC-RMF) model. Pairing correlations are treated in the BCS approximation using a separable pairing force of finite range. Pairing fluctuations are included as a collective variable using a constraint on particle-number dispersion. Fission paths are determined with the dynamic programming method by minimizing the action in multidimensional collective spaces. Results: The dynamics of spontaneous fission of 264Fm and 250Fm are explored. Fission paths, action integrals, and corresponding half-lives computed in the three-dimensional collective space of shape and pairing coordinates, using the relativistic functional DD-PC1 and a separable pairing force of finite range, are compared with results obtained without pairing fluctuations. Results for 264Fm are also discussed in relation with those recently obtained using the HFB model. Conclusions: The inclusion of pairing correlations in the space of collective coordinates favors axially symmetric shapes along the dynamic path of the fissioning system, amplifies pairing as the path traverses the fission barriers, significantly reduces the action integral, and shortens the

  20. Stochastic multi-scale models of competition within heterogeneous cellular populations: Simulation methods and mean-field analysis.

    PubMed

    Cruz, Roberto de la; Guerrero, Pilar; Spill, Fabian; Alarcón, Tomás

    2016-10-21

    We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age (i.e. time elapsed since they were born). The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. Once the birth rate is determined, we formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size (carrying capacity): cells consume oxygen which in turn fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. Besides the fact that this simple behaviour emerges from a rather complex model, this allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance