Existence of a solution to an equation arising from the theory of Mean Field Games
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).
A bilocal picture of quantum mechanics
International Nuclear Information System (INIS)
A new, bilocal picture of quantum mechanics is developed. We show that Born’s rule supports a virtual probability for a particle to arrive, as a wave, at any two locations (but no more). We discuss two ways to implement twin detectors suitable for detecting bilocal arrivals. The bilocal picture sheds light on currents in quantum mechanics. We find there are two types of bilocal current density, whose polar form and related mean velocities are given. In the bilocal context, the definitions of both current types simplify. In the unilocal case, the two types become the usual current and a fluctuation current. Their respective mean velocity fields are the usual de Broglie–Madelung–Bohm velocity and the imaginary (osmotic) velocity. We obtain a new, probabilistic Schrödinger equation for the bilocal probability by itself, solve the example of a free particle, develop the dyadic stationary states, and find that the von Neumann equation for time-varying density of states follows directly from the new equation. We also show how to include the electromagnetic potentials in this probabilistic Schrödinger equation. (paper)
On the dynamics of mean-field equations for stochastic neural fields with delays
Touboul, Jonathan
2011-01-01
The cortex is composed of large-scale cell assemblies sharing the same individual properties and receiving the same input, in charge of certain functions, and subject to noise. Such assemblies are characterized by specific space locations and space-dependent delayed interactions. The mean-field equations for such systems were rigorously derived in a recent paper for general models, under mild assumptions on the network, using probabilistic methods. We summarize and investigate general implications of this result. We then address the dynamics of these stochastic neural field equations in the case of firing-rate neurons. This is a unique case where the very complex stochastic mean-field equations exactly reduce to a set of delayed differential or integro-differential equations on the two first moments of the solutions, this reduction being possible due to the Gaussian nature of the solutions. The obtained equations differ from more customary approaches in that it incorporates intrinsic noise levels nonlinearly ...
Bound Pairs of Fronts in a Real Ginzburg-Landau Equation Coupled to a Mean Field
Herrero, H
1995-01-01
Motivated by the observation of localized traveling-wave states (`pulses') in convection in binary liquid mixtures, the interaction of fronts is investigated in a real Ginzburg-Landau equation which is coupled to a mean field. In that system the Ginzburg-Landau equation describes the traveling-wave amplitude and the mean field corrsponds to a concentration mode which arises due to the slowness of mass diffusion. For single fronts the mean field can lead to a hysteretic transition between slow and fast fronts. Its contribution to the interaction between fronts can be attractive as well as repulsive and depends strongly on their direction of propagation. Thus, the concentration mode leads to a new localization mechanism, which does not require any dispersion in contrast to that operating in the nonlinear Schrödinger equation. Based on this mechanism alone, pairs of fronts in binary-mixture convection are expected to form {\\it stable} pulses if they travel {\\it backward}, i.e. opposite to the phase velocity. Fo...
B-Spline Finite Elements and their Efficiency in Solving Relativistic Mean Field Equations
Pöschl, W
1997-01-01
A finite element method using B-splines is presented and compared with a conventional finite element method of Lagrangian type. The efficiency of both methods has been investigated at the example of a coupled non-linear system of Dirac eigenvalue equations and inhomogeneous Klein-Gordon equations which describe a nuclear system in the framework of relativistic mean field theory. Although, FEM has been applied with great success in nuclear RMF recently, a well known problem is the appearance of spurious solutions in the spectra of the Dirac equation. The question, whether B-splines lead to a reduction of spurious solutions is analyzed. Numerical expenses, precision and behavior of convergence are compared for both methods in view of their use in large scale computation on FEM grids with more dimensions. A B-spline version of the object oriented C++ code for spherical nuclei has been used for this investigation.
Chavanis, Pierre-Henri
2008-01-01
We consider a generalized class of Keller-Segel models describing the chemotaxis of biological populations (bacteria, amoebae, endothelial cells, social insects,...). We show the analogy with nonlinear mean field Fokker-Planck equations and generalized thermodynamics. As an illustration, we introduce a new model of chemotaxis incorporating both effects of anomalous diffusion and exclusion principle (volume filling). We also discuss the analogy between biological populations described by the Keller-Segel model and self-gravitating Brownian particles described by the Smoluchowski-Poisson system.
Tidal deformability of neutron and hyperon star with relativistic mean field equations of state
Kumar, Bharat; Patra, S K
2016-01-01
We systematically study the tidal deformability for neutron and hyperon stars using relativistic mean field (RMF) equations of state (EOSs). The tidal effect plays an important role during the early part of the evolution of compact binaries. Although, the deformability associated with the EOSs has a small correction, it gives a clean gravitational wave signature in binary inspiral. These are characterized by various love numbers kl (l=2, 3, 4), that depend on the EOS of a star for a given mass and radius. The tidal effect of star could be efficiently measured through advanced LIGO detector from the final stages of inspiraling binary neutron star (BNS) merger.
Mean-field potential calculations of high-pressure equation of state for BeO
Institute of Scientific and Technical Information of China (English)
Zhang Qi-Li; Zhang Ping; Song Hai-Feng; Liu Hai-Feng
2008-01-01
A systematic study of the Hugoniot equation of state, phase transition, and the other thermodynamic properties including the Hugoniot temperature, the electronic and ionic heat capacities, and the Griineisen parameter for shockcompressed BeO, has been carried out by calculating the total free energy. The method of calculations combines first-principles treatment for 0 K and finite-T electronic contribution and the mean-field-potential approach for the vibrational contribution of the lattice ion to the total energy. Our calculated Hugoniot is in good agreement with the experimental data.
Constraining mean-field models of the nuclear matter equation of state at low densities
Voskresenskaya, M D
2012-01-01
An extension of the generalized relativistic mean-field (gRMF) model with density dependent couplings is introduced in order to describe thermodynamical properties and the composition of dense nuclear matter for astrophysical applications. Bound states of light nuclei and two-nucleon scattering correlations are considered as explicit degrees of freedom in the thermodynamical potential. They are represented by quasiparticles with medium dependent properties. The model interpolates between the correct low-density limit, the model independent virial equation of state (VEoS), and the RMF description around nuclear saturation density where clusters are dissolved. A comparison between the fugacity expansions of the VEoS and the gRMF model provides consistency relations between the quasiparticles properties, the nucleon-nucleon scattering phase shifts and the meson-nucleon couplings of the gRMF model at zero density. Relativistic effects are found to be important at temperatures that are typical in astrophysical app...
Mean-field equations for stochastic neural fields with spatio-temporal delays
Touboul, Jonathan
2011-01-01
Neurons form large-scale cell assemblies sharing the same individual properties and receiving the same input, in charge of certain functions. Such assemblies have specific space locations and hence interact after some (space dependent) delay due the transport and transfer of the information. Both delays and spatial connectivity structures are understood to shape the collective response of neural assemblies and brain states that are observed through usual recording techniques. Abstracting this setting, we consider here the problem of the asymptotics, as the number of neurons increases, of bio-inspired neuronal networks composed of several populations (up to a continuum), interacting with spatio-temporal delays. The propagation of chaos property is proved under mild assumptions on the neuronal dynamics, valid for most models used in neuroscience, in both the case of finite number and infinite continuum populations (called neural fields). The mean-field equations in these cases are derived and analyzed from the ...
A Second Relativistic Mean Field and Virial Equation of State for Astrophysical Simulations
Shen, G; O'Connor, E
2011-01-01
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 non-ideal 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 $n_B$ = 10$^{-8}$ to 1.6 fm$^{-3}$, and the proton fraction range $Y_p$ = 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 ba...
Constraining mean-field models of the nuclear matter equation of state at low densities
Voskresenskaya, M. D.; Typel, S.
2012-08-01
An extension of the generalized relativistic mean-field (gRMF) model with density dependent couplings is introduced in order to describe thermodynamical properties and the composition of dense nuclear matter for astrophysical applications. Bound states of light nuclei and two-nucleon scattering correlations are considered as explicit degrees of freedom in the thermodynamical potential. They are represented by quasiparticles with medium-dependent properties. The model describes the correct low-density limit given by the virial equation of state (VEoS) and reproduces RMF results around nuclear saturation density where clusters are dissolved. A comparison between the fugacity expansions of the VEoS and the gRMF model provides consistency relations between the quasiparticles properties, the nucleon-nucleon scattering phase shifts and the meson-nucleon couplings of the gRMF model at zero density. Relativistic effects are found to be important at temperatures that are typical in astrophysical applications. Neutron matter and symmetric nuclear matter are studied in detail.
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.
Lahiri, T.; Pal Majumder, T.; Ghosh, N. K.
2014-07-01
Commercialization of ferroelectric liquid crystal displays (FLCDs) suffers from mechanical and electro-convective instabilities. Impurity ions play a pivotal role in the latter case, and therefore we developed a mean-field type model to understand the complex role of space charges, particularly ions in a ferroelectric liquid crystal. Considering an effective ion-chirality relation, we obtained a modified Poisson-Boltzmann equation for ions dissolved into a chiral solvent like the ferroelectric smectic phase. A nonuniform director profile induced by the mean electrostatic potential of the ions is then calculated by solving an Euler-Lagrange equation for a helically twisted smectic state. A combination of effects resulting from molecular chirality and an electrostatically driven twist created by the ions seems to produce this nonuniform fluctuation in the director orientation. Finally, both theoretical and experimental points of view are presented on the prediction of this mean-field model.
Jiang, Wei-Zhou; Li, Bao-An; Chen, Lie-Wen
2007-01-01
Using in-medium hadron properties according to the Brown-Rho scaling due to the chiral symmetry restoration at high densities and considering naturalness of the coupling constants, we have newly constructed several relativistic mean-field Lagrangians with chiral limits. The model parameters are adjusted such that the symmetric part of the resulting equation of state at supra-normal densities is consistent with that required by the collective flow data from high energy heavy-ion reactions, whi...
A mean field calculation of the equation of state of supernova matter
International Nuclear Information System (INIS)
The equation of state for hot dense matter occuring in stellar collapse is calculated using the Hartree-Fock approximation at finite temperature. The effective nucleon-nucleon interaction is a modified Skyrme force which gives a rather good value of the compression modulus in nuclear matter. Results are presented for the adiabat S=1 per baryon, with a fixed value of the electron fraction Ysub(e)=0.25, in the density range rho=0.02 to 0.07 baryons per fm3. We find that nuclei are still present in the medium. As a consequence the adiabatic index is slightly less than 4/3. We also discuss the presence of a transition, around half nuclear matter density, towards a phase made of bubbles
Hinschberger, Y.; Dixit, A.; Manfredi, G.; Hervieux, P.-A.
2015-01-01
We demonstrate the equivalence between (i) the semirelativistic limit (up to second order in the inverse of the speed of light) of the self-consistent Dirac-Maxwell equations and (ii) the Breit-Pauli equations in the mean-field (Hartree-like) approximation. We explain how the charge and current densities that act as sources in the Dirac-Maxwell equations are related to the microscopic two-electron interactions of the Breit-Pauli model (spin orbit, spin-other-orbit, and spin-spin). The key role played by the second-order corrections to the charge density is clarified.
Kraaij, Richard
2016-07-01
We prove the large deviation principle (LDP) for the trajectory of a broad class of finite state mean-field interacting Markov jump processes via a general analytic approach based on viscosity solutions. Examples include generalized Ehrenfest models as well as Curie-Weiss spin flip dynamics with singular jump rates. The main step in the proof of the LDP, which is of independent interest, is the proof of the comparison principle for an associated collection of Hamilton-Jacobi equations. Additionally, we show that the LDP provides a general method to identify a Lyapunov function for the associated McKean-Vlasov equation.
Malik, G P
2016-01-01
Given the Debye temperature of an elemental superconductor (SC) and its Tc, BCS theory enables one to predict the value of its gap 0 at T = 0, or vice versa. This monograph shows that non-elemental SCs can be similarly dealt with via the generalized BCS equations (GBCSEs) which, given any two parameters of the set {Tc, 10, 20 > 10}, enable one to predict the third. Also given herein are new equations for the critical magnetic field and critical current density of an elemental and a non-elemental SC — equations that are derived directly from those that govern pairing in them. The monograph includes topics that are usually not covered in any one text on superconductivity, e.g., BCS-BEC crossover physics, the long-standing puzzle posed by SrTiO3, and heavy-fermion superconductors — all of which are still imperfectly understood and therefore continue to avidly engage theoreticians. It suggests that addressing the Tcs, s and other properties (e.g., number densities of charge carriers) of high-Tc SCs via GBCSE...
International Nuclear Information System (INIS)
The su(3) mean field approximation describes collective nuclear rotation in a density matrix formalism. The densities ρ=q-i l/2 are 3x3 Hermitian matrices in the su(3) dual space, where q is the expectation of the quadrupole moment and l is the expectation of the angular momentum. The mean field approximation restricts these densities to a level surface of the su(3) Casimirs. Each level surface is a coadjoint orbit of the canonical transformation group SU(3). For each density ρ, the su(3) mean field Hamiltonian h[ρ] is an element of the su(3) Lie algebra. A model su(3) energy functional and the symplectic structure on the coadjoint orbit determine uniquely the su(3) mean field Hamiltonian. The densities in time-dependent su(3) mean field theory obey the dynamical equation i ρ radical = [h[ρ],ρ] on a coadjoint orbit. The cranked mean field Hamiltonian is hΩ=h+iΩ, where Ω is the angular velocity of the rotating principal axis frame. A rotating equilibrium density ρ-tilde in the body-fixed frame is a self-consistent solution to the equation [hΩ[ρ-tilde],ρ-tilde]=0. (author)
Risk-sensitive mean-field games
Tembine, Hamidou
2014-04-01
In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton -Jacobi- Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics. © 1963-2012 IEEE.
Bi-local holography in the SYK model
Jevicki, Antal; Suzuki, Kenta; Yoon, Junggi
2016-07-01
We discuss large N rules of the Sachdev-Ye-Kitaev model and the bi-local representation of holography of this theory. This is done by establishing 1 /N Feynman rules in terms of bi-local propagators and vertices, which can be evaluated following the recent procedure of Polchinski and Rosenhaus. These rules can be interpreted as Witten type diagrams of the dual AdS theory, which we are able to define at IR fixed point and off.
Extended Deterministic Mean-Field Games
Gomes, Diogo A.
2016-04-21
In this paper, we consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but also their collective behavior. To do so, we develop a random variable framework that is particularly convenient for these problems. We prove an existence result for extended mean-field games and establish uniqueness conditions. In the last section, we consider the Master Equation and discuss properties of its solutions.
Fattoyev, F. J.; Newton, W. G.; Xu, Jun; Li, Bao-An
2012-08-01
We study the nuclear symmetry energy S(ρ) and related quantities of nuclear physics and nuclear astrophysics predicted generically by relativistic mean-field (RMF) and Skyrme-Hartree-Fock (SHF) models. We establish a simple prescription for preparing equivalent RMF and SHF parametrizations starting from a minimal set of empirical constraints on symmetric nuclear matter, nuclear binding energy, and charge radii, enforcing equivalence of their Lorenz effective masses, and then using the pure neutron matter (PNM) equation of state obtained from ab initio calculations to optimize the pure isovector parameters in the RMF and SHF models. We find that the resulting RMF and SHF parametrizations give broadly consistent predictions of the symmetry energy J and its slope parameter L at saturation density within a tight range of ≲2 and ≲6 MeV, respectively, but that clear model dependence shows up in the predictions of higher-order symmetry energy parameters, leading to important differences in (a) the slope of the correlation between J and L from the confidence ellipse, (b) the isospin-dependent part of the incompressibility of nuclear matter Kτ, (c) the symmetry energy at suprasaturation densities, and (d) the predicted neutron star radii. The model dependence can lead to about 1-2 km difference in predictions of the neutron star radius given identical predicted values of J and L and symmetric nuclear matter (SNM) saturation properties. Allowing the full freedom in the effective masses in both models leads to constraints of 30≲J≲31.5 MeV, 35≲L≲60 MeV, and -330≲Kτ≲-216 MeV for the RMF model as a whole and 30≲J≲33 MeV, 28≲L≲65 MeV, and -420≲Kτ≲-325 MeV for the SHF model as a whole. Notably, given PNM constraints, these results place RMF and SHF models as a whole at odds with some constraints on Kτ inferred from giant monopole resonance and neutron skin experimental results.
Continuous time finite state mean field games
Gomes, Diogo A.
2013-04-23
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→∞ 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. © 2013 Springer Science+Business Media New York.
Pais, Helena
2016-01-01
The Vlasov formalism is extended to relativistic mean-field hadron models with non-linear terms up to fourth order and applied to the calculation of the crust-core transition density. The effect of the nonlinear $\\omega\\rho$ and $\\sigma\\rho$ 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$\\pm$0.3 km and a crust thickness of $1.36\\pm 0.06$km for a 1.4 $M_\\odot$ star.
Moghrabi, Kassem; Roca-Maza, Xavier; Colo', Gianluca
2012-01-01
In a quantum Fermi system the energy per particle calculated at the second order beyond the mean-field approximation diverges if a zero-range interaction is employed. We have previously analyzed this problem in symmetric nuclear matter by using a simplified nuclear Skyrme interaction, and proposed a strategy to treat such a divergence. In the present work, we extend the same strategy to the case of the full nuclear Skyrme interaction. Moreover we show that, in spite of the strong divergence ($\\sim$ $\\Lambda^5$, where $\\Lambda$ is the momentum cutoff) related to the velocity-dependent terms of the interaction, the adopted cutoff regularization can be always simultaneously performed for both symmetric and nuclear matter with different neutron-to-proton ratio. This paves the way to applications to finite nuclei.
Bi-Local Holography in the SYK Model: Perturbations
Jevicki, Antal
2016-01-01
We continue the study of the Sachdev-Ye-Kitaev model in the Large $N$ limit. Following our formulation in terms of bi-local collective fields with dynamical reparametrization symmetry, we perform perturbative calculations around the conformal IR point. These are based on an $\\varepsilon$ expansion which allows for analytical evaluation of correlators and finite temperature quantities.
Obstacle mean-field game problem
Gomes, Diogo A.
2015-01-01
In this paper, we introduce and study a first-order mean-field game obstacle problem. We examine the case of local dependence on the measure under assumptions that include both the logarithmic case and power-like nonlinearities. Since the obstacle operator is not differentiable, the equations for first-order mean field game problems have to be discussed carefully. Hence, we begin by considering a penalized problem. We prove this problem admits a unique solution satisfying uniform bounds. These bounds serve to pass to the limit in the penalized problem and to characterize the limiting equations. Finally, we prove uniqueness of solutions. © European Mathematical Society 2015.
Weak interactions in a bilocal chiral theory
International Nuclear Information System (INIS)
Relativistic covariant equations for quarkonia in the framework of a biolocal description are obtained. These equations can be used to find the solutions for the bound state functions for any given angular momentum. 13 refs.; 1 tab
Bosonic Dynamical Mean-Field Theory
Snoek, Michiel; Hofstetter, Walter
2013-02-01
We derive the bosonic dynamical mean-field equations for bosonic atoms in optical lattices with arbitrary lattice geometry. The equations are presented as a systematic expansion in 1/z, z being the number of lattice neighbours. Hence the theory is applicable in sufficiently high-dimensional lattices. We apply the method to a two-component mixture, for which a rich phase diagram with spin order is revealed.
Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras
Directory of Open Access Journals (Sweden)
Dangui Yan
2011-01-01
Full Text Available Let H be a complex Hilbert space and B(H the collection of all linear bounded operators, A is the closed subspace lattice including 0 an H, then A is a nest, accordingly alg A={T∈B(H:TN⊆N, ∀N∈A} is a nest algebra. It will be shown that of nest algebra, generalized derivations are generalized inner derivations, and bilocal Jordan derivations are inner derivations.
Mean field games for cognitive radio networks
Tembine, Hamidou
2012-06-01
In this paper we study mobility effect and power saving in cognitive radio networks using mean field games. We consider two types of users: primary and secondary users. When active, each secondary transmitter-receiver uses carrier sensing and is subject to long-term energy constraint. We formulate the interaction between primary user and large number of secondary users as an hierarchical mean field game. In contrast to the classical large-scale approaches based on stochastic geometry, percolation theory and large random matrices, the proposed mean field framework allows one to describe the evolution of the density distribution and the associated performance metrics using coupled partial differential equations. We provide explicit formulas and algorithmic power management for both primary and secondary users. A complete characterization of the optimal distribution of energy and probability of success is given.
On Mean Field Limits for Dynamical Systems
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.
Relativistic mean field for nuclear periphery
Gambhir, Y. K.; Bhagwat, A. A.
2002-09-01
The antiproton annihilation experiments help to extract so-called peripheral factors representing the ratio of neutron to proton densities at the annihilation site that is about 2.5 fm away from the half-density radius of the nucleus. The relativistic mean field (RMF) approach is used to calculate the peripheral factors. The RMF equations (with frozen gap) and relativistic Hartree-Bogoliubov (RHB) equations (with finite range Gogny interaction-D1S for pairing) are solved employing the basis expansion method. The RHB equations are also solved in the coordinate space using a large box (30 fm); with an effective zero range density dependent interaction (consistent with Gogny D1S interaction) for pairing. The results are analyzed to ascertain quantitatively the effect of using these different techniques for solving the RMF/RHB equations. The calculated peripheral factors obtained by solving RHB equations in the coordinate space are relatively closer to the corresponding experimental values.
A mean field approach to watershed hydrology
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.
Nonasymptotic mean-field games
Tembine, Hamidou
2014-12-01
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists of approximating large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networks with few entities. In this paper, we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through various examples including dynamic auction with asymmetric valuation distributions, and spiteful bidders.
Nonasymptotic mean-field games
Tembine, Hamidou
2014-12-01
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networked systems with few entities. In this paper we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through a dynamic auction with asymmetric valuation distributions.
Pedestrian Flow in the Mean Field Limit
Haji Ali, Abdul Lateef
2012-11-01
We study the mean-field limit of a particle-based system modeling the behavior of many indistinguishable pedestrians as their number increases. The base model is a modified version of Helbing\\'s social force model. In the mean-field limit, the time-dependent density of two-dimensional pedestrians satisfies a four-dimensional integro-differential Fokker-Planck equation. To approximate the solution of the Fokker-Planck equation we use a time-splitting approach and solve the diffusion part using a Crank-Nicholson method. The advection part is solved using a Lax-Wendroff-Leveque method or an upwind Backward Euler method depending on the advection speed. Moreover, we use multilevel Monte Carlo to estimate observables from the particle-based system. We discuss these numerical methods, and present numerical results showing the convergence of observables that were calculated using the particle-based model as the number of pedestrians increases to those calculated using the probability density function satisfying the Fokker-Planck equation.
Hassani, S Hamed; Urbanke, Ruediger
2011-01-01
We consider a collection of mean field spin systems, each of which is placed on the positions of a one-dimensional chain, coupled together by a Kac-type interaction along the chain. We analyze the simplest possible cases where the individual system is a Curie-Weiss model, possibly with a random field. We are interested in the regime where the size of each mean field model tends to infinity and, the length of the chain and range of the Kac interaction are large but finite. Below the critical temperature, there appears a series of equilibrium states representing kink-like interfaces between the two equilibrium states of the individual system. The van der Waals curve oscillates periodically around the Maxwell plateau. These oscillations have a period inversely proportional to the chain length and an amplitude exponentially small in the range of the interaction; in other words the spinodal points of the chain model lie exponentially close to the phase transition threshold. The amplitude of the oscillations is clo...
A Bilocal Model for the Relativistic Spinning Particle
Rempel, Trevor
2016-01-01
In this work we show that a relativistic spinning particle can be described at the classical and the quantum level as being composed of two physical constituents which are entangled and separated by a fixed distance. This bilocal model for spinning particles allows for a natural description of particle interactions as a local interaction at each of the constituents. This form of the interaction vertex provides a resolution to a long standing issue on the nature of relativistic interactions for spinning objects in the context of the worldline formalism. It also potentially brings a dynamical explanation for why massive fundamental objects are naturally of lowest spin. We analyze first a non-relativistic system where spin is modeled as an entangled state of two particles with the entanglement encoded into a set of constraints. It is shown that these constraints can be made relativistic and that the resulting description is isomorphic to the usual description of the phase space of massive relativistic particles ...
A simple derivation of mean field limits for quantum systems
Pickl, Peter
2009-01-01
We shall present a new strategy for handling mean field limits of quantum mechanical systems. The new method is simple and effective. It is simple, because it translates the idea behind the mean field description of a many particle quantum system directly into a mathematical algorithm. It is effective because the strategy yields with lesser effort better results than previously achieved. As an instructional example we treat a simple model for the time dependent Hartree equation which we derive under more general conditions than what has been considered so far. Other mean field scalings leading e.g. to the Gross-Pitaevskii equation can also be treated.
Bilocal bosonization of QCD and electroweak properties of light pseudoscalar mesons
International Nuclear Information System (INIS)
Quantum chromodynamic based analysis of the low energy electroweak properties of light pseudo-scalars is studied using an approximate bilocal bosonization technique. Particular attention is given to the problem of maintaining electroweak gauge invariance, and a bilocal Wilson-line technique is introduced to address this problem. The decay constants FK and Fπ and the π± charge radius are discussed in detail. 29 refs., 9 figs
The bilocated mind: new perspectives on self-localization and self-identification
Furlanetto, Tiziano; Bertone, Cesare; Becchio, Cristina
2013-01-01
Does the human mind allow for self-locating at more than one place at a time? Evidence from neurology, cognitive neuroscience, and experimental psychology suggests that mental bilocation is a complex, but genuine experience, occurring more frequently than commonly thought. In this article, we distinguish between different components of bilocated self-representation: self-localization in two different places at the same time, self-identification with another body, reduplication of first-person...
The bilocated mind: New perspectives on self-localization and self-identification
Cesare Bertone; Cristina Becchio
2013-01-01
Does the human mind allow for self-locating at more than one place at a time? Evidence from neurology, cognitive neuroscience, and experimental psychology suggests that mental bilocation is a complex, but genuine experience, occurring more frequently than commonly thought. In this article, we distinguish between different components of bilocated self-representation: self-localization in two different places at the same time, self-identification with another body, reduplication of first-person...
The bilocated mind: New perspectives on self-localization and self-identification
Directory of Open Access Journals (Sweden)
Tiziano eFurlanetto
2013-03-01
Full Text Available Does the human mind allow for self-locating at more than one place at a time? Evidence from neurology, cognitive neuroscience, and experimental psychology suggests that mental bilocation is a complex, but genuine experience, occurring more frequently than commonly thought. In this article, we distinguish between different components of bilocated self-representation: self-localization in two different places at the same time, self-identification with another body, reduplication of first-person perspective. We argue that different forms of mental bilocation may result from the combination of these components. To illustrate this, we discuss evidence of mental bilocation in pathological conditions such as heautoscopy, during immersion in virtual environments, and in everyday life, during social interaction. Finally, we consider the conditions for mental bilocation and speculate on the possible role of mental bilocation in the context of social interaction, suggesting that self-localization at two places at the same time may prove advantageous for the construction of a shared space.
Mean field limit of a continuous time finite state game
Gomes, Diogo A; Souza, Rafael R
2010-01-01
Mean field games is a recent area of study introduced by Lions and Lasry in a series of seminal papers in 2006. Mean field games model situations of competition between large number of rational agents that play non-cooperative dynamic games under certain symmetry assumptions. They key step is to develop a mean field model, in a similar way that what is done in statistical physics in order to construct a mathematically tractable model. A main question that arises in the study of such mean field problems is the rigorous justification of the mean field models by a limiting procedure. In this paper we consider the mean field limit of two-state Markov decision problem as the number of players $N\\to \\infty$. First we establish the existence and uniqueness of a symmetric partial information Markov perfect equilibrium. Then we derive a mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. Our main result is the c...
Mean-field models for disordered crystals
Cancès, Eric; Lewin, Mathieu
2012-01-01
In this article, we set up a functional setting for mean-field electronic structure models of Hartree-Fock or Kohn-Sham types for disordered crystals. The electrons are quantum particles and the nuclei are classical point-like articles whose positions and charges are random. We prove the existence of a minimizer of the energy per unit volume and the uniqueness of the ground state density of such disordered crystals, for the reduced Hartree-Fock model (rHF). We consider both (short-range) Yukawa and (long-range) Coulomb interactions. In the former case, we prove in addition that the rHF ground state density matrix satisfies a self-consistent equation, and that our model for disordered crystals is the thermodynamic limit of the supercell model.
Mean field interaction in biochemical reaction networks
Tembine, Hamidou
2011-09-01
In this paper we establish a relationship between chemical dynamics and mean field game dynamics. We show that chemical reaction networks can be studied using noisy mean field limits. We provide deterministic, noisy and switching mean field limits and illustrate them with numerical examples. © 2011 IEEE.
Mean Field Games Models-A Brief Survey
Gomes, Diogo A.
2013-11-20
The mean-field framework was developed to study systems with an infinite number of rational agents in competition, which arise naturally in many applications. The systematic study of these problems was started, in the mathematical community by Lasry and Lions, and independently around the same time in the engineering community by P. Caines, Minyi Huang, and Roland Malhamé. Since these seminal contributions, the research in mean-field games has grown exponentially, and in this paper we present a brief survey of mean-field models as well as recent results and techniques. In the first part of this paper, we study reduced mean-field games, that is, mean-field games, which are written as a system of a Hamilton-Jacobi equation and a transport or Fokker-Planck equation. We start by the derivation of the models and by describing some of the existence results available in the literature. Then we discuss the uniqueness of a solution and propose a definition of relaxed solution for mean-field games that allows to establish uniqueness under minimal regularity hypothesis. A special class of mean-field games that we discuss in some detail is equivalent to the Euler-Lagrange equation of suitable functionals. We present in detail various additional examples, including extensions to population dynamics models. This section ends with a brief overview of the random variables point of view as well as some applications to extended mean-field games models. These extended models arise in problems where the costs incurred by the agents depend not only on the distribution of the other agents, but also on their actions. The second part of the paper concerns mean-field games in master form. These mean-field games can be modeled as a partial differential equation in an infinite dimensional space. We discuss both deterministic models as well as problems where the agents are correlated. We end the paper with a mean-field model for price impact. © 2013 Springer Science+Business Media New York.
Back-reaction beyond the mean field approximation
International Nuclear Information System (INIS)
A method for solving an initial value problem of a closed system consisting of an electromagnetic mean field and its quantum fluctuations coupled to fermions is presented. By tailoring the large Nf expansion method to the Schwinger-Keldysh closed time path (CTP) formulation of the quantum effective action, causality of the resulting equations of motion is ensured, and a systematic energy conserving and gauge invariant expansion about the electromagnetic mean field in powers of 1/Nf is developed. The resulting equations may be used to study the quantum nonequilibrium effects of pair creation in strong electric fields and the scattering and transport processes of a relativistic e+e- plasma. Using the Bjorken ansatz of boost invariance initial conditions in which the initial electric mean field depends on the proper time only, we show numerical results for the case in which the Nf expansion is truncated in the lowest order, and compare them with those of a phenomenological transport equation
Nonequilibrium dynamical mean-field theory
Energy Technology Data Exchange (ETDEWEB)
Eckstein, Martin
2009-12-21
The aim of this thesis is the investigation of strongly interacting quantum many-particle systems in nonequilibrium by means of the dynamical mean-field theory (DMFT). An efficient numerical implementation of the nonequilibrium DMFT equations within the Keldysh formalism is provided, as well a discussion of several approaches to solve effective single-site problem to which lattice models such as the Hubbard-model are mapped within DMFT. DMFT is then used to study the relaxation of the thermodynamic state after a sudden increase of the interaction parameter in two different models: the Hubbard model and the Falicov-Kimball model. In the latter case an exact solution can be given, which shows that the state does not even thermalize after infinite waiting times. For a slow change of the interaction, a transition to adiabatic behavior is found. The Hubbard model, on the other hand, shows a very sensitive dependence of the relaxation on the interaction, which may be called a dynamical phase transition. Rapid thermalization only occurs at the interaction parameter which corresponds to this transition. (orig.)
Mean-field models and exotic nuclei
Energy Technology Data Exchange (ETDEWEB)
Bender, M.; Buervenich, T.; Maruhn, J.A.; Greiner, W. [Inst. fuer Theoretische Physik, Univ. Frankfurt (Germany); Rutz, K. [Inst. fuer Theoretische Physik, Univ. Frankfurt (Germany)]|[Gesellschaft fuer Schwerionenforschung mbH, Darmstadt (Germany); Reinhard, P.G. [Inst. fuer Theoretische Physik, Univ. Erlangen (Germany)
1998-06-01
We discuss two widely used nuclear mean-field models, the relativistic mean-field model and the (nonrelativistic) Skyrme-Hartree-Fock model, and their capability to describe exotic nuclei. Test cases are superheavy nuclei and neutron-rich Sn isotopes. New information in this regime helps to fix hitherto loosely determined aspects of the models. (orig.)
Large amplitude motion with a stochastic mean-field approach
Directory of Open Access Journals (Sweden)
Yilmaz Bulent
2012-12-01
Full Text Available In the stochastic mean-field approach, an ensemble of initial conditions is considered to incorporate correlations beyond the mean-field. Then each starting point is propagated separately using the Time-Dependent Hartree-Fock equation of motion. This approach provides a rather simple tool to better describe fluctuations compared to the standard TDHF. Several illustrations are presented showing that this theory can be rather effective to treat the dynamics close to a quantum phase transition. Applications to fusion and transfer reactions demonstrate the great improvement in the description of mass dispersion.
Socio-economic applications of finite state mean field games
Gomes, Diogo
2014-10-06
In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments,which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems.
General Relativistic Mean Field Theory for rotating nuclei
Energy Technology Data Exchange (ETDEWEB)
Madokoro, Hideki [Kyushu Univ., Fukuoka (Japan). Dept. of Physics; Matsuzaki, Masayuki
1998-03-01
The {sigma}-{omega} model Lagrangian is generalized to an accelerated frame by using the technique of general relativity which is known as tetrad formalism. We apply this model to the description of rotating nuclei within the mean field approximation, which we call General Relativistic Mean Field Theory (GRMFT) for rotating nuclei. The resulting equations of motion coincide with those of Munich group whose formulation was not based on the general relativistic transformation property of the spinor fields. Some numerical results are shown for the yrast states of the Mg isotopes and the superdeformed rotational bands in the A {approx} 60 mass region. (author)
Regularity theory for mean-field game systems
Gomes, Diogo A; Voskanyan, Vardan
2016-01-01
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Bauso, Dario
2014-05-07
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. © 2014 Bauso et al.
Microscopically constrained mean-field models from chiral nuclear thermodynamics
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.
From infinity to one: The reduction of some mean field games to a global control problem
Guéant, Olivier
2011-01-01
This paper presents recent results from Mean Field Game theory underlying the introduction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations introduced by J.M. Lasry and P.L. Lions and adapting them to games on graphs, we introduce a partial differential equation, often referred to as the Master equation, from which the MFG equations can be deduced. Then, this Master equation can be reinterpreted using a global control problem inducing the same behaviors as in the non-cooperative initial mean field game.
Pion mean fields and heavy baryons
Yang, Ghil-Seok; Polyakov, Maxim V; Praszałowicz, Michał
2016-01-01
We show that the masses of the lowest-lying heavy baryons can be very well described in a pion mean-field approach. We consider a heavy baryon as a system consisting of the $N_c-1$ light quarks that induce the pion mean field, and a heavy quark as a static color source under the influence of this mean field. In this approach we derive a number of \\textit{model-independent} relations and calculate the heavy baryon masses using those of the lowest-lying light baryons as input. The results are in remarkable agreement with the experimental data. In addition, the mass of the $\\Omega_b^*$ baryon is predicted.
Mean-field magnetohydrodynamics and dynamo theory
Krause, F
2013-01-01
Mean-Field Magnetohydrodynamics and Dynamo Theory provides a systematic introduction to mean-field magnetohydrodynamics and the dynamo theory, along with the results achieved. Topics covered include turbulence and large-scale structures; general properties of the turbulent electromotive force; homogeneity, isotropy, and mirror symmetry of turbulent fields; and turbulent electromotive force in the case of non-vanishing mean flow. The turbulent electromotive force in the case of rotational mean motion is also considered. This book is comprised of 17 chapters and opens with an overview of the gen
Mean-field models and superheavy elements
Reinhard, P G; Maruhn, J A
2000-01-01
We discuss the performance of two widely used nuclear mean-field models, the relativistic mean-field theory (RMF) and the non-relativistic Skyrme-Hartree-Fock approach (SHF), with particular emphasis on the description of superheavy elements (SHE). We provide a short introduction to the SHF and RMF, the relations between these two approaches and the relations to other nuclear structure models, briefly review the basic properties with respect to normal nuclear observables, and finally present and discuss recent results on the binding properties of SHE computed with a broad selection of SHF and RMF parametrisations.
Mean-field models and superheavy elements
International Nuclear Information System (INIS)
We discuss the performance of two widely used nuclear mean-field models, the relativistic mean-field theory (RMF) and the non-relativistic Skyrme-Hartree-Fock approach (SHF), with particular emphasis on the description of superheavy elements (SHE). We provide a short introduction to the SHF and RMF, the relations between these two approaches and the relations to other nuclear structure models, briefly review the basic properties with respect to normal nuclear observables, and finally present and discuss recent results on the binding properties of SHE computed with a broad selection of SHF and RMF parametrisations. (orig.)
Mean-field games with logistic population dynamics
Gomes, Diogo A.
2013-12-01
In its standard form, a mean-field game can be defined by coupled system of equations, a Hamilton-Jacobi equation for the value function of agents and a Fokker-Planck equation for the density of agents. Traditionally, the latter equation is adjoint to the linearization of the former. Since the Fokker-Planck equation models a population dynamic, we introduce natural features such as seeding and birth, and nonlinear death rates. In this paper we analyze a stationary meanfield game in one dimension, illustrating various techniques to obtain regularity of solutions in this class of systems. In particular we consider a logistic-type model for birth and death of the agents which is natural in problems where crowding affects the death rate of the agents. The introduction of these new terms requires a number of new ideas to obtain wellposedness. In a forthcoming publication we will address higher dimensional models. ©2013 IEEE.
Noise-induced behaviors in neural mean field dynamics
Touboul, Jonathan; Faugeras, Olivier
2011-01-01
The collective behavior of cortical neurons is strongly affected by the presence of noise at the level of individual cells. In order to study these phenomena in large-scale assemblies of neurons, we consider networks of firing-rate neurons with linear intrinsic dynamics and nonlinear coupling, belonging to a few types of cell populations and receiving noisy currents. Asymptotic equations as the number of neurons tends to infinity (mean field equations) are rigorously derived based on a probabilistic approach. These equations are implicit on the probability distribution of the solutions which generally makes their direct analysis difficult. However, in our case, the solutions are Gaussian, and their moments satisfy a closed system of nonlinear ordinary differential equations (ODEs), which are much easier to study than the original stochastic network equations, and the statistics of the empirical process uniformly converge towards the solutions of these ODEs. Based on this description, we analytically and numer...
A regularized stationary mean-field game
Yang, Xianjin
2016-04-19
In the thesis, we discuss the existence and numerical approximations of solutions of a regularized mean-field game with a low-order regularization. In the first part, we prove a priori estimates and use the continuation method to obtain the existence of a solution with a positive density. Finally, we introduce the monotone flow method and solve the system numerically.
Time-Dependent Mean-Field Games with Logarithmic Nonlinearities
Gomes, Diogo A.
2015-10-06
In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.
Ostwald ripening in Two Dimensions: Correlations and Scaling Beyond Mean Field
Levitan, Boris; Domany, Eytan
1997-01-01
We present a systematic quasi-mean field model of the Ostwald ripening process in two dimensions. Our approach yields a set of dynamic equations for the temporal evolution of the minority phase droplets' radii. The equations contain only pairwise interactions between the droplets; these interactions are evaluated in a mean- field type manner. We proceed to solve numerically the dynamic equations for systems of tens of thousands of interacting droplets. The numerical results are compared with ...
Mean-field learning for satisfactory solutions
Tembine, Hamidou
2013-12-01
One of the fundamental challenges in distributed interactive systems is to design efficient, accurate, and fair solutions. In such systems, a satisfactory solution is an innovative approach that aims to provide all players with a satisfactory payoff anytime and anywhere. In this paper we study fully distributed learning schemes for satisfactory solutions in games with continuous action space. Considering games where the payoff function depends only on own-action and an aggregate term, we show that the complexity of learning systems can be significantly reduced, leading to the so-called mean-field learning. We provide sufficient conditions for convergence to a satisfactory solution and we give explicit convergence time bounds. Then, several acceleration techniques are used in order to improve the convergence rate. We illustrate numerically the proposed mean-field learning schemes for quality-of-service management in communication networks. © 2013 IEEE.
Mean field and collisions in hot nuclei
International Nuclear Information System (INIS)
Collisions between heavy nuclei produce nuclear matter of high density and excitation. Brueckner methods are used to calculate the momentum and temperature dependent mean field for nucleons propagating through nuclear matter during these collisions. The mean field is complex and the imaginary part is related to the ''two-body'' collision, while the real part relates to ''one-body'' collisions. A potential model for the N-N interactions is avoided by calculating the Reaction matrix directly from the T-matrix (i.e., N-N phase shifts) using a version of Brueckner theory previously published by the author. Results are presented for nuclear matter at normal and twice normal density and for temperatures up to 50 MeV. 23 refs., 7 figs
Relativistic mean field description of exotic nuclei
Meng, Jie; Ring, Peter; Zhao, Pengwei; Zhou, Shan-Gui
In this chapter, we will present relativistic mean field (RMF) models with pairing treated by the Bardeen-Cooper-Schrieffer (BCS) and the relativistic Hartree-Bogoliubov (RHB) approaches and applications for exotic nuclear phenomena including nuclear halos, the position of the proton drip line and proton radioactivity, the surface diffuseness and its relation to nuclear exotic phenomena, and the effects of pairing correlations on the nuclear size.
Mean Field Studies of Exotic Nuclei}
Chinn, C. R.; Umar, A. S.; Vallières, M.; Strayer, M. R.
1994-01-01
{Full three dimensional static and dynamic mean field calculations using collocation basis splines with a Skyrme type Hamiltonian are described. This program is developed to address the difficult theoretical challenges offered by exotic nuclei. Ground state and deformation properties are calculated using static Hartree-Fock, Hartree-Fock+BCS and constrained Hartree-Fock models. Collective properties, such as reaction rates and resonances, are described using a new alternate method for evaluat...
Mean-field cooperativity in chemical kinetics
Di Biasio, Aldo; Agliari, Elena; Barra, Adriano; Burioni, Raffaella
2011-01-01
We consider cooperative reactions and we study the effects of the interaction strength among the system components on the reaction rate, hence realizing a connection between microscopic and macroscopic observables. Our approach is based on statistical mechanics models and it is developed analytically via mean-field techniques. First of all, we show that, when the coupling strength is set positive, the model is able to consistently recover all the various cooperative measures previously introd...
'Phase diagram' of a mean field game
Swiecicki, Igor; Ullmo, Denis
2015-01-01
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.Gu\\'eant, 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 agent 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...
Mean-field theory of echo state networks
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.
Mean-Field Dynamics: Singular Potentials and Rate of Convergence
Knowles, Antti
2009-01-01
We consider the time evolution of a system of $N$ identical bosons whose interaction potential is rescaled by $N^{-1}$. We choose the initial wave function to describe a condensate in which all particles are in the same one-particle state. It is well known that in the mean-field limit $N \\to \\infty$ the quantum $N$-body dynamics is governed by the nonlinear Hartree equation. Using a nonperturbative method, we extend previous results on the mean-field limit in two directions. First, we allow a large class of singular interaction potentials as well as strong, possibly time-dependent external potentials. Second, we derive bounds on the rate of convergence of the quantum $N$-body dynamics to the Hartree dynamics.
Derivation of mean-field dynamics for fermions
International Nuclear Information System (INIS)
In this work, we derive the time-dependent Hartree(-Fock) equations as an effective dynamics for fermionic many-particle systems. Our main results are the first for a quantum mechanical mean-field dynamics for fermions; in previous works, the mean-field limit is usually either coupled to a semiclassical limit, or the interaction is scaled down so much, that the system behaves freely for large particle number N. We mainly consider systems with total kinetic energy bounded by const.N and long-range interaction potentials, e.g., Coulomb interaction. Examples for such systems are large molecules or certain solid states. Our analysis also applies to attractive interactions, as, e.g., in fermionic stars. The fermionic Hartree(-Fock) equations are a standard tool to describe, e.g., excited states or chemical reactions of large molecules (like proteins). A deeper understanding of these equations as an approximation to the time evolution of a many body quantum system is thus highly relevant. We consider the fermionic Hartree equations (i.e., the Hartree-Fock equations without exchange term) in this work, since the exchange term is subleading in our setting. The main result is that the fermionic Hartree dynamics approximates the Schroedinger dynamics well for large N. This statement becomes exact in the thermodynamic limit N→∞. We give explicit values for the rates of convergence. We prove two types of results. The first type is very general and concerns arbitrary free Hamiltonians (e.g., relativistic, non-relativistic, with external fields) and arbitrary interactions. The theorems give explicit conditions on the solutions to the fermionic Hartree equations under which a derivation of the mean-field dynamics succeeds. The second type of results scrutinizes situations where the conditions are fulfilled. These results are about non-relativistic free Hamiltonians with external fields, systems with total kinetic energy bounded by const.N and with long-range interactions of
DEFF Research Database (Denmark)
Lerchner, Alexander; Sterner, G.; Hertz, J.;
2006-01-01
We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn, with a numerical procedure for solving the mean-field equations quantitatively. With our treatment, one can determine self-consistently both the firing rates and the firing correlations...
Mean field methods for cortical network dynamics
DEFF Research Database (Denmark)
Hertz, J.; Lerchner, Alexander; Ahmadi, M.
2004-01-01
We review the use of mean field theory for describing the dynamics of dense, randomly connected cortical circuits. For a simple network of excitatory and inhibitory leaky integrate- and-fire neurons, we can show how the firing irregularity, as measured by the Fano factor, increases...... with the strength of the synapses in the network and with the value to which the membrane potential is reset after a spike. Generalizing the model to include conductance-based synapses gives insight into the connection between the firing statistics and the high- conductance state observed experimentally in visual...
Dynamical mean-field theory for flat-band ferromagnetism
Nguyen, Hong-Son; Tran, Minh-Tien
2016-09-01
The magnetically ordered phase in the Hubbard model on the infinite-dimensional hyper-perovskite lattice is investigated within dynamical mean-field theory. It turns out for the infinite-dimensional hyper-perovskite lattice the self-consistent equations of dynamical mean-field theory are exactly solved, and this makes the Hubbard model exactly solvable. We find electron spins are aligned in the ferromagnetic or ferrimagnetic configuration at zero temperature and half filling of the edge-centered sites of the hyper-perovskite lattice. A ferromagnetic-ferrimagnetic phase transition driven by the energy level splitting is found and it occurs through a phase separation. The origin of ferromagnetism and ferrimagnetism arises from the band flatness and the virtual hybridization between macroscopically degenerate flat bands and dispersive ones. Based on the exact solution in the infinite-dimensional limit, a modified exact diagonalization as the impurity solver for dynamical mean-field theory on finite-dimensional perovskite lattices is also proposed and examined.
Numerical accuracy of mean-field calculations in coordinate space
Ryssens, W; Heenen, P -H
2015-01-01
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 on 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: The mean-field calculations have to be accurate enough in order to preserve the accuracy of the EDF. We study this numerical accuracy in detail for a specific numerical choice of representation for the mean-field equations that can accommodate any kind of symmetry breaking. Method: The method that we use is a particular implementation of 3-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 have examined the dependence of the results on these three factors...
Control and Nash Games with Mean Field Effect
Institute of Scientific and Technical Information of China (English)
Alain BENSOUSSAN; Jens FREHSE
2013-01-01
Mean field theory has raised a lot of interest in the recent years (see in particular the results of Lasry-Lions in 2006 and 2007,of Gueant-Lasry-Lions in 2011,of HuangCaines-Malham in 2007 and many others).There are a lot of applications.In general,the applications concern approximating an infinite number of players with common behavior by a representative agent.This agent has to solve a control problem perturbed by a field equation,representing in some way the behavior of the average infinite number of agents.This approach does not lead easily to the problems of Nash equilibrium for a finite number of players,perturbed by field equations,unless one considers averaging within different groups,which has not been done in the literature,and seems quite challenging.In this paper,the authors approach similar problems with a different motivation which makes sense for control and also for differential games.Thus the systems of nonlinear partial differential equations with mean field terms,which have not been addressed in the literature so far,are considered here.
Kinetic and mean field description of Gibrat's law
Toscani, Giuseppe
2016-11-01
I introduce and analyze a linear kinetic model that describes the evolution of the probability density of the number of firms in a society, in which the microscopic rate of change obeys to the so-called law of proportional effect proposed by Gibrat (1930, 1931). Despite its apparent simplicity, the possible mean field limits of the kinetic model are varied. In some cases, the asymptotic limit can be described by a first-order partial differential equation. In other cases, the mean field equation is a linear diffusion with a non constant diffusion coefficient that can be studied analytically, by virtue of a transformation of variables recently utilized in Iagar and Sánchez (2013) to study the heat equation in a nonhomogeneous medium with critical density. In this case, it is shown that the large-time behavior of the solution is represented, for a large class of initial data, by a lognormal distribution with constant mean value and variance increasing exponentially in time at a precise rate.
Mean-field theory and self-consistent dynamo modeling
Energy Technology Data Exchange (ETDEWEB)
Yoshizawa, Akira; Yokoi, Nobumitsu [Tokyo Univ. (Japan). Inst. of Industrial Science; Itoh, Sanae-I [Kyushu Univ., Fukuoka (Japan). Research Inst. for Applied Mechanics; Itoh, Kimitaka [National Inst. for Fusion Science, Toki, Gifu (Japan)
2001-12-01
Mean-field theory of dynamo is discussed with emphasis on the statistical formulation of turbulence effects on the magnetohydrodynamic equations and the construction of a self-consistent dynamo model. The dynamo mechanism is sought in the combination of the turbulent residual-helicity and cross-helicity effects. On the basis of this mechanism, discussions are made on the generation of planetary magnetic fields such as geomagnetic field and sunspots and on the occurrence of flow by magnetic fields in planetary and fusion phenomena. (author)
Dynamic Programming for Mean-field type Control
Laurière, Mathieu; Pironneau, Olivier
2014-01-01
For mean-field type control problems, stochastic dynamic programming requires adaptation. We propose to reformulate the problem as a distributed control problem by assuming that the PDF $\\rho$ of the stochastic process exists. Then we show that Bellman's principle applies to the dynamic programming value function $V(\\tau,\\rho_\\tau)$ where the dependency on $\\rho_\\tau$ is functional as in P.L. Lions' analysis of mean-filed games (2007). We derive HJB equations and apply them to two examples, a...
Mean-field approach for diffusion of interacting particles.
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
Invisible dynamo in mean-field models
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.
Dilution Robustness for Mean Field Ferromagnets
Barra, Adriano; Contucci, Pierluigi
2008-01-01
In this work we compare two different random dilution of a mean field ferromagnet: the first model is built on a Bernoulli-diluted network while the second lives on a Poisson-diluted network. While it is known that the two models have in the thermodynamic limit the same free energy we investigate on the structural constraints that the two models must fulfill. We rigorously derive for each model the set of identities for the multi-overlaps distribution using different methods for the two dilutions: constraints in the former model are obtained by studying the consequences of the self-averaging of the internal energy density, while in the latter are obtained by a stochastic-stability technique. Finally we prove that the identities emerging in the two models are the same, showing "robustness" of the ferromagnetic properties of diluted networks with respect to the details of dilution.
Mass Predictions from Mean-Field Calculations
International Nuclear Information System (INIS)
Several methods based on effective interactions or Lagrangians are available today. Although different in many respects (use of zero range or finite range interactions, relativistic or non relativistic framework, different treatments of pairing correlations), their applications to nuclei far from stability have shown converging results which still have to be incorporated in macroscopic approaches. Many efforts are also actually devoted to the improvements of the effective interactions, especially of the pairing force. Finally, developments are performed to include in a microscopic framework correlations beyond a mean-field (in particular, the correlations generated by rotation and vibration in the deformed nuclear potential). I shall review some key aspects of these developments and show how they affect the determination of nuclear masses in particular at the limits of stability
Kinetic and mean field description of Gibrat's law
Toscani, Giuseppe
2016-01-01
We introduce and analyze a linear kinetic model that describes the evolution of the probability density of the number of firms in a society, in which the microscopic rate of change obeys to the so-called law of proportional effect proposed by Gibrat. Despite its apparent simplicity, the possible mean field limits of the kinetic model are varied. In some cases, the asymptotic limit can be described by a first-order partial differential equation. In other cases, the mean field equation is a linear diffusion with a non constant diffusion coefficient that models also the geometric Brownian motion and can be studied analytically. In this case, it is shown that the large-time behavior of the solution is represented, for a large class of initial data, by a lognormal distribution with constant mean value and variance increasing exponentially in time at a precise rate. The relationship between the kinetic and the diffusion models allow to introduce an easy-to- implement expression for computing the Fourier transform o...
Nonlinear regimes in mean-field full-sphere dynamo
Pipin, V V
2016-01-01
The mean-field dynamo model is employed to study the non-linear dynamo regimes in a fully convective star of mass 0.3$M_{\\odot}$ rotating with period of 10 days. The differential rotation law was estimated using the mean-field hydrodynamic and heat transport equations. For the intermediate parameter of the turbulent magnetic Reynolds number, $Pm_{T}=3$ we found the oscillating dynamo regimes with period about 40Yr. The higher $Pm_{T}$ results to longer dynamo periods. The meridional circulation has one cell per hemisphere. It is counter-clockwise in the Northen hemisphere. The amplitude of the flow at the surface around 1 m/s. Tne models with regards for meridional circulation show the anti-symmetric relative to equator magnetic field. If the large-scale flows is fixed we find that the dynamo transits from axisymmetric to non-axisymmetric regimes for the overcritical parameter of the $\\alpha$effect. The change of dynamo regime occurs because of the non-axisymmetric non-linear $\\alpha$-effect. The situation pe...
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody J. H.
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. 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 k between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d<2k. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. This is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
A Mean-Field Description for AdS Black Hole
Dutta, Suvankar; P, Sachin Shain
2016-01-01
In this paper we find an equivalent mean-field description for asymptotically $AdS$ black hole in high temperature limit and in arbitrary dimensions. We obtain a class of mean-field potential for which the description is valid. We explicitly show that there is an one to one correspondence between the thermodynamics of a gas of interacting particles moving under a mean-field potential and an $AdS$ black hole, namely the equation of state, temperature, pressure, entropy and enthalpy of both the...
Thermal Effects in Dense Matter Beyond Mean Field Theory
Constantinou, Constantinos; Prakash, Madappa
2016-01-01
The formalism of next-to-leading order Fermi Liquid Theory is employed to calculate the thermal properties of symmetric nuclear and pure neutron matter in a relativistic many-body theory beyond the mean field level which includes two-loop effects. For all thermal variables, the semi-analytical next-to-leading order corrections reproduce results of the exact numerical calculations for entropies per baryon up to 2. This corresponds to excellent agreement down to sub-nuclear densities for temperatures up to $20$ MeV. In addition to providing physical insights, a rapid evaluation of the equation of state in the homogeneous phase of hot and dense matter is achieved through the use of the zero-temperature Landau effective mass function and its derivatives.
Low Densities Instability of Relativistic Mean Field Models
Sulaksono, A
2006-01-01
The effects of the symmetry energy softening of the relativistic mean field (RMF) models on the properties of matter with neutrino trapping are investigated. It is found that the effects are less significant than those in the case without neutrino trapping. The weak dependence of the equation of state on the symmetry energy is shown as the main reason of this finding. Using different RMF models the dynamical instabilities of uniform matters, with and without neutrino trapping, have been also studied. The interplay between the dominant contribution of the variation of matter composition and the role of effective masses of mesons and nucleons leads to higher critical densities for matter with neutrino trapping. Furthermore, the predicted critical density is insensitive to the number of trapped neutrinos as well as to the RMF model used in the investigation. It is also found that additional nonlinear terms in the Horowitz-Piekarewicz and Furnstahl-Serot-Tang models prevent another kind of instability, which occu...
Electrical Vehicles in the Smart Grid: A Mean Field Game Analysis
Couillet, Romain; Medina Perlaza, Samir; Tembine, Hamidou; Debbah, Mérouane
2012-01-01
In this article, we investigate the competitive interaction between electrical vehicles or hybrid oil-electricity vehicles in a Cournot market consisting of electricity transactions to or from an underlying electricity distribution network. We provide a mean field game formulation for this competition, and introduce the set of fundamental differential equations ruling the behavior of the vehicles at the feedback Nash equilibrium, referred here to as the mean field equilibrium. This framework ...
Relativistic mean field models for finite nuclei and neutron stars
Chen, Wei-Chia
In this dissertation we have created theoretical models for finite nuclei, nuclear matter, and neutron stars within the framework of relativistic mean field (RMF) theory, and we have used these models to investigate the elusive isovector sector and related physics, in particular, the neutron-skin thickness of heavy nuclei, the nuclear symmetry energy, and the properties of neutron stars. To build RMF models that incorporate collective excitations in finite nuclei in addition to their ground-state properties, we have extended the non-relativistic sum rule approach to the relativistic domain. This allows an efficient estimate of giant monopole energies. Moreover, we have combined an exact shell-model-like approach with the mean-field calculation to describe pairing correlations in open-shell nuclei. All the ingredients were then put together to establish the calibration scheme. We have also extended the transformation between model parameters and pseudo data of nuclear matter within the RMF context. Performing calibration in this pseudo data space can not only facilitate the searching algorithm but also make the pseudo data genuine model predictions. This calibration scheme is also supplemented by a covariance analysis enabling us to extract the information content of a model, including theoretical uncertainties and correlation coefficients. A series of RMF models subject to the same isoscalar constraints but one differing isovector assumption were then created using this calibration scheme. By comparing their predictions of the nuclear matter equation of state to both experimental and theoretical constraints, we found that a small neutron skin of about 0.16 fm in Pb208 is favored, indicating that the symmetry energy should be soft. To obtain stronger evidence, we proceeded to examine the evolution of the isotopic chains in both oxygen and calcium. Again, it was found that the model with such small neutron skin and soft symmetry energy can best describe both isotopic
Evolution of primordial magnetic fields in mean-field approximation
Campanelli, Leonardo
2013-01-01
We study the evolution of phase-transition-generated cosmic magnetic fields coupled to the primeval cosmic plasma in turbulent and viscous free-streaming regimes. The evolution laws for the magnetic energy density and correlation length, both in helical and non-helical cases, are found by solving the autoinduction and Navier-Stokes equations in mean-field approximation. Analytical results are derived in Minkowski spacetime and then extended to the case of a Friedmann universe with zero spatial curvature, both in radiation and matter dominated eras. The three possible viscous free-streaming phases are characterized by a drag term in the Navier-Stokes equation which depends on the free-steaming properties of neutrinos, photons, or hydrogen atoms, respectively. In the case of non-helical magnetic fields, the magnetic intensity $B$ and the magnetic correlation length $\\xi_B$ evolve asymptotically with the temperature $T$ as $B(T) \\simeq \\kappa_B (N_i v_i)^{\\varrho_1} (T/T_i)^{\\varrho_2}$ and $\\xi_B(T) \\simeq \\kap...
Mean-field approximation for spacing distribution functions in classical systems
González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.
2012-01-01
We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.
A Mean-Field Description for AdS Black Hole
Dutta, Suvankar
2016-01-01
In this paper we find an equivalent mean-field description for asymptotically $AdS$ black hole in high temperature limit and in arbitrary dimensions. We obtain a class of mean-field potential for which the description is valid. We explicitly show that there is an one to one correspondence between the thermodynamics of a gas of interacting particles moving under a mean-field potential and an $AdS$ black hole, namely the equation of state, temperature, pressure, entropy and enthalpy of both the systems match. In $3+1$ dimensions, in particular, the mean-field description can be thought of as an ensemble of tiny interacting {\\it asymptotically flat} black holes moving in volume $V$ and at temperature $T$. This motivates us to identify these asymptotically flat black holes as microstructure of asymptotically $AdS$ black holes in $3+1$ dimensions.
Time-Dependent Mean-Field Games in the Subquadratic Case
Gomes, Diogo A.
2014-10-14
In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence of classical solutions under a certain set of conditions depending on both the growth of the Hamiltonian and the dimension. This is done by combining regularity estimates for the Hamilton-Jacobi equation based on the Gagliardo-Nirenberg interpolation inequality with polynomial estimates for the Fokker-Planck equation. This technique improves substantially the previous results on the regularity of time-dependent mean-field games.
Mean-field theory of atomic self-organization in optical cavities
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.
Exact mean field dynamics for epidemic-like processes on heterogeneous networks
Lucas, Andrew
2012-01-01
We show that the mean field equations for the SIR epidemic can be exactly solved for a network with arbitrary degree distribution. Our exact solution consists of reducing the dynamics to a lone first order differential equation, which has a solution in terms of an integral over functions dependent on the degree distribution of the network, and reconstructing all mean field functions of interest from this integral. Irreversibility of the SIR epidemic is crucial for the solution. We also find exact solutions to the sexually transmitted disease SI epidemic on bipartite graphs, to a simplified rumor spreading model, and to a new model for recommendation spreading, via similar techniques. Numerical simulations of these processes on scale free networks demonstrate the qualitative validity of mean field theory in most regimes.
Lerchner, A; Hertz, J; Ahmadi, M
2004-01-01
We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn. The theory is complemented by a description of a numerical procedure for solving the mean-field equations quantitatively. With our treatment, we can determine self-consistently both the firing rates and the firing correlations, without being restricted to specific neuron models. Here, we solve the analytically derived mean-field equations numerically for integrate-and-fire neurons. Several known key properties of orientation selective cortical neurons emerge naturally from the description: Irregular firing with statistics close to -- but not restricted to -- Poisson statistics; an almost linear gain function (firing frequency as a function of stimulus contrast) of the neurons within the network; and a contrast-invariant tuning width of the neuronal firing. We find that the irregularity in firing depends sensitively on synaptic strengths. If Fano factors are bigger than 1, then they are so for all stim...
Development of mean field theories in nuclear physics and in desordered media
International Nuclear Information System (INIS)
This work, in two parts, deals with the development of mean field theories in nuclear physics (nuclei in balance and collisions of heavy ions) as well as in disordered media. In the first part, two different ways of tackling the problem of developments around mean field theories are explained. Possessing an approach wave function for the system, the natural idea for including the correlations is to develop the exact wave function of the system around the mean field wave function. The first two chapters show two different ways of dealing with this problem: the perturbative approach - Hartree-Fock equations with two body collisions and functional methods. In the second part: mean field theory for spin glasses. The problem for spin glasses is to construct a physically acceptable mean field theory. The importance of this problem in statistical mechanics is linked to the fact that the mean field theory provides a qualitative description of the low temperature phase and is the starting point needed for using more sophisticated methods (renormalization group). Two approaches to this problem are presented, one based on the Sherrington-Kirkpatrick model and the other based on a model of spins with purely local disorder and competitive interaction between the spins
Low density instability in relativistic mean field models
Sulaksono, A.; Mart, T.
2006-10-01
The effects of symmetry energy softening of relativistic mean field (RMF) models on the properties of matter with neutrino trapping are investigated. It is found that the effects are less significant than those in the case without neutrino trapping. The weak dependence of the equation of state on the symmetry energy is shown as the main reason for this finding. Using different RMF models the dynamical instabilities of uniform matters, with and without neutrino trapping, have been also studied. The interplay between the dominant contribution of the variation of matter composition and the role of effective masses of mesons and nucleons leads to higher critical densities for matter with neutrino trapping. Furthermore, the predicted critical density is insensitive to both the number of trapped neutrinos as well as the RMF model used in the investigation. It is also found that additional nonlinear terms in the Horowitz-Piekarewicz and Furnstahl-Serot-Tang models prevent another kind of instability, which occurs at relatively high densities, because the effective σ meson mass in their models increases as a function of matter density.
Modeling distributed axonal delays in mean-field brain dynamics
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.
Hot and dense matter beyond relativistic mean field theory
Zhang, Xilin
2016-01-01
Properties of hot and dense matter are calculated in the framework of quantum hadro-dynamics by including contributions from two-loop (TL) diagrams arising from the exchange of iso-scalar and iso-vector 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 iso-spin symmetric matter. Results of calculations from the MFT and TL approximations are compared for conditions of density, temperature, and proton fraction encountered in astrophysics applications involving compact objects. 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 neutron-star matter is substantially softer than its MFT counterpart, it is able to support a $2M_\\odot$ neutron star req...
Verbalization of Mean Field Utterances in German Instructions
Directory of Open Access Journals (Sweden)
Tayupova O. I.
2013-01-01
Full Text Available The article investigates ways of actualization of mean field utterances used in modern German instructions considering the type of the text. The author determines and analyzes similarities and differences in linguistic means used in mean field utterances in the context of such text subtypes as instructions to household appliances, cosmetic products directions and prescribing information for pharmaceutical drugs use.
Evolution of primordial magnetic fields in mean-field approximation
Campanelli, Leonardo
2014-01-01
We study the evolution of phase-transition-generated cosmic magnetic fields coupled to the primeval cosmic plasma in the turbulent and viscous free-streaming regimes. The evolution laws for the magnetic energy density and the correlation length, both in the helical and the non-helical cases, are found by solving the autoinduction and Navier-Stokes equations in the mean-field approximation. Analytical results are derived in Minkowski spacetime and then extended to the case of a Friedmann universe with zero spatial curvature, both in the radiation- and the matter-dominated era. The three possible viscous free-streaming phases are characterized by a drag term in the Navier-Stokes equation which depends on the free-streaming properties of neutrinos, photons, or hydrogen atoms, respectively. In the case of non-helical magnetic fields, the magnetic intensity and the magnetic correlation length evolve asymptotically with the temperature, , as and . Here, , , and are, respectively, the temperature, the number of magnetic domains per horizon length, and the bulk velocity at the onset of the particular regime. The coefficients , , , , , and , depend on the index of the assumed initial power-law magnetic spectrum, , and on the particular regime, with the order-one constants and depending also on the cutoff adopted for the initial magnetic spectrum. In the helical case, the quasi-conservation of the magnetic helicity implies, apart from logarithmic corrections and a factor proportional to the initial fractional helicity, power-like evolution laws equal to those in the non-helical case, but with equal to zero.
Statistical thermodynamics and mean-field theory for the alloy under irradiation model
International Nuclear Information System (INIS)
A generalization of statistical thermodynamics to the open systems case, is discussed, using as an example the alloy-under-irradiation model. The statistical properties of stationary states are described with the use of generalized thermodynamic potentials and 'quasi-interactions' determined from the master equation for micro-configuration probabilities. Methods for resolving this equation are illustrated by the mean-field type calculations of correlators, thermodynamic potentials and phase diagrams for disordered alloys
Expansion Around the Mean-Field Solution of the Bak-Sneppen Model
Marsili, Matteo; Rios, Paolo De Los; Maslov, Sergei
1997-01-01
We study a recently proposed equation for the avalanche distribution in the Bak-Sneppen model. We demonstrate that this equation indirectly relates $\\tau$,the exponent for the power law distribution of avalanche sizes, to $D$, the fractal dimension of an avalanche cluster.We compute this relation numerically and approximate it analytically up to the second order of expansion around the mean field exponents. Our results are consistent with Monte Carlo simulations of Bak-Sneppen model in one an...
An [imaginary time] Schr\\"odinger approach to mean field games
Swiecicki, Igor; Ullmo, Denis
2015-01-01
Mean Field Games (MFG) provide a theoretical frame to model socio-economic systems. In this letter, we study a particular class of MFG which shows strong analogies with the {\\em non-linear Schr\\"odinger and Gross-Pitaevski equations} introduced in physics to describe a variety of physical phenomena ranging from deep-water waves to interacting bosons. Using this bridge many results and techniques developed along the years in the latter context can be transferred to the former. As an illustration, we study in some details an example in which the "players" in the mean field game are under a strong incentive to coordinate themselves.
On the convergence of finite state mean-field games through Γ-convergence
Ferreira, Rita C.
2014-10-01
In this study, we consider the long-term convergence (trend toward an equilibrium) of finite state mean-field games using Γ-convergence. Our techniques are based on the observation that an important class of mean-field games can be viewed as the Euler-Lagrange equation of a suitable functional. Therefore, using a scaling argument, one can convert a long-term convergence problem into a Γ-convergence problem. Our results generalize previous results related to long-term convergence for finite state problems. © 2014 Elsevier Inc.
Single-particle potential in a relativistic Hartree-Fock mean field approximation
Jaminon, Martine; Mahaux, Claude; Rochus, Pierre
1981-01-01
A relativistic Hartree-Fock mean field approximation is investigated in a model in which the nucléon field interacts with scalar and vector meson fields. The Hartree-Fock potential felt by individual nucléons enters in a relativistic Dirac single-particle equation. It is shown that in the case of symmetric nuclear matter one can always find a potential which is fully equivalent to the most general mean field and which is only the sum of a Lorentz scalar, of one component of a Lorentz tensor a...
Quantum correlations in nuclear mean field theory through source terms
Lee, S J
1996-01-01
Starting from full quantum field theory, various mean field approaches are derived systematically. With a full consideration of external source dependence, the stationary phase approximation of an action gives a nuclear mean field theory which includes quantum correlation effects (such as particle-hole or ladder diagram) in a simpler way than the Brueckner-Hartree-Fock approach. Implementing further approximation, the result can be reduced to Hartree-Fock or Hartree approximation. The role of the source dependence in a mean field theory is examined.
Mean field theories and dual variation mathematical structures of the mesoscopic model
Suzuki, Takashi
2015-01-01
Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics. spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature. The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.
Mean-field instabilities and cluster formation in nuclear reactions
Colonna, M; Baran, V
2016-01-01
We review recent results on intermediate mass cluster production in heavy ion collisions at Fermi energy and in spallation reactions. Our studies are based on modern transport theories, employing effective interactions for the nuclear mean-field and incorporating two-body correlations and fluctuations. Namely we will consider the Stochastic Mean Field (SMF) approach and the recently developed Boltzmann-Langevin One Body (BLOB) model. We focus on cluster production emerging from the possible occurrence of low-density mean-field instabilities in heavy ion reactions. Within such a framework, the respective role of one and two-body effects, in the two models considered, will be carefully analysed. We will discuss, in particular, fragment production in central and semi-peripheral heavy ion collisions, which is the object of many recent experimental investigations. Moreover, in the context of spallation reactions, we will show how thermal expansion may trigger the development of mean-field instabilities, leading to...
Extrapolation of mean-field models to superheavy nuclei
International Nuclear Information System (INIS)
The extrapolation of self-consistent nuclear mean-field models to the region of superheavy elements is discussed with emphasis on the extrapolating power of the models. The predictions of modern mean-field models are confronted with recent experimental data. It is shown that a final conclusion about the location of the expected island of spherical doubly-magic superheavy nuclei cannot be drawn on the basis of the available data. (orig.)
Two-level interacting boson models beyond the mean field
Arias, J M; García-Ramos, J E; Vidal, J
2007-01-01
The phase diagram of two-level boson Hamiltonians, including the Interacting Boson Model (IBM), is studied beyond the standard mean field approximation using the Holstein-Primakoff mapping. The limitations of the usual intrinsic state (mean field) formalism concerning finite-size effects are pointed out. The analytic results are compared to numerics obtained from exact diagonalizations. Excitation energies and occupation numbers are studied in different model space regions (Casten triangle for IBM) and especially at the critical points.
Probabilistic data modelling with adaptive TAP mean-field theory
DEFF Research Database (Denmark)
Opper, M.; Winther, Ole
2001-01-01
We demonstrate for the case of single-layer neural networks how an extension of the TAP mean-field approach of disorder physics can be applied to the computation of approximate averages in probabilistic models for real data.......We demonstrate for the case of single-layer neural networks how an extension of the TAP mean-field approach of disorder physics can be applied to the computation of approximate averages in probabilistic models for real data....
Mean-Field Theory of the Solar Dynamo
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
Solution of the hyperon puzzle within a relativistic mean-field model
Energy Technology Data Exchange (ETDEWEB)
Maslov, K.A. [National Research Nuclear University (MEPhI), 115409 Moscow (Russian Federation); Kolomeitsev, E.E., E-mail: E.Kolomeitsev@gsi.de [Matej Bel University, SK-97401 Banska Bystrica (Slovakia); Voskresensky, D.N. [National Research Nuclear University (MEPhI), 115409 Moscow (Russian Federation)
2015-09-02
The equation of state of cold baryonic matter is studied within a relativistic mean-field model with hadron masses and coupling constants depending on the scalar field. All hadron masses undergo a universal scaling, whereas the couplings are scaled differently. The appearance of hyperons in dense neutron star interiors is accounted for, however the equation of state remains sufficiently stiff if the reduction of the ϕ meson mass is included. Our equation of state matches well the constraints known from analyses of the astrophysical data and particle production in heavy-ion collisions.
Short-time existence of solutions for mean-field games with congestion
Gomes, Diogo A.
2015-11-20
We consider time-dependent mean-field games with congestion that are given by a Hamilton–Jacobi equation coupled with a Fokker–Planck equation. These models are motivated by crowd dynamics in which agents have difficulty moving in high-density areas. The congestion effects make the Hamilton–Jacobi equation singular. The uniqueness of solutions for this problem is well understood; however, the existence of classical solutions was only known in very special cases, stationary problems with quadratic Hamiltonians and some time-dependent explicit examples. Here, we demonstrate the short-time existence of C∞ solutions for sub-quadratic Hamiltonians.
A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type
Energy Technology Data Exchange (ETDEWEB)
Hosking, John Joseph Absalom, E-mail: j.j.a.hosking@cma.uio.no [University of Oslo, Centre of Mathematics for Applications (CMA) (Norway)
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.
Neutron Stars in Relativistic Mean Field Theory with Isovector Scalar Meson
Kubis, S; Stachniewicz, S
1998-01-01
We study the equation of state of beta-stable dense matter and models of neutron stars in the relativistic mean field theory with the isovector scalar mean field corresponding to the delta-meson [a_0(980)]. A range of values of the delta-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E_s=30 MeV. We find that the quantity most sensitive to the delta-meson coupling is the proton fraction of neutron star matter. It increases significantly in the presence of the delta-field. The energy per baryon also increases but the effect is smaller. The equation of state becomes slightly stiffer and the maximum neutron star mass increases for stronger delta-meson coupling.
Accretion Disks and Dynamos: Toward a Unified Mean Field Theory
Blackman, Eric G
2012-01-01
Conversion of gravitational energy into radiation near stars and compact objects in accretion disks the origin of large scale magnetic fields in astrophysical rotators have long been distinct topics of active research in astrophysics. In semi-analytic work on both problems it has been useful to presume large scale symmetries, which necessarily results in mean field theories; magnetohydrodynamic turbulence makes the underlying systems locally asymmetric and highly nonlinear. Synergy between theory and simulations should aim for the development of practical, semi-analytic mean field models that capture the essential physics and can be used for observational modeling. Mean field dynamo (MFD) theory and alpha-viscosity accretion disc theory have exemplified such distinct pursuits. Both are presently incomplete, but 21st century MFD theory has nonlinear predictive power compared to 20th century MFD. in contrast, alpha-viscosity accretion theory is still in a 20th century state. In fact, insights from MFD theory ar...
Nonequilibrium Dynamical Mean-Field Theory for Bosonic Lattice Models
Strand, Hugo U. R.; Eckstein, Martin; Werner, Philipp
2015-01-01
We develop the nonequilibrium extension of bosonic dynamical mean-field theory and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong-coupling perturbative approaches, nonequilibrium bosonic dynamical mean-field theory captures not only dynamical transitions but also damping and thermalization effects at finite temperature. We apply the formalism to quenches in the Bose-Hubbard model, starting from both the normal and the Bose-condensed phases. Depending on the parameter regime, one observes qualitatively different dynamical properties, such as rapid thermalization, trapping in metastable superfluid or normal states, as well as long-lived or strongly damped amplitude oscillations. We summarize our results in nonequilibrium "phase diagrams" that map out the different dynamical regimes.
Noisy mean field game model for malware propagation in opportunistic networks
Tembine, Hamidou
2012-01-01
In this paper we present analytical mean field techniques that can be used to better understand the behavior of malware propagation in opportunistic large networks. We develop a modeling methodology based on stochastic mean field optimal control that is able to capture many aspects of the problem, especially the impact of the control and heterogeneity of the system on the spreading characteristics of malware. The stochastic large process characterizing the evolution of the total number of infected nodes is examined with a noisy mean field limit and compared to a deterministic one. The stochastic nature of the wireless environment make stochastic approaches more realistic for such types of networks. By introducing control strategies, we show that the fraction of infected nodes can be maintained below some threshold. In contrast to most of the existing results on mean field propagation models which focus on deterministic equations, we show that the mean field limit is stochastic if the second moment of the number of object transitions per time slot is unbounded with the size of the system. This allows us to compare one path of the fraction of infected nodes with the stochastic trajectory of its mean field limit. In order to take into account the heterogeneity of opportunistic networks, the analysis is extended to multiple types of nodes. Our numerical results show that the heterogeneity can help to stabilize the system. We verify the results through simulation showing how to obtain useful approximations in the case of very large systems. © 2012 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering.
Hot and dense matter beyond relativistic mean field theory
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
Suppression of oscillations in mean-field diffusion
Indian Academy of Sciences (India)
Neeraj Kumar Kamal; Pooja Rani Sharma; Manish Dev Shrimali
2015-02-01
We study the role of mean-field diffusive coupling on suppression of oscillations for systems of limit cycle oscillators. We show that this coupling scheme not only induces amplitude death (AD) but also oscillation death (OD) in coupled identical systems. The suppression of oscillations in the parameter space crucially depends on the value of mean-field diffusion parameter. It is also found that the transition from oscillatory solutions to OD in conjugate coupling case is different from the case when the coupling is through similar variable. We rationalize our study using linear stability analysis.
Derivation of mean-field dynamics for fermions
Petrat, Sören
2014-01-01
In dieser Arbeit werden die zeitabhängigen Hartree(-Fock) Gleichungen als effektive Dynamik für fermionische Vielteilchen-Systeme hergeleitet. Die Hauptresultate sind die ersten für eine quantenmechanische Mean-Field Dynamik ("Mittlere-Feld Dynamik") für Fermionen; in vorherigen Arbeiten ist der Mean-Field Limes üblicherweise entweder mit einem semiklassischen Limes gekoppelt oder die Wechselwirkung wird so stark runterskaliert, dass sich das System für große Teilchenzahl N frei verhält. Wir ...
Shapes and Dynamics from the Time-Dependent Mean Field
Stevenson, P D; Rios, A
2015-01-01
Explaining observed properties in terms of underlying shape degrees of freedom is a well--established prism with which to understand atomic nuclei. Self--consistent mean--field models provide one tool to understand nuclear shapes, and their link to other nuclear properties and observables. We present examples of how the time--dependent extension of the mean--field approach can be used in particular to shed light on nuclear shape properties, particularly looking at the giant resonances built on deformed nuclear ground states, and at dynamics in highly-deformed fission isomers. Example calculations are shown of $^{28}$Si in the first case, and $^{240}$Pu in the latter case.
Relativistic Chiral Mean Field Model for Finite Nuclei
Ogawa, Yoko; Toki, Hiroshi; Tamenaga, Setsuo; Haga, Akihiro
2012-01-01
We present a relativistic chiral mean field (RCMF) model, which is a method for the proper treatment of pion-exchange interaction in the nuclear many-body problem. There the dominant term of the pionic correlation is expressed in two-particle two-hole (2p-2h) states with particle-holes having pionic quantum number, J^{pi}. The charge-and-parity-projected relativistic mean field (CPPRMF) model developed so far treats surface properties of pionic correlation in 2p-2h states with J^{pi} = 0^{-} ...
Point-coupling models from mesonic hyper massive limit and mean-field approaches
Energy Technology Data Exchange (ETDEWEB)
Lourenco, O.; Dutra, M., E-mail: odilon@ita.br [Departamento de Fisica, Instituto Tecnologico da Aeronautica - CTA, Sao Jose dos Campos, SP (Brazil); Delfino, Antonio, E-mail: delfino@if.uff.br [Instituto de Fisica, Universidade Federal Fluminense, Niteroi, RJ (Brazil); Amaral, R.L.P.G. [Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA (United States)
2012-08-15
t In this work, we show how nonlinear point coupling models, described by a Lagrangian density containing only terms up to fourth order in the fermion condensate ({Psi}-bar{Psi}), are derived from a modified meson exchange nonlinear Walecka model. We present two methods of derivation, namely the hyper massive meson limit within a functional integral approach and the mean-field approximation, in which equations of state at zero temperature of the nonlinear point-coupling models are directly obtained. (author)
Nuclear magnetic moments and the spin-orbit current in the relativistic mean field theory
International Nuclear Information System (INIS)
The Dirac magnetic moments in the relativistic mean field theory are affected not only by the effective mass, but also by the spin-orbit current related to the spin-orbit force through the continuity equation. Previous arguments on the cancellation of the effective-mass effect in nuclear matter are not simply applied to finite nuclei to obtain the Schmidt values. Effects of the spin-orbit current on (e, e') response functions are also mentioned. (orig.)
A mean field theory for the cold quark gluon plasma applied to stellar structure
Energy Technology Data Exchange (ETDEWEB)
Fogaca, D. A.; Navarra, F. S.; Franzon, B. [Instituto de Fisica, Universidade de Sao Paulo Rua do Matao, Travessa R, 187, 05508-090 Sao Paulo, SP (Brazil); Horvath, J. E. [Instituto de Astronomia, Geofisica e Ciencias Atmosfericas, Universidade de Sao Paulo, Rua do Matao, 1226, 05508-090, Sao Paulo, SP (Brazil)
2013-03-25
An equation of state based on a mean-field approximation of QCD is used to describe the cold quark gluon plasma and also to study the structure of compact stars. We obtain stellar masses compatible with the pulsar PSR J1614-2230 that was determined to have a mass of (1.97 {+-} 0.04 M{sub Circled-Dot-Operator }), and the corresponding radius around 10-11 km.
Institute of Scientific and Technical Information of China (English)
GENG Li-Sheng; MENG Jie; Toki Hiroshi
2007-01-01
A reflection asymmetric relativistic mean field (RAS-RMF) approach is developed by expanding the equations of motion for both the nucleons and the mesons on the eigenfunctions of the two-centre harmonic-oscillator potential.The efficiency and reliability of the RAS-RMF approach are demonstrated in its application to the well-known octupole deformed nucleus 226Ra and the available data, including the binding energy and the deformation parameters, are well reproduced.
Mean field theory for lattice gauge systems with fermions
International Nuclear Information System (INIS)
We extend recent mean field calculations for lattice gauge theories to include fermions. We find that the addition of a Wilson fermion leads to an almost negligible change of the weak to strong coupling transition point. The plaquette average is also only weakly affected. (author)
Mean Field Approach to the Giant Wormhole Problem
Gamba, A.; Kolokolov, I.; Martellini, M.
1992-01-01
We introduce a gaussian probability density for the space-time distribution of wormholes, thus taking effectively into account wormhole interaction. Using a mean-field approximation for the free energy, we show that giant wormholes are probabilistically suppressed in a homogenous isotropic ``large'' universe.
Excitation energy of superdeformed bands in Relativistic Mean Field Theory
Lalazissis, G A
1998-01-01
Constrained Relativistic Mean Field (RMF) calculations have been carried out to estimate excitation energies relative to the ground state for superdeformed bands in the mass regions A $\\sim$ 190 and A $\\sim$ 150. It is shown that RMF theory is able to successfully reproduce the recently measured superdeformed minima in Hg and Pb nuclei.
Robust mean field games for coupled Markov jump linear systems
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.
Condition monitoring with Mean field independent components analysis
DEFF Research Database (Denmark)
Pontoppidan, Niels Henrik; Sigurdsson, Sigurdur; Larsen, Jan
2005-01-01
We discuss condition monitoring based on mean field independent components analysis of acoustic emission energy signals. Within this framework it is possible to formulate a generative model that explains the sources, their mixing and also the noise statistics of the observed signals. By using...
Merging Belief Propagation and the Mean Field Approximation
DEFF Research Database (Denmark)
Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro;
2010-01-01
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al., which allows to use the same objective function (Kullback-Leibler divergence) as a ...
Social networking and individual outcomes beyond the mean field case
Y.M. Ioannides; A.R. Soetevent
2007-01-01
We study individually optimized continuous outcomes in a dynamic environment in the presence of social interactions, and where the interaction topology may be either exogenous and time varying, or endogenous. The model accommodates more general social effects than those of the mean-field type. We ad
A Solvable Mean Field Model of a Gaussian Spin Glass
Barra, Adriano; Guerra, Francesco; Tantari, Daniele
2011-01-01
We introduce a mean field model for a spin glass with gaussian distribuited spin and pairwise interactions, whose also the couplings are drawn randomly from a gaussian distribution. We completely control the main thermodynamical properties of the model (free energy, phase diagram, fluctuations). In particular we prove that in thermodynamic limit the free energy of the model preserves the full symmetry between replicas.
Mean Field Approach to the Giant Wormhole Problem
Gamba, A.; Kolokolov, I.; Martellini, M.
We introduce a gaussian probability density for the space-time distribution of worm-holes, thus taking effectively into account wormhole interaction. Using a mean-field approximation for the free energy, we show that giant wormholes are probabilistically suppressed in a homogenous isotropic “large” universe.
Mean-field cosmological dynamos in Riemannian space with isotropic diffusion
de Andrade, L Garcia
2009-01-01
Mean-field cosmological dynamos in Riemannian space with isotropic diffusion}} Previous attempts for building a cosmic dynamo including preheating in inflationary universes [Bassett et al Phys Rev (2001)] has not included mean field or turbulent dynamos. In this paper a mean field dynamo in cosmic scales on a Riemannian spatial cosmological section background, is set up. When magnetic fields and flow velocities are parallel propagated along the Riemannian space dynamo action is obtained. Turbulent diffusivity ${\\beta}$ is coupled with the Ricci magnetic curvature, as in Marklund and Clarkson [MNRAS (2005)], GR-MHD dynamo equation. Mean electric field possesses an extra term where Ricci tensor couples with magnetic vector potential in Ohm's law. In Goedel universe induces a mean field dynamo growth rate ${\\gamma}=2{\\omega}^{2}{\\beta}$. In this frame kinetic helicity vanishes. In radiation era this yields ${\\gamma}\\approx{2{\\beta}{\\times}10^{-12}s^{-1}}$. In non-comoving the magnetic field is expressed as $B\\ap...
Chaotic time series prediction using mean-field theory for support vector machine
Institute of Scientific and Technical Information of China (English)
Cui Wan-Zhao; Zhu Chang-Chun; Bao Wen-Xing; Liu Jun-Hua
2005-01-01
This paper presents a novel method for predicting chaotic time series which is based on the support vector machines approach, and it uses the mean-field theory for developing an easy and efficient learning procedure for the support vector machine. The proposed method approximates the distribution of the support vector machine parameters to a Gaussian process and uses the mean-field theory to estimate these parameters easily, and select the weights of the mixture of kernels used in the support vector machine estimation more accurately and faster than traditional quadratic programming-based algorithms. Finally, relationships between the embedding dimension and the predicting performance of this method are discussed, and the Mackey-Glass equation is applied to test this method. The stimulations show that the mean-field theory for support vector machine can predict chaotic time series accurately, and even if the embedding dimension is unknown, the predicted results are still satisfactory. This result implies that the mean-field theory for support vector machine is a good tool for studying chaotic time series.
Nuclei, hypernuclei, and neutron stars in a relativistic mean-field model
International Nuclear Information System (INIS)
An essential aim of this thesis consisted in the obtainment of an optimal description of finite also strangeness carrying nuclei in the framework of a relativistic mean-field model. For this the model parameters were fitted to experimental nuclear and hypernuclear data. By the so optimized parametrizations the - among others - equations of state of neutron matter were extrapolated and by solving of the Oppenheimer-Volkoff equation neutron star properties calculated. In this connection also the possible existence of a quark phase in the interior of neutron stars was considered. (orig.)
Expansion Around the Mean-Field Solution of the Bak-Sneppen Model
Energy Technology Data Exchange (ETDEWEB)
Marsili, M. [Institut de Physique Theorique, Universite de Fribourg Perolles, Fribourg, CH-1700 (Switzerland); De Los Rios, P. [Max-Planck-Institut fuer Physik Komplexer Systeme, Noethnitzer Str.38, D-01187 Dresden (Germany); Maslov, S. [Department of Physics, Brookhaven National Laboratory, Upton, New York 11973 (United States)
1998-02-01
We study a recently proposed equation for the avalanche distribution in the Bak-Sneppen model. We demonstrate that this equation indirectly relates {tau} , the exponent for the power law distribution of avalanche sizes, to D , the fractal dimension of an avalanche cluster. We compute this relation numerically and approximate it analytically up to the second order of expansion around the mean-field exponents. Our results are consistent with Monte Carlo simulations of the Bak-Sneppen model in one and two dimensions. {copyright} {ital 1998} {ital The American Physical Society}
Merging Belief Propagation and the Mean Field Approximation: A Free Energy Approach
DEFF Research Database (Denmark)
Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro;
2013-01-01
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al. We show that the message passing fixed-point equations obtained with this combination...... correspond to stationary points of a constrained region-based free energy approximation. Moreover, we present a convergent implementation of these message passing fixed-point equations provided that the underlying factor graph fulfills certain technical conditions. In addition, we show how to include hard...
TURBULENT CONVECTION IN STELLAR INTERIORS. III. MEAN-FIELD ANALYSIS AND STRATIFICATION EFFECTS
Energy Technology Data Exchange (ETDEWEB)
Viallet, Maxime [Physics and Astronomy, University of Exeter, Stocker Road, Exeter, EX4 4QL (United Kingdom); Meakin, Casey; Mocak, Miroslav [Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Arnett, David [Steward Observatory, University of Arizona, Tucson, AZ 85721 (United States)
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.
Relativistic mean-field hadronic models under nuclear matter constraints
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
A Local Mean Field Analysis of Security Investments in Networks
Lelarge, Marc
2008-01-01
Getting agents in the Internet, and in networks in general, to invest in and deploy security features and protocols is a challenge, in particular because of economic reasons arising from the presence of network externalities. Our goal in this paper is to carefully model and quantify the impact of such externalities on the investment in, and deployment of, security features and protocols in a network. Specifically, we study a network of interconnected agents, which are subject to epidemic risks such as those caused by propagating viruses and worms, and which can decide whether or not to invest some amount to self-protect and deploy security solutions. We make three contributions in the paper. First, we introduce a general model which combines an epidemic propagation model with an economic model for agents which captures network effects and externalities. Second, borrowing ideas and techniques used in statistical physics, we introduce a Local Mean Field (LMF) model, which extends the standard mean-field approxi...
Nuclear collective vibrations in extended mean-field theory
Energy Technology Data Exchange (ETDEWEB)
Lacroix, D. [Lab. de Physique Corpusculaire/ ENSICAEN, 14 - Caen (France); Ayik, S. [Tennessee Technological Univ., Cookeville, TN (United States); Chomaz, Ph. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France)
2003-07-01
The extended mean-field theory, which includes both the incoherent dissipation mechanism due to nucleon-nucleon collisions and the coherent dissipation mechanism due to coupling to low-lying surface vibrations, is briefly reviewed. Expressions of the strength functions for the collective excitations are presented in the small amplitude limit of this approach. This fully microscopic theory is applied by employing effective Skyrme forces to various giant resonance excitations at zero and finite temperature. The theory is able to describe the gross properties of giant resonance excitations, the fragmentation of the strength distributions as well as their fine structure. At finite temperature, the success and limitations of this extended mean-field description are discussed. (authors)
Mean-Field Dynamical Semigroups on C*-ALGEBRAS
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}.
Progress in nuclear structure beyond the mean-field approximation
International Nuclear Information System (INIS)
Although self-consistent mean-field methods, or implementations of the density functional theory for atomic nuclei, are becoming increasingly accurate, some observables are not well reproduced by those models. In particular, the fragmentation and the decay properties of both single-particle and vibrational states cannot be accounted for. Models based on the introduction of further correlations or, in other words, that go beyond the mean-field approximation, have often been discussed in the past. We have recently developed a consistent model based on the use of a Skyrme-type force without the intervention of any other ad hoc parameter. A few typical results are discussed, after we have mentioned briefly the essential features of the model. Moreover, we discuss the necessity of fitting a new force within this context, the difficulties arising because of divergences that need to be renormalized, and our roadmap for curing these divergences
Analytic Beyond-Mean-Field BEC Wave Functions
Dunn, Martin; Laing, W. Blake; Watson, Deborah K.; Loeser, John G.
2006-05-01
We present analytic N-body beyond-mean-field wave functions for Bose-Einstein condensates. This extends our previous beyond-mean-field energy calculations to the substantially more difficult problem of determining correlated N-body wave functions for a confined system. The tools used to achieve this have been carefully chosen to maximize the use of symmetry and minimize the dependence on numerical computation. We handle the huge number of interactions when N is large (˜N^2/2 two-body interactions) by bringing together three theoretical methods. These are dimensional perturbation theory, the FG method of Wilson et al, and the group theory of the symmetric group. The wave function is then used to derive the density profile of a condensate in a cylindrical trap.This method makes no assumptions regarding the form or strength of the interactions and is applicable to both small-N and large-N systems.
Characterizing the mean-field dynamo in turbulent accretion disks
Gressel, Oliver
2015-01-01
The formation and evolution of a wide class of astrophysical objects is governed by turbulent, magnetized accretion disks. Understanding their secular dynamics is of primary importance. Apart from enabling mass accretion via the transport of angular momentum, the turbulence affects the long-term evolution of the embedded magnetic flux, which in turn regulates the efficiency of the transport. In this paper, we take a comprehensive next step towards an effective mean-field model for turbulent astrophysical disks by systematically studying the key properties of magnetorotational turbulence in vertically-stratified, isothermal shearing boxes. This allows us to infer emergent properties of the ensuing chaotic flow as a function of the shear parameter as well as the amount of net-vertical flux. Using the test-field method, we furthermore characterize the mean-field dynamo coefficients that describe the long-term evolution of large-scale fields. We simultaneously infer the vertical shape and the spectral scale depen...
Time-dependent mean-field games in the superquadratic case
Gomes, Diogo A.
2016-04-06
We investigate time-dependent mean-field games with superquadratic Hamiltonians and a power dependence on the measure. Such problems pose substantial mathematical challenges as key techniques used in the subquadratic case, which was studied in a previous publication of the authors, do not extend to the superquadratic setting. The main objective of the present paper is to address these difficulties. Because of the superquadratic structure of the Hamiltonian, Lipschitz estimates for the solutions of the Hamilton−Jacobi equation are obtained here through a novel set of techniques. These explore the parabolic nature of the problem through the nonlinear adjoint method. Well-posedness is proven by combining Lipschitz regularity for the Hamilton−Jacobi equation with polynomial estimates for solutions of the Fokker−Planck equation. Existence of classical solutions is then established under conditions depending only on the growth of the Hamiltonian and the dimension. Our results also add to current understanding of superquadratic Hamilton−Jacobi equations.
Nilsson parameters κ and μ in relativistic mean field models
Sulaksono, A.; Mart, T.; Bahri, C.
2005-03-01
Nilsson parameters κ and μ have been studied in the framework of relativistic mean field (RMF) models. They are used to investigate the reason why RMF models give a relatively good prediction of the spin-orbit splitting but fail to reproduce the placement of the states with different orbital angular momenta. Instead of the relatively small effective mass M*, the independence of M* from the angular momentum l is found to be the reason.
RPA correlations and nuclear densities in relativistic mean field approach
Energy Technology Data Exchange (ETDEWEB)
Van Giai, N. [Institut de Physique Nucleaire, CNRS, UMR 8608, F-91406 Orsay (France)]|[Universite Paris-Sud, F-91406 Orsay (France); Liang, H.Z. [Institut de Physique Nucleaire, CNRS, UMR 8608, F-91406 Orsay (France)]|[Universite Paris-Sud, F-91406 Orsay (France)]|[School of Physics, Peking University, 100871 Beijing (China); Meng, J. [School of Physics, Peking University, 100871 Beijing (China)
2007-02-15
The relativistic mean field approach (RMF) is well known for describing accurately binding energies and nucleon distributions in atomic nuclei throughout the nuclear chart. The random phase approximation (RPA) built on top of the RMF is also a good framework for the study of nuclear excitations. Here, we examine the consequences of long range correlations brought about by the RPA on the neutron and proton densities as given by the RMF approach. (authors)
Energy Dependent Isospin Asymmetry in Mean-Field Dynamics
Gaitanos, T
2011-01-01
The Lagrangian density of Relativistic Mean-Field (RMF) theory with non-linear derivative (NLD) interactions is applied to isospin asymmetric nuclear matter. We study the symmetry energy and the density and energy dependences of nucleon selfenergies. At high baryon densities a soft symmetry energy is obtained. The energy dependence of the isovector selfenergy suppresses the Lane-type optical potential with increasing energy and predicts a $\\rho$-meson induced mass splitting between protons and neutrons in isospin asymmetric matter.
Advanced Mean Field Theory of Restricted Boltzmann Machine
Huang, Haiping; Toyoizumi, Taro
2015-01-01
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...
Mean-field effects on matter and antimatter elliptic flow
International Nuclear Information System (INIS)
We report our recent work on mean-field potential effects on the elliptic flows of matters and antimatters in heavy ion collisions leading to the production of a baryon-rich matter. Within the framework of a multiphase transport (AMPT) model that includes both initial partonic and final hadronic interactions, we have found that including mean-field potentials in the hadronic phase leads to a splitting of the elliptic flows of particles and their antiparticles, providing thus a plausible explanation of the different elliptic flows between p and anti-p, K+ and K-, and π+ and π- observed by the STAR Collaboration in the Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider (RHIC). Using a partonic transport model based on the Nambu-Jona-Lasinio (NJL) model, we have also studied the effect of scalar and vector mean fields on the elliptic flows of quarks and antiquarks in these collisions. Converting quarks and antiquarks at hadronization to hadrons via the quark coalescence model, we have found that the elliptic flow differences between particles and antiparticles also depend on the strength of the quark vector coupling in baryon-rich quark-gluon plasma, providing thus the possibility of extracting information on the latter's properties from the BES program at RHIC. (authors)
Mean-field description of collapsing and exploding Bose-Einstein condensates
International Nuclear Information System (INIS)
We perform numerical simulations based on the time-dependent mean-field Gross-Pitaevskii equation to understand some aspects of a recent experiment by Donley et al. [Nature (London) 412, 295 (2001)] on the dynamics of collapsing and exploding Bose-Einstein condensates of 85Rb atoms. These authors manipulated the atomic interaction by an external magnetic field via a Feshbach resonance, thus changing the repulsive condensate into an attractive one, and vice versa. In the actual experiment they suddenly changed the scattering length of atomic interaction from a positive to a large negative value on a preformed condensate in an axially symmetric trap. Consequently, the condensate collapsed and ejected atoms via explosion. We find that the present mean-field analysis can explain some aspects of the dynamics of the collapsing and exploding Bose-Einstein condensates
Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis
Szabó-Solticzky, András; Kiss, Istvan Z; Simon, Péter L
2014-01-01
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. A compact pairwise approximation for the dynamic network case is also developed and, for the case of link-type independent rewiring, the outcome of epidemics and changes in network structure are concurrently presented in a single bifurcation diagram. 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.
Ion-metal and ion-atom collisions instant replays and mean-field theories
International Nuclear Information System (INIS)
In this paper, we describe the results of our general long-term programmatic goal of investigating the strengths and weaknesses of time-dependent mean-field theories for collisions. We have made some progress in: (a) obtaining a better formulation of the theory, which has the exact full Schroedinger equation as one limit and permits appropriate classical treatment of heavy particles correctly coupled to the quantally treated electrons; (b) restructuring our numerical treatment to make it fully three-dimensional, improve accuracy and decrease cycle time, so that larger problems more in keeping with the mean-field concept can be treated; and (c) incorporating the electrons in the conduction band of a metal into our quantal treatment, making possible the description of collisions of atoms and ions with solids. Numerical results for protons tranversing a thin metallic foil, among other examples, are presented and discussed
A mean-field monomer-dimer model with attractive interaction: Exact solution and rigorous results
Energy Technology Data Exchange (ETDEWEB)
Alberici, D., E-mail: diego.alberici2@unibo.it; Contucci, P., E-mail: pierluigi.contucci@unibo.it; Mingione, E., E-mail: emanuele.mingione2@unibo.it [Department of Mathematics, University of Bologna, Piazza di Porta San Donato 5, Bologna 40126 (Italy)
2014-06-15
A mean-field monomer-dimer model which includes an attractive interaction among both monomers and dimers is introduced and its exact solution rigorously derived. The Heilmann-Lieb method for the pure hard-core interacting case is used to compute upper and lower bounds for the pressure. The bounds are shown to coincide in the thermodynamic limit for a suitable choice of the monomer density m. The computation of the monomer density is achieved by solving a consistency equation in the phase space (h, J), where h tunes the monomer potential and J the attractive potential. The critical point and exponents are computed and show that the model is in the mean-field ferromagnetic universality class.
Damping of collective nuclear motion and thermodynamic properties of nuclei beyond mean field
International Nuclear Information System (INIS)
The dynamical description of correlated nuclear motion is based on a set of coupled equations of motion for the one-body density matrix ρ(11';t) and the two-body correlation function c2(12, 1'2';t), which is obtained from the density-matrix hierarchy beyond conventional mean-field approaches by truncating three-body correlations. The resulting equations non-perturbatively describe particle-particle collisions (short-range correlations) as well as particle-hole interactions (long-range correlations). Within a basis of time-dependent Hartree-Fock states these equations of motion are solved for collective vibrations of 40Ca at several finite thermal excitation energies corresponding to temperatures T = 0 - 6 MeV. Transport coefficients for friction and diffusion are extracted from the explicit solutions in comparison to the solutions of the associated TDHF, VUU, Vlasov or damped quantum oscillator equations of motion. We find that the actual magnitude of the transport coefficients is strongly influenced by particle-hole correlations at low temperature which generate large fluctuations in the nuclear shape degrees of freedom. Thermodynamically, the specific heat and the entropy of the system as a function of temperature does not differ much from the mean-field limit except for a bump in the specific heat around T ≅ 4 MeV which we attribute to the melting of shell effects in the correlated system
Modeling and computation of mean field equilibria in producers' game with emission permits trading
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.
Fictive impurity approach to dynamical mean field theory
Energy Technology Data Exchange (ETDEWEB)
Fuhrmann, A.
2006-10-15
A new extension of the dynamical mean-field theory was investigated in the regime of large Coulomb repulsion. A number of physical quantities such as single-particle density of states, spin-spin correlation, internal energy and Neel temperature, were computed for a two-dimensional Hubbard model at half-filling. The numerical data were compared to our analytical results as well as to the results computed using the dynamical cluster approximation. In the second part of this work we consider a two-plane Hubbard model. The transport properties of the bilayer were investigated and the phase diagram was obtained. (orig.)
Relativistic Mean Field Study on Halo Structures of Mirror Nuclei
Institute of Scientific and Technical Information of China (English)
LIANG Yu-Jie; LI Yan-Song; LIU Zu-Hua; ZHOU Hong-Yu
2009-01-01
Halo structures of some light mirror nuclei are investigated with the relativistic mean field (RMF) theory.The calculations show that the dispersion of the valence proton is larger than that of the valence neutron in its mirror nucleus,the difference between the root-mean-square (rms) radius of the valence nucleon in each pair of mirror nuclei becomes smailer with the increase of the mass number A,and all the ratios of the rms radius of the valence nucleon to that of the matter in each pair o~ mirror nuclei decrease almost linearly with the increase of the mass number A.
Relativistic mean field study of clustering in light nuclei
International Nuclear Information System (INIS)
The clustering phenomenon in light, stable and exotic nuclei is studied within the relativistic mean field (RMF) approach. Numerical calculations are done by using the axially deformed harmonic oscillator basis. The calculated nucleon density distributions and deformation parameters are analyzed to look for the cluster configurations. The calculations explain many of the well-established cluster structures in both the ground and intrinsic excited states. Comparisons of our results with other model calculations and the available experimental information suggest that the RMF theory is well suited for studying clustering in light nuclei. A few discrepancies and their possible sources are also discussed
A new Mean Field Approach for Exotic Nuclei
International Nuclear Information System (INIS)
We present a new phenomenological mean field approach aiming at the calculation of properties of exotic nuclei. This approach combines the microscopic description of the spin-orbit properties in terms of particle densities, but also vector spin-orbit densities, inspired by results obtained within the Skyrme Hartree-Fock formalism, thus including the contribution of the tensor force. At the same time, the new approach preserves the simplicity of the phenomenological Woods-Saxon calculations and, more importantly, the robustness of the latter towards extrapolations in terms of increasing number of particles and/or isospin. (author)
MAP segmentation of magnetic resonance images using mean field annealing
Logenthiran, Ambalavaner; Snyder, Wesley E.; Santago, Peter, II; Link, Kerry M.
1991-06-01
An algorithm is described which segments magnetic resonance images while removing the noise from the images without blurring or other distortion of edges. The problem of segmentation and noise removal is posed as a restoration of an uncorrupted image, given additive white Gaussian noise and a segmentation cost. The problem is solved using a strategy called Mean Field Annealing. An a priori statistical model of the image, which includes the region classification, is chosen which drives the minimization toward solutions which are locally homogeneous and globally classified. Application of the algorithm to brain and knee images is presented.
A mechanical approach to mean field spin models
Genovese, Giuseppe
2008-01-01
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 details 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.
A Mean Field Game Approach to Scheduling in Cellular Systems
Manjrekar, Mayank; Ramaswamy, Vinod; Shakkottai, Srinivas
2013-01-01
We study auction-theoretic scheduling in cellular networks using the idea of mean field equilibrium (MFE). Here, agents model their opponents through a distribution over their action spaces and play the best response. The system is at an MFE if this action is itself a sample drawn from the assumed distribution. In our setting, the agents are smart phone apps that generate service requests, experience waiting costs, and bid for service from base stations. We show that if we conduct a second-pr...
Benchmarking mean-field approximations to level densities
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
A mechanical approach to mean field spin models
Genovese, Giuseppe; Barra, Adriano
2008-01-01
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 details the simplest test case, namely the Curie-Weiss model. Further we report some applications also to models whose order parameters do not self-average, ...
Skymapping with OSSE via the Mean Field Annealing Pixon Technique
Dixon, D D; Zych, A D; Cheng, L X; Johnson, W N; Kurfess, J D; Pina, R K; Pütter, R C; Purcell, W R; Wheaton, W A; Wheaton, Wm. A.
1997-01-01
We present progress toward using scanned OSSE observations for mapping and sky survey work. To this end, we have developed a technique for detecting pointlike sources of unknown number and location, given that they appear in a background which is relatively featureless or which can be modeled. The technique, based on the newly developed concept and mean field annealing, is described, with sample reconstructions of data from the OSSE Virgo Survey. The results demonstrate the capability of reconstructing source information without any a priori information about the number and/or location of pointlike sources in the field-of-view.
Nuclear Density-Dependent Effective Coupling Constants in the Mean-Field Theory
Lee, J H; Lee, S J; Lee, Jae Hwang; Lee, Young Jae; Lee, Suk-Joon
1996-01-01
It is shown that the equation of state of nuclear matter can be determined within the mean-field theory of $\\sigma \\omega$ model provided only that the nucleon effective mass curve is given. We use a family of the possible nucleon effective mass curves that reproduce the empirical saturation point in the calculation of the nuclear binding energy curves in order to obtain density-dependent effective coupling constants. The resulting density-dependent coupling constants may be used to study a possible equation of state of nuclear system at high density or neutron matter. Within the constraints used in this paper to $M^*$ of nuclear matter at saturation point and zero density, neutron matter of large incompressibility is strongly bound at high density while soft neutron matter is weakly bound at low density. The study also exhibits the importance of surface vibration modes in the study of nuclear equation of state.
International Nuclear Information System (INIS)
We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green close-quote s functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article. copyright 1996 The American Physical Society
HBT pion interferometry with phenomenological mean field interaction
Hattori, Koichi
2010-01-01
In order to extract the information of the hadron production dynamics in ultra-relativistic heavy ion collisions, the space-time structure of the hadron source has been measured using Hanbury Brown and Twiss interferometry. We study the distortion of the source images due to the effect of a final state interaction. We describe the interactions, taking place while penetrating through the cloud formed by evaporating particles, in terms of an one-body mean field potential localized in the vicinity of the source region. Adopting the semi-classical method, the modification of the propagation of an emitted particle is examined. In analogy to the optical model applied to the nuclear reactions, our phenomenological model has an imaginary part of the potential, which describes the absorption in the cloud. In this work, we focus on the pion interferometry and the mean field interaction obtained using a phenomenological $\\pi\\pi$ forward scattering amplitude in the elastic channels. The p-wave scattering with rho meson r...
Non-local correlations within dynamical mean field theory
Energy Technology Data Exchange (ETDEWEB)
Li, Gang
2009-03-15
The contributions from the non-local fluctuations to the dynamical mean field theory (DMFT) were studied using the recently proposed dual fermion approach. Straight forward cluster extensions of DMFT need the solution of a small cluster, where all the short-range correlations are fully taken into account. All the correlations beyond the cluster scope are treated in the mean-field level. In the dual fermion method, only a single impurity problem needs to be solved. Both the short and long-range correlations could be considered on equal footing in this method. The weak-coupling nature of the dual fermion ensures the validity of the finite order diagram expansion. The one and two particle Green's functions calculated from the dual fermion approach agree well with the Quantum Monte Carlo solutions, and the computation time is considerably less than with the latter method. The access of the long-range order allows us to investigate the collective behavior of the electron system, e.g. spin wave excitations. (orig.)
Benchmarking mean-field approximations to level densities
Alhassid, Y; Gilbreth, C N; Nakada, H
2015-01-01
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 $^{162}$Dy, representing a heavy deformed nucleus, and $^{148}$Sm, 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 (SMMC) calculations, which are accurate up to well-controlled statistical errors. The main weak points in the mean-field treatments are seen 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 appr...
Non-local correlations within dynamical mean field theory
International Nuclear Information System (INIS)
The contributions from the non-local fluctuations to the dynamical mean field theory (DMFT) were studied using the recently proposed dual fermion approach. Straight forward cluster extensions of DMFT need the solution of a small cluster, where all the short-range correlations are fully taken into account. All the correlations beyond the cluster scope are treated in the mean-field level. In the dual fermion method, only a single impurity problem needs to be solved. Both the short and long-range correlations could be considered on equal footing in this method. The weak-coupling nature of the dual fermion ensures the validity of the finite order diagram expansion. The one and two particle Green's functions calculated from the dual fermion approach agree well with the Quantum Monte Carlo solutions, and the computation time is considerably less than with the latter method. The access of the long-range order allows us to investigate the collective behavior of the electron system, e.g. spin wave excitations. (orig.)
Mean field mutation dynamics and the continuous Luria-Delbr\\"uck distribution
Kashdan, Eugene
2011-01-01
The Luria-Delbr\\"uck mutation model has a long history and has been mathematically formulated in several different ways. Here we tackle the problem in the case of a continuous distribution using some mathematical tools from nonlinear statistical physics. Starting from the classical formulations we derive the corresponding differential models and show that under a suitable mean field scaling they correspond to generalized Fokker-Planck equations for the mutants distribution whose solutions are given by the corresponding Luria-Delbr\\"uck distribution. Numerical results confirming the theoretical analysis are also presented.
Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles
Chou, Yen-Liang; Ihle, Thomas
2014-01-01
A ring-kinetic theory for Vicsek-style models of self-propelled agents is derived 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 pre-collisional correlations and cluster formation which both seem 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 de...
Delta isobars in relativistic mean-field models with $\\sigma$-scaled hadron masses and couplings
Kolomeitsev, E E; Voskresensky, D N
2016-01-01
We extend the relativistic mean-field models with hadron masses and meson-baryon coupling constants dependent on the scalar $\\sigma$ field, studied previously to incorporate $\\Delta(1232)$ baryons. Available empirical information is analyzed to put constraints on the couplings of $\\Delta$s with meson fields. Conditions for the appearance of $\\Delta$s are studied. We demonstrate that with inclusion of the $\\Delta$s our equations of state continue to fulfill majority of known empirical constraints including the pressure-density constraint from heavy-ion collisions, the constraint on the maximum mass of the neutron stars, the direct Urca and the gravitational-baryon mass ratio constraints.
Pasta phases in neutron star studied with extended relativistic mean field models
Gupta, Neha
2013-01-01
To explain several properties of finite nuclei, infinite matter, and neutron stars in a unified way within the relativistic mean field models, it is important to extend them either with higher order couplings or with density-dependent couplings. These extensions are known to have strong impact in the high-density regime. Here we explore their role on the equation of state at densities lower than the saturation density of finite nuclei which govern the phase transitions associated with pasta structures in the crust of neutron stars.
Mean field games with nonlinear mobilities in pedestrian dynamics
Burger, Martin
2014-04-01
In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to the Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.
Nonhelical mean-field dynamos in a sheared turbulence
Rogachevskii, I
2008-01-01
Mechanisms of nonhelical large-scale dynamos (shear-current dynamo and effect of homogeneous kinetic helicity fluctuations with zero mean) in a homogeneous turbulence with large-scale shear are discussed. We have found that the shear-current dynamo can act even in random flows with small Reynolds numbers. However, in this case mean-field dynamo requires small magnetic Prandtl numbers (i.e., ${\\rm Pm} < {\\rm Pm}^{\\rm cr}<1$). The threshold in the magnetic Prandtl number, ${\\rm Pm}^{\\rm cr} = 0.24$, is determined using second order correlation approximation (or first-order smoothing approximation) for a background random flow with a scale-dependent viscous correlation time $\\tau_c=(\
Temperature dependent relativistic mean field for highly excited hot nuclei
Gambhir, Y. K.; Maharana, J. P.; Lalazissis, G. A.; Panos, C. P.; Ring, P.
2000-11-01
The temperature dependent relativistic mean field (RMF-T) results obtained by using nonlinear Lagrangian parameter set NL3 are presented for a few selected representative spherical and deformed nuclei. The calculated total binding energy (entropy) decrease (increase) as temperature (T) increases. The depths of the potentials and the single particle (sp) energies change very little with temperature. The density slightly spreads out; as a result the radius increases as temperature rises. For well deformed nuclei the shell effects disappear at around T~3 MeV. This value of T is relatively higher as compared to the corresponding value of T (~1.8 MeV) obtained in the Strutinsky-type calculations. This difference in the value of T is shown to be due to the use of the effective nucleon mass (RMF Lagrangian.
Relativistic Mean-Field Models and Nuclear Matter Constraints
Dutra, M; Carlson, B V; Delfino, A; Menezes, D P; Avancini, S S; Stone, J R; Providência, C; Typel, S
2013-01-01
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^3+\\sigma^4 models, (iii) \\sigma^3+\\sigma^4+\\omega^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.
Relativistic mean-field models and nuclear matter constraints
Dutra, M.; Lourenço, O.; Carlson, B. V.; Delfino, A.; Menezes, D. P.; Avancini, S. S.; Stone, J. R.; Providência, C.; Typel, S.
2013-05-01
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 σ3 + σ4 models, (iii) σ3 + σ4 + ω4 models, (iv) models containing mixing terms in the fields σ and ω, (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 σ (ω) field. The isospin dependence of the interaction is modeled by the ρ 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.
Relativistic Mean-Field Hadronic Models under Nuclear Matter Constraints
Dutra, M; Avancini, S S; Carlson, B V; Delfino, A; Menezes, D P; Providência, C; Typel, S; Stone, J R
2014-01-01
Relativistic mean-field (RMF) models have been widely used in the study of many hadronic frameworks 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. With the aim of identifying the models which best satisfy well known properties of nuclear matter, we have analyzed 263 parameterizations of seven different types of RMF models under three different sets of constraints related to symmetric nuclear matter, pure neutron matter, symmetry energy, and its derivatives. One of these (SET1) is formed of the same constraints used in a recent work in which we analyzed 240 Skyrme parameterizations. The results pointed to 2 models consistent with all constraints. Using another set of constraints, namely, SET2a, formed by the updated versions of the previous one, we found 4 models approved simultan...
Non-mean-field screening by multivalent counterions
Energy Technology Data Exchange (ETDEWEB)
Loth, M S; Shklovskii, B I, E-mail: loth@physics.umn.ed [Department of Physics, University of Minnesota, Minneapolis, MN 55455 (United States)
2009-10-21
Screening of a strongly charged macroion by its multivalent counterions cannot be described in the framework of a mean-field Poisson-Boltzmann (PB) theory because multivalent counterions form a strongly correlated liquid (SCL) on the surface of the macroion. It was predicted that a distant counterion polarizes the SCL as if it were a metallic surface and creates an electrostatic image. The attractive potential energy of the image is the reason why the charge density of counterions decreases faster with distance from the charged surface than in PB theory. Using the Monte Carlo method to find the equilibrium distribution of counterions around the macroion, we confirm the existence of the image potential energy. It is also shown that, due to the negative screening length of the SCL, -2xi, the effective metallic surface is actually above the SCL by |xi|.
Double binding energy differences: Mean-field or pairing effect?
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.
Nuclear Level Density: Shell Model vs Mean Field
Sen'kov, Roman
2015-01-01
The knowledge of the nuclear level density is necessary for understanding various reactions including those in the stellar environment. Usually the combinatorics of Fermi-gas plus pairing is used for finding the level density. Recently a practical algorithm avoiding diagonalization of huge matrices was developed for calculating the density of many-body nuclear energy levels with certain quantum numbers for a full shell-model Hamiltonian. The underlying physics is that of quantum chaos and intrinsic thermalization in a closed system of interacting particles. We briefly explain this algorithm and, when possible, demonstrate the agreement of the results with those derived from exact diagonalization. The resulting level density is much smoother than that coming from the conventional mean-field combinatorics. We study the role of various components of residual interactions in the process of thermalization, stressing the influence of incoherent collision-like processes. The shell-model results for the traditionally...
Spectral Synthesis via Mean Field approach Independent Component Analysis
Hu, Ning; Kong, Xu
2015-01-01
In this paper, we apply a new statistical analysis technique, Mean Field approach to Bayesian Independent Component Analysis (MF-ICA), on galaxy spectral analysis. This algorithm can compress the stellar spectral library into a few Independent Components (ICs), and galaxy spectrum can be reconstructed by these ICs. Comparing to other algorithms which decompose a galaxy spectrum into a combination of several simple stellar populations, MF-ICA approach offers a large improvement in the efficiency. To check the reliability of this spectral analysis method, three different methods are used: (1) parameter-recover for simulated galaxies, (2) comparison with parameters estimated by other methods, and (3) consistency test of parameters from the Sloan Digital Sky Survey galaxies. We find that our MF-ICA method not only can fit the observed galaxy spectra efficiently, but also can recover the physical parameters of galaxies accurately. We also apply our spectral analysis method to the DEEP2 spectroscopic data, and find...
Density Functional Plus Dynamical Mean Field Theory of Correlated Oxides
Millis, Andrew
2015-03-01
The density functional plus dynamical mean field method is outlined and a few recent successes including applications to spin crossover molecules, oxide superlattices and metal-insulator transitions in bulk transition metals are outlined. Insights from the method into the essential role played by lattice distortions (both rotations and bond length changes) in determining the phase diagrams of correlated materials are presented. The key theoretical issue of the double counting correction is outlined, different approaches are compared, and a connection to the energy level differences between strongly and weakly correlated orbitals is presented. Charge transfer across oxide interfaces shown to depend crucially on the double counting correction, suggesting that experiments on oxide superlattices may provide insights into this important problem. Future directions are discussed. This work is performed in collaboration with Jia Chen, Hung Dang, Hyowon Park and Chris Marianetti. This research supported by the DOE Office of Science, Grant ER 046169.
Shell Model and Mean-Field Description of Band Termination
Zalewski, M; Nazarewicz, W; Stoitcheva, G; Zdunczuk, H
2007-01-01
We study nuclear high-spin states undergoing the transition to the fully stretched configuration with maximum angular momentum I_max within the space of valence nucleons. To this end, we perform a systematic theoretical analysis of non-fully-stretched I_max-2 and I_max-1 f_{7/2}^n seniority isomers and d_{3/2}^{-1} f_{7/2}^{n+1} intruder states in the A~44 nuclei from the lower-fp shell. We employ two theoretical approaches: (i) the density functional theory based on the cranked self-consistent Skyrme-Hartree-Fock method, and (ii) the nuclear shell model in the full sdfp configuration space allowing for 1p-1h cross-shell excitations. We emphasize the importance of restoration of broken angular momentum symmetry inherently obscuring the mean-field treatment of high-spin states. Overall good agreement with experimental data is obtained.
Glauber Dynamics for the mean-field Potts Model
Cuff, Paul; Louidor, Oren; Lubetzky, Eyal; Peres, Yuval; Sly, Allan
2012-01-01
We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with $q\\geq 3$ states and show that it undergoes a critical slowdown at an inverse-temperature $\\beta_s(q)$ strictly lower than the critical $\\beta_c(q)$ for uniqueness of the thermodynamic limit. The dynamical critical $\\beta_s(q)$ is the spinodal point marking the onset of metastability. We prove that when $\\beta\\beta_s(q)$ the mixing time is exponentially large in $n$. Furthermore, as $\\beta \\uparrow \\beta_s$ with $n$, the mixing time interpolates smoothly from subcritical to critical behavior, with the latter reached at a scaling window of $O(n^{-2/3})$ around $\\beta_s$. These results form the first complete analysis of the critical slowdown of a dynamics with a first order phase transition.
A mean-field thermodynamic description of the kinetics of overdriven interfaces
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.
Mean-field/PDF numerical approach for polydispersed turbulent two-phase flows
Peirano, Eric; Pozorski, Jacek; Minier, Jean-Pierre
2010-01-01
The purpose of this paper is to give an overview in the realm of numerical computations of polydispersed turbulent two-phase flows, using a mean-field/PDF approach. In this approach, the numerical solution is obtained by resorting to a hybrid method where the mean fluid properties are computed by solving mean-field (RANS) equations with a classical finite volume procedure whereas the local instantaneous properties of the particles are determined by solving stochastic differential equations (SDEs). The fundamentals of the general formalism are recalled and particular attention is focused on a specific theoretical issue: the treatment of the multiscale character of the dynamics of the discrete particles, that is the consistency of the system of SDEs in asymptotic cases. Then, the main lines of the particle/mesh algorithm are given and some specific problems, related to the integration of the SDEs, are discussed, for example, issues related to the specificity of the treatment of the averaging and projection oper...
Quantum de Finetti theorems and mean-field theory from quantum phase space representations
International Nuclear Information System (INIS)
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. (paper)
Variational extensions of the time-dependent mean-field theory
International Nuclear Information System (INIS)
Using the Balian-Veneroni variational principle, we propose two consistent extensions of the time-dependent mean-field theory for many-boson systems. A first approximation, devised to take into account the effect of correlations, is obtained by means of a development of the optimal density operator suggested by the maximum entropy principle around a Gaussian operator. We discuss the relevance of the evolution equations and their possible generalizations. We present an application to an one-dimensional example. In a second type of approximation, to optimize the prediction of characteristic functions of one-body observables and of transition probabilities, we select for both, the variational observable and the density matrix, the class of exponential operators of quadratic forms. We obtain coupled evolution equations of an unusual kind called 'two-point boundary value problem'. To solve them, we construct a suitable numerical algorithm. A test of the method is presented on two examples in one dimension. In a first case, we study the collision of a particle against a Gaussian barrier. The method improves significantly mean-field predictions relative to reflexion and transmission ratios. The study of the motion of a particle in a quartic well reveals the existence of several different solutions for the transition probabilities predicted by the Balian-Veneroni method
International Nuclear Information System (INIS)
Neutron-rich nuclei of mass A=100-110 are of great interest for the study of nuclear structure far from stability. Previous experimental and theoretical studies suggest a complex evolution of deformation and collectivity in the isotopic chains of Zr, Mo, Ru and Pd. In order to extend information on the evolution of the collectivity towards higher spin states and more neutron-rich nuclei, lifetimes of excited states were measured in nuclei produced through a fusion-fission reaction in inverse kinematic at GANIL. Fission fragments were separated and identified in both A and Z with the high acceptance magnetic spectrometer VAMOS while the EXOGAM germanium detectors array was used for the coincident gamma-ray detection. Lifetimes of about twenty excited states were extracted using the plunger device of Cologne. This is the first RDDS measurement on fission fragments which are identified in A and Z on an event-by-event basis. The study of this mass region is completed by theoretical calculations using self consistent mean field and beyond mean field methods implemented with the Gogny force (D1S). The structure of the ground states and the excited states is described with Hartree-Fock-Bogoliubov calculations with constraints placed on the axial and triaxial deformations. Individual excitations are investigated through blocking calculations and the high spin states are studied through cranking calculations. Finally, an approximated generator coordinate method (GCM+GOA) using the 5DCH Hamiltonian is used to describe the low energy collective states and to interpret the experimental evolution of the collectivity. (author)
Individual based and mean-field modeling of direct aggregation
Burger, Martin
2013-10-01
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 firstorder 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. 2012 Elsevier B.V. All rights reserved.
Spectral Synthesis via Mean Field approach to Independent Component Analysis
International Nuclear Information System (INIS)
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. (paper)
A Mean-Field Theory for Coarsening Faceted Surfaces
Norris, Scott A
2009-01-01
A mean-field theory is developed for the scale-invariant length distributions observed during the coarsening of one-dimensional faceted surfaces. This theory closely follows the Lifshitz-Slyozov-Wagner theory of Ostwald ripening in two-phase systems [1-3], but the mechanism of coarsening in faceted surfaces requires the addition of convolution terms recalling the work of Smoluchowski [4] and Schumann [5] on coalescence. The model is solved by the exponential distribution, but agreement with experiment is limited by the assumption that neighboring facet lengths are uncorrelated. However, the method concisely describes the essential processes operating in the scaling state, illuminates a clear path for future refinement, and offers a framework for the investigation of faceted surfaces evolving under arbitrary dynamics. [1] I. Lifshitz, V. Slezov, Soviet Physics JETP 38 (1959) 331-339. [2] I. Lifshitz, V. Slyozov, J. Phys. Chem. Solids 19 (1961) 35-50. [3] C. Wagner, Elektrochemie 65 (1961) 581-591. [4] M. von S...
The quark mean field model with pion and gluon corrections
Xing, Xueyong; Shen, Hong
2016-01-01
The properties of nuclear matter and finite nuclei are studied within the quark mean field (QMF) model by taking the effects of pion and gluon into account at the quark level. The nucleon is described as the combination of three constituent quarks confined by a harmonic oscillator potential. To satisfy the spirit of QCD theory, the contributions of pion and gluon on the nucleon structure are treated in second-order perturbation theory. For the nuclear many-body system, nucleons interact with each other by exchanging mesons between quarks. With different constituent quark mass, $m_q$, we determine three parameter sets about the coupling constants between mesons and quarks, named as QMF-NK1, QMF-NK2, and QMF-NK3 by fitting the ground-state properties of several closed-shell nuclei. It is found that all of the three parameter sets can give satisfactory description on properties of nuclear matter and finite nuclei, meanwhile they can also predict the larger neutron star mass around $2.3M_\\odot$ without the hypero...
The hyperon mean free paths in the relativistic mean field
Wang, Q L; Ning, P Z; Zhong, X H
2005-01-01
The $\\Lambda$- and $\\Xi^-$-hyperon mean free paths in nuclei are firstly calculated in the relativistic mean field (RMF) theory. The real parts of the optical potential are derived from the RMF approach, while the imaginary parts are obtained from those of nucleons with the relations: $U^{\\mathrm{IY}}_{\\mathrm{S}} = \\alpha_{\\sigma \\mathrm{Y}}\\cdot U_{\\mathrm{S}}^{\\mathrm{IN}}$ and $U^{\\mathrm{IY}}_{\\mathrm{V}} = \\alpha_{\\omega \\mathrm{Y}}\\cdot U_{\\mathrm{V}}^{\\mathrm{IN}}$ . With the assumption, the depth of the imaginary potential for $\\Xi^-$ is $W_{\\Xi}\\simeq-$ 3.5 MeV, and for $\\Lambda$ is $W_{\\Lambda}\\simeq-$ 7 MeV at low incident energy. We find that, the hyperon mean free path decreases with the increase of the hyperon incident energies, from 200 MeV to 800 MeV; and in the interior of the nuclei, the mean free path is about $2\\sim 3$ fm for $\\Lambda$, and about $4\\sim 8$ fm for $\\Xi^-$, depending on the hyperon incident energy.
Quark mean field model with pion and gluon corrections
Xing, Xueyong; Hu, Jinniu; Shen, Hong
2016-10-01
The properties of nuclear matter and finite nuclei are studied within the quark mean field (QMF) model by taking the effects of pions and gluons into account at the quark level. The nucleon is described as the combination of three constituent quarks confined by a harmonic oscillator potential. To satisfy the spirit of QCD theory, the contributions of pions and gluons on the nucleon structure are treated in second-order perturbation theory. In a nuclear many-body system, nucleons interact with each other by exchanging mesons between quarks. With different constituent quark mass, mq, we determine three parameter sets for the coupling constants between mesons and quarks, named QMF-NK1, QMF-NK2, and QMF-NK3, by fitting the ground-state properties of several closed-shell nuclei. It is found that all of the three parameter sets can give a satisfactory description of properties of nuclear matter and finite nuclei, moreover they also predict a larger neutron star mass around 2.3 M⊙ without hyperon degrees of freedom.
Relativistic mean-field models and nuclear matter constraints
Energy Technology Data Exchange (ETDEWEB)
Dutra, M.; Lourenco, O.; Carlson, B. V. [Departamento de Fisica, Instituto Tecnologico de Aeronautica-CTA, 12228-900, Sao Jose dos Campos, SP (Brazil); Delfino, A. [Instituto de Fisica, Universidade Federal Fluminense, 24210-150, Boa Viagem, Niteroi, RJ (Brazil); Menezes, D. P.; Avancini, S. S. [Departamento de Fisica, CFM, Universidade Federal de Santa Catarina, CP. 476, CEP 88.040-900, Florianopolis, SC (Brazil); Stone, J. R. [Oxford Physics, University of Oxford, OX1 3PU Oxford (United Kingdom) and Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996 (United States); Providencia, C. [Centro de Fisica Computacional, Department of Physics, University of Coimbra, P-3004-516 Coimbra (Portugal); Typel, S. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Theorie, Planckstrasse 1,D-64291 Darmstadt (Germany)
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.
First principles based mean field model for oxygen reduction reaction.
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
Mean-field-diffusion-induced chimera death state
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.
Spectral Synthesis via Mean Field approach to Independent Component Analysis
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.
Classical mutual information in mean-field spin glass models
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.
Mean-field study of $^{12}$C+$^{12}$C fusion
Chien, Le Hoang; Khoa, Dao T
2016-01-01
The nuclear mean-field potential arising from the $^{12}$C+$^{12}$C interaction at the low energies relevant for the astrophysical carbon burning process has been constructed within the double-folding model, using the realistic nuclear ground-state density of the $^{12}$C nucleus and the effective M3Y nucleon-nucleon (NN) interaction constructed from the G-matrix of the Paris (free) NN potential. To explore the nuclear medium effect, both the original density independent M3Y-Paris interaction and its density dependent CDM3Y6 version have been used in the folding model calculation of the $^{12}$C+$^{12}$C potential. The folded potentials at the different energies were used in the optical model description of the elastic $^{12}$C+$^{12}$C scattering at the energies around and below the Coulomb barrier, as well as in the barrier penetration model to estimate the fusion cross section and astrophysical $S$ factor of the $^{12}$C+$^{12}$C reactions at the low energies. The obtained results are in good agreement wit...
Energy Technology Data Exchange (ETDEWEB)
Withers, L. P., E-mail: lpwithers@mitre.org [School of Physics, Astronomy, and Computational Science, George Mason University, Fairfax, Virginia 22030-4444 (United States); Narducci, F. A., E-mail: francesco.narducci@navy.mil [Naval Air Systems Command, Patuxent River, Maryland 20670 (United States)
2015-06-15
The recent single-photon double-slit experiment of Steinberg et al., based on a weak measurement method proposed by Wiseman, showed that, by encoding the photon’s transverse momentum behind the slits into its polarization state, the momentum profile can subsequently be measured on average, from a difference of the separated fringe intensities for the two circular polarization components. They then integrated the measured average velocity field, to obtain the average trajectories of the photons enroute to the detector array. In this paper, we propose a modification of their experiment, to demonstrate that the average particle velocities and trajectories change when the mode of detection changes. The proposed experiment replaces a single detector by a pair of detectors with a given spacing between them. The pair of detectors is configured so that it is impossible to distinguish which detector received the particle. The pair of detectors is then analogous to the simple pair of slits, in that it is impossible to distinguish which slit the particle passed through. To establish the paradoxical outcome of the modified experiment, the theory and explicit three-dimensional formulas are developed for the bilocal probability and current densities, and for the average velocity field and trajectories as the particle wavefunction propagates in the volume of space behind the Gaussian slits. Examples of these predicted results are plotted. Implementation details of the proposed experiment are discussed.
Active matter beyond mean-field: ring-kinetic theory for self-propelled particles.
Chou, Yen-Liang; Ihle, Thomas
2015-02-01
Recently, Hanke et al. [Phys. Rev. E 88, 052309 (2013)] 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. PMID:25768454
Avalanche shape and exponents beyond mean-field theory
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_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.
Mean Field Analysis of Stochastic Neural Network Models with Synaptic Depression
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.
Mean-field diffusion-limited aggregation: a "density" model for viscous fingering phenomena.
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
The electronic mean-field configuration interaction method. I. Theory and integral formulas
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.
Quantum correlated cluster mean-field theory applied to the transverse Ising model
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.
Quantum corrections to the Relativistic mean-field theory
MAYDANYUK, SERGEI P.; Zhang, Peng-Ming; Bakry, Ahmed
2016-01-01
In this paper, we compare the RMF theory and the model of deformed oscillator shells (DOS) in description of the quantum properties of the bound states of the spherically symmetric light nuclei. We obtain an explicit analytical relation between differential equations for the RMF theory and DOS model, which determine wave functions for nucleons. On such a basis we perform analysis of correspondence of quantum properties of nuclei. We find: (1) Potential $V_{RMF}$ of the RMF theory for nucleons...
Relativistic Nuclear Energy Density Functionals: Mean-Field and Beyond
Niksic, Tamara; Vretenar, Dario; Ring, Peter, 1941-
2011-01-01
Relativistic energy density functionals (EDF) have become a standard tool for nuclear structure calculations, providing a complete and accurate, global description of nuclear ground states and collective excitations. Guided by the medium dependence of the microscopic nucleon self-energies in nuclear matter, semi-empirical functionals have been adjusted to the nuclear matter equation of state and to bulk properties of finite nuclei, and applied to studies of arbitrarily heavy nuclei, exotic nu...
Antikaons in neutron star studied with recent versions of relativistic mean-field models
Gupta, Neha; Arumugam, P.
2013-03-01
We study the impact of additional couplings in the relativistic mean field (RMF) models, in conjunction with antikaon condensation, on various neutron star properties. We analyze different properties such as in-medium antikaon and nucleon effective masses, antikaon energies, chemical potentials and the mass-radius relations of neutron star (NS). We calculate the NS properties with the RMF (NL3), E-RMF (G1, G2) and FSU2.1 models, which are quite successful in explaining several finite nuclear properties. Our results show that the onset of kaon condensation in NS strongly depends on the parameters of the Lagrangian, especially the additional couplings which play a significant role at higher densities where antikaons dominate the behavior of equation of state.
Antikaons in neutron star studied with recent versions of relativistic mean-field models
Gupta, Neha
2013-01-01
We study the impact of additional couplings in the relativistic mean field (RMF) models, in conjunction with antikaon condensation, on various neutron star properties. We analyze different properties such as in-medium antikaon and nucleon effective masses, antikaon energies, chemical potentials and the mass-radius relations of neutron star (NS). We calculate the NS properties with the RMF (NL3), E-RMF (G1, G2) and FSU2.1 models, which are quite successful in explaining several finite nuclear properties. Our results show that the onset of kaon condensation in NS strongly depends on the parameters of the Lagrangian, especially the additional couplings which play a significant role at higher densities where antikaons dominate the behavior of equation of state.
A Fractional Micro-Macro Model for Crowds of Pedestrians based on Fractional Mean Field Games
Cao, Ke-cai; Stuart, Dan
2016-01-01
Modeling of crowds of pedestrians has been considered in this paper from different aspects. Based on fractional microscopic model that may be much more close to reality, a fractional macroscopic model has been proposed using conservation law of mass. Then in order to characterize the competitive and cooperative interactions among pedestrians, fractional mean field games are utilized in the modeling problem when the number of pedestrians goes to infinity and fractional dynamic model composed of fractional backward and fractional forward equations are constructed in macro scale. Fractional micro-macro model for crowds of pedestrians are obtained in the end. Simulation results are also included to illustrate the proposed fractional microscopic model and fractional macroscopic model respectively.
Gressel, Oliver
2010-01-01
Local shearing box simulations of stratified magneto rotational turbulence invariably exhibit cyclic field patterns which propagate away from the disc midplane. A common explanation for this is magnetic buoyancy. The recent analysis by Shi et al. however shows that the flow is buoyantly stable below one disc scale height H, necessitating an alternative explanation in this region. We here conduct and analyse direct numerical simulations to explain the observed behaviour by means of a mean-field description. Apart from the mean radial and azimuthal field, we monitor the small-scale current helicity, which we propose as a key indicator for saturation. Reconstructing the horizontally averaged field, we demonstrate that the problem can be reduced to a one-dimensional induction equation. By means of the so-called test field method, we then determine the underlying closure parameters. Our analysis shows that, apart from a possible direct MRI dynamo, two distinct indirect dynamo mechanisms operate in the disc. This r...
On the binding of small polarons in a mean-field quantum crystal
Lewin, Mathieu
2012-01-01
We consider a small multi-polaron model obtained by coupling the many-body Schr\\"odinger equation for N interacting electrons with the energy functional of a mean- field crystal with a localized defect, obtaining a highly non linear many-body problem. The physical picture is that the electrons constitue a charge defect in an otherwise perfect periodic crystal. A remarkable feature of such a system is the possibility to form a bound state of electrons via their interaction with the polarizable background. We first prove that a single polaron always binds, i.e. the energy functional has a minimizer for N = 1. Then we discuss the case of multi-polarons containing two electrons or more. We show that their existence is guaranteed when certain quantized binding inequalities of HVZ type are satisfied.
Economic dynamics with financial fragility and mean-field interaction: A model
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.
Andersen, J. O.; Haugerud, H.
2002-01-01
We consider the ground state of a trapped Bose-Einstein condensate in two dimensions. In the mean-field approximation, the ground state density profile satisfies the Gross-Pitaevskii equation. We compute the leading quantum corrections to the density profile to second order in an expansion around the Thomas-Fermi limit. By summing the ladder diagrams, we are generalizing Schick's result for the ground state energy of a homogeneouns Bose gas to the case of a trapped Bose gas.
Coagulation kinetics beyond mean field theory using an optimised Poisson representation
Energy Technology Data Exchange (ETDEWEB)
Burnett, James [Department of Mathematics, UCL, Gower Street, London WC1E 6BT (United Kingdom); Ford, Ian J. [Department of Physics and Astronomy, UCL, Gower Street, London WC1E 6BT (United Kingdom)
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.
Resonant Continuum in the Relativistic Mean-Field Theory
Institute of Scientific and Technical Information of China (English)
CAO Li-Gang; MA Zhong-Yu
2002-01-01
Energies, widths and wave functions of the single-particle resonant continuum are determined by solvingscattering states of the Dirac equation with proper asymptotic conditions for the continuous spectrum in the relativisticmean-field theory. The relativistic regular and irregular Coulomb wave functions are calculated numerically. Theresonance states in the continuum for some closed- or sub-closed-shell nucleus in Sn-isotopes, such as 1 14Sn, 1 16Sn, 1 18Sn,and 120Sn are calculated. Results show that the S-matrix method is a reliable and straightforward way in determiningenergies and widths of resonant states.
Tacla, Alexandre B.; Caves, Carlton M.
2013-02-01
We study the mean-field dynamics and the reduced-dimension character of two-mode Bose-Einstein condensates (BECs) in highly anisotropic traps. By means of perturbative techniques, we show that the tightly confined (transverse) degrees of freedom can be decoupled from the dynamical equations at the expense of introducing additional effective three-body, attractive, intra- and inter-mode interactions into the dynamics of the loosely confined (longitudinal) degrees of freedom. These effective interactions are mediated by changes in the transverse wave function. The perturbation theory is valid as long as the nonlinear scattering energy is small compared to the transverse energy scales. This approach leads to reduced-dimension mean-field equations that optimally describe the evolution of a two-mode condensate in general quasi-one-dimensional (1D) and quasi-two-dimensional geometries. We use this model to investigate the relative phase and density dynamics of a two-mode, cigar-shaped 87Rb BEC. We study the relative-phase dynamics in the context of a nonlinear Ramsey interferometry scheme, which has recently been proposed as a novel platform for high-precision interferometry. Numerical integration of the coupled, time-dependent, three-dimensional, two-mode Gross-Pitaevskii equations for various atom numbers shows that this model gives a considerably more refined analytical account of the mean-field evolution than an idealized quasi-1D description.
Exact mean-field theory of ionic solutions: non-Debye screening
Energy Technology Data Exchange (ETDEWEB)
Varela, L.M.; Garcia, Manuel; Mosquera, Victor
2003-07-01
The main aim of this report is to analyze the equilibrium properties of primitive model (PM) ionic solutions in the formally exact mean-field formalism. Previously, we review the main theoretical and numerical results reported throughout the last century for homogeneous (electrolytes) and inhomogeneous (electric double layer, edl) ionic systems, starting with the classical mean-field theory of electrolytes due to Debye and Hueckel (DH). In this formalism, the effective potential is derived from the Poisson-Boltzmann (PB) equation and its asymptotic behavior analyzed in the classical Debye theory of screening. The thermodynamic properties of electrolyte solutions are briefly reviewed in the DH formalism. The main analytical and numerical extensions of DH formalism are revised, ranging from the earliest extensions that overcome the linearization of the PB equation to the more sophisticated integral equation techniques introduced after the late 1960s. Some Monte Carlo and molecular dynamic simulations are also reviewed. The potential distributions in an inhomogeneous ionic system are studied in the classical PB framework, presenting the classical Gouy-Chapman (GC) theory of the electric double layer (edl) in a brief manner. The mean-field theory is adequately contextualized using field theoretic (FT) results and it is proven that the classical PB theory is recovered at the Gaussian or one-loop level of the exact FT, and a systematic way to obtain the corrections to the DH theory is derived. Particularly, it is proven following Kholodenko and Beyerlein that corrections to DH theory effectively lead to a renormalization of charges and Debye screening length. The main analytical and numerical results for this non-Debye screening length are reviewed, ranging from asymptotic expansions, self-consistent theory, nonlinear DH results and hypernetted chain (HNC) calculations. Finally, we study the exact mean-field theory of ionic solutions, the so-called dressed-ion theory
Quantum corrections to the Relativistic mean-field theory
Maydanyuk, Sergei P; Bakry, Ahmed
2016-01-01
In this paper, we compare the RMF theory and the model of deformed oscillator shells (DOS) in description of the quantum properties of the bound states of the spherically symmetric light nuclei. We obtain an explicit analytical relation between differential equations for the RMF theory and DOS model, which determine wave functions for nucleons. On such a basis we perform analysis of correspondence of quantum properties of nuclei. We find: (1) Potential $V_{RMF}$ of the RMF theory for nucleons has the wave functions $f$ and $g$ with joint part $h$ coincident exactly with the nucleon wave function of DOS model with potential $V_{\\rm shell}$. But, a difference between $V_{RMF}$ and $V_{\\rm shell}$ is essential for any nucleus. (2) The nucleon wave functions and densities obtained by the DOS and RMF theories are essentially different. The nucleon densities of the RMF theory contradict to knowledge about distribution of the proton and neutron densities inside the nuclei obtained from experimental data. This indica...
Dynamo action due to alpha fluctuations in a shear flow: mean--field theory
Sridhar, S
2013-01-01
We present an analytical theory of the growth of a large-scale mean magnetic field in a linear shear flow with fluctuations in time of the alpha parameter (equivalently, kinetic helicity). Using shearing coordinates and Fourier variables we derive a set of coupled integro-differential equations, governing the dynamics of the mean magnetic field, that are non perturbative in the rate of shear. When the alpha fluctuations are of white-noise form, the mean electromotive force (EMF) is identical to the negative diffusive form derived by Kraichnan for the case of no shear; the physical reason is that shear takes time to act, and white-noise fluctuations have zero correlation time. We demonstrate that the white-noise case does not allow for large-scale dynamo action. We then allow for a small but non zero correlation time and show that, for a slowly varying mean magnetic field, the mean EMF has additional terms that depend on a combination of shear and alpha fluctuations; the mean-field equations now reduce to a se...
The Accuracy of Mean-Field Approximation for Susceptible-Infected-Susceptible Epidemic Spreading
Qu, Bo
2016-01-01
The epidemic spreading has been studied for years by applying the mean-field approach in both homogeneous case, where each node may get infected by an infected neighbor with the same rate, and heterogeneous case, where the infection rates between different pairs of nodes are different. Researchers have discussed whether the mean-field approaches could accurately describe the epidemic spreading for the homogeneous cases but not for the heterogeneous cases. In this paper, we explore under what conditions the mean-field approach could perform well when the infection rates are heterogeneous. In particular, we employ the Susceptible-Infected-Susceptible (SIS) model and compare the average fraction of infected nodes in the metastable state obtained by the continuous-time simulation and the mean-field approximation. We concentrate on an individual-based mean-field approximation called the N-intertwined Mean Field Approximation (NIMFA), which is an advanced approach considered the underlying network topology. Moreove...
Ring, P; Lalazissis, G A
1997-01-01
A Fortran program for the calculation of the ground state properties of axially deformed even-even nuclei in the relativistic framework is presented. In this relativistic mean field (RMF) approach a set of coupled differential equations namely the Dirac equation with potential terms for the nucleons and the Glein-Gordon type equations with sources for the meson and the electromagnetic fields are to be solved self-consistently. The well tested basis expansion method is used for this purpose. Accordingly a set of harmonic oscillator basis generated by an axially deformed potential are used in the expansion. The solution gives the nucleon spinors, the fields and level occupancies, which are used in the calculation of the ground state properties.
Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model
Erban, Radek
2009-01-01
A framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs, for example, in the modeling of cell-cycle regulation. It is shown that the stochastic system possesses oscillatory solutions even for parameter values for which the mean-field model does not oscillate. The dependence of the mean period of these oscillations on the parameters of the model (kinetic rate constants) and the size of the system (number of molecules present) are studied. Our approach is based on the chemical Fokker-Planck equation. To gain some insight into the advantages and disadvantages of the method, a simple one-dimensional chemical switch is first analyzed, and then the chemical SNIPER problem is studied in detail. First, results obtained by solving the Fokker-Planck equation numerically are presented. Then an asymptotic analysis of the Fokker-Planck equation is used to derive explicit formulae for the period of oscillation as a function of the rate constants and as a function of the system size. © 2009 Society for Industrial and Applied Mathematics.
Mean-field dynamics versus two-body collisions at intermediate energy heavy-ion reactions
International Nuclear Information System (INIS)
Nucleus-nucleus collisions in the energy range from 10 MeV/u to 150 MeV/u are investigated in the framework of the Wigner transformed von-Neumann equation on the level of the one-body density matrix. Two-body collisions permitted by the Pauli principle are included via a collision term of the Uehling-Uhlenbeck type. The time evolution of the phase-space density is studied in detail for central collisions of 40Ca + 40Ca within a time-dependent finite two-center shell model. Special emphasis is ascribed to high momentum components in beam direction which are generated by the time-dependent mean field. These high momentum components, essentially decaying by two-body collisions, are energetic enough to allow for pion production already at 20 MeV/u laboratory bombarding energies in case of heavy nuclei. The competition between one-body and two-body effects is investigated with respect to decay times for primary distorted momentum distributions. Linear momentum transfer by one-body (wall) and two-body collisions turns out to be strongly correlated with nonequilibrium light particle emission in terms of Fermi-jets as well as scattered energetic nucleons. Double differential preequilibrium neutron spectra d2N/dTHETAdE in coincidence with central collisions of 40Ca + 40Ca at 20 MeV/u are calculated for primary and secondary emission processes. (orig.)
Effects of large-scale non-axisymmetric perturbations in the mean-field solar dynamo
Pipin, V V
2015-01-01
We explore a response of the non-linear non-axisymmetric mean-field solar dynamo model to the shallow non-axisymmetric perturbations with the strength of 1G. The amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, the depth of perturbation. It is found that perturbation which is anchored at the 0.9R have a profound effect and it produce the transient magnetic cycle of the axisymmetric magnetic field if it is initiated at the growing phase of the cycle. The non-symmetric about equator perturbation results the hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric field depends on how well the magnetic helicity is conserved. In the range of Rm=10^{4-6} the evolution returns to the normal course in the next cycle and the non-axisymmetric field is generated due to non-linear alpha-effect and the magnetic buoyancy. In the stationary state of evolution the large-scale magnetic field demonstrate, the phenomena of the "active...
Nucleon Finite Volume Effect and Nuclear Matter Properties in a Relativistic Mean-Field Theory
Institute of Scientific and Technical Information of China (English)
R. Costa; A.J. Santiago; H. Rodrigues; J. Sa Borges
2006-01-01
Effects of excluded volume of nucleons on nuclear matter are studied, and the nuclear properties that follow from different relativistic mean-field model parametrizations are compared. We show that, for all tested parametrizations,the resulting volume energy a1 and the symmetry energy J are around the acceptable values of 16 MeV and 30 MeV,and the density symmetry L is around 100 Me V. On the other hand, models that consider only linear terms lead to incompressibility K0 much higher than expected. For most parameter sets there exists a critical point (ρc,δc), where the minimum and the maximum of the equation of state are coincident and the incompressibility equals zero. This critical point depends on the excluded volume parameter r. If this parameter is larger than 0.5 fm, there is no critical point and the pure neutron matter is predicted to be bound. The maximum value for neutron star mass is 1.85M⊙, which is in agreement with the mass of the heaviest observed neutron star 4U0900-40 and corresponds to r = 0.72 fm. We also show that the light neutron star mass (1.2M⊙) is obtained for r (≌) 0.9 fm.
Hamiltonian mean field model: Effect of network structure on synchronization dynamics.
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
Nuclear matter fourth-order symmetry energy in relativistic mean field models
Cai, Bao-Jun
2011-01-01
Within the nonlinear relativistic mean field model, we derive the analytical expression of the nuclear matter fourth-order symmetry energy $E_{4}(\\rho)$. Our results show that the value of $E_{4}(\\rho)$ at normal nuclear matter density $\\rho_{0}$ is generally less than 1 MeV, confirming the empirical parabolic approximation to the equation of state for asymmetric nuclear matter at $\\rho_{0}$. On the other hand, we find that the $E_{4}(\\rho)$ may become nonnegligible at high densities. Furthermore, the analytical form of the $E_{4}(\\rho)$ provides the possibility to study the higher-order effects on the isobaric incompressibility of asymmetric nuclear matter, i.e., $K_{\\mathrm{sat}}(\\delta)=K_{0}+K_{\\mathrm{{sat},2}}\\delta ^{2}+K_{\\mathrm{{sat},4}}\\delta ^{4}+\\mathcal{O}(\\delta ^{6})$ where $\\delta =(\\rho_{n}-\\rho_{p})/\\rho $ is the isospin asymmetry, and we find that the value of $K_{\\mathrm{{sat},4}}$ is generally comparable with that of the $K_{\\mathrm{{sat},2}}$. In addition, we study the effects of the $E...
Nuclear matter EOS with light clusters within the mean-field approximation
Ferreira, Márcio
2013-01-01
The crust of a neutron star is essentially determined by the low-density region ($\\rho<\\rho_0\\approx0.15-0.16\\unit{fm}^{-3}$) of the equation of state. At the bottom of the inner crust, where the density is $\\rho\\lesssim0.1\\rho_0$, the formation of light clusters in nuclear matter will be energetically favorable at finite temperature. At very low densities and moderate temperatures, the few body correlations are expected to become important and light nuclei like deuterons, tritons, helions and $\\alpha$-particles will form. Due to Pauli blocking, these clusters will dissolve at higher densities $\\rho\\gtrsim 0.1\\rho_0$. The presence of these clusters influences the cooling process and quantities, such as the neutrino emissivity and gravitational waves emission. The dissolution density of these light clusters, treated as point-like particles, will be studied within the Relativistic Mean Field approximation. In particular, the dependence of the dissolution density on the clusters-meson couplings is studied.
Baladron, Javier; Fasoli, Diego; Faugeras, Olivier; Touboul, Jonathan
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 neu...
Lionel, Sittler
2008-01-01
In this paper we propose a solution for the time evolution of the island density with irreversible aggregation and a time dependent input of particle in the space dimensions $d=1,2$. For this purpose we use the rate equation resulting from a generalized mean field approach. A well-known technique for growing surfaces at the atomic scale is molecular beam epitaxy (MBE). Another approach is the pulsed laser deposition method (PLD). The main difference between MBE and PLD is that in the case of ...
Limit Theorems for Monomer-Dimer Mean-Field Models with Attractive Potential
Alberici, Diego; Contucci, Pierluigi; Fedele, Micaela; Mingione, Emanuele
2016-09-01
The number of monomers in a monomer-dimer mean-field model with an attractive potential fluctuates according to the central limit theorem when the parameters are outside the critical curve. At the critical point the model belongs to the same universality class of the mean-field ferromagnet. Along the critical curve the monomer and dimer phases coexist.
Rigorous mean-field dynamics of lattice bosons: quenches from the Mott insulator
M. Snoek
2011-01-01
We provide a rigorous derivation of Gutzwiller mean-field dynamics for lattice bosons, showing that it is exact on fully connected lattices. We apply this formalism to quenches in the interaction parameter from the Mott insulator to the superfluid state. Although within mean-field the Mott insulator
Amplitude pattern synthesis for conformal array antennas using mean-field neural networks
Castaldi, G.; Gerini, G.
2001-01-01
In this paper, we deal with the synthesis problem of conformai array antennas using a mean-field neural network. We applied a discrete version of mean-field neural network proposed by Vidyasagar [1], This technique is used to find the global minimum of the objective function, which represents the sq
State-of-the-art of beyond mean field theories with nuclear density functionals
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 discuss the
Corrected mean-field models for spatially dependent advection-diffusion-reaction phenomena
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.
1/N/sup 2/ expansion of the mean field for lattice chiral and gauge models
Energy Technology Data Exchange (ETDEWEB)
Brihaye, Y.; Taormina, A.
1985-08-21
For lattice chiral and gauge models the authors develop an /sup 1//N/sup 2/ expansion of the mean-field approximation. Special attention is paid to the free energy for which the effect of fluctuations around the mean-field solution is presented as an /sup 1//N/sup 2/ expansion. The differences between U(N) and SU(N) are pointed out. Finally, for the chiral model the mean-field saddle-point technique is applied to compute the two-point correlation function. (author).
Bose–Einstein condensation in self-consistent mean-field theory
International Nuclear Information System (INIS)
There is a wide-spread belief in the literature on Bose–Einstein condensation of interacting atoms that all variants of mean-field theory incorrectly describe the condensation phase transition, exhibiting, instead of the necessary second-order transition, a first-order transition, even for weakly interacting Bose gas. In the present paper, it is shown that a self-consistent mean-field approach is the sole mean-field theory that provides the correct second-order condensation transition for Bose systems with atomic interactions of arbitrary strength, whether weak or strong. (paper)
On the existence of classical solutions for stationary extended mean field games
Gomes, Diogo A.
2014-04-01
In this paper we consider extended stationary mean-field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean-field games in Gomes et al. (2012). In addition we use adjoint method techniques to obtain higher regularity bounds. Then we establish the existence of smooth solutions under fairly general conditions by applying the continuity method. When applied to standard stationary mean-field games as in Lasry and Lions (2006), Gomes and Sanchez-Morgado (2011) or Gomes et al. (2012) this paper yields various new estimates and regularity properties not available previously. We discuss additionally several examples where the existence of classical solutions can be proved. © 2013 Elsevier Ltd. All rights reserved.
Time-odd mean fields in covariant density functional theory: Rotating systems
Afanasjev, A V; 10.1103/PhysRev.82.034329
2010-01-01
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 dependences of their impact on the moments of inertia have been analysed 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 ...
Large-Scale Dynamics of Mean-Field Games Driven by Local Nash Equilibria
Degond, Pierre; Liu, Jian-Guo; Ringhofer, Christian
2014-02-01
We introduce a new mean field kinetic model for systems of rational agents interacting in a game-theoretical framework. This model is inspired from non-cooperative anonymous games with a continuum of players and Mean-Field Games. The large time behavior of the system is given by a macroscopic closure with a Nash equilibrium serving as the local thermodynamic equilibrium. An application of the presented theory to a social model (herding behavior) is discussed.
Beyond-mean-field corrections and effective interactions in the nuclear many-body problem
Moghrabi, Kassem
2013-01-01
Mean-field approaches successfully reproduce nuclear bulk properties like masses and radii within the Energy Density Functional (EDF) framework. However, complex correlations are missing in mean-field models and several observables related to single-particle and collective nuclear properties cannot be predicted accurately. The necessity to provide a precise description of the available data as well as reliable predictions in the exotic regions of the nuclear chart motivates the use of more so...
A Nash equilibrium macroscopic closure for kinetic models coupled with Mean-Field Games
Degond, Pierre; Liu, Jian-guo; Ringhofer, Christian
2012-01-01
We introduce a new mean field kinetic model for systems of rational agents interacting in a game theoretical framework. This model is inspired from non-cooperative anonymous games with a continuum of players and Mean-Field Games. The large time behavior of the system is given by a macroscopic closure with a Nash equilibrium serving as the local thermodynamic equilibrium. An application of the presented theory to a social model (herding behavior) is discussed.
Can realistic interaction be useful for nuclear mean-field approaches?
Nakada, H; Inakura, T; Margueron, J
2016-01-01
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 realistic interaction, which is derived from the base $2N$ and $3N$ interaction, furnish a new theoretical instrument for advancing nuclear mean-field approaches.
Magnetic moments in present relativistic nuclear theories: a mean-field problem
International Nuclear Information System (INIS)
We show that the magnetic moments of LS closed shell nuclei plus or minus one nucleon derived from non-relativistic Hartree-Fock mean-fields are as bad as those obtained in relativistic approaches of nuclear structure. Deviations with respect to more complete results in both cases are ascribed to the mean-field approximation which neglects some degrees of freedom in the nucleus description. 18 refs
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.
Revival of oscillation from mean-field-induced death: Theory and experiment
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.
Time-odd mean fields in covariant density functional theory: Rotating systems
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.
Time-odd mean fields in covariant density functional theory: Rotating systems
International Nuclear Information System (INIS)
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.
Relativistic Consistent Angular-Momentum Projected Shell-Model:Relativistic Mean Field
Institute of Scientific and Technical Information of China (English)
LI Yan-Song; LONG Gui-Lu
2004-01-01
We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shellmodel (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method.In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF)theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained.This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei 16O and 208Pb,the deformed nucleus 20Ne. Good agreement is obtained.
Ruan, Xinran; Cai, Yongyong; Bao, Weizhu
2016-06-01
We derive rigorously one- and two-dimensional mean-field equations for cigar- and pancake-shaped Bose–Einstein condensates (BECs) with higher-order interactions (HOIs), which originate from shape-dependent confinement corrections to the effective two-body atomic interaction potential. We show how the higher-order interaction modifies the contact interaction of the strongly confined particles. Surprisingly, we find that the usual Gaussian profile assumption for the strongly confining direction is inappropriate for the cigar-shaped BEC case, and a Thomas–Fermi-type profile should be adopted instead. Based on the derived mean-field equations, the Thomas–Fermi densities are analyzed in the presence of the contact interaction and HOI, and considering the limit of large contact interaction and HOI. For both box and harmonic traps in one, two and three dimensions, we identify the analytical Thomas–Fermi densities, which depend on the competition between the contact interaction and the HOI.
Study of the neutron skin thickness of ${}^{208}$Pb in mean field models
Roca-Maza, X; Viñas, X; Warda, M
2011-01-01
We study whether the neutron skin thickness $\\Delta r_{np}$ of ${}^{208}$Pb originates from the bulk or from the surface of the neutron and proton density distributions in mean field models. We find that the size of the bulk contribution to $\\Delta r_{np}$ of ${}^{208}$Pb strongly depends on the slope of the nuclear symmetry energy, while the surface contribution does not. We note that most mean field models predict a neutron density for ${}^{208}$Pb between the halo and skin type limits. We investigate the dependence of parity- violating electron scattering at the kinematics of the PREX experiment on the shape of the nucleon densities predicted by the mean field models for ${}^{208}$Pb. We find an approximate formula for the parity-violating asymmetry in terms of the central radius and the surface diffuseness of the nucleon densities of ${}^{208}$Pb in these models.
A beyond-mean-field example with zero-range effective interactions in infinite nuclear matter
Moghrabi, K; Roca-Maza, X; Coló, G; Van Giai, N; 10.1051/epjconf/20123806002
2013-01-01
Zero-range effective interactions are commonly used in nuclear physics to describe a many-body system in the mean-field framework. If they are employed in beyond- mean-field models, an artificial ultraviolet divergence is generated by the zero-range of the interaction. We analyze this problem in symmetric nuclear matter with the t0-t3 Skyrme model. In this case, the second-order energy correction diverges linearly with the momentum cutoff. After that, we extend the work to the case of nuclear matter with the full Skyrme interaction. A strong divergence related to the velocity-dependent terms of the interaction is obtained. Moreover, a global fit can be simultaneously performed for both symmetric and nuclear matter with different neutron-to-proton ratios. These results pave the way for applications to finite nuclei in the framework of beyond mean-field theories.
On the gap problem for the Mott--Hubbard transition within Dynamical Mean-Field Theory
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.
Nuclear Matter in Relativistic Mean Field Theory with Isovector Scalar Meson
Kubis, S
1997-01-01
Relativistic mean field (RMF) theory of nuclear matter with the isovector scalar mean field corresponding to the delta-meson [a_0(980)] is studied. While the delta-meson mean field vanishes in symmetric nuclear matter, it can influence properties of asymmetric nuclear matter in neutron stars. The RMF contribution due to delta-field to the nuclear symmetry energy is negative. To fit the empirical value, E_s=30 MeV, a stronger rho-meson coupling is required than in the absence of the delta-field. The energy per particle of neutron matter is then larger at high densities than the one with no delta-field included. Also, the proton fraction of beta-stable matter increases. Splitting of proton and neutron effective masses due to the delta-field can affect transport properties of neutron star matter.
Energy Technology Data Exchange (ETDEWEB)
Typel, S.; Wolter, H.H. [Sektion Physik, Univ. Muenchen, Garching (Germany)
1998-06-01
Nuclear matter and ground state properties for (proton and neutron) semi-closed shell nuclei are described in relativistic mean field theory with coupling constants which depend on the vector density. The parametrization of the density dependence for {sigma}-, {omega}- and {rho}-mesons is obtained by fitting to properties of nuclear matter and some finite nuclei. The equation of state for symmetric and asymmetric nuclear matter is discussed. Finite nuclei are described in Hartree approximation, including a charge and an improved center-of-mass correction. Pairing is considered in the BCS approximation. Special attention is directed to the predictions for properties at the neutron and proton driplines, e.g. for separation energies, spin-orbit splittings and density distributions. (orig.)
Excitation dynamics in a lattice Bose gas within the time-dependent Gutzwiller mean-field approach
Energy Technology Data Exchange (ETDEWEB)
Krutitsky, Konstantin V. [Fakultaet fuer Physik der Universitaet Duisburg-Essen, Campus Duisburg, Lotharstrasse 1, D-47048 Duisburg (Germany); Navez, Patrick [Fakultaet fuer Physik der Universitaet Duisburg-Essen, Campus Duisburg, Lotharstrasse 1, D-47048 Duisburg (Germany); Institut fuer Theoretische Physik, TU Dresden, D-01062 Dresden (Germany)
2011-09-15
The dynamics of the collective excitations of a lattice Bose gas at zero temperature is systematically investigated using the time-dependent Gutzwiller mean-field approach. The excitation modes are determined within the framework of the linear-response theory as solutions of the generalized Bogoliubov-de Gennes equations valid in the superfluid and Mott-insulator phases at arbitrary values of parameters. The expression for the sound velocity derived in this approach coincides with the hydrodynamic relation. We calculate the transition amplitudes for the excitations in the Bragg scattering process and show that the higher excitation modes make significant contributions. We simulate the dynamics of the density perturbations and show that their propagation velocity in the limit of week perturbation is satisfactorily described by the predictions of the linear-response analysis.
Skyrme mean-field studies of nuclei far from the stability line
Heenen, P H; Cwiok, S; Nazarewicz, W; Valor, A
1999-01-01
Two applications of mean-field calculations based on 3D coordinate-space techniques are presented. The first concerns the structure of odd-N superheavy elements that have been recently observed experimentally and shows the ability of the method to describe, in a self-consistent way, very heavy odd-mass nuclei. Our results are consistent with the experimental data. The second application concerns the introduction of correlations beyond a mean-field approach by means of projection techniques and configuration mixing. Results for Mg isotopes demonstrate that the restoration of rotational symmetry plays a crucial role in the description of 32Mg.
Many-body dynamics of p-wave Feshbach molecule production: a mean-field approach
Austen, L.; Cook, L.; Lee, M. D.; Mur-Petit, Jordi
2012-01-01
We study the mean-field dynamics of p-wave Feshbach molecule production in an ultra cold gas of Fermi atoms in the same internal state. We derive a separable potential to describe the low-energy scattering properties of such atoms, and use this potential to solve the mean-field dynamics during a magnetic field sweep. Initially, on the negative scattering length side of a Feshbach resonance the gas is described by the BCS theory. We adapt the method by Szyma\\'{n}ska et al. [Phys. Rev. Lett. 94...
Adaptive and self-averaging Thouless-Anderson-Palmer mean-field theory for probabilistic modeling
DEFF Research Database (Denmark)
Opper, Manfred; Winther, Ole
2001-01-01
We develop a generalization of the Thouless-Anderson-Palmer (TAP) mean-field approach of disorder physics. which makes the method applicable to the computation of approximate averages in probabilistic models for real data. In contrast to the conventional TAP approach, where the knowledge of the d......We develop a generalization of the Thouless-Anderson-Palmer (TAP) mean-field approach of disorder physics. which makes the method applicable to the computation of approximate averages in probabilistic models for real data. In contrast to the conventional TAP approach, where the knowledge...
A Modified Mean Field Theory for Spin Systems with Orbital Degeneracy
Institute of Scientific and Technical Information of China (English)
施大宁
2003-01-01
In order to understand the ground state of spin systems with orbital degeneracy, we present a modified mean-field theory that includes four order parameters. Our mean-field results suggest that for a small Hund interaction,the flavour liquid state is still stable against the solid state, but long-range orders may be attained in the system with sufficient deviation from the SU(4) limit. Finally, the implications for the experimental observations on the system LaMnO3 are discussed.
Mean field theory of nuclei and shell model. Present status and future outlook
International Nuclear Information System (INIS)
Many of the recent topics of the nuclear structure are concerned on the problems of unstable nuclei. It has been revealed experimentally that the nuclear halos and the neutron skins as well as the cluster structures or the molecule-like structures can be present in the unstable nuclei, and the magic numbers well established in the stable nuclei disappear occasionally while new ones appear. The shell model based on the mean field approximation has been successfully applied to stable nuclei to explain the nuclear structure as the finite many body system quantitatively and it is considered as the standard model at present. If the unstable nuclei will be understood on the same model basis or not is a matter related to fundamental principle of nuclear structure theories. In this lecture, the fundamental concept and the framework of the theory of nuclear structure based on the mean field theory and the shell model are presented to make clear the problems and to suggest directions for future researches. At first fundamental properties of nuclei are described under the subtitles: saturation and magic numbers, nuclear force and effective interactions, nuclear matter, and LS splitting. Then the mean field theory is presented under subtitles: the potential model, the mean field theory, Hartree-Fock approximation for nuclear matter, density dependent force, semiclassical mean field theory, mean field theory and symmetry, Skyrme interaction and density functional, density matrix expansion, finite range interactions, effective masses, and motion of center of mass. The subsequent section is devoted to the shell model with the subtitles: beyond the mean field approximation, core polarization, effective interaction of shell model, one-particle wave function, nuclear deformation and shell model, and shell model of cross shell. Finally structure of unstable nuclei is discussed with the subtitles: general remark on the study of unstable nuclear structure, asymptotic behavior of wave
Streamlined mean field variational Bayes for longitudinal and multilevel data analysis.
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.
Non-mean-field effects in systems with long-range forces in competition.
Bachelard, R; Staniscia, F
2012-11-01
We investigate the canonical equilibrium of systems with long-range forces in competition. These forces create a modulation in the interaction potential and modulated phases appear at the system scale. The structure of these phases differentiate this system from monotonic potentials, where only the mean-field and disordered phases exist. With increasing temperature, the system switches from one ordered phase to another through a first-order phase transition. Both mean-field and modulated phases may be stable, even at zero temperature, and the long-range nature of the interaction will lead to metastability characterized by extremely long time scales.
The crossover from mean-field to 3D-Ising critical behaviour in a 3-component microemulsion
DEFF Research Database (Denmark)
Seto, H.; Schwahn, D.; Yokoi, E.;
1995-01-01
Density fluctuations and associated critical phenomena of water droplets in a water-in-oil microemulsion system have been studied, We have recently found a mean-field behavior in the ''near-critical region'', and this evidence suggested that a crossover from mean-field to non-mean-field behavior...
Mean field limit for bosons and infinite dimensional phase-space analysis
Zied, Ammari
2007-01-01
This article proposes the construction of Wigner measures in the infinite dimensional bosonic quantum field theory, with applications to the derivation of the mean field dynamics. Once these asymptotic objects are well defined, it is shown how they can be used to make connections between different kinds of results or to prove new ones.
Shape Coexistence in Neutron-Deficient At Isotopes in Relativistic Mean-Field Model
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The potential energy surfaces are calculated for neutron-deficient At isotopes from A = 190 to 207 in an axiaJJy deformed relativistic mean-field approach, using a quadratic constraint scheme for the first time. We find several minima in the potential energy surface for each nucleus, shape-coexistence, and quadratic deform are discussed.
A simplified BBGKY hierarchy for correlated fermionic systems from a Stochastic Mean-Field approach
Lacroix, Denis; Ayik, Sakir; Yilmaz, Bulent
2015-01-01
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 sho...
Feng, Shui
1994-01-01
A large deviation system is established for the empirical processes of a mean-field interacting particle system with unbounded jump rates under assumptions that are satisfied by many interesting models including the first and the second Schlogl models. The action functional obtained has a form that is very useful for applications.
A Two-Mode Mean-Field Optimal Switching Problem for the Full Balance Sheet
Directory of Open Access Journals (Sweden)
Boualem Djehiche
2014-01-01
a two-mode optimal switching problem of mean-field type, which can be described by a system of Snell envelopes where the obstacles are interconnected and nonlinear. The main result of the paper is a proof of a continuous minimal solution to the system of Snell envelopes, as well as the full characterization of the optimal switching strategy.
A simplified BBGKY hierarchy for correlated fermions from a stochastic mean-field approach
Energy Technology Data Exchange (ETDEWEB)
Lacroix, Denis; Tanimura, Yusuke [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France); Ayik, Sakir [Tennessee Technological University, Physics Department, Cookeville, TN (United States); Yilmaz, Bulent [Ankara University, Physics Department, Faculty of Sciences, Ankara (Turkey)
2016-04-15
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. (orig.)
Mott-Hubbard and Anderson transitions in dynamical mean-field theory
Energy Technology Data Exchange (ETDEWEB)
Byczuk, Krzysztof [Institute of Theoretical Physics, Warsaw University, ul. Hoza 69, PL-00-681 Warsaw (Poland)]. E-mail: byczuk@fuw.edu.pl; Hofstetter, Walter [Condensed Matter Theory Group, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Vollhardt, Dieter [Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute for Physics, University of Augsburg, D-86135 Augsburg (Germany)
2005-04-30
The Anderson-Hubbard Hamiltonian at half-filling is investigated within dynamical mean-field theory at zero temperature. The local density of states is calculated by taking the geometric and arithmetic mean, respectively. The non-magnetic ground state phase diagrams obtained within the different averaging schemes are compared.
Mean-field theory of spin-glasses with finite coordination number
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.
Shape Coexistence for 179Hg in Relativistic Mean-Field Theory
Institute of Scientific and Technical Information of China (English)
WANG Nan; MENG Jie; ZHAO En-Guang
2005-01-01
The potential energy surface of179 Hg is traced and the multi-shape coexistence phenomenon in that nucleus is studied within the relativistic mean-field theory with quadrupole moment constraint. The calculation results of binding energies and charge radii of mercury isotopes are in good agreement with the experimental data.
Time-dependent mean field description of a two-level bosonic model
International Nuclear Information System (INIS)
A time-dependent mean field approximation is applied to a simple bosonic model that is related to the phase transition from spherical to deformed nuclei. It is shown that this approximation is very appropriate for the detection of this phase transition. A method for extracting matrix elements is developed and applied for the two-particle transfer operator in this model
Institute of Scientific and Technical Information of China (English)
XueJianjun; YouXiaohu
1997-01-01
Channel equalization is essential in the Pan-European GSM mobile communication system.The maximum likelihood sequence estimation(MLSE) using the Viterbi algorithm(VA)iscommonly recommended for the dqualization,which can only accommodate the channels with limited time delay spread.In[1],we presented a mean field annealing(MFA)partially connected neural equalizer for the GSM system,in which the complexity is linearly proportional to the time delay spread and therefore relatively fast convergence speed is achieved.But the annealing coefficient of the MFA equalizer is fixed,which is not flexible in timing-varying circumstance such as mobile communications.To decrease the computation of MFA approach so as to make it more easy for practical use,the MFA approach is reated as a homotopy problem.The ordinary equations which the MFA approach should obey are derived.These equations can be used to reflect the deviation of the iteration result from the track of MFA approach.Based on this tesult,an adaptive annealing control algorithm is proposed,which can dynamically control the annealing coefficient according to the iteration deviation.Computer simulations show that our approach can provide a much higher convergence speed and performance improvement over 16-state and 32-state VA's which are usually suggested for practical applications.
The relativistic mean-field description of nuclei and nuclear dynamics
International Nuclear Information System (INIS)
The relativistic mean-field model of the nucleus is reviewed. It describes the nucleus as a system of Dirac-Nucleons which interact in a relativistic covariant manner via meson fields. The meson fields are treated as mean fields, i.e. as non quantal c-number fields. The effects of the Dirac sea of the nucleons is neglected. The model is interpreted as a phenomenological ansatz providing a selfconsistent relativistic description of nuclei and nuclear dynamics. It is viewed, so to say, as the relativistic generalisation of the Skyrme-Hartree-Fock ansatz. The capability and the limitations of the model to describe nuclear properties are discussed. Recent applications to spherical and deformed nuclei and to nuclear dynamics are presented. (orig.)
Macroscopic and large scale phenomena coarse graining, mean field limits and ergodicity
Rademacher, Jens; Zagaris, Antonios
2016-01-01
This book is the offspring of a summer school school “Macroscopic and large scale phenomena: coarse graining, mean field limits and ergodicity”, which was held in 2012 at the University of Twente, the Netherlands. The focus lies on mathematically rigorous methods for multiscale problems of physical origins. Each of the four book chapters is based on a set of lectures delivered at the school, yet all authors have expanded and refined their contributions. Francois Golse delivers a chapter on the dynamics of large particle systems in the mean field limit and surveys the most significant tools and methods to establish such limits with mathematical rigor. Golse discusses in depth a variety of examples, including Vlasov--Poisson and Vlasov--Maxwell systems. Lucia Scardia focuses on the rigorous derivation of macroscopic models using $\\Gamma$-convergence, a more recent variational method, which has proved very powerful for problems in material science. Scardia illustrates this by various basic examples and a mor...
Beyond the mean field in the particle-vibration coupling scheme
Baldo, M; Colo', G; Rizzo, D; Sciacchitano, L
2015-01-01
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 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 single particle energies, trying to keep the ground state energy sufficiently well reproduced. An alternative route, that has been developed along several years, for solving this problem is to introduce the mean field fluctuations, as represented by t...
Orientational quadrupolar glass in ortho-para hydrogen mixtures. I. Mean-field microscopic theory
International Nuclear Information System (INIS)
The mean-field theory of the quadrupolar glass (QG) is presented using a microscopic approach. It is shown that the reaction-polarization effects caused by short-range spatial correlations are well distinguished from those of random-bond spin glasses. They control the QG concentration threshold and result in an incomplete orientational order. The QG ground state (zero quadrupolization, unsaturated Edwards-Anderson-type orientational order parameter) is predicted. Thermodynamic characteristics, namely entropy, pressure and free energy as well as the related heat capacity and Gruneisen parameter are estimated. The ground-state findings (incomplete order, residual entropy) are similar to those of short-range Potts glasses. A correspondence between density matrix and mean field treatment to the QG problem is also discussed
Beyond-mean-field approach to low-lying spectra of $\\Lambda$ hypernuclei
Hagino, K; Yao, J M; Motoba, T
2015-01-01
Taking the hypernucleus $^{13}_{~\\Lambda}$C as an example, we illustrate the miscroscopic particle-rotor model for low-lying spectra of hypernuclei. This approach is based on the beyond-mean-field method, with the particle number and angular momentum projections. The quantum fluctuation of the mean-field is also taken into account for the core nucleus using the generator coordinate method. We show that the impurity effect of $\\Lambda$ hyperon, such as a change in $B(E2)$, is well described with this model. Our calculation indicates that the most important impurity effect in $sd$-shell hypernuclei is a change in a deformation parameter rather than in a nuclear size.
Mean-Field Dynamics and Fisher Information in Matter Wave Interferometry.
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.
Spectral properties of the one-dimensional Hubbard model: cluster dynamical mean-field approaches
Go, Ara; Jeon, Gun Sang
2011-03-01
We investigate static and dynamic properties of the one-dimensional Hubbard model using cluster extensions of the dynamical mean-field theory. It is shown that the two different extensions, the cellular dynamical mean-field theory and the dynamic cluster approximation, yield the ground-state properties which are qualitatively in good agreement with each other. We compare the results with the Bethe ansatz results to check the accuracy of the calculation with finite sizes of clusters. We also analyze the spectral properties of the model with the focus on the spin-charge separation and discuss the dependency on the cluster size in the two approaches. This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2010-0010937).
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
Mean-Field Dynamics and Fisher Information in Matter Wave Interferometry.
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
Yao, J M; Hagino, K; Ring, P; Meng, J
2014-01-01
We report a systematic study of nuclear matrix elements (NMEs) in neutrinoless double-beta decays with 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 which are found to be consistent with the results of previous beyond non-relativistic mean-field calculation based on a Gogny force with the exception of $^{150}$Nd. Our study shows that the total NMEs can be well approximated by the pure axial-vector coupling term, the calculation of which is computationally much cheaper than that of full terms.
International Nuclear Information System (INIS)
Nuclear structure is subject to a major renewal linked with the development of radioactive ion beams (such as the SPIRAL 1 and 2 beams at GANIL). Mean-field and density-functional methods are among the best suited for studying nuclei produced at such facilities. The present work aims at demonstrating how existing functionals can be improved so as to exhibit a better predictive power in little-explored regions of the nuclear chart. We propose a better description of the isospin-dependence of the effective interaction, and examine the relevance of adding a tensor coupling. We also show how a new generation of functionals can be better constrained by considering results obtained beyond the mean-field approximation. Finally, we attempt establishing a link with the bare nucleon-nucleon potential for the description of pairing, thus participating in the construction of a non-empirical functional. (author)
Mean-Field Dynamics and Fisher Information in Matter Wave Interferometry
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.
Heterogeneous mean field for neural networks with short-term plasticity
di Volo, Matteo; Burioni, Raffaella; Casartelli, Mario; Livi, Roberto; Vezzani, Alessandro
2014-08-01
We report about the main dynamical features of a model of leaky integrate-and-fire excitatory neurons with short-term plasticity defined on random massive networks. We investigate the dynamics by use of a heterogeneous mean-field formulation of the model that is able to reproduce dynamical phases characterized by the presence of quasisynchronous events. This formulation allows one to solve also the inverse problem of reconstructing the in-degree distribution for different network topologies from the knowledge of the global activity field. We study the robustness of this inversion procedure by providing numerical evidence that the in-degree distribution can be recovered also in the presence of noise and disorder in the external currents. Finally, we discuss the validity of the heterogeneous mean-field approach for sparse networks with a sufficiently large average in-degree.
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.
State-of-the-art of beyond mean field theories with nuclear density functionals
Egido, J Luis
2016-01-01
We present an overview of beyond mean field theories (BMFT) based on the generator coordinate method (GCM) and the recovery of symmetries used in nuclear physics with effective forces. After a reminder of the Hartree-Fock-Bogoliubov (HFB) theory a discussion of the shortcomings of any mean field approximation (MFA) 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 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. The lack of fluctuations around the average values of the MFA is a shortcoming of this approach. To build in correlations in BMFT one selects the relevant degrees of freedom: quadrupole, octupole and the pairing vibrations as well as the single particle ones. In the GCM the operators representing these degrees of f...
Strange quark matter in a chiral SU(3) quark mean field model
Wang, P.; Lyubovitskij, V. E.; Gutsche, Th.; Faessler, Amand
2002-01-01
We apply the chiral SU(3) quark mean field model to investigate strange quark matter. The stability of strange quark matter with different strangeness fraction is studied. The interaction between quarks and vector mesons destabilizes the strange quark matter. If the strength of the vector coupling is the same as in hadronic matter, strangelets can not be formed. For the case of beta equilibrium, there is no strange quark matter which can be stable against hadron emission even without vector m...
Inverse magnetic catalysis in Nambu-Jona-Lasinio model beyond mean field
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.
Existence for stationary mean-field games with congestion and quadratic Hamiltonians
Gomes, Diogo A.
2015-09-03
Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular behavior is caused by congestion. Thanks to a new class of a priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions. © 2015 Springer Basel
Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states
AMMARI, Zied; Nier, Francis
2011-01-01
International audience Contrary to the finite dimensional case, Weyl and Wick quantizations are no more asymptotically equivalent in the infinite dimensional bosonic second quantization. Moreover neither the Weyl calculus defined for cylindrical symbols nor the Wick calculus defined for polynomials are preserved by the action of a nonlinear flow. Nevertheless taking advantage carefully of the information brought by these two calculuses in the mean field asymptotics, the propagation of Wign...
AMMARI, Zied; Nier, Francis
2015-01-01
49 pages International audience We consider the quantum dynamics of many bosons systems in the mean field limit with a singular pair-interaction potential, including the attractive or repulsive Coulombic case in three dimensions. By using a measure transportation technique, we show that Wigner measures propagate along the nonlinear Hartree flow. Such property was previously proved only for bounded potentials in our previous works with a slightly different strategy.
Ammari, Zied
2011-01-01
We consider the quantum dynamics of many bosons systems in the mean field limit with a singular pair-interaction potential, including the attractive or repulsive Coulombic case in three dimensions. By using a measure transportation technique, we show that Wigner measures propagate along the nonlinear Hartree flow. Such property was previously proved only for bounded potentials in our previous works with a slightly different strategy.
Thermal properties of a rotating nucleus in a fluctuating mean field approach
B K Agrawal; Ansari, A
1993-01-01
The static path approximation to the path integral representation of partition function provides a natural microscopic basis to deal with thermal fluctuations around mean field configurations. Using this approach for one-dimensional cranking Hamiltonian with quadrupole- quadrupole interaction term we have studied a few properties like energy, level density, level density parameter($a$) and moment of inertia as a function of temperature and spin for $^{64}Zn$ taking it as an illustrative examp...
Raedler, Karl-Heinz; Rheinhardt, Matthias
2006-01-01
There are various analytical approaches to the mean electromotive force $\\cal E =$ crucial in mean--field electrodynamics, with $\\vec{u}$ and $\\vec{b}$ being velocity and magnetic field fluctuations. In most cases the traditional approach, restricted to the second--order correlation approximation, has been used. Its validity is only guaranteed for a range of conditions, which is narrow in view of many applications, e.g., in astrophysics. With the intention to have a wi...
Nilsson parameters kappa and mu in the relativistic mean field models
Sulaksono, A; Bahri, C
2005-01-01
Nilsson parameters kappa and mu have been studied in the framework of the relativistic mean field (RMF) models. They are used to investigate the reason that the RMF models give a relatively well prediction of the spin-orbit splitting, but fail to reproduce the placement of the states with different orbital angular momenta. Instead of the relatively small effective mass M*, the independence of M* from the angular momentum l is found to be the reason.
New mean field theories for the liquid-vapor transition of charged hard spheres
Caillol, J. -M.
2004-01-01
The phase behavior of the primitive model of electrolytes is studied in the framework of various mean field approximations obtained recently by means of methods pertaining to statistical field theory (CAILLOL, J.-M., 2004, \\textit{J. Stat. Phys.}, \\textbf{115}, 1461). The role of the regularization of the Coulomb potential at short distances is discussed in details and the link with more traditional approximations of the theory of liquids is discussed. The values computed for the critical tem...
The D-D¯ mesons matter in Walecka's mean field theory
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 = 0 and the 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.
Time-odd mean fields in covariant density functional theory: Rotating systems
Afanasjev, A. V.; Abusara, H.
2010-01-01
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 dependences of their impact on the moments of inertia have been analysed in a systematic way. Nuclear magnetism can also considerably modify the band crossing features such...
Mean Field Theory of Sandpile Avalanches: from the Intermittent to the Continuous Flow Regime
Benza, V. G.; Nori, Franco; Pla, Oscar
1993-01-01
We model the dynamics of avalanches in granular assemblies in partly filled rotating cylinders using a mean-field approach. We show that, upon varying the cylinder angular velocity $\\omega$, the system undergoes a hysteresis cycle between an intermittent and a continuous flow regimes. In the intermittent flow regime, and approaching the transition, the avalanche duration exhibits critical slowing down with a temporal power-law divergence. Upon adding a white noise term, and close to the trans...
Mean-Field Calculations for the Three-Dimensional Holstein Model
Institute of Scientific and Technical Information of China (English)
罗强; 刘川
2002-01-01
The electron-phonon Holstein model is studied in three spatial dimensions. It is argued that this model can be used to account for major features of the high-To BaPb1-xBixO3 and BaxK1-xBiO3 systems. Mean-field calculations are performed via a path integral representation of the model. Charge-density-wave order parameters and transition temperatures are obtained.
Inverse Magnetic Catalysis in Nambu--Jona-Lasinio Model beyond Mean Field
Mao, Shijun
2016-01-01
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.
Gaussian and Mean Field Approximations for Reduced Yang-Mills Integrals
Oda, Satsuki; Sugino, Fumihiko
2000-01-01
In this paper, we consider bosonic reduced Yang-Mills integrals by using some approximation schemes, which are a kind of mean field approximation called Gaussian approximation and its improved version. We calculate the free energy and the expectation values of various operators including Polyakov loop and Wilson loop. Our results nicely match to the exact and the numerical results obtained before. Quite good scaling behaviors of the Polyakov loop and of the Wilson loop can be seen under the '...
Mean field description of the ground state of many boson systems relevant to nuclei
International Nuclear Information System (INIS)
In the present paper we give the explicit expressions for the ground state of a many boson system in different mean field approximations, such as Hartree-Bose, Bogoliubov, the particle-hole random phase approximation (RPA), and its coupling with the particle-particle (RPA). The ground states obtained satisfy the requirement that the annihilation operators of the ''elementary excitations'' annihilates them. In all cases the ground state wave functions can be understood as a condensate of pairs of bosons
Mean field and collisional dynamics of interacting fermion-boson systems the Jaynes-Cummings model
Takano-Natti, E R
1996-01-01
A general time-dependent projection technique is applied to the study of the dynamics of quantum correlations in a system consisting of interacting fermionic and bosonic subsystems, described by the Jaynes-Cummings Hamiltonian. The amplitude modulation of the Rabi oscillations which occur for a strong, coherent initial bosonic field is obtained from the spin intrinsic depolarization resulting from collisional corrections to the mean-field approximation.
Sun, Bao-Xi; Lu, Xiao-Fu; Shen, Peng-Nian; Zhao, En-Guang
2002-01-01
The Debye screening masses of the $\\sigma$, $\\omega$ and neutral $\\rho$ mesons and the photon are calculated in the relativistic mean-field approximation. As the density of the nucleon increases, all the screening masses of mesons increase. It shows a different result with Brown-Rho scaling, which implies a reduction in the mass of all the mesons in the nuclear matter except the pion. Replacing the masses of the mesons with their corresponding screening masses in Walecka-1 model, five saturat...
Niksic, T.; Vretenar, D.; Ring, P.
2006-01-01
We report the first study of restoration of rotational symmetry and fluctuations of the quadrupole deformation in the framework of relativistic mean-field models. A model is developed which uses the generator coordinate method to perform configuration mixing calculations of angular momentum projected wave functions, calculated in a relativistic point-coupling model. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the...
Spinodal Instabilities in Nuclear Matter in a Stochastic Relativistic Mean-Field Approach
Ayik, S.; Yilmaz, O.; Er, N.; Gokalp, A.; Ring, P.
2009-01-01
Spinodal instabilities and early growth of baryon density fluctuations in symmetric nuclear matter are investigated in the basis of stochastic extension of relativistic mean-field approach in the semi-classical approximation. Calculations are compared with the results of non-relativistic calculations based on Skyrme-type effective interactions under similar conditions. A qualitative difference appears in the unstable response of the system: the system exhibits most unstable behavior at higher...
Isospin dependence of incompressibility in relativistic and non-relativistic mean field calculations
Sagawa, Hiroyuki; Yoshida, Satoshi; Zeng, Guo-Mo; Gu, Jian-Zhong; Zhang, Xi-Zhen
2007-01-01
The isospin dependence of incompressibility is investigated in the Skyrme Hartree-Fock (SHF) and relativistic mean field (RMF) models. The correlations between the nuclear matter incompressibility and the isospin dependent term of the finite nucleus incompressibility is elucidated by using the Thomas-Fermi approximation. The Coulomb term is also studied by using various different Skyrme Hamiltonians and RMF Lagrangians. The symmetry energy coefficient of incompressibility is extracted to be K...
Mean field dynamics of superfluid-insulator phase transition in a gas of ultra cold atoms
Zakrzewski, Jakub
2004-01-01
A large scale dynamical simulation of the superfluid to Mott insulator transition in the gas of ultra cold 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 [Nature 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 re...
Self-consistent chaotic transport in a high-dimensional mean-field Hamiltonian map model
Martínez-del-Río, D; Olvera, A; Calleja, R
2016-01-01
Self-consistent chaotic transport is studied in a Hamiltonian mean-field model. The model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Self-consistency is incorporated through a mean-field that couples all the degrees-of-freedom. The model is formulated as a large set of $N$ coupled standard-like area-preserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherent structures. Numerical simulations show that self-consistency leads to the formation of a coherent macro-particle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a non-autonomous map that allows a detailed study of th...
Particle-number projection in the finite-temperature mean-field approximation
Fanto, P; Bertsch, G F
2016-01-01
Calculation of statistical properties of nuclei in a finite-temperature mean-field theory requires projection onto good particle number, since the theory is formulated in the grand canonical ensemble. This projection is usually carried out in a saddle-point approximation. Here we derive formulas for an exact particle-number projection of the finite-temperature mean-field solution. We consider both deformed nuclei, in which the pairing condensate is weak and the Hartree-Fock (HF) approximation is the appropriate mean-field theory, and nuclei with strong pairing condensates, in which the appropriate theory is the Hartree-Fock-Bogoliubov (HFB) approximation, a method that explicitly violates particle-number conservation. For the HFB approximation, we present a general projection formula for a condensate that is time-reversal invariant and a simpler formula for the Bardeen-Cooper-Schrieffer (BCS) limit, which is realized in nuclei with spherical condensates. We apply the method to three heavy nuclei: a typical de...
Mean-Field Approximation to the Hydrophobic Hydration in the Liquid-Vapor Interface of Water.
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
Antimagnetic rotation in 108,110In with tilted axis cranking relativistic mean-field approach
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)
Rios, Arnau; Buchler, Mark; Danielewicz, Pawel
2010-01-01
Nonequilibrium Green's function methods allow for an intrinsically consistent description of the evolution of quantal many-body body systems, with inclusion of different types of correlations. In this paper, we focus on the practical developments needed to build a Green's function methodology for nuclear reactions. We start out by considering symmetric collisions of slabs in one dimension within the mean-field approximation. We concentrate on two issues of importance for actual reaction simulations. First, the preparation of the initial state within the same methodology as for the reaction dynamics is demonstrated by an adiabatic switching on of the mean-field interaction, which leads to the mean-field ground state. Second, the importance of the Green's function matrix-elements far away from the spatial diagonal is analyzed by a suitable suppression process that does not significantly affect the evolution of the elements close to the diagonal. The relative lack of importance of the far-away elements is tied t...
International Nuclear Information System (INIS)
The ground-state properties of the nucleus 100Sn have been studied by the non-relativistic mean-field approach with Skyrme interactions, the relativistic mean-field approach with the Hartree approximation and the density-dependent relativistic mean-field approach. We compare and discuss the numerical results of average binding energies, and matter root-mean-square radii of proton and neutron distributions. It is shown that the non-relativistic, relativistic and density-dependent relativistic mean-field theories can be successfully applied to the nucleus near the proton drip line. (author)
Continuum theory of critical phenomena in polymer solutions: Formalism and mean field approximation
Goldstein, Raymond E.; Cherayil, Binny J.
1989-06-01
A theoretical description of the critical point of a polymer solution is formulated directly from the Edwards continuum model of polymers with two- and three-body excluded-volume interactions. A Hubbard-Stratonovich transformation analogous to that used in recent work on the liquid-vapor critical point of simple fluids is used to recast the grand partition function of the polymer solution as a functional integral over continuous fields. The resulting Landau-Ginzburg-Wilson (LGW) Hamiltonian is of the form of a generalized nonsymmetric n=1 component vector model, with operators directly related to certain connected correlation functions of a reference system. The latter is taken to be an ensemble of Gaussian chains with three-body excluded-volume repulsions, and the operators are computed in three dimensions by means of a perturbation theory that is rapidly convergent for long chains. A mean field theory of the functional integral yields a description of the critical point in which the power-law variations of the critical polymer volume fraction φc, critical temperature Tc, and critical amplitudes on polymerization index N are essentially identical to those found in the Flory-Huggins theory. In particular, we find φc ˜N-1/2, Tθ-Tc˜N-1/2 with (Tθ the theta temperature), and that the composition difference between coexisting phases varies with reduced temperature t as N-1/4t1/2. The mean field theory of the interfacial tension σ between coexisting phases near the critical point, developed by considering the LGW Hamiltonian for a weakly inhomogeneous solution, yields σ˜N-1/4t3/2, with the correlation length diverging as ξ˜N1/4t-1/2 within the same approximation, consistent with the mean field limit of de Gennes' scaling form. Generalizations to polydisperse systems are discussed.
Transport in multilayered nanostructures the dynamical mean-field theory approach
Freericks, James K
2016-01-01
Over the last 25 years, dynamical mean-field theory (DMFT) has emerged as one of the most powerful new developments in many-body physics. Written by one of the key researchers in the field, this book presents the first comprehensive treatment of this ever-developing topic. Transport in Mutlilayered Nanostructures is varied and modern in its scope, and: A series of over 50 problems help develop the skills to allow readers to reach the level of being able to contribute to research. This book is suitable for an advanced graduate course in DMFT, and for individualized study by graduate students, postdoctoral fellows and advanced researchers wishing to enter the field.
Doping Induced Spin State Transition in LaCoO3: Dynamical Mean-Field Study
Augustinský, P.; Křápek, V.; Kuneš, J.
2013-06-01
Hole and electron doped LaCoO3 is studied using dynamical mean-field theory. The one-particle spectra are analyzed and compared to the available experimental data, in particular the x-ray absorption spectra. Analyzing the temporal spin-spin correlation functions we find the atomic intermediate spin state is not important for the observed Curie-Weiss susceptibility. Contrary to the commonly held view about the roles played by the t2g and eg electrons we find narrow quasiparticle bands of t2g character crossing the Fermi level accompanied by strongly damped eg excitations.
Systematic analysis of shape evolution for N=60 isotonic chain in relativistic mean-field model
International Nuclear Information System (INIS)
The shape phase transition between spherical U(5) and axially SU(3) deformed nuclei is investigated systemically for N=60 isotonic chain by the constrained relativistic mean-field theory with the interactions NL3 and PK1. The values of bind energy and quadruple deformation β2 are calculated and a good agreement is obtained as compared with the experiments. By examining the potential energy curve and single particle spectra obtained with this microscopic approach, the possible critical point nuclei with the structure of shape phase transition are suggested to be 114Xe and 116Ba, which is favored by the experiments. (authors)
Mean-field theory of photoinduced formation of surface reliefs in side-chain azobenzene polymers
DEFF Research Database (Denmark)
Pedersen, Thomas Garm; Johansen, Per Michael; Holme, N.C.R.;
1998-01-01
A mean-field model of photoinduced surface reliefs in dye containing side-chain polymers is presented. It is demonstrated that photoinduced ordering of dye molecules subject to anisotropic intermolecular interactions leads to mass transport even when the intensity of the incident light is spatially...... uniform. Theoretical profiles are obtained using a simple variational method and excellent agreement with experimental surface reliefs recorded under various polarization configurations is found. The polarization dependence of both period and shape of the profiles is correctly reproduced by the model....
A mean field game analysis of electric vehicles in the smart grid
Couillet, Romain; Medina Perlaza, Samir; Tembine, Hamidou; Debbah, Mérouane
2012-01-01
In this article, we develop a mean field game model for the economical analysis of the integration of purely electrical vehicles (EV) or electrical hybrid oil-electricity vehicles (PHEV) in the smart grid energy market. The framework we develop allows for a consistent analysis of the evolution of the price of electricity, of the timely demand, and possibly of the energy reserves in the grid, when EV or PHEV owners buy and sell electricity from their cars, selfishly but rationally, based on co...
Magnetic material in mean-field dynamos driven by small scale helical flows
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
I. M. Sokolov; Yuste, S. B.; Ruiz-Lorenzo, J. J.; Lindenberg, Katja
2008-01-01
We present a mean field model for coagulation ($A+A\\to A$) and annihilation ($A+A\\to 0$) reactions on lattices of traps with a distribution of depths reflected in a distribution of mean escape times. The escape time from each trap is exponentially distributed about the mean for that trap, and the distribution of mean escape times is a power law. Even in the absence of reactions, the distribution of particles over sites changes with time as particles are caught in ever deeper traps, that is, t...
Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states
Ammari, Zied
2010-01-01
Contrary to the finite dimensional case, Weyl and Wick quantizations are no more asymptotically equivalent in the infinite dimensional bosonic second quantization. Moreover neither the Weyl calculus defined for cylindrical symbols nor the Wick calculus defined for polynomials are preserved by the action of a nonlinear flow. Nevertheless taking advantage carefully of the information brought by these two calculuses in the mean field asymptotics, the propagation of Wigner measures for general states can be proved, extending to the infinite dimensional case a standard result of semiclassical analysis.
Shell evolution at N=20 in the constrained relativistic mean field approach
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The shell evolution at N = 20, a disappearing neutron magic number observed experimentally in very neutron-rich nuclides, is investigated in the constrained relativistic mean field (RMF) theory. The trend of the shell closure observed experimentally towards the neutron drip-line can be reproduced. The predicted two-neutron separation energies, neutron shell gap energies and deformation parameters of ground states are shown as well. These results are compared with the recent Hartree-Fock-Bogliubov (HFB-14) model and the available experimental data. The perspective towards a better understanding of the shell evolution is discussed.
One-Proton Halo in 31Cl with Relativistic Mean-Field Theory
Institute of Scientific and Technical Information of China (English)
蔡翔舟; 沈文庆; 任中洲; 蒋维洲; 方德清; 张虎勇; 钟晨; 魏义彬; 郭威; 马余刚; 朱志远
2002-01-01
We investigate proton-rich isotopes s1,32Cl using the nonlinear relativistic mean-field model. It is shown that this model can reproduce the properties of these nuclei well. A long tail appears in the calculated proton density distribution of 31 Cl. The results of relativistic density-dependent Hartree theory show a similar trend of tail density distribution. It is strongly suggested that there is a proton halo in 31Cl and it is indicated that there may be a proton skin in 32 Cl. The relation between the proton halo in 31Cl and the new proton magic number is discussed.
Temperature Dependence of the Nuclear Energy in Relativistic Mean-Field Theory
Nerlo-Pomorska, B.; Pomorski, K.; Sykut, J.; Bartel, J.
Self-consistent relativistic mean-field (RMF) calculations with the NL3 parameter set were performed for 171 spherical even-even nuclei with 16≤A≤224 at temperatures in the range 0≤T≤4 MeV. For this sample of nuclei single-particle level densities are determined by analyzing the data obtained for various temperatures. A new shell-correction method is used to evaluate shell effects at all temperatures. The single-particle level density is expressed as function of mass number A and relative isospin I and compared with previous estimates.
A Bayesian mean field game approach to supply demand analysis of the smart grid
Kamgarpour, Maryam
2013-07-01
We explore a game theoretic framework for multiple energy producers competing in energy market. Each producer, referred to as a player, optimizes its own objective function given the demand utility. The equilibrium strategy of each player depends on the production cost, referred to as type, of the other players. We show that as the number of players increases, the mean of the types is sufficient for finding the equilibrium. For finite number of players, we design a mean field distributed learning algorithm that converges to equilibrium. We discuss extensions of our model to include several realistic aspects of the energy market. © 2013 IEEE.
Spinodal instabilities in nuclear matter in a stochastic relativistic mean-field approach
International Nuclear Information System (INIS)
Spinodal instabilities and early growth of baryon density fluctuations in symmetric nuclear matter are investigated in the basis of the stochastic extension of the relativistic mean-field approach in the semiclassical approximation. Calculations are compared with the results of nonrelativistic calculations based on Skyrme-type effective interactions under similar conditions. A qualitative difference appears in the unstable response of the system: the system exhibits most unstable behavior at higher baryon densities around ρb=0.4ρ0 in the relativistic approach while most unstable behavior occurs at lower baryon densities around ρb=0.2ρ0 in the nonrelativistic calculations
Systematic study of Bh isotopes in a relativistic mean field formalism
International Nuclear Information System (INIS)
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
Ginzburg criterion for the mean-field to three-dimensional Ising crossover in polymer blends
DEFF Research Database (Denmark)
Schwahn, D.; Schmackers, T.; Mortensen, K.
1995-01-01
Composition fluctuations within the mean-field and three-dimensional Ising range were measured in a homogeneous binary polymer blend by small angle neutron scattering as a function of temperature and pressure. The experimental data were analyzed in terms of the crossover function of Belyakov and...... Kiselev [Physica A 190, 75 (1992)]. It is shown that the reduced-crossover-temperature, the Ginzburg number Gi, decreases with pressure sensitively, in accordance with the prediction of Belyakov and Kiselev. On the other hand, de Gennes' crossover criterion for polymer blends predicts an increase of Gi...
Low Complexity Sparse Bayesian Learning for Channel Estimation Using Generalized Mean Field
DEFF Research Database (Denmark)
Pedersen, Niels Lovmand; Manchón, Carles Navarro; Fleury, Bernard Henri
2014-01-01
We derive low complexity versions of a wide range of algorithms for sparse Bayesian learning (SBL) in underdetermined linear systems. The proposed algorithms are obtained by applying the generalized mean field (GMF) inference framework to a generic SBL probabilistic model. In the GMF framework, we...... constrain the auxiliary function approximating the posterior probability density function of the unknown variables to factorize over disjoint groups of contiguous entries in the sparse vector - the size of these groups dictates the degree of complexity reduction. The original high-complexity algorithms......, by choosing small group sizes, the resulting algorithms perform nearly as well as their original counterparts but with much less computational complexity....
Beyond the relativistic mean-field approximation (III): collective Hamiltonian in five dimensions
Niksic, T; Vretenar, D; Prochniak, L; Meng, J; Ring, P
2008-01-01
The framework of relativistic energy density functionals is extended to include correlations related to restoration of broken symmetries and fluctuations of collective variables. A model is developed for the solution of the eigenvalue problem of a five-dimensional collective Hamiltonian for quadrupole vibrational and rotational degrees of freedom, with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The model is tested in a series of illustrative calculations of potential energy surfaces and the resulting collective excitation spectra and transition probabilities of the chain of even-even gadolinium isotopes.
Mean-field approximation for a limit order driven market model.
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
Mean-field approximation for a limit order driven market model
Frantisek Slanina
2001-01-01
The 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 he 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 ...
Phase transitions and topology in 2+k XY mean-field models.
Angelani, L; Ruocco, G
2007-11-01
The thermodynamics and topology of mean-field models with 2+k body interaction terms (generalizing XY model) are derived. Focusing on two particular cases (2+4 and 2+6 body interaction terms), a comparison between thermodynamic (phase transition energy, thermodynamically forbidden energy regions) and topological (singularity and curvature of saddle entropy) properties is performed. We find that (i) a topological change is present at the phase transition energy; however, (ii) only one topological change occurs, also for those models exhibiting two phase transitions; (iii) the order of a phase transition is not completely signaled by the curvature of topological quantities.
Institute of Scientific and Technical Information of China (English)
舒崧; 李家荣
2012-01-01
We used the Cornwall, Jackiw and Tomboulis （CJT） resummation scheme to study nuclear matter. In the CJT formalism the meson propagators are treated as the bare propagators and the the higher order loop corrections of the thermodynamic potential are evaluated at the Hartree approximation, while the vacuum fluctuations are ignored. Under these treatments in the CJT formalism we derived exact mean-field theory （MFT） results for the nuclear matter. The results are thermodynamically consistent, and our study indicates that the MFT result is the lowest order resummation result in the CJT resummation scheme. The relation between CJT formalism and MFT is clearly presented through the calculations.
High-conductance states in a mean-field cortical network model
Lerchner, A; Hertz, J
2004-01-01
Measured responses from visual cortical neurons show that spike times tend to be correlated rather than exactly Poisson distributed. Fano factors vary and are usually greater than 1 due to the tendency of spikes being clustered into bursts. We show that this behavior emerges naturally in a balanced cortical network model with random connectivity and conductance-based synapses. We employ mean field theory with correctly colored noise to describe temporal correlations in the neuronal activity. Our results illuminate the connection between two independent experimental findings: high conductance states of cortical neurons in their natural environment, and variable non-Poissonian spike statistics with Fano factors greater than 1.
Ground state properties of La isotopes in reflection asymmetric relativistic mean field theory
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The ground state properties of La isotopes are investigated with the reflection asymmetric relativistic mean field(RAS-RMF) model.The calculation results of binding energies and the quadrupole moments are in good agreements with the experiment.The calculation results indicate the change of the quadrupole deformation with the nuclear mass number.The "kink" on the isotope shifts is observed at A = 139 where the neutron number is the magic number N = 82.It is also found that the octupole deformations may exist in the La isotopes with mass number A ～ 145-155.
Ground state properties of La isotopes in reflection asymmetric relativistic mean field theory
Institute of Scientific and Technical Information of China (English)
WANG Nan; GUO Lu
2009-01-01
The ground state properties of La isotopes are investigated with the reflection asymmetric relativistic mean field (RAS-RMF) model.The calculation results of binding energies and the quadrupole moments are in good agreements with the experiment.The calculation results indicate the change of the quadrupole deformation with the nuclear mass number.The "kink" on the isotope shifts is observed at A=139 where the neutron number is the magic number N=82.It is also found that the octupole deformations may exist in the La isotopes with mass number A～ 145-155.
Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
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.
Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
Tanizaki, Yuya; Kashiwa, Kouji
2015-01-01
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.
Strange baryons, nuclear dripline and shrinkage : A Relativistic Mean Field study
Bhowmick, Bipasha; Gangopadhyay, G; 10.1142/S0218301313500122
2013-01-01
Neutron and proton driplines of single-$\\Lambda$ and double-$\\Lambda$ hypernuclei, $\\Xi^{-}$ hypernuclei as well as normal nuclei are studied within a relativistic mean field approach using an extended form of the FSU Gold Lagrangian density. Hyperons are found to produce bound nuclei beyond the normal nuclear driplines. Radii are found to decrease in hypernuclei near the driplines, in line with observations in light $\\Lambda$ hypernuclei near the stability valley, The inclusion of a $\\Xi^{-}$ introduces a much larger change in radii than one or more $\\Lambda$'s.
Coexistence of nuclear shapes: self-consistent mean-field and beyond
Li, Zhipan; Vretenar, Dario
2015-01-01
A quantitative analysis of the evolution of nuclear shapes and shape phase transitions, including regions of short-lived nuclei that are becoming accessible in experiments at radioactive-beam facilities, necessitate accurate modeling of the underlying nucleonic dynamics. Important theoretical advances have recently been made in studies of complex shapes and the corresponding excitation spectra and electromagnetic decay patterns, especially in the "beyond mean-field" framework based on nuclear density functionals. Interesting applications include studies of shape evolution and coexistence in N = 28 isotones, the structure of lowest $0^+$ excitations in deformed N $\\approx$ 90 rare-earth nuclei, and quadrupole and octupole shape transitions in thorium isotopes.
Magnetic material in mean-field dynamos driven by small scale helical flows
International Nuclear Information System (INIS)
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<=μr<=20. Our results may be used for the development of global large scale models with recirculation flow and realistic boundary
Speed of sound in quark gluon plasma with one loop correction in mean field potential
Singh, S Somorendro
2015-01-01
We study thermodynamic properties and speed of sound in a free en- ergy evolution of quark-gluon plasma (QGP) with one loop correction factor in the mean-field potential. The values of the thermodynamic prop- erties like pressure, entropy and specific heat are calculated for a range of temperatures. The results agree with the recent lattice results. The speed of sound is found to be C2 s = 0.3 independent of parameters used in the loop correction which matches almost with lattice calculations.
Investigations on Nuclei near Z- 82 in Relativistic Mean Field Theory with FSUGold
Institute of Scientific and Technical Information of China (English)
圣宗强; 任中洲
2012-01-01
In this work, the ground-state properties of Pt, Hg, Pb, and Po isotopes have been systematically investigated in the deformed relativistic mean field (RMF) theory with the new parameter set FSUGold. The calculated results show that FSUGold is as successful as NL3 in reproducing the ground-state binding energies of the nuclei in this region. The calculated two- neutron separation energies, quadrupole deformations, and root-mean-square charge radii are in agreement with the experimental data. The parameter set FSUGold can successfully describe the shell effect of the neutron magic number N = 126 and give smaller neutron skin thicknesses than NL3 for all the nuclei considered.
Baryon resonances in the mean field approach and a simple explanation of the Theta+ pentaquark
Diakonov, Dmitri
2008-01-01
We suggest to classify baryon resonances as single-quark states in a mean field, and/or as its collective excitations. Identifying the Roper resonance N(1440), the nucleon resonance N(1535), and the singlet hyperon Lambda(1405) as single-quark excitations, we find that there must be an exotic S=+1 baryon resonance Theta+ (the "pentaquark") with a mass about 1440+1535-1405=1570 MeV and spin-parity one-half-plus. We argue that Theta+ is an analog of the Gamov--Teller excitation long known in nuclear physics.
From energy-density functionals to mean field potentials: a systematic derivation
Energy Technology Data Exchange (ETDEWEB)
Chomaz, Ph.; Hasnaoui, K.H.O. [GANIL, DSM-CEA/IN2P3-CNRS, B.P.5027, F-14076 Caen cedex 5 (France); Gulminelli, F. [LPC, IN2P3-CNRS/Ensicaen et Universite, F-14050 Caen cedex (France)
2006-10-15
The density functional theory (DFT) is one of the most powerful theories to deal with the intractable quantum many body problem for interacting systems with an arbitrary number of constituents. In this paper we present a systematic method to solve the variational problem of the derivation of a self-consistent Kohn-Sham field from an arbitrary local energy functional. We illustrate this formalism with an application in nuclear physics and give the general mean field associated to the widely used Skyrme effective interaction. (authors)
Phase transitions in social sciences: two-populations mean field theory
Contucci, P; Menconi, G; Contucci, Pierluigi; Gallo, Ignacio; Menconi, Giulia
2007-01-01
A mean field statistical mechanics model of two interacting groups of spins is introduced and the phase transition 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.
High-conductance states in a mean-field cortical network model
DEFF Research Database (Denmark)
Lerchner, Alexander; Ahmadi, Mandana; Hertz, John
2004-01-01
Measured responses from visual cortical neurons show that spike times tend to be correlated rather than exactly Poisson distributed. Fano factors vary and are usually greater than 1, indicating a tendency toward spikes being clustered. We show that this behavior emerges naturally in a balanced...... cortical network model with random connectivity and conductance-based synapses. We employ mean-field theory with correctly colored noise to describe temporal correlations in the neuronal activity. Our results illuminate the connection between two independent experimental findings: high-conductance states...
Analytical results on the magnetization of the Hamiltonian Mean-Field model
Energy Technology Data Exchange (ETDEWEB)
Bachelard, R., E-mail: romain.bachelard@synchrotron-soleil.f [Synchrotron Soleil, L' Orme des Merisiers, Saint-Aubin, BP 48, F-91192 Gif-sur-Yvette cedex (France); Chandre, C. [Centre de Physique Theorique, CNRS - Aix-Marseille Universites, Campus de Luminy, case 907, F-13288 Marseille cedex 09 (France); Ciani, A.; Fanelli, D. [Dipartimento di Energetica ' Sergio Stecco' , Universita di Firenze, via s. Marta 3, 50139 Firenze (Italy)] [Centro interdipartimentale per lo Studio delle Dinamiche Complesse - CSDC (Italy)] [INFN (Italy); Yamaguchi, Y.Y. [Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, 606-8501 Kyoto (Japan)
2009-11-09
The violent relaxation and the metastable states of the Hamiltonian Mean-Field model, a paradigmatic system of long-range interactions, is studied using a Hamiltonian formalism. Rigorous results are derived algebraically for the time evolution of selected macroscopic observables, e.g., the global magnetization. The high- and low-energy limits are investigated and the analytical predictions are compared with direct N-body simulations. The method we use enables us to re-interpret the out-of-equilibrium phase transition separating magnetized and (almost) unmagnetized regimes.
One-pion exchange current corrections for nuclear magnetic moments in relativistic mean field theory
Li, Jian; Meng, J; Arima, A
2010-01-01
The one-pion exchange current corrections to isoscalar and isovector magnetic moments of double-closed shell nuclei plus and minus one nucleon with $A=15,17,39$ and 41 have been studied in the relativistic mean field (RMF) theory and compared with previous relativistic and non-relativistic results. It has been found that the one-pion exchange current gives a negligible contribution to the isoscalar magnetic moments but a significant correction to the isovector ones. However, the one-pion exchange current doesn't improve the description of nuclear isovector magnetic moments for the concerned nuclei.
Cassam-Chenaï, Patrick; Suo, Bingbing; Liu, Wenjian
2015-07-01
We introduce the electron-nucleus mean-field configuration-interaction (EN-MFCI) approach. It consists in building an effective Hamiltonian for the electrons taking into account a mean field due to the nuclear motion and, conversely, in building an effective Hamiltonian for the nuclear motion taking into account a mean field due to the electrons. The eigenvalue problems of these Hamiltonians are solved in basis sets giving partial eigensolutions for the active degrees of freedom (DOF's), that is to say, either for the electrons or for nuclear motion. The process can be iterated or electron and nuclear motion DOF's can be contracted in a CI calculation. In the EN-MFCI reduction of the molecular Schrödinger equation to an electronic and a nuclear problem, the electronic wave functions do not depend parametrically upon nuclear coordinates. So, it is different from traditional adiabatic methods. Furthermore, when contracting electronic and nuclear functions, a direct product basis set is built in contrast with methods which treat electrons and nuclei on the same footing, but where electron-nucleus explicitly correlated coordinates are used. Also, the EN-MFCI approach can make use of the partition of molecular DOF's into translational, rotational, and internal DOF's. As a result, there is no need to eliminate translations and rotations from the calculation, and the convergence of vibrational levels is facilitated by the use of appropriate internal coordinates. The method is illustrated on diatomic molecules.
Engl, Thomas; Richter, Klaus
2015-01-01
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, non-perturbative solutions of the, typically non-linear, wave equation of the classical (mean-field) limit. To this end we construct the semiclassical approximation for both the smooth and oscillatory part 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 like 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 brea...
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
Hadron resonance gas and mean-field nuclear matter for baryon number fluctuations
Fukushima, Kenji
2014-01-01
We give an estimate for the skewness and the kurtosis of the baryon number distribution in two representative models; i.e., models for a hadron resonance gas and relativistic mean-field nuclear matter. We emphasize formal similarity between these two descriptions. The hadron resonance gas leads to a deviation from the Skellam distribution if quantum statistical correlation is taken into account at high baryon density, but this effect is not strong enough to explain fluctuation data seen in the beam-energy scan at RHIC/STAR. In the calculation of mean-field nuclear matter the density correlation with the vector \\omega-field rather than the effective mass with the scalar \\sigma-field renders the kurtosis suppressed at higher baryon density so as to account for the observed behavior of the kurtosis. We finally discuss the difference between the baryon number and the proton number fluctuations from correlation effects in isospin space. Our numerical results suggest that such effects are only minor even in the cas...
Atomically flat superconducting nanofilms: multiband properties and mean-field theory
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.
Implementing the density matrix embedding theory with the hierarchical mean-field approach
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.
Mean-field Theory for Some Bus Transport Networks with Random Overlapping Clique Structure
International Nuclear Information System (INIS)
Transport networks, such as railway networks and airport networks, are a kind of random network with complex topology. Recently, more and more scholars paid attention to various kinds of transport networks and try to explore their inherent characteristics. Here we study the exponential properties of a recently introduced Bus Transport Networks (BTNs) evolution model with random overlapping clique structure, which gives a possible explanation for the observed exponential distribution of the connectivities of some BTNs of three major cities in China. Applying mean-field theory, we analyze the BTNs model and prove that this model has the character of exponential distribution of the connectivities, and develop a method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the exponents. By comparing mean-field based theoretic results with the statistical data of real BTNs, we observe that, as a whole, both of their data show similar character of exponential distribution of the connectivities, and their exponents have same order of magnitude, which show the availability of the analytical result of this paper. (general)
Characteristic Feature of Self-Consistent Mean-Field in Level Crossing Region
Guo, L; Zhao, E G; Guo, Lu; Sakata, Fumihiko; Zhao, En-Guang
2004-01-01
A shape change of the self-consistent mean-field induced by a configuration change is discussed within the conventional constrained Hartree-Fock (CHF) theory. It is stressed that a single-particle level crossing dynamics should be treated carefully, because the shape of the mean-field in such a finite many-body system as the nucleus strongly changes depending on its configuration. This situation is clearly shown by applying an adiabatic assumption, where the most energetically favorable single-particle states are assumed to be occupied. The excited HF states and the continuously-connected potential energy curves are given by applying the configuration dictated CHF method. The effect of pairing correlation is discussed in the level crossing region. Triaxial deformed results in our Hartree-Fock-Bogoliubov (HFB) calculation with Gogny force nicely reproduce the available experimental data of Ge isotopes. From our numerical calculation, it is concluded that the CHFB state is more fragile than the CHF state in the...
Beyond mean-field study of elastic and inelastic electron scattering off nuclei
Yao, J M; Heenen, P -H
2014-01-01
[Background] Electron scattering provides a powerful tool to determine charge distributions and transition densities of nuclei. This tool will soon be available for short-lived neutron-rich nuclei. [Purpose] Beyond mean-field methods have been successfully applied to the study of excitation spectra of nuclei in the whole nuclear chart. These methods permit to determine energies and transition probabilities starting from an effective in-medium nucleon-nucleon interaction but without other phenomenological ingredients. Such a method has recently been extended to calculate the charge density of nuclei deformed at the mean-field level of approximation [J. M. Yao et al., Phys. Rev. C86, 014310 (2012)]. The aim of this work is to further extend the method to the determination of transition densities between low-lying excited states. [Method] The starting point of our method is a set of Hartree-Fock-Bogoliubov wave functions generated with a constraint on the axial quadrupole moment and using a Skyrme energy density...
Effects of anisotropy of turbulent convection in mean-field solar dynamo models
Pipin, V V
2013-01-01
We study how anisotropy of turbulent convection affects diffusion of large-scale magnetic fields and the dynamo process on the Sun. The effect of anisotropy is calculated in a mean-field magneto-hydrodynamics framework using the minimal $\\tau$-approximation. We examine two types of mean-field dynamo models: the well-known benchmark flux-transport model, and a distributed-dynamo model with the subsurface rotational shear layer. For both models we investigate effects of the double-cell meridional circulation, recently suggested by helioseismology. We introduce a parameter of anisotropy as a ratio of the radial and horizontal intensity of turbulent mixing, to characterize the anisotropy effects. It is found that the anisotropy of turbulent convection 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 d...
$\\sigma$-SCF: A Direct Energy-targeting Method To Mean-field Excited States
Ye, Hong-Zhou; Ricke, Nathan D; Van Voorhis, Troy
2016-01-01
The mean-field solutions of electronic excited states are much less accessible than ground state (e.g.\\ Hartree-Fock) solutions. Energy-based optimization methods for excited states, like $\\Delta$-scf, tend to fall into the lowest solution consistent with a given symmetry -- a problem known as "variational collapse". In this work, we combine the ideas of direct energy-targeting and variance-based optimization in order to describe excited states at the mean-field level. The resulting method, $\\sigma$-scf, has several advantages. First, it allows one to target any desired excited state by specifying a single parameter: a guess of the energy of that state. It can therefore, in principle, find \\emph{all} excited states. Second, it avoids variational collapse by using a variance-based, unconstrained local minimization. As a consequence, all states -- ground or excited -- are treated on an equal footing. Third, it provides an alternate approach to locate $\\Delta$-scf solutions that are otherwise inaccessible by the...
Shell structure of superheavy nuclei in self-consistent mean-field models
Bender, M; Reinhard, P G; Maruhn, J A; Greiner, W
1999-01-01
We study the extrapolation of nuclear shell structure to the region of superheavy nuclei in self-consistent mean-field models -- the Skyrme-Hartree-Fock approach and the relativistic mean-field model -- using a large number of parameterizations. Results obtained with the Folded-Yukawa potential are shown for comparison. We focus on differences in the isospin dependence of the spin-orbit interaction and the effective mass between the models and their influence on single-particle spectra. While all relativistic models give a reasonable description of spin-orbit splittings, all non-relativistic models show a wrong trend with mass number. The spin-orbit splitting of heavy nuclei might be overestimated by 40%-80%. Spherical doubly-magic superheavy nuclei are found at (Z=114,N=184), (Z=120,N=172) or (Z=126,N=184) depending on the parameterization. The Z=114 proton shell closure, which is related to a large spin-orbit splitting of proton 2f states, is predicted only by forces which by far overestimate the proton spi...
Mean field game theoretic approach for security in mobile ad-hoc networks
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.
On a mean field game optimal control approach modeling fast exit scenarios in human crowds
Burger, Martin
2013-12-01
The understanding of fast exit and evacuation situations in crowd motion research has received a lot of scientific interest in the last decades. Security issues in larger facilities, like shopping malls, sports centers, or festivals necessitate a better understanding of the major driving forces in crowd dynamics. In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. The model is formulated in the framework of mean field games and based on a parabolic optimal control problem. We consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position and velocity, the overall density of people, and the time to exit. This microscopic setup leads in a mean-field formulation to a nonlinear macroscopic optimal control problem, which raises challenging questions for the analysis and numerical simulations.We discuss different aspects of the mathematical modeling and illustrate them with various computational results. ©2013 IEEE.
From effective field theories to effective density functionals in and beyond the mean field
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.
Resonating Valence Bonds and Mean-Field d-Wave Superconductivity in Graphite
Energy Technology Data Exchange (ETDEWEB)
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.
Preequilibrium neutron emission in heavy ion reaction: Mean field effect and multiple emission
Paul, Sabyasachi; Nandy, Maitreyee; Mohanty, A. K.; Gambhir, Y. K.
2016-09-01
Effects of nuclear mean field and of multiple preequilibrium (PEQ) emission on double differential neutron multiplicity distribution from heavy ion reactions (12C+165Ho and 20Ne+165Ho ) at 10-30 MeV/u have been investigated in the framework of the semiclassical formalism for heavy ion reaction (henceforth termed "HION") developed earlier. HION follows the equilibration of a target+projectile composite system through the kinematics of two-body scattering. In the present work nuclear density distribution in the composite system is estimated in the relativistic mean field (RMF) approach. The nucleon-nucleon collision rates and subsequently the nucleon emission probability are calculated from this density distribution. A second approach based on a semiphenomenological formalism is also used for nuclear density distribution. Energy-angle distribution of neutron multiplicities calculated with this modified HION model coupled with multiple PEQ emission could reproduce the measured data of earlier workers in the projectile energy range of 10-30 MeV/u.
Cluster Mean-Field Approach to the Steady-State Phase Diagram of Dissipative Spin Systems
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.
Quantum fluctuations, mean field methods and the simulation of continuous quantum systems
Energy Technology Data Exchange (ETDEWEB)
Kadar, Zoltan; Keyl, Michael; Zimboras, Zoltan [ISI Foundation, Torino (Italy)
2012-07-01
The fluctuations of a discrete quantum system behave in the infinite particle limit like a continuous system. This fact can be used to simulate a continuous system in terms of finitely many qubits. Experimental applications of this observation include the implementation of ''quantum memory'', which can be used to store the state of (one mode) of a light field in an atomic ensemble at room temperature. A very convenient tool to treat such models is mean field theory, where the fluctuations around a mean field observable are described in terms of ''fluctuation operators''. In this context we will show how products of the latter converge in a weak sense to polynomials of position and momentum of the continuous system. Based on that the relation between discreet and continuous dynamics will be analyzed, and quadratic Hamiltonians are discussed in greater detail. Finally we will have a particular look at cases where the continuous Hamiltonian is a Schroedinger operator which does not admit a selfadjoint extension.
Maximizing Influence in an Ising Network: A Mean-Field Optimal Solution
Lynn, Christopher
2016-01-01
The problem of influence maximization in social networks has typically been studied in the context of contagion models and irreversible processes. In this paper, we consider an alternate model that treats individual opinions as spins in an Ising network at dynamic equilibrium. We formalize the Ising influence maximization (IIM) problem, which has a physical interpretation as the maximization of the magnetization given a budget of external magnetic field. Under the mean-field (MF) approximation, we develop a number of sufficient conditions for when the problem is convex and exactly solvable, and we provide a gradient ascent algorithm that efficiently achieves an $\\epsilon$-approximation to the optimal solution. We show that optimal strategies exhibit a phase transition from focusing influence on high-degree individuals at high interaction strengths to spreading influence among low-degree individuals at low interaction strengths. We also establish a number of novel results about the structure of steady-states i...
Angular momentum projection for a Nilsson mean-field plus pairing model
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.
Magnetic helicity in non-axisymmetric mean-field solar dynamo
Pipin, V V
2016-01-01
The paper address the effects of magnetic helicity conservation in a non-linear nonaxisymmetric mean-field solar dynamo model. We study the evolution of the shallow non-axisymmetric magnetic field perturbation with the strength about 10G in the solar convection zone. The dynamo evolves from the pure axisymmetric stage through the short (about 2 years) transient phase when the non-axisymmetric m=1 dynamo mode is dominant to the final stage where the axisymmetry of the dynamo is almost restored. It is found that magnetic helicity is transferred forth and back over the spectral space during the transient phase. Also our simulations shows that the non-axisymmetric distributions of magnetic helicity tend to follows the regions of the Hale polarity rule.
Following Gibbs states adiabatically: the energy landscape of mean field glassy systems
Energy Technology Data Exchange (ETDEWEB)
Zdeborova, Lenka [Los Alamos National Laboratory; Krzakala, Florent [ESPCI
2009-01-01
We introduce a generalization of the cavity, or Bethe-Peierls, method that allows to follow Gibbs states when an external parameter, e.g. the temperature, is adiabatically changed. This allows to obtain new quantitative results on the static and dynamic behavior of mean field disordered systems such as models of glassy and amorphous materials or random constraint satisfaction problems. As a first application, we discuss the residual energy after a very slow annealing, the behavior of out-of-equilibrium states, and demonstrate the presence of temperature chaos in equilibrium. We also explore the energy landscape, and identify a new transition from an computationally easier canyons-dominated region to a harder valleys-dominated one.
A fully covariant mean-field dynamo closure for numerical 3+1 resistive GRMHD
Bucciantini, N
2012-01-01
The powerful high-energy phenomena typically encountered in astrophysics invariably involve physical engines, like neutron stars and black hole accretion disks, characterized by a combination of highly magnetized plasmas, strong gravitational fields, and relativistic motions. In recent years numerical schemes for General Relativistic MHD (GRMHD) have been developed to model the multidimensional dynamics of such systems, including the possibility of an evolving spacetime. Such schemes have been also extended beyond the ideal limit including the effects of resistivity, in an attempt to model dissipative physical processes acting on small scales (sub-grid effects) over the global dynamics. Along the same lines, magnetic fields could be amplified by the presence of turbulent dynamo processes, as often invoked to explain the high values of magnetization required in accretion disks and neutron stars. Here we present, for the first time, a further extension to include the possibility of a mean-field dynamo action wi...
Ground state phase transition in the Nilsson mean-field plus standard pairing model
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.
Pair quenched mean-field theory for the susceptible-infected-susceptible model on complex networks
Mata, Angélica S
2013-01-01
We present quenched mean-field (QMF) theory for the dynamics of the susceptible-infected-susceptible (SIS) epidemic model on complex networks where dynamical correlations between connected vertices are taken into account by means of a pair approximation. We present analytical expressions for the epidemic thresholds for the star and wheel graphs and for random regular networks. For random networks with a power law degree distribution, the thresholds are numerically determined via an eigenvalue problem. The pair and one-vertex QMF theories yield the same scaling for the thresholds as function of the network size. However, comparisons with quasi-stationary simulations of the SIS dynamics on large networks show that the former is quantitatively much more accurate than the latter. Our results demonstrate the central role played by dynamical correlations on the epidemic spreading and introduce an efficient way to theoretically access the thresholds of very large networks that can be extended to dynamical processes ...
Beyond mean-field boson-fermion model for odd-mass nuclei
Nomura, K; Vretenar, D
2016-01-01
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.
Time-dependent Relativistic Mean-field Theory and Random Phase Approximation
Institute of Scientific and Technical Information of China (English)
P.Ring; D.Vretenar; A.Wandelt; NguyenVanGiai; MAZhong-yu; CAOLi-gang
2001-01-01
The relativistic random phase approximation (RRPA) is derived from the time-dependent relativistic mean field (TD RMF) theory in the limit of small amplitude oscillations. In the no-sea approximation of the RMF theory, the RRPA configuration space includes not only the usual particle-hole ph-states, but also ah configurations, i.e. pairs formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The contribution of the negative energy states to the RRPA matrices is examined in a schematic model, and the large effect of Dirac sea states on isoscalar strength distributions is illustrated for the giant monopole resonance in 116Sn. It is shown that
Mean-field-like behavior of the generalized voter-model-class kinetic Ising model
Krause, Sebastian M; Bornholdt, Stefan; 10.1103/PhysRevE.85.031126
2012-01-01
We analyze a kinetic Ising model with suppressed bulk noise which is a prominent representative of the generalized voter model phase transition. On the one hand we discuss the model in the context of social systems, and opinion formation in the presence of a tunable social temperature. On the other hand we characterize the abrupt phase transition. The system shows non-equilibrium dynamics in the presence of absorbing states. We slightly change the system to get a stationary state model variant exhibiting the same kind of phase transition. Using a Fokker-Planck description and comparing to mean field calculations, we investigate the phase transition, finite size effects and the effect of the absorbing states resulting in a dynamic slowing down.
Hyperons in neutron star matter within relativistic mean-field models
Oertel, M; Gulminelli, F; Raduta, A R
2014-01-01
Since the discovery of neutron stars with masses around 2 solar masses the composition of matter in the central part of these massive stars has been intensively discussed. Within this paper we will (re)investigate the question of the appearance of hyperons. To that end we will perform an extensive parameter study within relativistic mean field models. We will show that it is possible to obtain high mass neutron stars (i) with a substantial amount of hyperons, (ii) radii of 12-13 km for the canonical mass of 1.4 solar masses, and (iii) a spinodal instability at the onset of hyperons. The results depend strongly on the interaction in the hyperon-hyperon channels, on which only very little information is available from terrestrial experiments up to now.
The role of disorder in the dynamics of critical fluctuations of mean field models
Collet, Francesca
2011-01-01
The purpose of this paper is to analyze how the disorder affects the dynamics of critical fluctuations for two different types of interacting particle system: the Curie-Weiss and Kuramoto model. The models under consideration are a collection of spins and rotators respectively. They both are subject to a mean field interaction and embedded in a site-dependent, i.i.d. random environment. As the number of particles goes to infinity their limiting dynamics become deterministic and exhibit phase transition. The main result concern the fluctuations around this deterministic limit at the critical point in the thermodynamic limit. From a qualitative point of view, it indicates that when disorder is added spin and rotator systems belong to two different classes of universality, which is not the case for the homogeneous models (i.e., without disorder).
Rhythmic behavior in a two-population mean field Ising model
Collet, Francesca; Tovazzi, Daniele
2016-01-01
Many real systems comprised of a large number of interacting components, as for instance neural networks , may exhibit collective periodic behavior even though single components have no natural tendency to behave periodically. Macroscopic oscillations are indeed one of the most common self-organized behavior observed in living systems. In the present paper we study some dynamical features of a two-population generalization of the mean field Ising model with the scope of investigating simple mechanisms capable to generate rhythm in large groups of interacting individuals. We show that the system may undergo a transition from a disordered phase, where the magnetization of each population fluctuates closely around zero, to a phase in which they both display a macroscopic regular rhythm. In particular, there exists a region in the parameter space where having two groups of spins with inter- and intra-population interactions of different strengths suffices for the emergence of a robust periodic behavior.
Mean-Field Theory of Intra-Molecular Charge Ordering in (TTM--TTP)I3
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.
Application of Gaussian expansion method to nuclear mean-field calculations with deformation
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.
Application of Gaussian expansion method to nuclear mean-field calculations with deformation
Nakada, H
2008-01-01
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 of the single-particle bases, 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 $^{40}$Mg.
Cluster Mean-Field Signature of Entanglement Entropy in Bosonic Superfluid-Insulator Transitions
Zhang, Li; Ke, Yongguan; Lee, Chaohong
2016-01-01
Entanglement entropy (EE), a fundamental conception in quantum information for characterizing entanglement, has been extensively employed to explore quantum phase transitions (QPTs). Although the conventional single-site mean-field (MF) approach successfully predicts the emergence of QPTs, it fails to include any entanglement. Here, for the first time, in the framework of a cluster MF treatment, we extract the signature of EE in the bosonic superfluid-insulator transitions. We consider a trimerized Kagome lattice of interacting bosons, in which each trimer is treated as a cluster, and implement the cluster MF treatment by decoupling all inter-trimer hopping. In addition to superfluid and integer insulator phases, we find that fractional insulator phases appear when the tunneling is dominated by the intra-trimer part. To quantify the residual bipartite entanglement in a cluster, we calculate the second-order Renyi entropy, which can be experimentally measured by quantum interference of many-body twins. The sec...
Faster is More Different: Mean-Field Dynamics of Innovation Diffusion
Baek, Seung Ki; Kim, Mina
2013-01-01
Based on a recent model of paradigm shifts by Bornholdt et al., we studied mean-field opinion dynamics in an infinite population where an infinite number of ideas compete simultaneously with their values publicly known. We found that a highly innovative society is not characterized by heavy concentration in highly valued ideas: Rather, ideas are more broadly distributed in a more innovative society with faster progress, provided that the rate of adoption is constant, which suggests a positive correlation between innovation and technological disparity. Furthermore, the distribution is generally skewed in such a way that the fraction of innovators is substantially smaller than has been believed in conventional innovation-diffusion theory based on normality. Thus, the typical adoption pattern is predicted to be asymmetric with slow saturation in the ideal situation, which is compared with empirical data sets.
Investigation of A＋c- and Ab-Hypernuclei in Relativistic Mean-Field Model
Institute of Scientific and Technical Information of China (English)
TANYu-Hong; CAIChong-Hai; LILei; NINGPing-Zhi
2003-01-01
We investigate the properties of A+c- and Ab-hypernuclei within the framework of the relativistic mean-field model (RMF). It is found that no A+c bound states can exist if the A+c potential well depth |UA+c| in nuclear matter is less than 10 MeV. If |UA+c|is less than 20 MeV, A+c cannot bind to the heavier nuclei with atomic number larger than 100. We suggest it is preferable to search the A+c-hypernuclei from medium-heavy nuclear systems in experiment. Very small spin-orbit splitting for the A+c in hypernuclei is a/so observed, and for the Ab it is nearly zero.
Sharma, Mahesh K; Sharma, Manoj K; Patra, S K
2015-01-01
We have studied the ground state properties (binding energy and charge radius) using relativistic mean filed formalism (RMF) for Mg-isotopes in the valley of stability to drip line region. The RMF densities have been analyzed in context of reaction dynamics. The calculated results of $^{24-40}$Mg+$^{12}$C reactions at projectile energy 240 AMeV using Glauber model with the conjunction of densities from relativistic mean field formalism are compared with experimental data. We found remarkable agreement of estimated values of reaction cross sections with experimental data except for $^{37}$Mg isotope. In view of this, the halo status of $^{37}$Mg is examined through higher magnitude of rms radius and small value of longitudinal momentum distribution. Finally, an effort is made to explore the structure of $^{37}$Mg halo candidate using Glauber few body formalism.
Beyond-mean-field boson-fermion model for odd-mass nuclei
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.
Isospin-symmetry-breaking effects in A∼70 nuclei within beyond-mean-field approach
Energy Technology Data Exchange (ETDEWEB)
Petrovici, A.; Andrei, O. [National Institute for Physics and Nuclear Engineering, R-077125 Bucharest (Romania)
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.
Orbital magnetism of ultracold fermionic gases in a lattice: Dynamical mean-field approach
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.
A scalable theoretical mean-field model for the electron component of an ultracold neutral plasma
Guthrie, John
2015-01-01
The electron component of an ultracold neutral plasma (UCP) is modeled based on a scalable method using a self-consistently determined mean-field approximation. Representative sampling of discrete electrons within the UCP are used to project the electron spatial distribution onto an expansion of orthogonal basis functions. A collision operator acting on the sample electrons is employed in order to drive the distribution toward thermal equilibrium. These equilibrium distributions can be determined for non-zero electron temperatures even in the presence of spherical symmetry-breaking applied electric fields. This is useful for predicting key macroscopic UCP parameters, such as the depth of the electrons' confining potential. Dynamics such as electron oscillations in UCPs with non-uniform density distributions can also be treated by this model.
Description of 178 Hfm2 in the Constrained Relativistic Mean Field Theory
Institute of Scientific and Technical Information of China (English)
ZHANG Wei; PENG Jing; ZHANG Shuang-Quan
2009-01-01
Properties of the ground state of 178 Hf and the isomeric state 178Hfn2 are studied within the adiabatic and diabatic constrained relativistic mean field (RMF) approaches. The RMF calculations reproduce well the binding energy and the deformation for the ground state of 178Hf. Using the ground state single-particle eigenvalues obtained in the present calculation, the lowest excitation configuration with Kπ = 16+ is found to be v(7/2- [514])-1 (9/2+ [624])1 π(7/2+ [404])-1 (9/2-[514])1. Its excitation energy calculated by the RMF theory with time-odd fields taken into account is equal to 2.801 MeV, i.e., close to the 178 Hfm2 experimental excitation energy 2.446 MeV. The self-consistent procedure accounting for the time-odd component of the meson fields is the most important aspect of the present calculation.
Ground-State Properties of Z = 59 Nuclei in the Relativistic Mean-Field Theory
Institute of Scientific and Technical Information of China (English)
ZHOU Yong; MA Zhong-Yu; CHEN Bao-Qiu; LI Jun-Qing
2000-01-01
Ground-state properties of Pr isotopes are studied in a framework of the relativistic mean-field (RMF) theory using the recently proposed parameter set TM1. Bardeen-Cooper-Schrieffer (BCS) pproximation and blocking method is adopted to deal with pairing interaction and the odd nucleon, respectively. The pairing forces are taken to be isospin dependent. The domain of the validity of the BCS theory and the positions of neutron and proton drip lines are studied. It is shown that RMF theory has provided a good description of the binding energy,isotope shifts and deformation of nuclei over a large range of Pr isotopes, which are in good agreement with those obtained in the finite-range droplet model.
Criterion for DNA melting in the mean-field modified self-consistent phonon theory
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.
Internal stucture of clusters in $^{112-122}$Ba nuclei within relativistic mean field theory
Bhuyan, M; Arumugam, P; Gupta, Raj K
2009-01-01
We study the clustering structure and the internal or sub-structure of clusters in $^{112-122}$Ba nuclei within the framework of relativistic mean field theory in an axially deformed cylindrical co-ordinate. We calculate the total density distribution, and the individual neutrons and protons density distributions. From the analysis of the clustering confugurations of the density distributions of various shapes, we find different sub-structures inside the Ba nuclei considered here. The important step, carried out for the first time, is the counting of number of protons and neutrons present in the clustering region(s). $^{12}$C is shown to consitute the cluster configuration of Ba nuclei in most cases, with $^{2,3}$H and $^4$He constituting the neck between two fissioning symmetrical fragments.
Bilayer Hubbard model for 3He: a cluster dynamical mean-field calculation
International Nuclear Information System (INIS)
Inspired by recent experiments on bilayer 3He, we consider a bilayer Hubbard model on a triangular lattice. For appropriate model parameters, we observe a band-selective Mott transition at a critical chemical potential, μc, corresponding to the solidification of the fermions in the first layer. The growth of the effective mass on the metallic side (μ c) is cut off by a first order transition in which the first layer fermions drop out of the Luttinger volume and their spin degrees of freedom become locked in a spin singlet state. These results are obtained from a cluster dynamical mean-field calculation on an eight-site cluster with a quantum Monte Carlo cluster solver.
Mean-field dynamic criticality and geometric transition in the Gaussian core model
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.
β-decay of magic nuclei: Beyond mean-field description
International Nuclear Information System (INIS)
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
Modeling of coherent ultrafast magneto-optical experiments: Light-induced molecular mean-field model
Energy Technology Data Exchange (ETDEWEB)
Hinschberger, Y. [Instituto de Física dos Materiais da Universidade do Porto, Departamento de Física et Astronomia, Rua do campo Alegre, 687, 4169-007 Porto (Portugal); Hervieux, P.-A. [Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS UMR 7504 BP 43 - F-67034 Strasbourg Cedex 2 (France)
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.
β-decay of magic nuclei: Beyond mean-field description
Energy Technology Data Exchange (ETDEWEB)
Niu, Yifei, E-mail: nyfster@gmail.com [Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900 (China); INFN, Sezione di Milano, via Celoria 16, I-20133 Milano (Italy); Niu, Zhongming [School of Physics and Material Science, Anhui University, Hefei 230601 (China); Colò, Gianluca [Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, I-20133 Milano (Italy); INFN, Sezione di Milano, via Celoria 16, I-20133 Milano (Italy); Vigezzi, Enrico [INFN, Sezione di Milano, via Celoria 16, I-20133 Milano (Italy)
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.
Out-of-equilibrium mean-field dynamics of a model for wave-particle interaction
de Buyl, Pierre; Bachelard, Romain; De Ninno, Giovanni
2009-01-01
The out-of-equilibrium mean-field dynamics of a model for wave-particle interaction is investigated. Such a model can be regarded as a general formulation for all those applications where the complex interplay between particles and fields is known to be central, e.g., electrostatic instabilities in plasma physics, particle acceleration and free-electron lasers. The latter case is here assumed as a paradigmatic example. A transition separating different macroscopic regimes is numerically identified and interpreted by making use of the so-called violent relaxation theory. In this context, the transition is explained as a dynamical switch between two metastable regimes, and related to the change of nature of a stationary point of an entropic functional.
Magnetic moments of 33Mg in the time-odd relativistic mean field approach
Institute of Scientific and Technical Information of China (English)
LI Jian; ZHANG Ying; YAO JiangMing; MENG Jie
2009-01-01
The configuration-fixed deformation constrained relativistic mean field approach with time-odd component has been applied to investigate the ground state properties of 33Mg with effective interaction PK1.The ground state of 33Mg has been found to be prolate deformed,β2=0.23,with the odd neutron in 1/2[330]orbital and the energy-251.85 MeV which is close to the data-252.06 MeV.The magnetic moment-0.9134μN is obtained with the effective electromagnetic current which well reproduces the data -0.7456 μN self-consistently without introducing any parameter.The energy splittings of time reversal conjugate states,the neutron current,the energy contribution from the nuclear magnetic potential,and the effect of core polarization are discussed in detail.
Magnetic moments of 33Mg in the time-odd relativistic mean field approach
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The configuration-fixed deformation constrained relativistic mean field approach with time-odd component has been applied to investigate the ground state properties of 33Mg with effective interaction PK1.The ground state of 33Mg has been found to be prolate deformed,β2=0.23,with the odd neutron in 1/2[330] orbital and the energy -251.85 MeV which is close to the data -252.06 MeV.The magnetic moment -0.9134 μN is obtained with the effective electromagnetic current which well reproduces the data -0.7456 μN self-consistently without introducing any parameter.The energy splittings of time reversal conjugate states,the neutron current,the energy contribution from the nuclear magnetic potential,and the effect of core polarization are discussed in detail.
Estimating the relevance of predictions from nuclear mean-field models
Reinhard, P -G
2015-01-01
This contribution reviews the present status of the Skyrme-Hartree-Fock (SHF) approach as one of the leading self-consistent mean-field models in the physics of atomic nuclei. It starts with a brief summary of the formalism and strategy for proper calibration of the SHF functional. The main emphasis lies on an exploration of the reliability of predictions, particularly in the regime of extrapolations. Various strategies are discussed to explore the statistical and systematic errors of SHF. The strategies are illustrated on examples from actual applications. Variations of model and fit data are used to get an idea about systematic errors. The statistical error is evaluated in straightforward manner by statistical analysis based on $\\chi^2$ fits. This also allows also to evaluate the correlations (covariances) between observables which provides useful insights into the structure of the model and of the fitting strategy.
Magnetic Field Line Random Walk in Isotropic Turbulence with Varying Mean Field
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.
Perturbative Calculation of Quasi-Potential in Non-equilibrium Diffusions: A Mean-Field Example
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 http://arxiv.org/abs/1404.6466" TargetType="URL"/> , 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
A systematic study of even-even nuclei in the nuclear chart by the relativistic mean field theory
Energy Technology Data Exchange (ETDEWEB)
Sumiyoshi, K.; Hirata, D.; Tanihata, I.; Sugahara, Y.; Toki, H. [Institute of Physical and Chemical Research, Wako, Saitama (Japan)
1997-03-01
We study systematically the properties of nuclei in the whole mass range up to the drip lines by the relativistic mean field (RMF) theory with deformations as a microscopic framework to provide the data of nuclear structure in the nuclear chart. The RMF theory is a phenomenological many-body framework, in which the self-consistent equations for nucleons and mesons are solved with arbitrary deformation, and has a potential ability to provide all the essential information of nuclear structure such as masses, radii and deformations together with single particle states and wave functions from the effective lagrangian containing nuclear interaction. As a first step toward the whole project, we study the ground state properties of even-even nuclei ranging from Z=8 to Z=120 up to the proton and neutron drip lines in the RMF theory. We adopt the parameter set TMA, which has been determined by the experimental masses and charge radii in a wide mass range, for the effective lagrangian of the RMF theory. We take into account the axially symmetric deformation using the constrained method on the quadrupole moment. We provide the properties of all even-even nuclei with all the possible ground state deformations extracted from the deformation energy curves by the constrained calculations. By studying the calculated ground state properties systematically, we aim to explore the general trend of masses, radii and deformations in the whole region of the nuclear chart. We discuss the agreement with experimental data and the predictions such as magicness and triaxial deformations beyond the experimental frontier. (author)
Brenna, M; Roca-Maza, X; Bortignon, P F; Moghrabi, K; Grasso, M
2013-01-01
A completely microscopic beyond mean-field approach has been elaborated to overcome some intrinsic limitations of self-consistent mean-field schemes applied to nuclear systems, such as the incapability to produce some properties of single-particle states (e.g. spectroscopic factors), as well as of collective states (e.g. their damping width and their gamma decay to the ground state or to low lying states). Since commonly used effective interactions are fitted at the mean-field level, one should aim at refitting them including the desired beyond mean-field contributions in the refitting procedure. If zero-range interactions are used, divergences arise. We present some steps towards the refitting of Skyrme interactions, for its application in finite nuclei.
International Nuclear Information System (INIS)
The two-plane HUBBARD model, which is a model for some electronic properties of undoped YBCO superconductors as well as displays a MOTT metal-to-insulator transition and a metal-to-band insulator transition, is studied within Dynamical Mean-Field Theory using HIRSCH-FYE Monte Carlo. In order to find the different transitions and distinguish the types of insulator, we calculate the single-particle spectral densities, the self-energies and the optical conductivities. We conclude that there is a continuous transition from MOTT to band insulator. In the second part, ground state properties of a diagonally disordered HUBBARD model is studied using a generalisation of Path Integral Renormalisation Group, a variational method which can also determine low-lying excitations. In particular, the distribution of antiferromagnetic properties is investigated. We conclude that antiferromagnetism breaks down in a percolation-type transition at a critical disorder, which is not changed appreciably by the inclusion of correlation effects, when compared to earlier studies. Electronic and excitation properties at the system sizes considered turn out to primarily depend on the geometry. (orig.)
Magnetic material in mean-field dynamos driven by small scale helical flows
Giesecke, Andre; Gerbeth, Gunter
2014-01-01
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-K\\'arm\\'an-Sodium (VKS) dynamo. For both examined flow configurations the consideration of magnetic material within...
A mean field approach to Coulomb blockade for a disordered assembly of quantum dots
Indian Academy of Sciences (India)
Akashdeep Kamra; Praveen Pathak; Vijay A Singh
2008-02-01
The Coulomb blockade (CB) in quantum dots (QDs) is by now well documented. It has been used to guide the fabrication of single electron transistors. Even the most sophisticated techniques for synthesizing QDs (e.g. MOCVD/MBE) result in an assembly in which a certain amount of disorder is inevitable. On the other hand, theoretical approaches to CB limit themselves to an analysis of a single QD. In the present work we consider two types of disorders: (i) size disorder; e.g. QDs have a distribution of sizes which could be unimodal or bimodal in nature. (ii) Potential disorder with the confining potential assuming a variety of shapes depending on growth condition and external fields. We assume a Gaussian distribution in disorder in both size and potential and employ a simplified mean field theory. To do this we rely on the scaling laws for the CB (also termed as Hubbard ) obtained for an isolated QD [1]. We analyze the distribution in the Hubbard as a consequence of disorder and observe that Coulomb blockade is partially suppressed by the disorder. Further, the distribution in is a skewed Gaussian with enhanced broadening.
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.
Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy*
Kechedzhi, Kostyantyn; Smelyanskiy, Vadim N.
2016-04-01
Real-life quantum computers are inevitably affected by intrinsic noise resulting in dissipative nonunitary dynamics realized by these devices. We consider an open-system quantum annealing algorithm optimized for such a realistic analog quantum device which takes advantage of noise-induced thermalization and relies on incoherent quantum tunneling at finite temperature. We theoretically analyze the performance of this algorithm considering a p -spin model that allows for a mean-field quasiclassical solution and, at the same time, demonstrates the first-order phase transition and exponential degeneracy of states, typical characteristics of spin glasses. We demonstrate that finite-temperature effects introduced by the noise are particularly important for the dynamics in the presence of the exponential degeneracy of metastable states. We determine the optimal regime of the open-system quantum annealing algorithm for this model and find that it can outperform simulated annealing in a range of parameters. Large-scale multiqubit quantum tunneling is instrumental for the quantum speedup in this model, which is possible because of the unusual nonmonotonous temperature dependence of the quantum-tunneling action in this model, where the most efficient transition rate corresponds to zero temperature. This model calculation is the first analytically tractable example where open-system quantum annealing algorithm outperforms simulated annealing, which can, in principle, be realized using an analog quantum computer.
Thermal properties of a rotating nucleus in a fluctuating mean-field approach
International Nuclear Information System (INIS)
The static-path approximation to the path integral representation of partition function provides a natural microscopic basis to deal with thermal fluctuations around mean-field configurations. Using this approach for a one-dimensional cranking hamiltonian with quadrupole-quadrupole interaction term we have studied a few properties like energy, level-density, level-density parameter (a) and moment of inertia as a function of temperature and spin for 64Zn taking it as an illustrative example. We have also investigated the effects of variation in interaction strength on the level density and the parameter a as a function of temperature. The moment of inertia, I, versus rotational frequency, ω, plot shows a sudden rise in the value of I due to the rotation alignment of Og9/2 orbitals at ω ∼ 1.0 MeV for a small temperature T ∼ 0.5 MeV. At high T ∼ 2.0 MeV about 40-45% of each angular momentum is generated by the alignment of Og9/2 orbitals with an interesting result that at ω ∼ 1.0 MeV and spin J ∼ 16 the moment of inertia has almost a constant, temperature-independent value. (orig.)
Impacts of Parameters Adjustment of Relativistic Mean Field Model on Neutron Star Properties
Kasmudin; Sulaksono, A.
Analysis of the parameters adjustment effects in isovector as well as in isoscalar sectors of effective field based relativistic mean field (E-RMF) model in the symmetric nuclear matter and neutron-rich matter properties has been performed. The impacts of the adjustment on slowly rotating neutron star are systematically investigated. It is found that the mass-radius relation obtained from adjusted parameter set G2** is compatible not only with neutron stars masses from 4U 0614+09 and 4U 1636-536, but also with the ones from thermal radiation measurement in RX J1856 and with the radius range of canonical neutron star of X7 in 47 Tuc, respectively. It is also found that the moment inertia of PSR J073-3039A and the strain amplitude of gravitational wave at the Earth's vicinity of PSR J0437-4715 as predicted by the E-RMF parameter sets used are in reasonable agreement with the extracted constraints of these observations from isospin diffusion data.
Peng, J.; Zhao, P. W.
2015-04-01
The self-consistent tilted axis cranking relativistic mean-field (TAC-RMF) theory based on a point-coupling interaction is applied to investigate the observed magnetic and antimagnetic rotations in the nucleus 110Cd . The energy spectra, the relation between the spin and the rotational frequency, the deformation parameters, and the reduced M 1 and E 2 transition probabilities are studied with the various configurations. It is found that the configuration has to be changed to reproduce the energy spectra and the relations between the spin and the rotational frequency for both the magnetic and antimagnetic rotational bands. The shears mechanism for the magnetic rotation and the two-shears-like mechanism for the antimagnetic rotation are examined by investigating the orientation of the neutron and proton angular momenta. The calculated electromagnetic transitions B (M 1 ) and B (E 2 ) are in reasonable agreement with the data, and their tendencies are coincident with the typical characteristics of the magnetic and antimagnetic rotations.
Mass predictions of the relativistic mean-field model with the radial basis function approach
Zheng, J. S.; Wang, N. Y.; Wang, Z. Y.; Niu, Z. M.; Niu, Y. F.; Sun, B.
2014-07-01
The radial basis function (RBF) is a powerful tool to improve mass predictions of nuclear models. By combining the RBF approach with the relativistic mean-field (RMF) model, the systematic deviations between mass predictions of the RMF model and the experimental data are eliminated to a large extent and the resulting rms deviation is reduced from 2.217 to 0.488 MeV. Furthermore, it is found that the RBF approach has a relatively reliable extrapolative power along the distance from the β-stability line except for a large uncertainty around the region at magic number. From the deduced neutron separation energies, we found that the description of the nuclear shell structure and shape transition is also significantly improved by the RBF approach, thus improving agreement with the solar r-process abundances before A =130 and speeding up the r-matter flow. Therefore, a shorter irradiation time is enough to reproduce the solar r-process abundance distribution for the improved RMF mass model, which is closer to the irradiation time for those sophisticated mass models.
Generalized mean-field description of entanglement in dimerized spin systems
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.
Kaon Condensation and Lambda-Nucleon Loop in the Relativistic Mean-Field Approach
Energy Technology Data Exchange (ETDEWEB)
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.
The evaporation residue of 112-134Ba within relativistic mean field theory
International Nuclear Information System (INIS)
The phenomenon of nuclear fission was discovered about 75 years back, still many crucial features of its dynamics are yet to be explained. The exploration is possible when one can view such aspects from the microscopic theoretical point of view. Usually, the common methods used in such investigations are non-relativistic and relativistic self-consistent mean-field theories. These theories are capable for finding the static fission path through entire potential energy landscape spanned over relevant degrees of freedom. The extension of these model calculations for unstable nuclei up to the drip lines is still a challenge. We then choose the relativistic mean theory (RMF) to explore the origin of neck configuration, assumed to be preformed clusters in the fission state, i.e., the formation of elongated neck in the fission state of a nucleus. First of all, we have presented the gross nuclear properties, like the binding energy, deformation parameter β2, charge radius rch and the nucleonic density distributions for the isotopic chain 112-134Ba, using an axially deformed RMF theory with NL3 parameter set
Kaon Condensation and Lambda-Nucleon Loop in the Relativistic Mean-Field Approach
International Nuclear Information System (INIS)
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 Ks state carrying the same quantum numbers as the antikaon. The appearance of the Ks 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-Kbars 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-Kbars condensation for high-energy heavy-ion collisions are briefly mentioned
Kaon condensation and lambda-nucleon loop in the relativistic mean-field approach
International Nuclear Information System (INIS)
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-bar s state carrying the same quantum numbers as the antikaon. The appearance of the K-bar 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-K-bar 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 Λ-mixing effects in the ground state of high-density matter. Implications of KK-bar s condensation for high-energy heavy-ion collisions are briefly mentioned
Energy Technology Data Exchange (ETDEWEB)
Heilmann, D.B.
2007-02-15
The two-plane HUBBARD model, which is a model for some electronic properties of undoped YBCO superconductors as well as displays a MOTT metal-to-insulator transition and a metal-to-band insulator transition, is studied within Dynamical Mean-Field Theory using HIRSCH-FYE Monte Carlo. In order to find the different transitions and distinguish the types of insulator, we calculate the single-particle spectral densities, the self-energies and the optical conductivities. We conclude that there is a continuous transition from MOTT to band insulator. In the second part, ground state properties of a diagonally disordered HUBBARD model is studied using a generalisation of Path Integral Renormalisation Group, a variational method which can also determine low-lying excitations. In particular, the distribution of antiferromagnetic properties is investigated. We conclude that antiferromagnetism breaks down in a percolation-type transition at a critical disorder, which is not changed appreciably by the inclusion of correlation effects, when compared to earlier studies. Electronic and excitation properties at the system sizes considered turn out to primarily depend on the geometry. (orig.)
Morawetz, K.
2013-08-01
The general possible form of mean-field parametrization in a running frame in terms of current, energy, and density functionals is examined under the restrictions of Galilean invariance. It is found that only two density-dependent parameters remain which are usually condensed in a position-dependent effective mass and the self-energy formed by current and mass. The position-dependent mass induces a position-dependent local current, which is identified for different nonlinear frames. In a second step the response to an external perturbation and relaxation towards a local equilibrium is investigated. The response function is found to be universal in the sense that the actual parametrization of the local equilibrium does not matter and is eliminated from the theory due to the conservation laws. The explicit form of the response with respect to density, momentum, and energy is derived. The compressibility sum rule as well as the sum rule by first- and third-order frequency moments are proved analytically to be fulfilled simultaneously. The results are presented for Bose or Fermi systems in one, two, and three dimensions.
Nuclear mean field and double-folding model of the nucleus-nucleus optical potential
Khoa, Dao T; Loan, Doan Thi; Loc, Bui Minh
2016-01-01
Realistic density dependent CDM3Yn versions of the M3Y interaction have been used in an extended Hartree-Fock (HF) calculation of nuclear matter (NM), with the nucleon single-particle potential determined from the total NM energy based on the Hugenholtz-van Hove theorem that gives rise naturally to a rearrangement term (RT). Using the RT of the single-nucleon potential obtained exactly at different NM densities, the density- and energy dependence of the CDM3Yn interactions was modified to account properly for both the RT and observed energy dependence of the nucleon optical potential. Based on a local density approximation, the double-folding model of the nucleus-nucleus optical potential has been extended to take into account consistently the rearrangement effect and energy dependence of the nuclear mean-field potential, using the modified CDM3Yn interactions. The extended double-folding model was applied to study the elastic $^{12}$C+$^{12}$C and $^{16}$O+$^{12}$C scattering at the refractive energies, wher...
Stable oscillations of a predator-prey probabilistic cellular automaton: a mean-field approach
Energy Technology Data Exchange (ETDEWEB)
Tome, Tania; Carvalho, Kelly C de [Instituto de FIsica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970 Sao Paulo (Brazil)
2007-10-26
We analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator-prey system. The individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired by the processes of the Lotka-Volterra model. Two levels of mean-field approximations are set up. The simple approximation is equivalent to an extended patch model, a simple metapopulation model with patches colonized by prey, patches colonized by predators and empty patches. This approximation is capable of describing the limited available space for species occupancy. The pair approximation is moreover able to describe two types of coexistence of prey and predators: one where population densities are constant in time and another displaying self-sustained time oscillations of the population densities. The oscillations are associated with limit cycles and arise through a Hopf bifurcation. They are stable against changes in the initial conditions and, in this sense, they differ from the Lotka-Volterra cycles which depend on initial conditions. In this respect, the present model is biologically more realistic than the Lotka-Volterra model.
Multidimensionally-constrained relativistic mean-field study of triple-humped barriers in actinides
Zhao, Jie; Vretenar, Dario; Zhao, En-Guang; Zhou, Shan-Gui
2014-01-01
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 one was predicted by macroscopic-microscopic model calculations in the 1970s but contradictory results were later obtained with a number of different models. In this paper, triple-humped barriers in actinide nuclei are investigated with covariant density functional theory (CDFT). Calculations are performed using the multidimensionally-constrained relativistic mean field (MDC-RMF) model, with functionals PC-PK1 and DD-ME2 in the particle-hole channel, while pairing correlations are treated in the BCS approximation with a separable and finite range pairing force. Two-dimensional PES's of $^{226,228,230,232}$Th and $^{232,234,236,238}$U are mapped and the third minima on these surfaces are located. In a second step the one-dimensional potential energy curves along the fission path are analyzed in detail and the energies of the second ...
Allen, James T; Richardson, Chris T; Ferland, Gary J; Baldwin, Jack A
2013-01-01
We present an analysis of the optical spectra of narrow emission-line galaxies, based on mean field independent component analysis (MFICA). Samples of galaxies were drawn from the Sloan Digital Sky Survey (SDSS) and used to generate compact sets of `continuum' and `emission-line' component spectra. These components can be linearly combined to reconstruct the observed spectra of a wider sample of galaxies. Only 10 components - five continuum and five emission line - are required to produce accurate reconstructions of essentially all narrow emission-line galaxies; the median absolute deviations of the reconstructed emission-line fluxes, given the signal-to-noise ratio (S/N) of the observed spectra, are 1.2-1.8 sigma for the strong lines. After applying the MFICA components to a large sample of SDSS galaxies we identify the regions of parameter space that correspond to pure star formation and pure active galactic nucleus (AGN) emission-line spectra, and produce high S/N reconstructions of these spectra. The phys...
T-->0 mean-field population dynamics approach for the random 3-satisfiability problem.
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
Kaon Condensation and Lambda-Nucleon Loop in the Relativistic Mean-Field Approach
Maruyama, T; Tatsumi, T; Tsushima, K; Thomas, A W; Maruyama, Tomoyuki; Muto, Takumi; Tatsumi, Toshitaka; Tsushima, Kazuo; Thomas, Anthony W.
2005-01-01
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 ${\\bar K}_s$ state carrying the same quantum numbers as the antikaon. The appearance of the ${\\bar K}_s$ 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 $K$-${\\bar K}_s$ 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 $K{\\bar K}_s$ condensation for high-energy heavy-ion collisions are briefly mentioned.
Properties and structure of N=Z nuclei within relativistic mean field theory
Institute of Scientific and Technical Information of China (English)
GAO Yuan; DONG Jian-Min; ZHANG Hong-Fei; ZUO Wei; LI Jun-Qing
2009-01-01
The axially deformed relativistic mean field theory with the force NLSH has been performed in the blocked BCS approximation to investigate the properties and structure of N=Z nuclei from Z=20 to Z=48.Some ground state quantities such as binding energies, quadrupole deformations, one/two-nucleon separation energies, root-mean-square (rms) radii of charge and neutron, and shell gaps have been calculated.The results suggest that large deformations can be found in medium-heavy nuclei with N=Z=38-42.The charge and neutron rms radii increase rapidly beyond the magic number N=Z=28 until Z=42 with increasing nucleon number, which is similar to isotope shift, yet beyond Z=42, they decrease dramatically as the structure changes greatly from Z=42 to Z=43.The evolution of shell gaps with proton number Z can be clearly observed.Besides the appearance of possible new shell closures, some conventional shell closures have been found to disappear in some region.In addition, we found that the Coulomb interaction is not strong enough to breakdown the shell structure of protons in the current region.
Dynamical mean field theory of the repulsive BCS+U model
Energy Technology Data Exchange (ETDEWEB)
Park, Kwon [School of Physics, Korea Institute for Advanced Study, Seoul 130-722 (Korea, Republic of)], E-mail: kpark@kias.re.kr
2009-07-15
The Gutzwiller-projected BCS Hamiltonian is a useful model for high-temperature superconductivity due to its equivalence to the Heisenberg model at half filling and a close connection to the t-J model at moderate doping. In this work, a dynamical mean field theory (DMFT) is developed for the BCS Hamiltonian with d-wave pairing subject to on-site repulsive interaction, U, which we call the BCS+U model. The large-U limit corresponds to the Gutzwiller-projected BCS Hamiltonian. It is shown that the equivalence between the Heisenberg and the Gutzwiller-projected BCS model is a manifestation of a broader duality in the BCS+U model: for any finite U, the local dynamics of the BCS+U model is dual at half filling with respect to the exchange between the hopping parameter, t, and the pairing amplitude, {delta}. It is explicitly demonstrated in our DMFT analysis that the real superconducting gap, determined from the sharp coherence peaks in the local density of states, shows strong renormalization from its bare value as a function of U.
Multigrid Hirsch-Fye quantum Monte Carlo solver for dynamical mean-field theory
International Nuclear Information System (INIS)
The dynamical mean-field theory (DMFT) is a nonperturbative approach to Hubbard-type models in which an impurity model has to be solved self-consistently. This is possible nonperturbatively using the Hirsch-Fye quantum Monte-Carlo (HF-QMC) algorithm which introduces an imaginary-time discretization Δτ. The associated Trotter error impacts all ''raw'' HF-QMC results including phase boundaries, Green functions, spectra, and scalar observables such as energies and quasiparticle weights. Unbiased estimates of scalar observables can be derived from HF-QMC data by extrapolation Δτ→ 0, with high precision and efficiency. However, this a posteriori correction of the Trotter error is problematic close to phase boundaries and could so far not be applied to Green functions and spectra. In this talk, I show how numerically exact Green functions can be extrapolated from HF-QMC estimates and construct a multigrid HF-QMC algorithm which eliminates the discretization error within the DMFT self-consistency cycle. In contrast to conventional HF-QMC, the multigrid algorithm converges to the numerically exact fixed point(s) and allows for the direct determination of phase boundaries without further extrapolation. It extends the useful range of Δτ values and yields unbiased estimates of observables with high precision and efficiency, even close to phase transitions
Study of neutron magic drip-line nuclei within relativistic mean-field plus BCS approach
International Nuclear Information System (INIS)
Encouraged by the success of relativistic mean-field plus BCS (RMF + BCS) approach for the description of the ground state properties of the chains of isotopes of proton magic nuclei with proton number Z = 8, 20, 28, 50 and 82 as well as those of proton sub-magic nuclei with Z = 40, we have further employed it, in an analogous manner, for a detailed calculations of the ground state properties of the neutron magic isotones with neutron number N = 8, 20, 28, 50, 82 and 126 as well as those of neutron sub-magic isotones with N = 40 using the TMA force parametrizations in order to explore low lying resonance and other exotic phenomenon near drip-lines. The results of these calculations for wave function, single particle pairing gaps etc. are presented here to demonstrate the general validity of our RMF + BCS approach. It is found that, in some of the proton-rich nuclei in the vicinity of the proton drip-line, the main contribution to the pairing correlations is provided by the low-lying resonant states, in addition to the contributions coming from the states close to the Fermi surface, which results extended proton drip-line for isotonic chain. (author)
Effective meson masses in a non-linear relativistic mean field model
International Nuclear Information System (INIS)
Full text: Relativistic mean field theories, with (σ, ω)-fields mediating the baryonic interaction, reproduce many important properties of the symmetric nuclear matter. This kind of models, where the nonlinear Walecka's model is a prototype, also has been widely applied to the description of the hadron phase for the thermodynamic treatment of the hadron to quark-gluon phase transition. However the conventional theory does not consider the interaction between the mesonic fields. This kind of interaction could be relevant when applying the theory to the situation involving nucleon and antinuclear matter. In this work we discuss the inclusion of meson-meson interaction in the theory in order to investigate the properties of nucleon-antinucleon matter at high temperature and low net baryonic density regime. This situation is of interest in describing the highest energy density states of the heavy ion collision at ultra-relativistic energies. Our present study includes the interaction between σ-ω mesons for different net baryonic densities by changing the ratio of nucleons to antinucleons densities. The particular scenario with null net baryonic density (the so-called 'no-sea' approximation) was already studied in Refs., but without taking into account the interaction between mesons. In the present work, with the interaction between meson included, we also determine the effective masses of the (σ, ω)-fields. (author)
A mean-field theory on the differential capacitance of asymmetric ionic liquid electrolytes
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.
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.
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.
Lu, Bing-Nan; Zhao, En-Guang; Zhou, Shan-Gui
2013-01-01
In this contribution we present some results of potential energy surfaces of actinide and transfermium nuclei from multi-dimensional constrained relativistic mean field (MDC-RMF) models. Recently we developed multi-dimensional constrained covariant density functional theories (MDC-CDFT) in which all shape degrees of freedom $\\beta_{\\lambda\\mu}$ with even $\\mu$ are allowed and the functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the non-linear or density-dependent couplings. In MDC-RMF models, the pairing correlations are treated with the BCS method. With MDC-RMF models, the potential energy surfaces of even-even actinide nuclei were investigated and the effect of triaxiality on the fission barriers in these nuclei was discussed. The non-axial reflection-asymmetric $\\beta_{32}$ shape in some transfermium nuclei with $N=150$, namely $^{246}$Cm, $^{248}$Cf, $^{250}$Fm, and $^{252}$No were also studied.
van Albada, S J; Gray, R T; Drysdale, P M; Robinson, P A
2009-04-21
Neuronal correlates of Parkinson's disease (PD) include a shift to lower frequencies in the electroencephalogram (EEG) and enhanced synchronized oscillations at 3-7 and 7-30 Hz in the basal ganglia, thalamus, and cortex. This study describes the dynamics of a recent physiologically based mean-field model of the basal ganglia-thalamocortical system, and shows how it accounts for many key electrophysiological correlates of PD. Its detailed functional connectivity comprises partially segregated direct and indirect pathways through two populations of striatal neurons, a hyperdirect pathway involving a corticosubthalamic projection, thalamostriatal feedback, and local inhibition in striatum and external pallidum (GPe). In a companion paper, realistic steady-state firing rates were obtained for the healthy state, and after dopamine loss modeled by weaker direct and stronger indirect pathways, reduced intrapallidal inhibition, lower firing thresholds of the GPe and subthalamic nucleus (STN), a stronger projection from striatum to GPe, and weaker cortical interactions. Here it is shown that oscillations around 5 and 20 Hz can arise with a strong indirect pathway, which also causes increased synchronization throughout the basal ganglia. Furthermore, increased theta power with progressive nigrostriatal degeneration is correlated with reduced alpha power and peak frequency, in agreement with empirical results. Unlike the hyperdirect pathway, the indirect pathway sustains oscillations with phase relationships that coincide with those found experimentally. Alterations in the responses of basal ganglia to transient stimuli accord with experimental observations. Reduced cortical gains due to both nigrostriatal and mesocortical dopamine loss lead to slower changes in cortical activity and may be related to bradykinesia. Finally, increased EEG power found in some studies may be partly explained by a lower effective GPe firing threshold, reduced GPe-GPe inhibition, and/or weaker
Macromolecular Stabilization by Excluded Cosolutes: Mean Field Theory of Crowded Solutions.
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.
MAGNETIC FIELD LINE RANDOM WALK IN ISOTROPIC TURBULENCE WITH ZERO MEAN FIELD
International Nuclear Information System (INIS)
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 << 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
MAGNETIC FIELD LINE RANDOM WALK IN ISOTROPIC TURBULENCE WITH ZERO MEAN FIELD
Energy Technology Data Exchange (ETDEWEB)
Sonsrettee, W.; Ruffolo, D.; Snodin, A. P.; Wongpan, P. [Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400 (Thailand); Subedi, P.; Matthaeus, W. H. [Bartol Research Institute, University of Delaware, Newark, DE 19716 (United States); Chuychai, P., E-mail: bturbulence@gmail.com, E-mail: david.ruf@mahidol.ac.th, E-mail: andrew.snodin@gmail.com, E-mail: pat.wongpan@postgrad.otago.ac.nz, E-mail: piyanate@gmail.com, E-mail: prasub@udel.edu, E-mail: whm@udel.edu [Thailand Center of Excellence in Physics, CHE, Ministry of Education, Bangkok 10400 (Thailand)
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.
Magnetic Field Line Random Walk in Isotropic Turbulence with Zero Mean Field
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.
Double Dynamo Signatures in a Global MHD Simulation and Mean-field Dynamos
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.
The ground state energy of the mean field spin glass model
Koukiou, Flora
2008-01-01
From the study of a functional equation of Gibbs measures we calculate the limiting free energy of the Sherrington-Kirkpatrick spin glass model at a particular value of (low) temperature. This implies the following lower bound for the ground state energy $\\epsilon_0$ \\[\\epsilon_0\\geq -0.7833\\cdots,\\] close to the replica symmetry breaking and numerical simulations values.
The ground state energy of the mean field spin glass model
Koukiou, Flora
2008-01-01
From the study of a functional equation of Gibbs measures we calculate the limiting free energy of the Sherrington-Kirkpatrick spin glass model at a particular value of (low) temperature. This implies the following lower bound for the ground state energy $\\epsilon_0$ \\[\\epsilon_0\\geq -0.7833...,\\] close to the replica symmetry breaking and numerical simulations values.
Hartree-Fock mean-field theory for trapped dirty bosons
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.
Mean-field theory of atomic self-organization in optical cavities
Jäger, Simon B.; Schütz, Stefan; Morigi, Giovanna
2016-01-01
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 fu...
Multidimensionally constrained relativistic mean-field study of triple-humped barriers in actinides
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
An effective correlated mean-field theory applied in the spin-1/2 Ising ferromagnetic model
Energy Technology Data Exchange (ETDEWEB)
Roberto Viana, J.; Salmon, Octávio R. [Universidade Federal do Amazonas – UFAM, Manaus 69077-000, AM (Brazil); Ricardo de Sousa, J. [Universidade Federal do Amazonas – UFAM, Manaus 69077-000, AM (Brazil); National Institute of Science and Technology for Complex Systems, Universidade Federal do Amazonas, 3000, Japiim, 69077-000 Manaus, AM (Brazil); Neto, Minos A.; Padilha, Igor T. [Universidade Federal do Amazonas – UFAM, Manaus 69077-000, AM (Brazil)
2014-11-15
We developed a new treatment for mean-field theory applied in spins systems, denominated effective correlated mean-field (ECMF). We apply this theory to study the spin-1/2 Ising ferromagnetic model with nearest-neighbor interactions on a square lattice. We use clusters of finite sizes and study the criticality of the ferromagnetic system, where we obtain a convergence of critical temperature for the value k{sub B}T{sub c}/J≃2.27905±0.00141. Also the behavior of magnetic and thermodynamic properties, using the condition of minimum energy of the physical system is obtained. - Highlights: • We developed spin models to study real magnetic systems. • We study the thermodynamic and magnetic properties of the ferromagnetism. • We enhanced a mean-field theory applied in spins models.
Energy Technology Data Exchange (ETDEWEB)
Rodrigues, Serafim [Department of Mathematical Sciences, Loughborough University, Leicestershire, LE11 3TU (United Kingdom); Terry, John R. [Department of Mathematical Sciences, Loughborough University, Leicestershire, LE11 3TU (United Kingdom)]. E-mail: j.r.terry@lboro.ac.uk; Breakspear, Michael [Black Dog Institute, Randwick, NSW 2031 (Australia); School of Psychiatry, UNSW, NSW 2030 (Australia)
2006-07-10
In this Letter, the genesis of spike-wave activity-a hallmark of many generalized epileptic seizures-is investigated in a reduced mean-field model of human neural activity. Drawing upon brain modelling and dynamical systems theory, we demonstrate that the thalamic circuitry of the system is crucial for the generation of these abnormal rhythms, observing that the combination of inhibition from reticular nuclei and excitation from the cortical signal, interplay to generate the spike-wave oscillation. The mechanism revealed provides an explanation of why approaches based on linear stability and Heaviside approximations to the activation function have failed to explain the phenomena of spike-wave behaviour in mean-field models. A mathematical understanding of this transition is a crucial step towards relating spiking network models and mean-field approaches to human brain modelling.
International Nuclear Information System (INIS)
In this Letter, the genesis of spike-wave activity-a hallmark of many generalized epileptic seizures-is investigated in a reduced mean-field model of human neural activity. Drawing upon brain modelling and dynamical systems theory, we demonstrate that the thalamic circuitry of the system is crucial for the generation of these abnormal rhythms, observing that the combination of inhibition from reticular nuclei and excitation from the cortical signal, interplay to generate the spike-wave oscillation. The mechanism revealed provides an explanation of why approaches based on linear stability and Heaviside approximations to the activation function have failed to explain the phenomena of spike-wave behaviour in mean-field models. A mathematical understanding of this transition is a crucial step towards relating spiking network models and mean-field approaches to human brain modelling
Solving the inverse Ising problem by mean-field methods in a clustered phase space with many states
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).
DEFF Research Database (Denmark)
Sakellariou, Jason; Roudi, Yasser; Mezard, Marc;
2012-01-01
We study how the degree of symmetry in the couplings influences the performance of three mean field methods used for solving the direct and inverse problems for generalized Sherrington-Kirkpatrick models. In this context, the direct problem is predicting the potentially time-varying magnetizations....... The three theories include the first and second order Plefka expansions, referred to as naive mean field (nMF) and TAP, respectively, and a mean field theory which is exact for fully asymmetric couplings. We call the last of these simply MF theory. We show that for the direct problem, nMF performs worse...... than the other two approximations, TAP outperforms MF when the coupling matrix is nearly symmetric, while MF works better when it is strongly asymmetric. For the inverse problem, MF performs better than both TAP and nMF, although an ad hoc adjustment of TAP can make it comparable to MF. For high...
International Nuclear Information System (INIS)
Fluctuations in the Sun's magnetic activity, including episodes of grand minima such as the Maunder minimum have important consequences for space and planetary environments. However, the underlying dynamics of such extreme fluctuations remain ill-understood. Here, we use a novel mathematical model based on stochastically forced, non-linear delay differential equations to study solar cycle fluctuations in which time delays capture the physics of magnetic flux transport between spatially segregated dynamo source regions in the solar interior. Using this model, we explicitly demonstrate that the Babcock-Leighton poloidal field source based on dispersal of tilted bipolar sunspot flux, alone, cannot recover the sunspot cycle from a grand minimum. We find that an additional poloidal field source effective on weak fields—e.g., the mean-field α effect driven by helical turbulence—is necessary for self-consistent recovery of the sunspot cycle from grand minima episodes.
Hazra, Soumitra; Nandy, Dibyendu
2013-01-01
Fluctuations in the Sun's magnetic activity, including episodes of grand minima such as the Maunder minimum have important consequences for space and planetary environments. However, the underlying dynamics of such extreme fluctuations remain ill-understood. Here we use a novel mathematical model based on stochastically forced, non-linear delay differential equations to study solar cycle fluctuations, in which, time delays capture the physics of magnetic flux transport between spatially segregated dynamo source regions in the solar interior. Using this model we explicitly demonstrate that the Babcock-Leighton poloidal field source based on dispersal of tilted bipolar sunspot flux, alone, can not recover the sunspot cycle from a grand minimum. We find that an additional poloidal field source effective on weak fields--the mean-field alpha-effect driven by helical turbulence--is necessary for self-consistent recovery of the sunspot cycle from grand minima episodes.
Energy Technology Data Exchange (ETDEWEB)
Snoek, M; Titvinidze, I; Toeke, C; Hofstetter, W [Institut fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, 60438 Frankfurt/Main (Germany); Byczuk, K [Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute for Physics, University of Augsburg, 86135 Augsburg (Germany)], E-mail: snoek@itp.uni-frankfurt.de
2008-09-15
We apply dynamical mean-field theory to strongly interacting fermions in an inhomogeneous environment. With the help of this real-space dynamical mean-field theory (R-DMFT) we investigate antiferromagnetic states of repulsively interacting fermions with spin1/2 in a harmonic potential. Within R-DMFT, antiferromagnetic order is found to be stable in spatial regions with total particle density close to one, but persists also in parts of the system where the local density significantly deviates from half filling. In systems with spin imbalance, we find that antiferromagnetism is gradually suppressed and phase separation emerges beyond a critical value of the spin imbalance.
Mean-field model of interaction between bright vortex solitons in Bose-Einstein condensates
International Nuclear Information System (INIS)
Using the explicit numerical solution of the axially symmetric Gross-Pitaevskii equation we study the dynamics of interaction among vortex solitons in a rotating matter-wave bright soliton train in a radially trapped and axially free Bose-Einstein condensate to understand certain features of the experiment by Strecker et al (2002 Nature 417 150). In a soliton train, solitons of opposite phase (phase δ = π) repel and stay apart without changing shape; solitons with π = 0 attract, interact and coalesce, but eventually come out; solitons with a general δ usually repel but interact inelastically by exchanging matter. We study this and suggest future experiments with vortex solitons
Kalikmanov, V.I.; De Leeuw, S.W.
2002-01-01
We propose a self-consistent mean-field lattice-gas theory of intercalation compounds based on effective interactions between interstitials in the presence of the host atoms. In addition to short-range screened Coulomb repulsions, usually discussed in the lattice gas models, the present theory takes
Waldorp, Lourens J
2016-01-01
It was recently shown how graphs can be used to provide descriptions of psychopathologies, where symptoms of, say, depression, affect each other and certain configurations determine whether someone could fall into a sudden depression. To analyse changes over time and characterise possible future behaviour is rather difficult for large graphs. We describe the dynamics of networks using one-dimensional discrete time dynamical systems theory obtained from a mean field approach to (elementary) probabilistic cellular automata (PCA). Often the mean field approach is used on a regular graph (a grid or torus) where each node has the same number of edges and the same probability of becoming active. We show that we can use variations of the mean field of the grid to describe the dynamics of the PCA on a random and small-world graph. Bifurcation diagrams for the mean field of the grid, random, and small-world graphs indicate possible phase transitions for certain parameter settings. Extensive simulations indicate for di...
Fraaije, JGEM; vanVlimmeren, BAC; Maurits, NM; Postma, M; Evers, OA; Hoffmann, C; Altevogt, P; GoldbeckWood, G
1997-01-01
In this paper we discuss a new generalized time-dependent Ginzburg-Landau theory for the numerical calculation of polymer phase separation kinetics in 3D. The thermodynamic forces are obtained by a mean-field density functional method, using a Gaussian chain as a molecular model. The method is espec
Absence of the Twisted Superfluid State in a mean field model of bosons on a Honeycomb Lattice
Choudhury, Sayan; Mueller, Erich J.
2012-01-01
Motivated by recent observations (P. Soltan-Panahi {\\it et al.}, Nature Physics {\\bf 8}, 71-75 (2012)), we study the stability of a Bose-Einstein Condensate within a spin-dependent honeycomb lattice towards forming a "Twisted Superfluid" state. Our exhaustive numerical search fails to find this phase, pointing to possible non-mean field physics.
Building relativistic mean field models for finite nuclei and neutron stars
Chen, Wei-Chia; Piekarewicz, J.
2014-10-01
Background: Theoretical approaches based on density functional theory provide the only tractable method to incorporate the wide range of densities and isospin asymmetries required to describe finite nuclei, infinite nuclear matter, and neutron stars. Purpose: A relativistic energy density functional (EDF) is developed to address the complexity of such diverse nuclear systems. Moreover, a statistical perspective is adopted to describe the information content of various physical observables. Methods: We implement the model optimization by minimizing a suitably constructed χ2 objective function using various properties of finite nuclei and neutron stars. The minimization is then supplemented by a covariance analysis that includes both uncertainty estimates and correlation coefficients. Results: A new model, "FSUGold2," is created that can well reproduce the ground-state properties of finite nuclei, their monopole response, and that accounts for the maximum neutron-star mass observed up to date. In particular, the model predicts both a stiff symmetry energy and a soft equation of state for symmetric nuclear matter, suggesting a fairly large neutron-skin thickness in Pb208 and a moderate value of the nuclear incompressibility. Conclusions: We conclude that without any meaningful constraint on the isovector sector, relativistic EDFs will continue to predict significantly large neutron skins. However, the calibration scheme adopted here is flexible enough to create models with different assumptions on various observables. Such a scheme—properly supplemented by a covariance analysis—provides a powerful tool to identify the critical measurements required to place meaningful constraints on theoretical models.
Valor, A; Bonche, P
2000-01-01
We present in this paper the general framework of a method which permits to restore the rotational and particle number symmetries of wave functions obtained in Skyrme HF+BCS calculations. This restoration is nothing but a projection of mean-field intrinsic wave functions onto good particle number and good angular momentum. The method allows also to mix projected wave functions. Such a configuration mixing is discussed for sets of HF+BCS intrinsic states generated in constrained calculations with suitable collective variables. This procedure gives collective states which are eigenstates of the particle number and the angular momentum operators and between which transition probabilities are calculated. An application to 24Mg is presented, with mean-field wave functions generated by axial quadrupole constraints. Theoretical spectra and transition probabilities are compared to the experiment.