Many-Body Mean-Field Equations: Parallel implementation
International Nuclear Information System (INIS)
Vallieres, M.; Umar, S.; Chinn, C.; Strayer, M.
1993-01-01
We describe the implementation of Hartree-Fock Many-Body Mean-Field Equations on a Parallel Intel iPSC/860 hypercube. We first discuss the Nuclear Mean-Field approach in physical terms. Then we describe our parallel implementation of this approach on the Intel iPSC/860 hypercube. We discuss and compare the advantages and disadvantages of the domain partition versus the Hilbert space partition for this problem. We conclude by discussing some timing experiments on various computing platforms
Nonlocal structures: bilocal photon
International Nuclear Information System (INIS)
Clapp, R.E.
1980-01-01
It is postulated that all particles and fields are built from a single primitive field, a massless fermion with a σ spin of one-half. Two helicities are embodied in a tau spin of one-half. The vacuum is an open Fermi sea whose height is a wave number kappa. Elementary particles are structures having the form of standing-wave systems floating on the vacuum sea. A bilocal photon starts with a function describing two primitive quanta with parallel σ spin and opposite tau spin. A centroid-time wave equation then couples-in and infinite set of orthogonal functions. The introduction of an operator Qlambda permits the reduction of the infinite secular determinant to finite six-by-six determinant. Solutions are obtained describing photons with right-handed and left-handed polarizations. Electric and magnetic field vectors satisfying the vacuum Maxwell equations, are obtained from a bilocal Hertz vector. (author)
Parallel implementation of many-body mean-field equations
International Nuclear Information System (INIS)
Chinn, C.R.; Umar, A.S.; Vallieres, M.; Strayer, M.R.
1994-01-01
We describe the numerical methods used to solve the system of stiff, nonlinear partial differential equations resulting from the Hartree-Fock description of many-particle quantum systems, as applied to the structure of the nucleus. The solutions are performed on a three-dimensional Cartesian lattice. Discretization is achieved through the lattice basis-spline collocation method, in which quantum-state vectors and coordinate-space operators are expressed in terms of basis-spline functions on a spatial lattice. All numerical procedures reduce to a series of matrix-vector multiplications and other elementary operations, which we perform on a number of different computing architectures, including the Intel Paragon and the Intel iPSC/860 hypercube. Parallelization is achieved through a combination of mechanisms employing the Gram-Schmidt procedure, broadcasts, global operations, and domain decomposition of state vectors. We discuss the approach to the problems of limited node memory and node-to-node communication overhead inherent in using distributed-memory, multiple-instruction, multiple-data stream parallel computers. An algorithm was developed to reduce the communication overhead by pipelining some of the message passing procedures
Non-degeneracy, Mean Field Equations and the Onsager Theory of 2D Turbulence
Bartolucci, Daniele; Jevnikar, Aleks; Lee, Youngae; Yang, Wen
2018-04-01
The understanding of some large energy, negative specific heat states in the Onsager description of 2D turbulence seem to require the analysis of a subtle open problem about bubbling solutions of the mean field equation. Motivated by this application we prove that, under suitable non-degeneracy assumptions on the associated m-vortex Hamiltonian, the m-point bubbling solutions of the mean field equation are non-degenerate as well. Then we deduce that the Onsager mean field equilibrium entropy is smooth and strictly convex in the high energy regime on domains of second kind.
On the initial conditions of time-dependent mean-field equations of evolution. Pt. 2
International Nuclear Information System (INIS)
Troudet, T.; Paris-11 Univ., 91 - Orsay
1986-01-01
We analyze the problem so far untouched of determining the initial mean-field wavefunction in the context of zero-temperature mean-field descriptions of time-dependent expectation values and quantum fluctuations of nuclear observables. The nucleus, at zero temperature, is taken to be in a low-lying excited many-body eigenstate and is approximated by the corresponding RPA wavefunction as a continuous superposition of coherent states (i.e. Slater determinants). A generating function Gsub(A)(lambda) for time-dependent expectation values and quantum fluctuations is constructed within the formalism of functional integration. By applying the saddle-point method to the functional action of Gsub(A)(lambda) and then taking its lambda-derivatives, we recover the well-known TDHF theory and propose a simple determination of the initial Slater determinant for an appropriate mean-field description of time-dependent expectation values. The analog mean-field description of quadratic-quantum fluctuations proceeds similarly and in addition includes the contribution of the uncorrelated TDHF-RPA phonons coupled to collective excitations of the initial (static) mean-field configuration. When the collective TDHF-RPA excitations are solely taken into account, we obtain an improved version of the Balian-Veneroni dispersion formula by showing how to determine the initial mean-field wavefunction. By first taking the lambda-derivatives of Gsub(A)(lambda) before applying the saddle-point method, the initial mean-field wavefunction is found to be non-linearly coupled to the mean-field dynamics themselves. In return, and in contrast to the first quantization scheme, these both depend non-trivially upon the observable A being measured so that approximations must be proposed to simplify the resulting mean-field equations. (orig.)
International Nuclear Information System (INIS)
Bender, C.M.; Cooper, F.
1985-01-01
An apparent difference between formulating mean field perturbation theory for lambdaphi 4 field theory via path integrals or via functional differential equations when there are external sources present is shown not to exist when mean field theory is considered as the N = 1 limit of the 0(N)lambdaphi 4 field theory. A simply method is given for determining the 1/N expansion for the Green's functions in the presence of external sources by directly solving the functional differential equations order by order in 1/N. The 1/N expansion for the effective action GAMMA(phi,chi) is obtained by directly integrating the functional differential equations for the fields phi and chi (equivalent1/2lambda/Nphi/sub α/phi/sup α/-μ 2 ) in the presence of two external sources j = -deltaGAMMA/deltaphi, S = -deltaGAMMA/deltachi
Energy Technology Data Exchange (ETDEWEB)
Haertle, Rainer [Institut fuer Theoretische Physik, Georg-August-Universitaet Goettingen, Goettingen (Germany); Millis, Andrew J. [Department of Physics, Columbia University, New York (United States)
2016-07-01
We present a new impurity solver for real-time and nonequilibrium dynamical mean field theory applications, based on the recently developed hierarchical quantum master equation approach. Our method employs a hybridization expansion of the time evolution operator, including an advanced, systematic truncation scheme. Convergence to exact results for not too low temperatures has been demonstrated by a direct comparison to quantum Monte Carlo simulations. The approach is time-local, which gives us access to slow dynamics such as, e.g., in the presence of magnetic fields or exchange interactions and to nonequilibrium steady states. Here, we present first results of this new scheme for the description of strongly correlated materials in the framework of dynamical mean field theory, including benchmark and new results for the Hubbard and periodic Anderson model.
Nuclear structure information studied through Dirac equation with deformed mean fields
International Nuclear Information System (INIS)
Dudek, J.
2000-01-01
Complete text of publication follows. Relativistic mean-field theory provides a formal expression for the Dirac equation for the nucleonic motion in an atomic nucleus. The 'potentials' within such a formalism are given in terms of the meson fields, the latter obtained through a coupled system of equations of the Klein-Grodon type. Usually the whole system is being solved by using a Hartree approximation by employing an iterative selfonsistent algorithms. On a more phenomenological level one can parametrize the potentials that enter into a Dirac equation rather than obtain the selfconsistently; such a simplification was suggested some time ago by the Munich group. We introduce a Woods-Saxon type parametrisation and verify by a non-linear search routine what are the 'best fit potential parameters' that reproduce the single particle excitations in the double-magic spherical nuclei as well as the band-head properties in some hundreds of deformed nuclei. Next, by introducing a low-energy reduction of the Dirac equation, one may obtain in a natural way a Pauli Schrodinger type equation with a position dependent effective mass. The role of the corresponding term in a description of single particle energies of the nucleons is illustrated and the implications for the cranking equation are discussed in some detail. (author)
Out-of-equilibrium dynamical mean-field equations for the perceptron model
Agoritsas, Elisabeth; Biroli, Giulio; Urbani, Pierfrancesco; Zamponi, Francesco
2018-02-01
Perceptrons are the building blocks of many theoretical approaches to a wide range of complex systems, ranging from neural networks and deep learning machines, to constraint satisfaction problems, glasses and ecosystems. Despite their applicability and importance, a detailed study of their Langevin dynamics has never been performed yet. Here we derive the mean-field dynamical equations that describe the continuous random perceptron in the thermodynamic limit, in a very general setting with arbitrary noise and friction kernels, not necessarily related by equilibrium relations. We derive the equations in two ways: via a dynamical cavity method, and via a path-integral approach in its supersymmetric formulation. The end point of both approaches is the reduction of the dynamics of the system to an effective stochastic process for a representative dynamical variable. Because the perceptron is formally very close to a system of interacting particles in a high dimensional space, the methods we develop here can be transferred to the study of liquid and glasses in high dimensions. Potentially interesting applications are thus the study of the glass transition in active matter, the study of the dynamics around the jamming transition, and the calculation of rheological properties in driven systems.
Second relativistic mean field and virial equation of state for astrophysical simulations
International Nuclear Information System (INIS)
Shen, G.; Horowitz, C. J.; 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 nonideal gas for matter at low density. For this EOS we use the RMF effective interaction FSUGold, whereas our earlier EOS was based on the RMF effective interaction NL3. The FSUGold interaction has a lower pressure at high densities compared to the NL3 interaction. We calculate the resulting EOS at over 100 000 grid points in the temperature range T=0 to 80 MeV, the density range n 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-based EOS, and previous EOSs by Lattimer-Swesty and H. Shen et al. for the thermodynamic properties, composition, and neutron star structure. The original FSUGold interaction produces an EOS, which we call FSU1.7, that has a maximum neutron star mass of 1.7 solar masses. A modification in the high-density EOS is introduced to increase the maximum neutron star mass to 2.1 solar masses and results in a slightly different EOS that we call FSU2.1. The EOS tables for FSU1.7 and FSU2.1 are available for download.
Kelly, Aaron; Brackbill, Nora; Markland, Thomas E
2015-03-07
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
Energy Technology Data Exchange (ETDEWEB)
Kelly, Aaron; Markland, Thomas E., E-mail: tmarkland@stanford.edu [Department of Chemistry, Stanford University, Stanford, California 94305 (United States); Brackbill, Nora [Department of Physics, Stanford University, Stanford, California 94305 (United States)
2015-03-07
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
Lumping of degree-based mean-field and pair-approximation equations for multistate contact processes
Kyriakopoulos, Charalampos; Grossmann, Gerrit; Wolf, Verena; Bortolussi, Luca
2018-01-01
Contact processes form a large and highly interesting class of dynamic processes on networks, including epidemic and information-spreading networks. While devising stochastic models of such processes is relatively easy, analyzing them is very challenging from a computational point of view, particularly for large networks appearing in real applications. One strategy to reduce the complexity of their analysis is to rely on approximations, often in terms of a set of differential equations capturing the evolution of a random node, distinguishing nodes with different topological contexts (i.e., different degrees of different neighborhoods), such as degree-based mean-field (DBMF), approximate-master-equation (AME), or pair-approximation (PA) approaches. The number of differential equations so obtained is typically proportional to the maximum degree kmax of the network, which is much smaller than the size of the master equation of the underlying stochastic model, yet numerically solving these equations can still be problematic for large kmax. In this paper, we consider AME and PA, extended to cope with multiple local states, and we provide an aggregation procedure that clusters together nodes having similar degrees, treating those in the same cluster as indistinguishable, thus reducing the number of equations while preserving an accurate description of global observables of interest. We also provide an automatic way to build such equations and to identify a small number of degree clusters that give accurate results. The method is tested on several case studies, where it shows a high level of compression and a reduction of computational time of several orders of magnitude for large networks, with minimal loss in accuracy.
Gomes, Diogo A.
2014-01-06
In this talk we will report on new results concerning the existence of smooth solutions for time dependent mean-field games. This new result is established through a combination of various tools including several a-priori estimates for time-dependent mean-field games combined with new techniques for the regularity of Hamilton-Jacobi equations.
Gomes, Diogo A.
2014-01-01
In this talk we will report on new results concerning the existence of smooth solutions for time dependent mean-field games. This new result is established through a combination of various tools including several a-priori estimates for time-dependent mean-field games combined with new techniques for the regularity of Hamilton-Jacobi equations.
International Nuclear Information System (INIS)
Mieck, B.
2007-01-01
We consider bosonic atoms with a repulsive contact interaction in a trap potential for a Bose-Einstein condensation (BEC) and additionally include a random potential. The ensemble averages for two models of static (I) and dynamic (II) disorder are performed and investigated in parallel. The bosonic many body systems of the two disorder models are represented by coherent state path integrals on the Keldysh time contour which allow exact ensemble averages for zero and finite temperatures. These ensemble averages of coherent state path integrals therefore present alternatives to replica field theories or super-symmetric averaging techniques. Hubbard-Stratonovich transformations (HST) lead to two corresponding self-energies for the hermitian repulsive interaction and for the non-hermitian disorder-interaction. The self-energy of the repulsive interaction is absorbed by a shift into the disorder-self-energy which comprises as an element of a larger symplectic Lie algebra sp(4M) the self-energy of the repulsive interaction as a subalgebra (which is equivalent to the direct product of M x sp(2); 'M' is the number of discrete time intervals of the disorder-self-energy in the generating function). After removal of the remaining Gaussian integral for the self-energy of the repulsive interaction, the first order variations of the coherent state path integrals result in the exact mean field or saddle point equations, solely depending on the disorder-self-energy matrix. These equations can be solved by continued fractions and are reminiscent to the 'Nambu-Gorkov' Green function formalism in superconductivity because anomalous terms or pair condensates of the bosonic atoms are also included into the selfenergies. The derived mean field equations of the models with static (I) and dynamic (II) disorder are particularly applicable for BEC in d=3 spatial dimensions because of the singularity of the density of states at vanishing wavevector. However, one usually starts out from
International Nuclear Information System (INIS)
Jiang Weizhou; Li Baozn; Chen Liewen
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, while the resulting density dependence of the symmetry energy at sub-saturation densities agrees with that extracted from the recent isospin diffusion data from intermediate energy heavy-ion reactions. The resulting equations of state have the special feature of being soft at intermediate densities but stiff at high densities naturally. With these constrained equations of state, it is found that the radius of a 1.4M o canonical neutron star is in the range of 11.9 km≤R≤13.1 km, and the maximum neutron star mass is around 2.0M o close to the recent observations
Analytic equation of state for FCC C60 solid based on analytic mean-field potential approach
International Nuclear Information System (INIS)
Sun Jiuxun
2006-01-01
The analytic mean-field approach (AMFP) was applied to the FCC C60 solid. For the intermolecular forces the Girifalco potential has been utilized. The analytic expressions for the Helmholtz free energy, internal energy and equation of state have been derived. The numerical results of thermodynamic quantities are compared with the molecular dynamic (MD) simulations and the unsymmetrized self-consistent field approach (CUSF) in the literature. It is shown that our AMFP results are in good agreement with the MD data both at low and high temperatures. The results of CUSF are in accordance with the AMFP at low temperature, but at high temperature the difference becomes prominent. Especially the AMFP predicted that the FCC C60 solid is stable upto 2202 K, the spinodal temperature, in good agreement with 2320 K from the MD simulation. However, the CUST just gives 1916 K, a temperature evidently lower than the MD data. The AMFP qualifies as a useful approach that can reasonably consider the anharmonic effects at high temperature
Gravitation and bilocal field theory
International Nuclear Information System (INIS)
Vollendorf, F.
1975-01-01
The starting point is the conjecture that a field theory of elementary particles can be constructed only in a bilocal version. Thus the 4-dimensional space time has to be replaced by the 8-dimensional manifold R 8 of all ordered pairs of space time events. With special reference to the Schwarzschild metric it is shown that the embedding of the time space into the manifold R 8 yields a description of the gravitational field. (orig.) [de
Spin geometry of entangled qubits under bilocal decoherence modes
International Nuclear Information System (INIS)
Durstberger, Katharina
2008-01-01
The Lindblad generators of the master equation define which kind of decoherence happens in an open quantum system. We are working with a two qubit system and choose the generators to be projection operators on the eigenstates of the system and unitary bilocal rotations of them. The resulting decoherence modes are studied in detail. Besides the general solutions we investigate the special case of maximally entangled states-the Bell singlet states. The results are depicted in the so-called spin geometry picture which allows to illustrate the evolution of the (nonlocal) correlations stored in a certain state. The question for which conditions the path traced out in the geometric picture depends only on the relative angle between the bilocal rotations is addressed
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...
Relativistic mechanics of two interacting particles and bilocal theory
International Nuclear Information System (INIS)
Takabayasi, Takehiko
1975-01-01
New relativistic mechanics of two-particle system is set forth, where the two constituent particles are interacting by an arbitrary (central) action-at-a-distance. The fundamental equations are presented in a form covariant under general transformation of parameters parametrizing the world lines of constituent particles. The theory represents the proper relativistic generalization of the usual Newtonian mechanics in the sense that it tends in the non-relativistic (and weak interaction) limit to the usual mechanics of two particles moving under a corresponding non-relativistic potential. For the analysis of theory it is convenient to choose a certain particular gauge (i.e., parametrization) fixed by two gauge relations. This brings the theory to a canonical formalism accompanied by two weak equations, and in this gauge quantization can be performed. The result verifies that the relativistic quantum mechanics for two particles interacting by an action-at-a-distance is just represented by a bilocal wave equation and a subsidiary condition, with the clarification of its correspondence-theoretical foundation and internal dynamics. As an example the case of Hooke-type force is illustrated, where the internal motions are elliptic oscillations in the center-of-mass frame. Its quantum theory just reproduces the original form of bilocal theory giving bound states lying on a straightly rising trajectory and on its daughter trajectories. (auth.)
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.
Risk-sensitive mean-field games
Tembine, Hamidou; Zhu, Quanyan; Başar, Tamer
2014-01-01
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.
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.
Extended Deterministic Mean-Field Games
Gomes, Diogo A.; Voskanyan, Vardan K.
2016-01-01
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.
Euclidean scalar field theory in the bilocal approximation
Nagy, S.; Polonyi, J.; Steib, I.
2018-04-01
The blocking step of the renormalization group method is usually carried out by restricting it to fluctuations and to local blocked action. The tree-level, bilocal saddle point contribution to the blocking, defined by the infinitesimal decrease of the sharp cutoff in momentum space, is followed within the three dimensional Euclidean ϕ6 model in this work. The phase structure is changed, new phases and relevant operators are found, and certain universality classes are restricted by the bilocal saddle point.
Continuous time finite state mean field games
Gomes, Diogo A.; Mohr, Joana; Souza, Rafael Rigã o
2013-01-01
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ 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.
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.
Continuous Time Finite State Mean Field Games
Energy Technology Data Exchange (ETDEWEB)
Gomes, Diogo A., E-mail: dgomes@math.ist.utl.pt [Instituto Superior Tecnico, Center for Mathematical Analysis, Geometry, and Dynamical Systems, Departamento de Matematica (Portugal); Mohr, Joana, E-mail: joana.mohr@ufrgs.br; Souza, Rafael Rigao, E-mail: rafars@mat.ufrgs.br [UFRGS, Instituto de Matematica (Brazil)
2013-08-01
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N{yields}{infinity} of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games.
Continuous Time Finite State Mean Field Games
International Nuclear Information System (INIS)
Gomes, Diogo A.; Mohr, Joana; Souza, Rafael Rigão
2013-01-01
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ 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
Obstacle mean-field game problem
Gomes, Diogo A.; Patrizi, Stefania
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.
Towards an effective bilocal theory from QCD in a background
International Nuclear Information System (INIS)
Magpantay, J.A.
1982-05-01
Using the path integral, we show how we can get background gauge invariant bilocals (to be identified with mesons) from QCD in a nontrivial ground state. We discuss in this paper mainly the formal manipulations, especially how to deal with the zero modes. We also discuss the large N limit of QCD in a background. (author)
Effective potential for bilocal composite fields and its ambiguity
International Nuclear Information System (INIS)
Muta, T.
1988-01-01
It is discussed that an ambiguity exists in the definition of the effective potential for bilocal composite fields which is an indispensable tool to discuss dynamical symmetry breaking. The ambiguity gives warning to arguments on the stability of ground states based on the curvature of the effective potential
Bi-local holography in the SYK model: perturbations
Energy Technology Data Exchange (ETDEWEB)
Jevicki, Antal; Suzuki, Kenta [Department of Physics, Brown University,182 Hope Street, Providence, RI 02912 (United States)
2016-11-08
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 ε expansion which allows for analytical evaluation of correlators and finite temperature quantities.
Borgs, C.; Chayes, J.T.; Hofstad, van der R.W.; Slade, G.
1999-01-01
We introduce a mean-field model of lattice trees based on embeddings into d of abstract trees having a critical Poisson offspring distribution. This model provides a combinatorial interpretation for the self-consistent mean-field model introduced previously by Derbez and Slade [9], and provides an
Mean Field Type Control with Congestion
Energy Technology Data Exchange (ETDEWEB)
Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr; Laurière, Mathieu [Univ. Paris Diderot, Sorbonne Paris Cité, Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRS (France)
2016-06-15
We analyze some systems of partial differential equations arising in the theory of mean field type control with congestion effects. We look for weak solutions. Our main result is the existence and uniqueness of suitably defined weak solutions, which are characterized as the optima of two optimal control problems in duality.
Stochastic quantization and mean field approximation
International Nuclear Information System (INIS)
Jengo, R.; Parga, N.
1983-09-01
In the context of the stochastic quantization we propose factorized approximate solutions for the Fokker-Planck equation for the XY and Zsub(N) spin systems in D dimensions. The resulting differential equation for a factor can be solved and it is found to give in the limit of t→infinity the mean field or, in the more general case, the Bethe-Peierls approximation. (author)
Nonasymptotic mean-field games
Tembine, Hamidou
2014-01-01
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
Mean Field Games with a Dominating Player
Energy Technology Data Exchange (ETDEWEB)
Bensoussan, A., E-mail: axb046100@utdallas.edu [The University of Texas at Dallas, International Center for Decision and Risk Analysis, Jindal School of Management (United States); Chau, M. H. M., E-mail: michaelchaumanho@gmail.com; Yam, S. C. P., E-mail: scpyam@sta.cuhk.edu.hk [The Chinese University of Hong Kong, Department of Statistics (Hong Kong, People’s Republic of China) (China)
2016-08-15
In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the dominating player. We first provide the general theory and discuss the necessary condition for the optimal controls and equilibrium condition by adopting adjoint equation approach. We then present a special case in the context of linear-quadratic framework, in which a necessary and sufficient condition can be asserted by stochastic maximum principle; we finally establish the sufficient condition that guarantees the unique existence of the equilibrium control. The proof of the convergence result of finite player game to mean field counterpart is provided in Appendix.
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.
Chen, Jiamin; Luo, Xiaofeng; Liu, Feng; Nara, Yasushi
2018-01-01
We perform a systematic study of elliptic flow (v 2) in Au+Au collisions at \\sqrt{{s}NN}}=5 {GeV} by using a microscopic transport model, JAM. The centrality, pseudorapidity, transverse momentum and beam energy dependence of v 2 for charged as well as identified hadrons are studied. We investigate the effects of both the hadronic mean-field and the softening of equation of state (EoS) on elliptic flow. The softening of the EoS is realized by imposing attractive orbits in two body scattering, which can reduce the pressure of the system. We found that the softening of the EoS leads to the enhancement of v 2, while the hadronic mean-field suppresses v 2 relative to the cascade mode. It indicates that elliptic flow at high baryon density regions is highly sensitive to the EoS and the enhancement of v 2 may probe the signature of a first-order phase transition in heavy-ion collisions at beam energies of a strong baryon stopping region. Supported by the MoST of China 973-Project (2015CB856901), NSFC (11575069, 11221504). Y. N. is supported by the Grants-in-Aid for Scientific Research from JSPS (15K05079, 15K05098)
Nonasymptotic mean-field games
Tembine, Hamidou
2014-01-01
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.
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.
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.
Bauso, Dario; Dia, Ben Mansour; Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul
2014-01-01
The myth of marriage has been and is still a fascinating historical societal phenomenon. Paradoxically, the empirical divorce rates are at an all-time high. This work describes a unique paradigm for preserving relationships and marital stability from mean-field game theory. We show that optimizing the long-term well-being via effort and society feeling state distribution will help in stabilizing relationships.
Bauso, Dario
2014-01-06
The myth of marriage has been and is still a fascinating historical societal phenomenon. Paradoxically, the empirical divorce rates are at an all-time high. This work describes a unique paradigm for preserving relationships and marital stability from mean-field game theory. We show that optimizing the long-term well-being via effort and society feeling state distribution will help in stabilizing relationships.
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.
Mean field interaction in biochemical reaction networks
Tembine, Hamidou; Tempone, Raul; Vilanova, Pedro
2011-01-01
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
Mean Field Games for Stochastic Growth with Relative Utility
Energy Technology Data Exchange (ETDEWEB)
Huang, Minyi, E-mail: mhuang@math.carleton.ca [Carleton University, School of Mathematics and Statistics (Canada); Nguyen, Son Luu, E-mail: sonluu.nguyen@upr.edu [University of Puerto Rico, Department of Mathematics (United States)
2016-12-15
This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation error estimate.
Mean Field Games for Stochastic Growth with Relative Utility
International Nuclear Information System (INIS)
Huang, Minyi; Nguyen, Son Luu
2016-01-01
This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation error estimate.
Energy Technology Data Exchange (ETDEWEB)
Graber, P. Jameson, E-mail: jameson-graber@baylor.edu [Baylor University, Department of Mathematics (United States)
2016-12-15
We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of Riccati equations. In certain cases, the solution to the mean field type control is also the equilibrium strategy for a class of mean field games. We use this fact to study an economic model of production of exhaustible resources.
Bi-local baryon interpolating fields with two flavors
Energy Technology Data Exchange (ETDEWEB)
Dmitrasinovic, V. [Belgrade University, Institute of Physics, Pregrevica 118, Zemun, P.O. Box 57, Beograd (RS); Chen, Hua-Xing [Institutos de Investigacion de Paterna, Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Valencia (Spain); Peking University, Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Beijing (China)
2011-02-15
We construct bi-local interpolating field operators for baryons consisting of three quarks with two flavors, assuming good isospin symmetry. We use the restrictions following from the Pauli principle to derive relations/identities among the baryon operators with identical quantum numbers. Such relations that follow from the combined spatial, Dirac, color, and isospin Fierz transformations may be called the (total/complete) Fierz identities. These relations reduce the number of independent baryon operators with any given spin and isospin. We also study the Abelian and non-Abelian chiral transformation properties of these fields and place them into baryon chiral multiplets. Thus we derive the independent baryon interpolating fields with given values of spin (Lorentz group representation), chiral symmetry (U{sub L}(2) x U{sub R}(2) group representation) and isospin appropriate for the first angular excited states of the nucleon. (orig.)
Bilocal bosonization of QCD and electroweak properties of light pseudoscalar mesons
International Nuclear Information System (INIS)
Belyea, C.I.; McKellar, B.H.J.
1991-01-01
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 F K and F π and the π ± charge radius are discussed in detail. 29 refs., 9 figs
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.
Time dependent mean-field games
Gomes, Diogo A.
2014-01-06
We consider time dependent mean-field games (MFG) with a local power-like dependence on the measure and Hamiltonians satisfying both sub and superquadratic growth conditions. We establish existence of smooth solutions under a certain set of conditions depending both on the growth of the Hamiltonian as well as on the dimension. In the subquadratic case this is done by combining a Gagliardo-Nirenberg type of argument with a new class of polynomial estimates for solutions of the Fokker-Planck equation in terms of LrLp- norms of DpH. These techniques do not apply to the superquadratic case. In this setting we recur to a delicate argument that combines the non-linear adjoint method with polynomial estimates for solutions of the Fokker-Planck equation in terms of L1L1-norms of DpH. Concerning the subquadratic case, we substantially improve and extend the results previously obtained. Furthermore, to the best of our knowledge, the superquadratic case has not been addressed in the literature yet. In fact, it is likely that our estimates may also add to the current understanding of Hamilton-Jacobi equations with superquadratic Hamiltonians.
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 fields and self consistent normal ordering of lattice spin and gauge field theories
International Nuclear Information System (INIS)
Ruehl, W.
1986-01-01
Classical Heisenberg spin models on lattices possess mean field theories that are well defined real field theories on finite lattices. These mean field theories can be self consistently normal ordered. This leads to a considerable improvement over standard mean field theory. This concept is carried over to lattice gauge theories. We construct first an appropriate real mean field theory. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean field theory are derived. (orig.)
Mean Field Games Models-A Brief Survey
Gomes, Diogo A.; Saú de, Joã o
2013-01-01
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.
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)
Kluger, Y.
1993-01-01
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 N f 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/N f 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 N f expansion is truncated in the lowest order, and compare them with those of a phenomenological transport equation
A Maximum Principle for SDEs of Mean-Field Type
Energy Technology Data Exchange (ETDEWEB)
Andersson, Daniel, E-mail: danieand@math.kth.se; Djehiche, Boualem, E-mail: boualem@math.kth.se [Royal Institute of Technology, Department of Mathematics (Sweden)
2011-06-15
We study the optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state of the process. Moreover the cost functional is also of mean-field type, which makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. Under the assumption of a convex action space a maximum principle of local form is derived, specifying the necessary conditions for optimality. These are also shown to be sufficient under additional assumptions. This maximum principle differs from the classical one, where the adjoint equation is a linear backward SDE, since here the adjoint equation turns out to be a linear mean-field backward SDE. As an illustration, we apply the result to the mean-variance portfolio selection problem.
A Maximum Principle for SDEs of Mean-Field Type
International Nuclear Information System (INIS)
Andersson, Daniel; Djehiche, Boualem
2011-01-01
We study the optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state of the process. Moreover the cost functional is also of mean-field type, which makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. Under the assumption of a convex action space a maximum principle of local form is derived, specifying the necessary conditions for optimality. These are also shown to be sufficient under additional assumptions. This maximum principle differs from the classical one, where the adjoint equation is a linear backward SDE, since here the adjoint equation turns out to be a linear mean-field backward SDE. As an illustration, we apply the result to the mean-variance portfolio selection problem.
A diffusion model of protected population on bilocal habitat with generalized resource
Vasilyev, Maxim D.; Trofimtsev, Yuri I.; Vasilyeva, Natalya V.
2017-11-01
A model of population distribution in a two-dimensional area divided by an ecological barrier, i.e. the boundaries of natural reserve, is considered. Distribution of the population is defined by diffusion, directed migrations and areal resource. The exchange of specimens occurs between two parts of the habitat. The mathematical model is presented in the form of a boundary value problem for a system of non-linear parabolic equations with variable parameters of diffusion and growth function. The splitting space variables, sweep method and simple iteration methods were used for the numerical solution of a system. A set of programs was coded in Python. Numerical simulation results for the two-dimensional unsteady non-linear problem are analyzed in detail. The influence of migration flow coefficients and functions of natural birth/death ratio on the distributions of population densities is investigated. The results of the research would allow to describe the conditions of the stable and sustainable existence of populations in bilocal habitat containing the protected and non-protected zones.
Momentum and density dependence of the nuclear mean field
International Nuclear Information System (INIS)
Behera, B.; Routray, T.R.
1999-01-01
The purpose of this is to analyse the momentum, density and temperature dependence of the mean field in nuclear matter derived from finite range effective interactions and to examine the influence of the functional form of the interaction on the high momentum behaviour of the mean field. Emphasis will be given to use very simple parametrizations of the effective interaction with a minimum number of adjustable parameters and yet capable of giving a good description of the mean field in nuclear matter over a wide range of momentum, density and temperature. As an application of the calculated equation of state of nuclear matter, phase transitions to quark-gluon plasma is studied where the quark phase is described by a zeroth order bag model equation of state
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.)
Nonequilibrium dynamical mean-field theory
International Nuclear Information System (INIS)
Eckstein, Martin
2009-01-01
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.)
Instabilities constraint and relativistic mean field parametrization
International Nuclear Information System (INIS)
Sulaksono, A.; Kasmudin; Buervenich, T.J.; Reinhard, P.-G.; Maruhn, J.A.
2011-01-01
Two parameter sets (Set 1 and Set 2) of the standard relativistic mean field (RMF) model plus additional vector isoscalar nonlinear term, which are constrained by a set of criteria 20 determined by symmetric nuclear matter stabilities at high densities due to longitudinal and transversal particle–hole excitation modes are investigated. In the latter parameter set, δ meson and isoscalar as well as isovector tensor contributions are included. The effects in selected finite nuclei and nuclear matter properties predicted by both parameter sets are systematically studied and compared with the ones predicted by well-known RMF parameter sets. The vector isoscalar nonlinear term addition and instability constraints have reasonably good effects in the high-density properties of the isoscalar sector of nuclear matter and certain finite nuclei properties. However, even though the δ meson and isovector tensor are included, the incompatibility with the constraints from some experimental data in certain nuclear properties at saturation point and the excessive stiffness of the isovector nuclear matter equation of state at high densities as well as the incorrect isotonic trend in binding the energies of finite nuclei are still encountered. It is shown that the problem may be remedied if we introduce additional nonlinear terms not only in the isovector but also in the isoscalar vectors. (author)
Mean-field approach to unconventional superconductivity
International Nuclear Information System (INIS)
Sacks, William; Mauger, Alain; Noat, Yves
2014-01-01
Highlights: • A model Hamiltonian for unconventional superconductivity (SC) is proposed. • The pseudogap (PG) state is described in terms of pair fluctuations. • SC coherence is restored by a new pair–pair interaction, which counteracts fluctuations. • Given the temperature dependence of the parameters, the SC to PG transition is examined. • The theory fits the ‘peak–dip–hump’ features of cuprate and pnictide excitation spectra. - Abstract: We propose a model that connects the quasiparticle spectral function of high-T c superconductors to the condensation energy. Given the evidence for pair correlations above T c , we consider a coarse-grain Hamiltonian of fluctuating pairs describing the incoherent pseudogap (PG) state, together with a novel pair–pair interaction term that restores long-range superconducting (SC) coherence below T c . A mean-field solution then leads to a self-consistent gap equation containing the new pair–pair coupling. The corresponding spectral function A(k,E) reveals the characteristic peak–dip–hump features of cuprates, now observed on iron pnictides (LiFeAs). The continuous transition from SC to PG states is discussed
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.)
Mean-field models and exotic nuclei
International Nuclear Information System (INIS)
Bender, M.; Buervenich, T.; Maruhn, J.A.; Greiner, W.; Rutz, K.; Reinhard, P.G.
1998-01-01
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.)
Quantum mean-field theory of collective dynamics and tunneling
International Nuclear Information System (INIS)
Negele, J.W.; Massachusetts Inst. of Tech., Cambridge
1981-01-01
In collaboration with Shimon Levit and Zvi Paltiel, significant progress has been made recently in formulating the quantum many-body problem in terms of an expansion about solutions to time-dependent mean-field equations. The essential ideas, principal results, and illustrative examples will be summarized here. (orig./HSI)
Mean-field theory of nuclear structure and dynamics
International Nuclear Information System (INIS)
Negele, J.W.
1982-01-01
The physical and theoretical foundations are presented for the mean-field theory of nuclear structure and dynamics. Salient features of the many-body theory of stationary states are reviewed to motivate the time-dependent mean-field approximation. The time-dependent Hartree-Fock approximation and its limitations are discussed and general theoretical formulations are presented which yield time-dependent mean-field equations in lowest approximation and provide suitable frameworks for overcoming various conceptual and practical limitations of the mean-field theory. Particular emphasis is placed on recent developments utilizing functional integral techniques to obtain a quantum mean-field theory applicable to quantized eigenstates, spontaneous fission, the nuclear partition function, and scattering problems. Applications to a number of simple, idealized systems are presented to verify the approximations for solvable problems and to elucidate the essential features of mean-field dynamics. Finally, calculations utilizing moderately realistic geometries and interactions are reviewed which address heavy-ion collisions, fusion, strongly damped collisions, and fission
Time independent mean-field theory
International Nuclear Information System (INIS)
Negele, J.W.
1980-02-01
The physical and theoretical motivations for the time-dependent mean-field theory are presented, and the successes and limitations of the time-dependent Hartree-Fock initial-vaue problem are reviewed. New theoretical developments are described in the treatment of two-body correlations and the formulation of a quantum mean-field theory of large-amplitude collective motion and tunneling decay. Finally, the mean-field theory is used to obtain new insights into the phenomenon of pion condensation in finite nuclei. 18 figures
Socio-economic applications of finite state mean field games
Gomes, Diogo A.
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.
Socio-economic applications of finite state mean field games.
Gomes, Diogo; Velho, Roberto M; Wolfram, Marie-Therese
2014-11-13
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. © 2014 The Author(s) Published by the Royal Society. All rights reserved.
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)
Relativistic mean-field mass models
Energy Technology Data Exchange (ETDEWEB)
Pena-Arteaga, D.; Goriely, S.; Chamel, N. [Universite Libre de Bruxelles, Institut d' Astronomie et d' Astrophysique, CP-226, Brussels (Belgium)
2016-10-15
We present a new effort to develop viable mass models within the relativistic mean-field approach with density-dependent meson couplings, separable pairing and microscopic estimations for the translational and rotational correction energies. Two interactions, DD-MEB1 and DD-MEB2, are fitted to essentially all experimental masses, and also to charge radii and infinite nuclear matter properties as determined by microscopic models using realistic interactions. While DD-MEB1 includes the σ, ω and ρ meson fields, DD-MEB2 also considers the δ meson. Both mass models describe the 2353 experimental masses with a root mean square deviation of about 1.1 MeV and the 882 measured charge radii with a root mean square deviation of 0.029 fm. In addition, we show that the Pb isotopic shifts and moments of inertia are rather well reproduced, and the equation of state in pure neutron matter as well as symmetric nuclear matter are in relatively good agreement with existing realistic calculations. Both models predict a maximum neutron-star mass of more than 2.6 solar masses, and thus are able to accommodate the heaviest neutron stars observed so far. However, the new Lagrangians, like all previously determined RMF models, present the drawback of being characterized by a low effective mass, which leads to strong shell effects due to the strong coupling between the spin-orbit splitting and the effective mass. Complete mass tables have been generated and a comparison with other mass models is presented. (orig.)
Mean field games for cognitive radio networks
Tembine, Hamidou; Tempone, Raul; Vilanova, Pedro
2012-01-01
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
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.
Mean field approach to nuclear structure
International Nuclear Information System (INIS)
Nazarewicz, W.; Tennessee Univ., Knoxville, TN
1993-01-01
Several examples of mean-field calculations, relevant to the recent and planned low-spin experimental works, are presented. The perspectives for future studies (mainly related to spectroscopy of exotic nuclei) are reviewd
Weakly coupled mean-field game systems
Gomes, Diogo A.; Patrizi, Stefania
2016-01-01
Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized problem
Bauso, Dario; Dia, Ben Mansour; Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul
2014-01-01
This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple’s network on their feeling states and their well-being. PMID:24804835
Bauso, Dario; Dia, Ben Mansour; Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul
2014-01-01
This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple's network on their feeling states and their well-being. © 2014 Bauso et al.
Mean-field games for marriage.
Directory of Open Access Journals (Sweden)
Dario Bauso
Full Text Available 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.
Mean-field approximation minimizes relative entropy
International Nuclear Information System (INIS)
Bilbro, G.L.; Snyder, W.E.; Mann, R.C.
1991-01-01
The authors derive the mean-field approximation from the information-theoretic principle of minimum relative entropy instead of by minimizing Peierls's inequality for the Weiss free energy of statistical physics theory. They show that information theory leads to the statistical mechanics procedure. As an example, they consider a problem in binary image restoration. They find that mean-field annealing compares favorably with the stochastic approach
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.
Regularity Theory for Mean-Field Game Systems
Gomes, Diogo A.
2016-09-14
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.
Regularity Theory for Mean-Field Game Systems
Gomes, Diogo A.; Pimentel, Edgard A.; Voskanyan, Vardan K.
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.
Mean field approximation versus exact treatment of collisions in few-body systems
International Nuclear Information System (INIS)
Lemm, J.; Weiguny, A.; Giraud, B.G.
1990-01-01
A variational principle for calculating matrix elements of the full resolvent operator for a many-body system is studied. Its mean field approximation results in non-linear equations of Hartree (-Fock) type, with initial and final channel wave functions as driving terms. The mean field equations will in general have many solutions whereas the exact problem being linear, has a unique solution. In a schematic model with separable forces the mean field equations are analytically soluble, and for the exact problem the resulting integral equations are solved numerically. Comparing exact and mean field results over a wide range of system parameters, the mean field approach proves to be a very reliable approximation, which is not plagued by the notorious problem of defining asymptotic channels in the time-dependent mean field method. (orig.)
Uncertainty quantification for mean field games in social interactions
Dia, Ben Mansour
2016-01-09
We present an overview of mean field games formulation. A comparative analysis of the optimality for a stochastic McKean-Vlasov process with time-dependent probability is presented. Then we examine mean-field games for social interactions and we show that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize couple (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. Finally we introduce the Wiener chaos expansion for the construction of solution of stochastic differential equations of Mckean-Vlasov type. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and allow to quantify the uncertainty in the optimality system.
Uncertainty quantification for mean field games in social interactions
Dia, Ben Mansour
2016-01-01
We present an overview of mean field games formulation. A comparative analysis of the optimality for a stochastic McKean-Vlasov process with time-dependent probability is presented. Then we examine mean-field games for social interactions and we show that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize couple (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. Finally we introduce the Wiener chaos expansion for the construction of solution of stochastic differential equations of Mckean-Vlasov type. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and allow to quantify the uncertainty in the optimality system.
Towards an effective bilocal theory from quantum chromodynamics in a background field
International Nuclear Information System (INIS)
Magpantay, J.A.
1983-01-01
Using the path integral, we show how we can get background gauge-invariant bilocals (to be identified with mesons) from QCD in a nontrivial ground state. We discuss in this paper mainly the formal manipulations, especially how to deal with the zero modes
Representations of the Poincare group, position operator and the bi-local model
International Nuclear Information System (INIS)
Sohkawa, Tohru
1978-01-01
We propose two types of representations of the Poincare group which give general frameworks for introduction of internal degrees of freedom of a particle. The bi-local model recently proposed by Takabayasi is constructed through our frameworks. In this study, new covariant and non-covariant position operators are introduced and discussed. (author)
Band mixing effects in mean field theories
International Nuclear Information System (INIS)
Kuyucak, S.; Morrison, I.
1989-01-01
The 1/N expansion method, which is an angular momentum projected mean field theory, is used to investigate the nature of electromagnetic transitions in the interacting boson model (IBM). Conversely, comparison with the exact IBM results sheds light on the range of validity of the mean field theory. It is shown that the projected mean field results for the E2 transitions among the ground, β and γ bands are incomplete for the spin dependent terms and it is essential to include band mixing effect for a correct (Mikhailov) analysis of E2 data. The algebraic expressions derived are general and will be useful in the analysis of experimental data in terms of both the sd and sdg boson models. 17 refs., 7 figs., 8 tabs
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
International Nuclear Information System (INIS)
Reinhard, P.G.; Bender, M.; Maruhn, J.A.; Frankfurt Univ.
2001-03-01
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. (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.
Mean-field games with logistic population dynamics
Gomes, Diogo A.; De Lima Ribeiro, Ricardo
2013-01-01
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.
A regularized stationary mean-field game
Yang, Xianjin
2016-01-01
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.
Mean-field theory and solitonic matter
International Nuclear Information System (INIS)
Cohen, T.D.
1989-01-01
Finite density solitonic matter is considered in the context of quantum field theory. Mean-field theory, which provides a reasonable description for single-soliton properties gives rise to a crystalline description. A heuristic description of solitonic matter is given which shows that the low-density limit of solitonic matter (the limit which is presumably relevant for nuclear matter) does not commute with the mean-field theory limit and gives rise to a Fermi-gas description of the system. It is shown on the basis of a formal expansion of simple soliton models in terms of the coupling constant why one expects mean-field theory to fail at low densities and why the corrections to mean-field theory are nonperturbative. This heuristic description is tested against an exactly solvable 1+1 dimensional model (the sine-Gordon model) and found to give the correct behavior. The relevance of these results to the program of doing nuclear physics based on soliton models is discussed. (orig.)
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.
Weakly coupled mean-field game systems
Gomes, Diogo A.
2016-07-14
Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized problem. Finally, by a limiting procedure, we obtain solutions to the MFG problem. © 2016 Elsevier Ltd
Mean-field Ensemble Kalman Filter
Law, Kody; Tembine, Hamidou; Tempone, Raul
2015-01-01
A proof of convergence of the standard EnKF generalized to non-Gaussian state space models is provided. A density-based deterministic approximation of the mean-field limiting EnKF (MFEnKF) is proposed, consisting of a PDE solver and a quadrature
International Nuclear Information System (INIS)
Guerra, E.M. de
2001-01-01
In these talks, we review non relativistic selfconsistent mean field theories, their scope and limitations. We first discuss static and time dependent mean field approaches for particles and quasiparticles, together with applications. We then discuss extensions that go beyond the non-relativistic independent particle limit. On the one hand, we consider extensions concerned with restoration of symmetries and with the treatment of collective modes, particularly by means of quantized ATDHF. On the other hand, we consider extensions concerned with the relativistic dynamics of bound nucleons. We present data on nucleon momentum distributions that show the need for relativistic mean field approach and probe the limits of the mean field concept. Illustrative applications of various methods are presented stressing the role that selfconsistency plays in providing a unifying reliable framework to study all sorts of properties and phenomena. From global properties such as size, mass, lifetime,.., to detailed structure in excitation spectra (high spin, RPA modes,..), as well as charge, magnetization and velocity distributions. (orig.)
Configuration mixing of mean-field states
International Nuclear Information System (INIS)
Bender, M; Heenen, P-H
2005-01-01
Starting from self-consistent mean-field models, we discuss how to include correlations from fluctuations in collective degrees of freedom through symmetry restoration and configuration mixing, which give access to ground-state correlations and collective excitations. As an example for the method, we discuss the spectroscopy of neutron-deficient Pb isotopes
Time-Dependent Mean-Field Games with Logarithmic Nonlinearities
Gomes, Diogo A.; Pimentel, Edgard
2015-01-01
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.
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.
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.
Derivation of mean-field dynamics for fermions
International Nuclear Information System (INIS)
Petrat, Soeren
2014-01-01
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
Heavy-ion interactions in relativistic mean-field models
International Nuclear Information System (INIS)
Rashdan, M.
1996-01-01
The interaction potential between spherical nuclei and the elastic scattering cross section are calculated within relativistic mean-field (linear and non-linear) models, using a generalized relativistic local density approximation. The nuclear densities are calculated self-consistently from the solution of the relativistic mean-field equations. It is found that both the linear and non-linear models predict the characteristic switching-over phenomenon of the heavy-ion nuclear potential, where the potential gets attraction with increasing energy up to some value where it reverses this behaviour. The non-linear NLC model predicts a deeper potential than the linear LW model. The elastic scattering cross section calculated within the non-linear NLC model is in better agreement with experiments than that calculated within the linear LW model. (orig.)
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 starting point. In this method message passing fixed point equations (which correspond to the update rules in a message passing algorithm) are then obtained by imposing different region-based approximations and constraints on the mean field and belief propagation parts of the corresponding factor graph....... Our results can be applied, for example, to algorithms that perform joint channel estimation and decoding in iterative receivers. This is demonstrated in a simple example....
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...
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...
Probabilistic theory of mean field games with applications
Carmona, René
2018-01-01
This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic...
Applicability of self-consistent mean-field theory
International Nuclear Information System (INIS)
Guo Lu; Sakata, Fumihiko; Zhao Enguang
2005-01-01
Within the constrained Hartree-Fock (CHF) theory, an analytic condition is derived to estimate whether a concept of the self-consistent mean field is realized in the level repulsive region. The derived condition states that an iterative calculation of the CHF equation does not converge when the quantum fluctuations coming from two-body residual interaction and quadrupole deformation become larger than a single-particle energy difference between two avoided crossing orbits. By means of numerical calculation, it is shown that the analytic condition works well for a realistic case
Mean-field theory and self-consistent dynamo modeling
International Nuclear Information System (INIS)
Yoshizawa, Akira; Yokoi, Nobumitsu
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)
Relativistic mean field calculations in neutron-rich nuclei
Energy Technology Data Exchange (ETDEWEB)
Gangopadhyay, G.; Bhattacharya, Madhubrata [Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700 009 (India); Roy, Subinit [Saha Institute of Nuclear Physics, Block AF, Sector 1, Kolkata- 700 064 (India)
2014-08-14
Relativistic mean field calculations have been employed to study neutron rich nuclei. The Lagrange's equations have been solved in the co-ordinate space. The effect of the continuum has been effectively taken into account through the method of resonant continuum. It is found that BCS approximation performs as well as a more involved Relativistic Continuum Hartree Bogoliubov approach. Calculations reveal the possibility of modification of magic numbers in neutron rich nuclei. Calculation for low energy proton scattering cross sections shows that the present approach reproduces the density in very light neutron rich nuclei.
Mean-field level analysis of epidemics in directed networks
Energy Technology Data Exchange (ETDEWEB)
Wang, Jiazeng [School of Mathematical Sciences, Peking University, Beijing 100871 (China); Liu, Zengrong [Mathematics Department, Shanghai University, Shanghai 200444 (China)], E-mail: wangjiazen@yahoo.com.cn, E-mail: zrongliu@online.sh.cn
2009-09-04
The susceptible-infected-removed spreading model in a directed graph is studied. The mean-field level rate equations are built with the degree-degree connectivity correlation element and the (in, out)-degree distribution. And the outbreak threshold is obtained analytically-it is determined by the combination of connectivity probability and the degree distribution. Furthermore, the methods of calculating the degree-degree correlations in directed networks are presented. The numerical results of the discrete epidemic processes in networks verify our analyses.
Mean-field level analysis of epidemics in directed networks
International Nuclear Information System (INIS)
Wang, Jiazeng; Liu, Zengrong
2009-01-01
The susceptible-infected-removed spreading model in a directed graph is studied. The mean-field level rate equations are built with the degree-degree connectivity correlation element and the (in, out)-degree distribution. And the outbreak threshold is obtained analytically-it is determined by the combination of connectivity probability and the degree distribution. Furthermore, the methods of calculating the degree-degree correlations in directed networks are presented. The numerical results of the discrete epidemic processes in networks verify our analyses.
Pedestrian Flow in the Mean Field Limit
Haji Ali, Abdul Lateef
2012-01-01
-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
Superheavy nuclei: a relativistic mean field outlook
International Nuclear Information System (INIS)
Afanasjev, A.V.
2006-01-01
The analysis of quasi-particle spectra in the heaviest A∼250 nuclei with spectroscopic data provides an additional constraint for the choice of effective interaction for the description of superheavy nuclei. It strongly suggests that only the parametrizations which predict Z = 120 and N = 172 as shell closures are reliable for superheavy nuclei within the relativistic mean field theory. The influence of the central depression in the density distribution of spherical superheavy nuclei on the shell structure is studied. A large central depression produces large shell gaps at Z = 120 and N = 172. The shell gaps at Z = 126 and N = 184 are favoured by a flat density distribution in the central part of the nucleus. It is shown that approximate particle number projection (PNP) by means of the Lipkin-Nogami (LN) method removes pairing collapse seen at these gaps in the calculations without PNP
Effective masses and the nuclear mean field
International Nuclear Information System (INIS)
Mahaux, C.; Sartor, R.
1985-01-01
The effective mass characterizes the energy dependence of the empirical average nuclear potential. This energy dependence has two different sources, namely the nonlocality in space of the microscopic mean field on the one hand, and its true energy dependence on the other hand. Correspondingly it is convenient to divide the effective mass into two components, the k-mass and the ω-mass. The latter is responsible for the existence of a peak in the energy dependence of the effective mass. This peak is located near the Fermi energy in nuclear matter and in nuclei, as well as in the electron gas, the hard sphere Fermi gas and liquid helium 3. A related phenomenon is the existence of a low energy anomaly in the energy dependence of the optical model potential between two heavy ions. (orig.)
Mean-field Ensemble Kalman Filter
Law, Kody
2015-01-07
A proof of convergence of the standard EnKF generalized to non-Gaussian state space models is provided. A density-based deterministic approximation of the mean-field limiting EnKF (MFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for d < 2 . The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods
Machado Velho, Roberto
2017-01-01
-economic sciences. Examples include paradigm shifts in the scientific community and the consumer choice behavior in a free market. The corresponding finite-state mean-field game models are hyperbolic systems of partial differential equations, for which we propose
Quantum mean-field theory of collective dynamics and tunneling
International Nuclear Information System (INIS)
Negele, J.W.
1981-01-01
A fundamental problem in quantum many-body theory is formulation of a microscopic theory of collective motion. For self-bound, saturating systems like finite nuclei described in the context of nonrelativistic quantum mechanics with static interactions, the essential problem is how to formulate a systematic quantal theory in which the relevant collective variables and their dynamics arise directly and naturally from the Hamiltonian and the system under consideration. Significant progress has been made recently in formulating the quantum many-body problem in terms of an expansion about solutions to time-dependent mean-field equations. The essential ideas, principal results, and illustrative examples are summarized. An exact expression for an observable of interest is written using a functional integral representation for the evolution operator, and tractable time-dependent mean field equations are obtained by application of the stationary-phase approximation (SPA) to the functional integral. Corrections to the lowest-order theory may be systematically enumerated. 6 figures
A Stochastic Maximum Principle for General Mean-Field Systems
International Nuclear Information System (INIS)
Buckdahn, Rainer; Li, Juan; Ma, Jin
2016-01-01
In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and we extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.
Displacement Convexity for First-Order Mean-Field Games
Seneci, Tommaso
2018-05-01
In this thesis, we consider the planning problem for first-order mean-field games (MFG). These games degenerate into optimal transport when there is no coupling between players. Our aim is to extend the concept of displacement convexity from optimal transport to MFGs. This extension gives new estimates for solutions of MFGs. First, we introduce the Monge-Kantorovich problem and examine related results on rearrangement maps. Next, we present the concept of displacement convexity. Then, we derive first-order MFGs, which are given by a system of a Hamilton-Jacobi equation coupled with a transport equation. Finally, we identify a large class of functions, that depend on solutions of MFGs, which are convex in time. Among these, we find several norms. This convexity gives bounds for the density of solutions of the planning problem.
A Stochastic Maximum Principle for General Mean-Field Systems
Energy Technology Data Exchange (ETDEWEB)
Buckdahn, Rainer, E-mail: Rainer.Buckdahn@univ-brest.fr [Université de Bretagne-Occidentale, Département de Mathématiques (France); Li, Juan, E-mail: juanli@sdu.edu.cn [Shandong University, Weihai, School of Mathematics and Statistics (China); Ma, Jin, E-mail: jinma@usc.edu [University of Southern California, Department of Mathematics (United States)
2016-12-15
In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and we extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.
Mean Field Analysis of Quantum Annealing Correction.
Matsuura, Shunji; Nishimori, Hidetoshi; Albash, Tameem; Lidar, Daniel A
2016-06-03
Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the p-body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for p=2, where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p≥3, where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder.
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody
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.
Relativistic mean field theory for unstable nuclei
International Nuclear Information System (INIS)
Toki, Hiroshi
2000-01-01
We discuss the properties of unstable nuclei in the framework of the relativistic mean field (RMF) theory. We take the RMF theory as a phenomenological theory with several parameters, whose form is constrained by the successful microscopic theory (RBHF), and whose values are extracted from the experimental values of unstable nuclei. We find the outcome with the newly obtained parameter sets (TM1 and TMA) is promising in comparison with various experimental data. We calculate systematically the ground state properties of even-even nuclei up to the drip lines; about 2000 nuclei. We find that the neutron magic shells (N=82, 128) at the standard magic numbers stay at the same numbers even far from the stability line and hence provide the feature of the r-process nuclei. However, many proton magic numbers disappear at the neutron numbers far away from the magic numbers due to the deformations. We discuss how to describe giant resonances for the case of the non-linear coupling terms for the sigma and omega mesons in the relativistic RPA. We mention also the importance of the relativistic effect on the spin observables as the Gamow-Teller strength and the longitudinal and transverse spin responses. (author)
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody; Tembine, Hamidou; Tempone, Raul
2016-01-01
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.
Time dependent mean-field games
Gomes, Diogo A.; Pimentel, Edgard; Sá nchez-Morgado, Hé ctor
2014-01-01
In this setting we recur to a delicate argument that combines the non-linear adjoint method with polynomial estimates for solutions of the Fokker-Planck equation in terms of L1L1-norms of DpH. Concerning the subquadratic case, we substantially improve and extend the results previously obtained. Furthermore, to the best of our knowledge, the superquadratic case has not been addressed in the literature yet. In fact, it is likely that our estimates may also add to the current understanding of Hamilton-Jacobi equations with superquadratic Hamiltonians.
Generalized continuity equations from two-field Schrödinger Lagrangians
Spourdalakis, A. G. B.; Pappas, G.; Morfonios, C. Â. V.; Kalozoumis, P. A.; Diakonos, F. K.; Schmelcher, P.
2016-11-01
A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields and whose global invariance under dilation and phase variations leads to a mixed continuity equation for the two fields. In combination with discrete spatial symmetries of the underlying Hamiltonian, the mixed continuity equation is shown to produce bilocal conservation laws for a single field. This leads to generalized conserved charges for vanishing boundary currents and to divergenceless bilocal currents for stationary states. The formalism reproduces the bilocal continuity equation obtained in the special case of P T -symmetric quantum mechanics and paraxial optics.
Pairing gaps from nuclear mean-field models
International Nuclear Information System (INIS)
Bender, M.; Rutz, K.; Maruhn, J.A.
2000-01-01
We discuss the pairing gap, a measure for nuclear pairing correlations, in chains of spherical, semi-magic nuclei in the framework of self-consistent nuclear mean-field models. The equations for the conventional BCS model and the approximate projection-before-variation Lipkin-Nogami method are formulated in terms of local density functionals for the effective interaction. We calculate the Lipkin-Nogami corrections of both the mean-field energy and the pairing energy. Various definitions of the pairing gap are discussed as three-point, four-point and five-point mass-difference formulae, averaged matrix elements of the pairing potential, and single-quasiparticle energies. Experimental values for the pairing gap are compared with calculations employing both a delta pairing force and a density-dependent delta interaction in the BCS and Lipkin-Nogami model. Odd-mass nuclei are calculated in the spherical blocking approximation which neglects part of the the core polarization in the odd nucleus. We find that the five-point mass difference formula gives a very robust description of the odd-even staggering, other approximations for the gap may differ from that up to 30% for certain nuclei. (orig.)
Spin and orbital exchange interactions from Dynamical Mean Field Theory
Energy Technology Data Exchange (ETDEWEB)
Secchi, A., E-mail: a.secchi@science.ru.nl [Radboud University, Institute for Molecules and Materials, 6525 AJ Nijmegen (Netherlands); Lichtenstein, A.I., E-mail: alichten@physnet.uni-hamburg.de [Universitat Hamburg, Institut für Theoretische Physik, Jungiusstraße 9, D-20355 Hamburg (Germany); Katsnelson, M.I., E-mail: m.katsnelson@science.ru.nl [Radboud University, Institute for Molecules and Materials, 6525 AJ Nijmegen (Netherlands)
2016-02-15
We derive a set of equations expressing the parameters of the magnetic interactions characterizing a strongly correlated electronic system in terms of single-electron Green's functions and self-energies. This allows to establish a mapping between the initial electronic system and a spin model including up to quadratic interactions between the effective spins, with a general interaction (exchange) tensor that accounts for anisotropic exchange, Dzyaloshinskii–Moriya interaction and other symmetric terms such as dipole–dipole interaction. We present the formulas in a format that can be used for computations via Dynamical Mean Field Theory algorithms. - Highlights: • We give formulas for the exchange interaction tensor in strongly correlated systems. • Interactions are written in terms of electronic Green's functions and self-energies. • The method is suitable for a Dynamical Mean Field Theory implementation. • No quenching of the orbital magnetic moments is assumed. • Spin and orbital contributions to magnetism can be computed separately.
Coalescing colony model: Mean-field, scaling, and geometry
Carra, Giulia; Mallick, Kirone; Barthelemy, Marc
2017-12-01
We analyze the coalescing model where a `primary' colony grows and randomly emits secondary colonies that spread and eventually coalesce with it. This model describes population proliferation in theoretical ecology, tumor growth, and is also of great interest for modeling urban sprawl. Assuming the primary colony to be always circular of radius r (t ) and the emission rate proportional to r (t) θ , where θ >0 , we derive the mean-field equations governing the dynamics of the primary colony, calculate the scaling exponents versus θ , and compare our results with numerical simulations. We then critically test the validity of the circular approximation for the colony shape and show that it is sound for a constant emission rate (θ =0 ). However, when the emission rate is proportional to the perimeter, the circular approximation breaks down and the roughness of the primary colony cannot be discarded, thus modifying the scaling exponents.
Explicit Solutions for One-Dimensional Mean-Field Games
Prazeres, Mariana
2017-04-05
In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or without congestion. Our aim is to understand the qualitative features of these games through the analysis of explicit solutions. We are particularly interested in MFGs with a nonmonotonic behavior, which corresponds to situations where agents tend to aggregate. First, we derive the MFG equations from control theory. Then, we compute explicit solutions using the current formulation and examine their behavior. Finally, we represent the solutions and analyze the results. This thesis main contributions are the following: First, we develop the current method to solve MFG explicitly. Second, we analyze in detail non-monotonic MFGs and discover new phenomena: non-uniqueness, discontinuous solutions, empty regions and unhappiness traps. Finally, we address several regularization procedures and examine the stability of MFGs.
Trapped Bose gas. Mean-field approximation and beyond
International Nuclear Information System (INIS)
Pitaevskii, L.P.
1998-01-01
The recent realization of Bose-Einstein condensation in atomic gases opens new possibilities for observation of macroscopic quantum phenomena. There are two important features of the system - weak interaction and significant spatial inhomogeneity. Because of this inhomogeneity a non-trivial 'zeroth-order' theory exists, compared to the 'first-order' Bogoliubov theory. This theory is based on the mean-field Gross-Pitaevskii equation for the condensate ψ -function. The equation is classical in its essence but contains the ℎ constant explicitly. Phenomena such as collective modes, interference, tunneling, Josephson-like current and quantized vortex lines can be described using this equation. The study of deviations from the zeroth-order theory arising from zero-point and thermal fluctuations is also of great interest. Thermal fluctuations are described by elementary excitations which define the thermodynamic behaviour of the system and result in Landau-type damping of collective modes. Fluctuations of the phase of the condensate wave function restrict the monochromaticity of the Josephson current. Fluctuations of the numbers of quanta result in the quantum collapse-revival of the collective oscillations. This phenomenon is considered in some details. Collapse time for the JILA experimental conditions turns out to be of the order of seconds. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd)
Short-time existence of solutions for mean-field games with congestion
Gomes, Diogo A.; Voskanyan, Vardan K.
2015-01-01
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
Directory of Open Access Journals (Sweden)
Jürgen Dorbritz
2013-03-01
When looking at wave one and wave two in comparison (i.e. a time period of one year, profound changes have already occurred regarding continuation or breakup. From those bilocal relationships found in wave one, more than half of the age-group questioned had not changed their chosen relationship type. The smaller portion of respondents had separated and thus ended bilocality (just over 10 %. The remaining bilocal relationships had increased their level of institutionalisation by becoming spouses or cohabitants. As regarding the development from wave one to wave two, it becomes apparent through the results of a multivariate analysis that the general circumstances of older respondents should be judged differently than those of younger ones. The work-related constellation between the two partners, spatial proximity, educational homogamy, previous experience in cohabitating and intentions in regard to separation or moving in together are explaining factors for the continuation of a bilocal relationship, the set-up of a shared household or a breakup.
Mean field theory for non-abelian gauge theories and fluid dynamics. A brief progress report
International Nuclear Information System (INIS)
Wadia, Spenta R.
2009-01-01
We review the long standing problem of 'mean field theory' for non-abelian gauge theories. As a consequence of the AdS/CFT correspondence, in the large N limit, at strong coupling, and high temperatures and density, the 'mean field theory' is described by the Navier-Stokes equations of fluid dynamics. We also discuss and present results on the non-conformal fluid dynamics of the D1 brane in 1+1 dim. (author)
Nuclear response beyond mean field theory
International Nuclear Information System (INIS)
Brand, M.G.E.; Allaart, K.; Dickhoff, W.H.
1990-01-01
An extension of the RPA equations is derived, with emphasis on the relation between the single-particle Green function and the polarization propagator. Including second order self-energy contributions the resulting particle-hole interaction includes the coupling to two-particle-two-hole (2p2h) states and the resulting response satisfies relevant conservation laws. This aspect of the theory is shown to be essential to obtain reliable and meaningful results for excitation strengths and to avoid ghost solutions. This method is applied to electromagnetic and charge exchange excitations in 48 Ca up to 100 MeV. A G-matrix interaction based on meson exchange is used which takes care of short-range correlations. The results compare favourably with measured excitation strengths and electromagnetic form factors both at low energy as well as in the giant resonance region. Remaining discrepancies point in the direction of further strength reduction due to short-range correlations as well as a possible stronger coupling to 2p2h states at low energy. (orig.)
Classification of networks of automata by dynamical mean field theory
International Nuclear Information System (INIS)
Burda, Z.; Jurkiewicz, J.; Flyvbjerg, H.
1990-01-01
Dynamical mean field theory is used to classify the 2 24 =65,536 different networks of binary automata on a square lattice with nearest neighbour interactions. Application of mean field theory gives 700 different mean field classes, which fall in seven classes of different asymptotic dynamics characterized by fixed points and two-cycles. (orig.)
Derivation and precision of mean field electrodynamics with mesoscale fluctuations
Zhou, Hongzhe; Blackman, Eric G.
2018-06-01
Mean field electrodynamics (MFE) facilitates practical modelling of secular, large scale properties of astrophysical or laboratory systems with fluctuations. Practitioners commonly assume wide scale separation between mean and fluctuating quantities, to justify equality of ensemble and spatial or temporal averages. Often however, real systems do not exhibit such scale separation. This raises two questions: (I) What are the appropriate generalized equations of MFE in the presence of mesoscale fluctuations? (II) How precise are theoretical predictions from MFE? We address both by first deriving the equations of MFE for different types of averaging, along with mesoscale correction terms that depend on the ratio of averaging scale to variation scale of the mean. We then show that even if these terms are small, predictions of MFE can still have a significant precision error. This error has an intrinsic contribution from the dynamo input parameters and a filtering contribution from differences in the way observations and theory are projected through the measurement kernel. Minimizing the sum of these contributions can produce an optimal scale of averaging that makes the theory maximally precise. The precision error is important to quantify when comparing to observations because it quantifies the resolution of predictive power. We exemplify these principles for galactic dynamos, comment on broader implications, and identify possibilities for further work.
A General Stochastic Maximum Principle for SDEs of Mean-field Type
International Nuclear Information System (INIS)
Buckdahn, Rainer; Djehiche, Boualem; Li Juan
2011-01-01
We study the optimal control for stochastic differential equations (SDEs) of mean-field type, in which the coefficients depend on the state of the solution process as well as of its expected value. Moreover, the cost functional is also of mean-field type. This makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. For a general action space a Peng’s-type stochastic maximum principle (Peng, S.: SIAM J. Control Optim. 2(4), 966–979, 1990) is derived, specifying the necessary conditions for optimality. This maximum principle differs from the classical one in the sense that here the first order adjoint equation turns out to be a linear mean-field backward SDE, while the second order adjoint equation remains the same as in Peng’s stochastic maximum principle.
Linear–Quadratic Mean-Field-Type Games: A Direct Method
Directory of Open Access Journals (Sweden)
Tyrone E. Duncan
2018-02-01
Full Text Available In this work, a multi-person mean-field-type game is formulated and solved that is described by a linear jump-diffusion system of mean-field type and a quadratic cost functional involving the second moments, the square of the expected value of the state, and the control actions of all decision-makers. We propose a direct method to solve the game, team, and bargaining problems. This solution approach does not require solving the Bellman–Kolmogorov equations or backward–forward stochastic differential equations of Pontryagin’s type. The proposed method can be easily implemented by beginners and engineers who are new to the emerging field of mean-field-type game theory. The optimal strategies for decision-makers are shown to be in a state-and-mean-field feedback form. The optimal strategies are given explicitly as a sum of the well-known linear state-feedback strategy for the associated deterministic linear–quadratic game problem and a mean-field feedback term. The equilibrium cost of the decision-makers are explicitly derived using a simple direct method. Moreover, the equilibrium cost is a weighted sum of the initial variance and an integral of a weighted variance of the diffusion and the jump process. Finally, the method is used to compute global optimum strategies as well as saddle point strategies and Nash bargaining solution in state-and-mean-field feedback form.
Self-consistent mean field forces in turbulent plasmas: Current and momentum relaxation
International Nuclear Information System (INIS)
Hegna, C.C.
1997-08-01
The properties of turbulent plasmas are described using the two-fluid equations. Under some modest assumptions, global constraints for the turbulent mean field forces that act on the ion and electron fluids are derived. These constraints imply a functional form for the parallel mean field forces in the Ohm's law and the momentum balance equation. These forms suggest that the fluctuations attempt to relax the plasma to a state where both the current and the bulk plasma momentum are aligned along the mean magnetic field with proportionality constants that are global constants. Observations of flow profile evolution during discrete dynamo activity in reversed field pinch experiments are interpreted
Time-Dependent Mean-Field Games in the Subquadratic Case
Gomes, Diogo A.; Pimentel, Edgard A.; Sá nchez-Morgado, Hé ector
2014-01-01
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.
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 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.
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...
One-Dimensional Forward–Forward Mean-Field Games
Energy Technology Data Exchange (ETDEWEB)
Gomes, Diogo A., E-mail: diogo.gomes@kaust.edu.sa; Nurbekyan, Levon; Sedjro, Marc [King Abdullah University of Science and Technology (KAUST), CEMSE Division (Saudi Arabia)
2016-12-15
While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward–forward problem is still poorly understood—even in the one-dimensional setting. Here, we consider one-dimensional forward–forward MFGs, study the existence of solutions and their long-time convergence. First, we discuss the relation between these models and systems of conservation laws. In particular, we identify new conserved quantities and study some qualitative properties of these systems. Next, we introduce a class of wave-like equations that are equivalent to forward–forward MFGs, and we derive a novel formulation as a system of conservation laws. For first-order logarithmic forward–forward MFG, we establish the existence of a global solution. Then, we consider a class of explicit solutions and show the existence of shocks. Finally, we examine parabolic forward–forward MFGs and establish the long-time convergence of the solutions.
One-Dimensional Forward–Forward Mean-Field Games
Gomes, Diogo A.; Nurbekyan, Levon; Sedjro, Marc
2016-01-01
While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward–forward problem is still poorly understood—even in the one-dimensional setting. Here, we consider one-dimensional forward–forward MFGs, study the existence of solutions and their long-time convergence. First, we discuss the relation between these models and systems of conservation laws. In particular, we identify new conserved quantities and study some qualitative properties of these systems. Next, we introduce a class of wave-like equations that are equivalent to forward–forward MFGs, and we derive a novel formulation as a system of conservation laws. For first-order logarithmic forward–forward MFG, we establish the existence of a global solution. Then, we consider a class of explicit solutions and show the existence of shocks. Finally, we examine parabolic forward–forward MFGs and establish the long-time convergence of the solutions.
One-Dimensional Forward–Forward Mean-Field Games
Gomes, Diogo A.
2016-11-01
While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward–forward problem is still poorly understood—even in the one-dimensional setting. Here, we consider one-dimensional forward–forward MFGs, study the existence of solutions and their long-time convergence. First, we discuss the relation between these models and systems of conservation laws. In particular, we identify new conserved quantities and study some qualitative properties of these systems. Next, we introduce a class of wave-like equations that are equivalent to forward–forward MFGs, and we derive a novel formulation as a system of conservation laws. For first-order logarithmic forward–forward MFG, we establish the existence of a global solution. Then, we consider a class of explicit solutions and show the existence of shocks. Finally, we examine parabolic forward–forward MFGs and establish the long-time convergence of the solutions.
Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods
Machado Velho, Roberto
2017-09-10
In this dissertation, we present two research projects, namely finite-state mean-field games and the Hughes model for the motion of crowds. In the first part, we describe finite-state mean-field games and some applications to socio-economic sciences. Examples include paradigm shifts in the scientific community and the consumer choice behavior in a free market. The corresponding finite-state mean-field game models are hyperbolic systems of partial differential equations, for which we propose and validate a new numerical method. Next, we consider the dual formulation to two-state mean-field games, and we discuss numerical methods for these problems. We then depict different computational experiments, exhibiting a variety of behaviors, including shock formation, lack of invertibility, and monotonicity loss. We conclude the first part of this dissertation with an investigation of the shock structure for two-state problems. In the second part, we consider a model for the movement of crowds proposed by R. Hughes in [56] and describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an Eikonal equation with Dirichlet or Neumann data. We first establish a priori estimates for the solutions. Next, we consider radial solutions, and we identify a shock formation mechanism. Subsequently, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. We also propose a new numerical method for the solution of Fokker-Planck equations and then to systems of PDEs composed by a Fokker-Planck equation and a potential type equation. Finally, we illustrate the use of the numerical method both to the Hughes model and mean-field games. We also depict cases such as the evacuation of a room and the movement of persons around Kaaba (Saudi Arabia).
Two Populations Mean-Field Monomer-Dimer Model
Alberici, Diego; Mingione, Emanuele
2018-04-01
A two populations mean-field monomer-dimer model including both hard-core and attractive interactions between dimers is considered. The pressure density in the thermodynamic limit is proved to satisfy a variational principle. A detailed analysis is made in the limit of one population is much smaller than the other and a ferromagnetic mean-field phase transition is found.
Exotic nuclei in self-consistent mean-field models
International Nuclear Information System (INIS)
Bender, M.; Rutz, K.; Buervenich, T.; Reinhard, P.-G.; Maruhn, J. A.; Greiner, W.
1999-01-01
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 with emphasis on neutron-rich tin isotopes and superheavy nuclei. (c) 1999 American Institute of Physics
Modification of linear response theory for mean-field approximations
Hütter, M.; Öttinger, H.C.
1996-01-01
In the framework of statistical descriptions of many particle systems, the influence of mean-field approximations on the linear response theory is studied. A procedure, analogous to one where no mean-field approximation is involved, is used in order to determine the first order response of the
Conservation laws arising in the study of forward-forward Mean-Field Games
Gomes, Diogo A.; Nurbekyan, Levon; Sedjro, Marc
2017-01-01
We consider forward-forward Mean Field Game (MFG) models that arise in numerical approximations of stationary MFGs. First, we establish a link between these models and a class of hyperbolic conservation laws as well as certain nonlinear wave equations. Second, we investigate existence and long-time behavior of solutions for such models.
Conservation laws arising in the study of forward-forward Mean-Field Games
Gomes, Diogo A.
2017-04-24
We consider forward-forward Mean Field Game (MFG) models that arise in numerical approximations of stationary MFGs. First, we establish a link between these models and a class of hyperbolic conservation laws as well as certain nonlinear wave equations. Second, we investigate existence and long-time behavior of solutions for such models.
Development of mean field theories in nuclear physics and in desordered media
International Nuclear Information System (INIS)
Orland, Henri.
1981-04-01
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 [fr
A Stochastic Maximum Principle for Risk-Sensitive Mean-Field Type Control
Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul
2015-01-01
In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends the risk-sensitive SMP (without mean-field coupling) of Lim and Zhou (2005), derived for feedback (or Markov) type optimal controls, to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. In our approach to the risk-sensitive SMP, the smoothness assumption on the value-function imposed in Lim and Zhou (2005) needs not be satisfied. For a general action space a Peng's type SMP is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type SMP under linear stochastic dynamics with exponential quadratic cost function. Explicit solutions are given for both mean-field free and mean-field models.
A Stochastic Maximum Principle for Risk-Sensitive Mean-Field Type Control
Djehiche, Boualem
2015-02-24
In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends the risk-sensitive SMP (without mean-field coupling) of Lim and Zhou (2005), derived for feedback (or Markov) type optimal controls, to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. In our approach to the risk-sensitive SMP, the smoothness assumption on the value-function imposed in Lim and Zhou (2005) needs not be satisfied. For a general action space a Peng\\'s type SMP is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type SMP under linear stochastic dynamics with exponential quadratic cost function. Explicit solutions are given for both mean-field free and mean-field models.
Statistical thermodynamics and mean-field theory for the alloy under irradiation model
International Nuclear Information System (INIS)
Kamyshendo, V.
1993-01-01
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
On Social Optima of Non-Cooperative Mean Field Games
Energy Technology Data Exchange (ETDEWEB)
Li, Sen; Zhang, Wei; Zhao, Lin; Lian, Jianming; Kalsi, Karanjit
2016-12-12
This paper studies the social optima in noncooperative mean-field games for a large population of agents with heterogeneous stochastic dynamic systems. Each agent seeks to maximize an individual utility functional, and utility functionals of different agents are coupled through a mean field term that depends on the mean of the population states/controls. The paper has the following contributions. First, we derive a set of control strategies for the agents that possess *-Nash equilibrium property, and converge to the mean-field Nash equilibrium as the population size goes to infinity. Second, we study the social optimal in the mean field game. We derive the conditions, termed the socially optimal conditions, under which the *-Nash equilibrium of the mean field game maximizes the social welfare. Third, a primal-dual algorithm is proposed to compute the *-Nash equilibrium of the mean field game. Since the *-Nash equilibrium of the mean field game is socially optimal, we can compute the equilibrium by solving the social welfare maximization problem, which can be addressed by a decentralized primal-dual algorithm. Numerical simulations are presented to demonstrate the effectiveness of the proposed approach.
On the convergence of finite state mean-field games through Γ-convergence
Ferreira, Rita C.; Gomes, Diogo A.
2014-01-01
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.
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.
Non-equilibrium mean-field theories on scale-free networks
International Nuclear Information System (INIS)
Caccioli, Fabio; Dall'Asta, Luca
2009-01-01
Many non-equilibrium processes on scale-free networks present anomalous critical behavior that is not explained by standard mean-field theories. We propose a systematic method to derive stochastic equations for mean-field order parameters that implicitly account for the degree heterogeneity. The method is used to correctly predict the dynamical critical behavior of some binary spin models and reaction–diffusion processes. The validity of our non-equilibrium theory is further supported by showing its relation with the generalized Landau theory of equilibrium critical phenomena on networks
Some approximate calculations in SU2 lattice mean field theory
International Nuclear Information System (INIS)
Hari Dass, N.D.; Lauwers, P.G.
1981-12-01
Approximate calculations are performed for small Wilson loops of SU 2 lattice gauge theory in mean field approximation. Reasonable agreement is found with Monte Carlo data. Ways of improving these calculations are discussed. (Auth.)
Socio-economic applications of finite state mean field games
Gomes, Diogo A.; Machado Velho, Roberto; Wolfram, Marie Therese
2014-01-01
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
Explicit Solutions for One-Dimensional Mean-Field Games
Prazeres, Mariana
2017-01-01
In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or without congestion. Our aim is to understand the qualitative features of these games through the analysis of explicit solutions. We are particularly interested
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.
Generalized quantum mean-field systems and their application to ultracold atoms
International Nuclear Information System (INIS)
Trimborn-Witthaut, Friederike Annemarie
2011-01-01
-symmetric states and discuss their representation by quantum phase space distributions in terms of generalized coherent states. In particular, this allows for an explicit calculation of the evolution equations and bounds for the ground state energy. In the second part of this thesis we analyse the dynamics of ultracold atoms in optical lattices described by the Bose-Hubbard Hamiltonian, which provide an important example of the generalized quantum mean-field systems treated in the first part. In the mean-field limit the dynamics is described by the (discrete) Gross-Pitaevskii equation. We give a detailed analysis of the interplay between dissipation and strong interactions in different dynamical settings, where we especially focus on the relation between the mean-field description and the full many-particle dynamics given by a master equation. (orig.)
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.
Solution of the hyperon puzzle within a relativistic mean-field model
Directory of Open Access Journals (Sweden)
K.A. Maslov
2015-09-01
Full Text Available 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.
Mean-field Ohm's law and coaxial helicity injection in force-free plasmas
International Nuclear Information System (INIS)
Weening, R. H.
2011-01-01
A theoretical analysis of steady-state coaxial helicity injection (CHI) in force-free plasmas is presented using a parallel mean-field Ohm's law that includes resistivity η and hyper-resistivity Λ terms. Using Boozer coordinates, a partial differential equation is derived for the time evolution of the mean-field poloidal magnetic flux, or magnetic Hamiltonian function, from the parallel mean-field Ohm's law. A general expression is obtained from the mean-field theory for the efficiency of CHI current drive in force-free plasmas. Inductances of internal energy, magnetic helicity, and poloidal magnetic flux are used to characterize axisymmetric plasma equilibria that have a model current profile. Using the model current profile, a method is suggested to determine the level of magnetohydrodynamic activity at the magnetic axis and the consequent deviation from the completely relaxed Taylor state. The mean-field Ohm's law model suggests that steady-state CHI can be viewed most simply as a boundary layer problem.
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.
A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type
International Nuclear Information System (INIS)
Hosking, John Joseph Absalom
2012-01-01
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.
Dynamical Mean Field Approximation Applied to Quantum Field Theory
Akerlund, Oscar; Georges, Antoine; Werner, Philipp
2013-12-04
We apply the Dynamical Mean Field (DMFT) approximation to the real, scalar phi^4 quantum field theory. By comparing to lattice Monte Carlo calculations, perturbation theory and standard mean field theory, we test the quality of the approximation in two, three, four and five dimensions. The quantities considered in these tests are the critical coupling for the transition to the ordered phase and the associated critical exponents nu and beta. We also map out the phase diagram in four dimensions. In two and three dimensions, DMFT incorrectly predicts a first order phase transition for all bare quartic couplings, which is problematic, because the second order nature of the phase transition of lattice phi^4-theory is crucial for taking the continuum limit. Nevertheless, by extrapolating the behaviour away from the phase transition, one can obtain critical couplings and critical exponents. They differ from those of mean field theory and are much closer to the correct values. In four dimensions the transition is sec...
Mean field strategies induce unrealistic nonlinearities in calcium puffs
Directory of Open Access Journals (Sweden)
Guillermo eSolovey
2011-08-01
Full Text Available Mean field models are often useful approximations to biological systems, but sometimes, they can yield misleading results. In this work, we compare mean field approaches with stochastic models of intracellular calcium release. In particular, we concentrate on calcium signals generated by the concerted opening of several clustered channels (calcium puffs. To this end we simulate calcium puffs numerically and then try to reproduce features of the resulting calcium distribution using mean field models were all the channels open and close simultaneously. We show that an unrealistic nonlinear relationship between the current and the number of open channels is needed to reproduce the simulated puffs. Furthermore, a single channel current which is five times smaller than the one of the stochastic simulations is also needed. Our study sheds light on the importance of the stochastic kinetics of the calcium release channel activity to estimate the release fluxes.
Self-consistent mean-field models for nuclear structure
International Nuclear Information System (INIS)
Bender, Michael; Heenen, Paul-Henri; Reinhard, Paul-Gerhard
2003-01-01
The authors review the present status of self-consistent mean-field (SCMF) models for describing nuclear structure and low-energy dynamics. These models are presented as effective energy-density functionals. The three most widely used variants of SCMF's based on a Skyrme energy functional, a Gogny force, and a relativistic mean-field Lagrangian are considered side by side. The crucial role of the treatment of pairing correlations is pointed out in each case. The authors discuss other related nuclear structure models and present several extensions beyond the mean-field model which are currently used. Phenomenological adjustment of the model parameters is discussed in detail. The performance quality of the SCMF model is demonstrated for a broad range of typical applications
Symplectic manifolds, coadjoint orbits, and Mean Field Theory
International Nuclear Information System (INIS)
Rosensteel, G.
1986-01-01
Mean field theory is given a geometrical interpretation as a Hamiltonian dynamical system. The Hartree-Fock phase space is the Grassmann manifold, a symplectic submanifold of the projective space of the full many-fermion Hilbert space. The integral curves of the Hartree-Fock vector field are the time-dependent Hartree-Fock solutions, while the critical points of the energy function are the time-independent states. The mean field theory is generalized beyond determinants to coadjoint orbit spaces of the unitary group; the Grassmann variety is the minimal coadjoint orbit
A mean field theory of coded CDMA systems
International Nuclear Information System (INIS)
Yano, Toru; Tanaka, Toshiyuki; Saad, David
2008-01-01
We present a mean field theory of code-division multiple-access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean-field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems
A mean field theory of coded CDMA systems
Energy Technology Data Exchange (ETDEWEB)
Yano, Toru [Graduate School of Science and Technology, Keio University, Hiyoshi, Kohoku-ku, Yokohama-shi, Kanagawa 223-8522 (Japan); Tanaka, Toshiyuki [Graduate School of Informatics, Kyoto University, Yoshida Hon-machi, Sakyo-ku, Kyoto-shi, Kyoto 606-8501 (Japan); Saad, David [Neural Computing Research Group, Aston University, Birmingham B4 7ET (United Kingdom)], E-mail: yano@thx.appi.keio.ac.jp
2008-08-15
We present a mean field theory of code-division multiple-access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean-field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems.
Shapes and dynamics from the time-dependent mean field
International Nuclear Information System (INIS)
Stevenson, P.D.; Goddard, P.M.; 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
Mean field with corrections in lattice gauge theory
International Nuclear Information System (INIS)
Flyvbjerg, H.; Zuber, J.B.; Lautrup, B.
1981-12-01
A systematic expansion of the path integral for lattice gauge theory is performed around the mean field solution. In this letter the authors present the results for the pure gauge groups Z(2), SU(2) and SO(3). The agreement with Monte Carlo calculations is excellent. For the discrete group the calculation is performed with and without gauge fixing, whereas for the continuous groups gauge fixing is mandatory. In the case of SU(2) the absence of a phase transition is correctly signalled by mean field theory. (Auth.)
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.
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.
A New Method and a New Scaling for Deriving Fermionic Mean-Field Dynamics
International Nuclear Information System (INIS)
Petrat, Sören; Pickl, Peter
2016-01-01
We introduce a new method for deriving the time-dependent Hartree or Hartree-Fock equations as an effective mean-field dynamics from the microscopic Schrödinger equation for fermionic many-particle systems in quantum mechanics. The method is an adaption of the method used in Pickl (Lett. Math. Phys. 97 (2) 151–164 2011) for bosonic systems to fermionic systems. It is based on a Gronwall type estimate for a suitable measure of distance between the microscopic solution and an antisymmetrized product state. We use this method to treat a new mean-field limit for fermions with long-range interactions in a large volume. Some of our results hold for singular attractive or repulsive interactions. We can also treat Coulomb interaction assuming either a mild singularity cutoff or certain regularity conditions on the solutions to the Hartree(-Fock) equations. In the considered limit, the kinetic and interaction energy are of the same order, while the average force is subleading. For some interactions, we prove that the Hartree(-Fock) dynamics is a more accurate approximation than a simpler dynamics that one would expect from the subleading force. With our method we also treat the mean-field limit coupled to a semiclassical limit, which was discussed in the literature before, and we recover some of the previous results. All results hold for initial data close (but not necessarily equal) to antisymmetrized product states and we always provide explicit rates of convergence.
Hydrodynamic mean-field solutions of 1D exclusion processes with spatially varying hopping rates
Energy Technology Data Exchange (ETDEWEB)
Lakatos, Greg; O' Brien, John; Chou, Tom [Department of Biomathematics and Institute for Pure and Applied Mathematics, UCLA, Los Angeles, CA 90095 (United States)
2006-03-10
We analyse the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean-field limit. The mean-field equations for particle densities are written in terms of Ricatti equations with the steady-state current J as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents J are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for J from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean-field currents asymptotically approach the exact currents in the hydrodynamic limit, as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions.
Hydrodynamic mean-field solutions of 1D exclusion processes with spatially varying hopping rates
International Nuclear Information System (INIS)
Lakatos, Greg; O'Brien, John; Chou, Tom
2006-01-01
We analyse the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean-field limit. The mean-field equations for particle densities are written in terms of Ricatti equations with the steady-state current J as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents J are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for J from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean-field currents asymptotically approach the exact currents in the hydrodynamic limit, as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions
Applying Mean-Field Approximation to Continuous Time Markov Chains
Kolesnichenko, A.V.; Senni, Valerio; Pourranjabar, Alireza; Remke, A.K.I.; Stoelinga, M.I.A.
2014-01-01
The mean-field analysis technique is used to perform analysis of a system with a large number of components to determine the emergent deterministic behaviour and how this behaviour modifies when its parameters are perturbed. The computer science performance modelling and analysis community has found
Mean-field theory of anyons near Bose statistics
International Nuclear Information System (INIS)
McCabe, J.; MacKenzie, R.
1992-01-01
The validity of a mean-field approximation for a boson-based free anyon gas near Bose statistics is shown. The magnetic properties of the system is discussed in the approximation that the statistical magnetic field is uniform. It is proved that the anyon gas does not exhibit a Meissner effect in the domain of validity the approximation. (K.A.) 7 refs
Constrained deterministic leader-follower mean field control
Möller, L.; Gentile, B.; Parise, F.; Grammatico, S.; Lygeros, J.
2016-01-01
We consider a mean field game among a large population of noncooperative agents divided into two categories: leaders and followers. Each agent is subject to heterogeneous convex constraints and minimizes a quadratic cost function; the cost of each leader is affected by the leaders' aggregate
A mean-field game economic growth model
Gomes, Diogo A.; Lafleche, Laurent; Nurbekyan, Levon
2016-01-01
Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative, rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent seeks
Two numerical methods for mean-field games
Gomes, Diogo A.
2016-01-09
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
Two numerical methods for mean-field games
Gomes, Diogo A.
2016-01-01
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
Two Numerical Approaches to Stationary Mean-Field Games
Almulla, Noha; Ferreira, Rita; Gomes, Diogo A.
2016-01-01
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
Halo nuclei studied by relativistic mean-field approach
International Nuclear Information System (INIS)
Gmuca, S.
1997-01-01
Density distributions of light neutron-rich nuclei are studied by using the relativistic mean-field approach. The effective interaction which parameterizes the recent Dirac-Brueckner-Hartree-Fock calculations of nuclear matter is used. The results are discussed and compared with the experimental observations with special reference to the neutron halo in the drip-line nuclei. (author)
Two Numerical Approaches to Stationary Mean-Field Games
Almulla, Noha
2016-10-04
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
One-Dimensional Stationary Mean-Field Games with Local Coupling
Gomes, Diogo A.; Nurbekyan, Levon; Prazeres, Mariana
2017-01-01
A standard assumption in mean-field game (MFG) theory is that the coupling between the Hamilton–Jacobi equation and the transport equation is monotonically non-decreasing in the density of the population. In many cases, this assumption implies the existence and uniqueness of solutions. Here, we drop that assumption and construct explicit solutions for one-dimensional MFGs. These solutions exhibit phenomena not present in monotonically increasing MFGs: low-regularity, non-uniqueness, and the formation of regions with no agents.
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...
One-Dimensional Stationary Mean-Field Games with Local Coupling
Gomes, Diogo A.
2017-05-25
A standard assumption in mean-field game (MFG) theory is that the coupling between the Hamilton–Jacobi equation and the transport equation is monotonically non-decreasing in the density of the population. In many cases, this assumption implies the existence and uniqueness of solutions. Here, we drop that assumption and construct explicit solutions for one-dimensional MFGs. These solutions exhibit phenomena not present in monotonically increasing MFGs: low-regularity, non-uniqueness, and the formation of regions with no agents.
A dynamic mean-field glass model with reversible mode coupling and a trivial Hamiltonian
International Nuclear Information System (INIS)
Kawasaki, Kyozi; Kim, Bongsoo
2002-01-01
Often the current mode coupling theory (MCT) of glass transitions is compared with mean field theories. We explore this possible correspondence. After showing a simple-minded derivation of MCT with some difficulties we give a concise account of our toy model developed to gain more insight into MCT. We then reduce this toy model by adiabatically eliminating rapidly varying velocity-like variables to obtain a Fokker-Planck equation for the slowly varying density-like variables where the diffusion matrix can be singular. This gives room for non-ergodic stationary solutions of the above equation. (author)
Mean field limit for bosons with compact kernels interactions by Wigner measures transportation
International Nuclear Information System (INIS)
Liard, Quentin; Pawilowski, Boris
2014-01-01
We consider a class of many-body Hamiltonians composed of a free (kinetic) part and a multi-particle (potential) interaction with a compactness assumption on the latter part. We investigate the mean field limit of such quantum systems following the Wigner measures approach. We prove in particular the propagation of these measures along the flow of a nonlinear (Hartree) field equation. This enhances and complements some previous results of the same type shown in Z. Ammari and F. Nier and Fröhlich et al. [“Mean field limit for bosons and propagation of Wigner measures,” J. Math. Phys. 50(4), 042107 (2009); Z. Ammari and F. Nier and Fröhlich et al., “Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states,” J. Math. Pures Appl. 95(6), 585–626 (2011); Z. Ammari and F. Nier and Fröhlich et al., “Mean-field- and classical limit of many-body Schrödinger dynamics for bosons,” Commun. Math. Phys. 271(3), 681–697 (2007)
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.
Time-dependent mean-field games in the superquadratic case
Gomes, Diogo A.; Pimentel, Edgard; Sá nchez-Morgado, Hé ctor
2016-01-01
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.
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)
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...... a novelty approach we may detect unseen faulty signals as indeed faulty with high precision, even though the model learns only from normal signals. This is done by evaluating the likelihood that the model generated the signals and adapting a simple threshold for decision. Acoustic emission energy signals...... from a large diesel engine is used to demonstrate this approach. The results show that mean field independent components analysis gives a better detection of fault compared to principal components analysis, while at the same time selecting a more compact model...
Instability in relativistic mean-field theories of nuclear matter
International Nuclear Information System (INIS)
Friman, B.L.; Henning, P.A.
1988-01-01
We investigate the stability of the nuclear matter ground state with respect to small-perturbations of the meson fields in relativistic mean-field theories. The popular σ-ω model is shown to have an instability at about twice the nuclear density, which gives rise to a new ground state with periodic spin alignment. Taking into account the contributions of the Dirac sea properly, this instability vanishes. Consequences for relativistic heavy-ion-collisions are discussed briefly. (orig.)
Retardation and dispersive effects in the nuclear mean field
International Nuclear Information System (INIS)
Mahaux, C.; Davies, K.T.R.; Satchler, G.R.
1993-01-01
We consider several parametrizations of the energy dependence of the imaginary part of the mean field, for nucleons as well as heavy ions. These parametrizations specify the energy dependence of the corresponding real part, because the real and imaginary parts are connected by a dispersion relation. The latter can be viewed as equivalent to the causality property. Since Hilbert transforms appear in the dispersion relation and since Fourier transforms give the correspondence between energy dependence and temporal nonlocality, we derive several properties of these transforms which are of particular interest in the present context. The most useful one is that the Fourier transform of a function F(E) which is analytic in the upper half of the complex E-plane can be expressed in terms of the Fourier transform of the imaginary part of F(E) alone. We investigate several schematic models for the mean field. They fall into two main categories. These correspond to the two main definitions which have been proposed for the mean field, namely the self-energy and Feshbach's potential. Both of these definitions can be used for the nucleon-nucleus system, in which case they correspond to two different ways of handling the combined influence of ground state correlations and antisymmetrization. The resulting two mean fields have different energy dependences and, correspondingly, temporal nonlocalities. Feshbach's approach can also be applied to the nucleus-nucleus system. Our schematic models are semi-realistic, in the sense that they all take account of the 'Fermi surface anomaly' for the nucleon-nucleus system or of the 'threshold anomaly' for the nucleus-nucleus case. The temporal nonlocality is investigated for each model. A physical interpretation of this nonlocality is given in terms delay of the response of the medium, in which an incident wave is partially trapped in nonelastic channels and subsequently reemitted. (orig./HSI)
RPA correlations and nuclear densities in relativistic mean field approach
International Nuclear Information System (INIS)
Van Giai, N.; Liang, H.Z.; Meng, J.
2007-02-01
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)
Instability in relativistic mean-field theories of nuclear matter
International Nuclear Information System (INIS)
Friman, B.L.; Henning, P.A.
1988-01-01
We investigate the stability of the nuclear matter ground state with respect to small perturbations of the meson fields in relativistic mean-field theories. The popular σ-ω model is shown to have an instability at about twice the nuclear density, which gives rise to a new ground state with periodic spin alignment. Taking into account the contributions of the Dirac sea properly, this instability vanishes. Consequences for relativistic heavy-ion collisions are discussed briefly. (orig.)
Neutron-skin thickness of finite nuclei in relativistic mean-field models with chiral limits
International Nuclear Information System (INIS)
Jiang Weizhou; Li Baoan; Chen Liewen
2007-01-01
We study several structure properties of finite nuclei using relativistic mean-field Lagrangians constructed according to the Brown-Rho scaling due to the chiral symmetry restoration at high densities. The models are consistent with current experimental constraints for the equations of state of symmetric matter at both normal and supranormal densities and of asymmetric matter at subsaturation densities. It is shown that these models can successfully describe the binding energies and charge radii of finite nuclei. Compared to calculations with usual relativistic mean-field models, these models give a reduced thickness of neutron skin in 208 Pb between 0.17 fm and 0.21 fm. The reduction of the predicted neutron skin thickness is found to be due to not only the softening of the symmetry energy but also the scaling property of ρ meson required by the partial restoration of chiral symmetry
Mean Field Limits for Interacting Diffusions in a Two-Scale Potential
Gomes, S. N.; Pavliotis, G. A.
2018-06-01
In this paper, we study the combined mean field and homogenization limits for a system of weakly interacting diffusions moving in a two-scale, locally periodic confining potential, of the form considered in Duncan et al. (Brownian motion in an N-scale periodic potential, arXiv:1605.05854, 2016b). We show that, although the mean field and homogenization limits commute for finite times, they do not, in general, commute in the long time limit. In particular, the bifurcation diagrams for the stationary states can be different depending on the order with which we take the two limits. Furthermore, we construct the bifurcation diagram for the stationary McKean-Vlasov equation in a two-scale potential, before passing to the homogenization limit, and we analyze the effect of the multiple local minima in the confining potential on the number and the stability of stationary solutions.
Advances in dynamic and mean field games theory, applications, and numerical methods
Viscolani, Bruno
2017-01-01
This contributed volume considers recent advances in dynamic games and their applications, based on presentations given at the 17th Symposium of the International Society of Dynamic Games, held July 12-15, 2016, in Urbino, Italy. Written by experts in their respective disciplines, these papers cover various aspects of dynamic game theory including mean-field games, stochastic and pursuit-evasion games, and computational methods for dynamic games. Topics covered include Pedestrian flow in crowded environments Models for climate change negotiations Nash Equilibria for dynamic games involving Volterra integral equations Differential games in healthcare markets Linear-quadratic Gaussian dynamic games Aircraft control in wind shear conditions Advances in Dynamic and Mean-Field Games presents state-of-the-art research in a wide spectrum of areas. As such, it serves as a testament to the continued vitality and growth of the field of dynamic games and their applications. It will be of interest to an interdisciplinar...
Neutron stars in relativistic mean field theory with isovector scalar meson
Energy Technology Data Exchange (ETDEWEB)
Kubis, S.; Kutschera, M.; Stachniewicz, S. [H. Niewodniczanski Institute of Nuclear Physics, Cracow (Poland)
1998-03-01
We study the equation of state (EOS) of {beta}-stable dense matter and models of neutron stars in the relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the {delta}-meson (a{sub 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{sub s}{approx}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 EOS becomes slightly stiffer and the maximum neutron star mass increases for stronger {delta}-meson coupling. (author) 8 refs, 6 figs, 2 tabs
Neutron stars in relativistic mean field theory with isovector scalar meson
International Nuclear Information System (INIS)
Kubis, S.; Kutschera, M.; Stachniewicz, S.
1996-12-01
We study the equation of state (EOS) of neutron star matter in a relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the δ-meson [a 0 (980)]. A range of values of the δ-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 proton fraction of neutron star matter is higher in the presence of the δ-field whereas the energy per particle is lower. The EOS becomes slightly stiffer and the maximum mass of the neutron star increased with increasing δmeson coupling. The effect is stronger for soft EOS. (author). 7 refs, 6 figs, 1 tab
Neutron stars in relativistic mean field theory with isovector scalar meson
International Nuclear Information System (INIS)
Kubis, S.; Kutschera, M.; Stachniewicz, S.
1998-01-01
We study the equation of state (EOS) of β-stable dense matter and models of neutron stars in the relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the δ-meson (a 0 (980)). A range of values of the δ-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 δ-meson coupling is the proton fraction of neutron star matter. It increases significantly in the presence of the δ-field. The energy per baryon also increases but the effect is smaller. The EOS becomes slightly stiffer and the maximum neutron star mass increases for stronger δ-meson coupling. (author)
Neutron stars in relativistic mean field theory with isovector scalar meson
Energy Technology Data Exchange (ETDEWEB)
Kubis, S.; Kutschera, M.; Stachniewicz, S. [Institute of Nuclear Physics, Cracow (Poland)
1996-12-01
We study the equation of state (EOS) of neutron star matter in a relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the {delta}-meson [a{sub 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{sub s} {approx} 30 MeV. We find that proton fraction of neutron star matter is higher in the presence of the {delta}-field whereas the energy per particle is lower. The EOS becomes slightly stiffer and the maximum mass of the neutron star increased with increasing {delta}meson coupling. The effect is stronger for soft EOS. (author). 7 refs, 6 figs, 1 tab.
Short-range correlations in an extended time-dependent mean-field theory
International Nuclear Information System (INIS)
Madler, P.
1982-01-01
A generalization is performed of the time-dependent mean-field theory by an explicit inclusion of strong short-range correlations on a level of microscopic reversibility relating them to realistic nucleon-nucleon forces. Invoking a least action principle for correlated trial wave functions, equations of motion for the correlation functions and the single-particle model wave function are derived in lowest order of the FAHT cluster expansion. Higher order effects as well as long-range correlations are consider only to the extent to which they contribute to the mean field via a readjusted phenomenological effective two-body interaction. The corresponding correlated stationary problem is investigated and appropriate initial conditions to describe a heavy ion reaction are proposed. The singleparticle density matrix is evaluated
Perturbative renormalization of composite operators via flow equations. Pt. 2
International Nuclear Information System (INIS)
Keller, G.; Kopper, C.
1993-01-01
We give a rigorous and very detailed derivation of the short distance expansion for a product of two arbitrary composite operators in the framework of the perturbative Euclidean massive Φ 4 4 . The technically almost trivial proof rests on an extension of the differential flow equation method to Green functions with bilocal insertions, for which we also establish a set of generalized Zimmermann identities and Lowenstein rules. (orig.)
Nonlinear mean field theory for nuclear matter and surface properties
International Nuclear Information System (INIS)
Boguta, J.; Moszkowski, S.A.
1983-01-01
Nuclear matter properties are studied in a nonlinear relativistic mean field theory. We determine the parameters of the model from bulk properties of symmetric nuclear matter and a reasonable value of the effective mass. In this work, we stress the nonrelativistic limit of the theory which is essentially equivalent to a Skyrme hamiltonian, and we show that most of the results can be obtained, to a good approximation, analytically. The strength of the required parameters is determined from the binding energy and density of nuclear matter and the effective nucleon mass. For realistic values of the parameters, the nonrelativistic approximation turns out to be quite satisfactory. Using reasonable values of the parameters, we can account for other key properties of nuclei, such as the spin-orbit coupling, surface energy, and diffuseness of the nuclear surface. Also the energy dependence of the nucleon-nucleus optical model is accounted for reasonably well except near the Fermi surface. It is found, in agreement with empirical results, that the Landau parameter F 0 is quite small in normal nuclear matter. Both density dependence and momentum dependence of the NN interaction, but especially the former, are important for nuclear saturation. The required scalar and vector coupling constants agree fairly well with those obtained from analyses of NN scattering phase shifts with one-boson-exchange models. The mean field theory provides a semiquantitative justification for the weak Skyrme interaction in odd states. The strength of the required nonlinear term is roughly consistent with that derived using a new version of the chiral mean field theory in which the vector mass as well as the nucleon mass is generated by the sigma-field. (orig.)
The mean field in many body quantum physics
International Nuclear Information System (INIS)
Llano, M. de
1984-01-01
As an introduction to the quantum problem of many bodies we present a panoramic view of the most elementary theories called mean field theories. They comprise: i) the fermions ideal gas theory which implies, in a simple manner, the stability of white dwarf stars and of neutron stars, ii) the Hartree-Fock approximation for thermodynamical systems which is presented here in the context of a liquid-crystal phase transition, and iii) the Thomas-Fermi theory which is applied to the total binding energy of neutral atoms. (author)
A mean-field game economic growth model
Gomes, Diogo A.
2016-08-05
Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative, rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent seeks to maximize his/her utility by taking into account statistical data about the whole population. The individual actions drive the evolution of the players, and a market-clearing condition determines the relative price of capital and consumer goods. We study the existence and uniqueness of optimal strategies of the agents and develop numerical methods to compute these strategies and the equilibrium price.
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.)
Surface incompressibility from semiclassical relativistic mean field calculations
International Nuclear Information System (INIS)
Patra, S.K.; Centelles, M.; Vinas, X.; Estal, M. del
2002-01-01
By using the scaling method and the Thomas-Fermi and extended Thomas-Fermi approaches to relativistic mean field theory the surface contribution to the leptodermous expansion of the finite nuclei incompressibility K A has been self-consistently computed. The validity of the simplest expansion, which contains volume, volume-symmetry, surface, and Coulomb terms, is examined by comparing it with self-consistent results of K A for some currently used nonlinear σ-ω parameter sets. A numerical estimate of higher-order contributions to the leptodermous expansion, namely, the curvature and surface-symmetry terms, is made
First-order, stationary mean-field games with congestion
Evangelista, David
2018-04-30
Mean-field games (MFGs) are models for large populations of competing rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas. Here, we study stationary MFGs with congestion with quadratic or power-like Hamiltonians. First, using explicit examples, we illustrate two main difficulties: the lack of classical solutions and the existence of areas with vanishing densities. Our main contribution is a new variational formulation for MFGs with congestion. With this formulation, we prove the existence and uniqueness of solutions. Finally, we consider applications to numerical methods.
Mean field dynamics of some open quantum systems.
Merkli, Marco; Rafiyi, Alireza
2018-04-01
We consider a large number N of quantum particles coupled via a mean field interaction to another quantum system (reservoir). Our main result is an expansion for the averages of observables, both of the particles and of the reservoir, in inverse powers of [Formula: see text]. The analysis is based directly on the Dyson series expansion of the propagator. We analyse the dynamics, in the limit [Formula: see text], of observables of a fixed number n of particles, of extensive particle observables and their fluctuations, as well as of reservoir observables. We illustrate our results on the infinite mode Dicke model and on various energy-conserving models.
Mean-field theory for a ferroelectric transition
International Nuclear Information System (INIS)
Dobry, A.; Greco, A.; Stachiotti, M.
1990-01-01
For the treatment of anharmonic models of solids presenting structural transitions, a commonly used approximation is that of self-consistent phonons. Rather than the usual site decoupling, this mean-field theory is based on decoupling of modes in reciprocal space. A self-consistent phonon approximation for the non-linear polarizability model is developed in this work. The model describes the dynamical properties of ferroelectric materials. Phase diagrams as a function of relevant model parameters are presented. An analysis is made of critical behaviour and it is shown that the approximation leads to the same anomalies found in other models. (Author). 9 refs., 3 figs
Mean field dynamics of some open quantum systems
Merkli, Marco; Rafiyi, Alireza
2018-04-01
We consider a large number N of quantum particles coupled via a mean field interaction to another quantum system (reservoir). Our main result is an expansion for the averages of observables, both of the particles and of the reservoir, in inverse powers of √{N }. The analysis is based directly on the Dyson series expansion of the propagator. We analyse the dynamics, in the limit N →∞ , of observables of a fixed number n of particles, of extensive particle observables and their fluctuations, as well as of reservoir observables. We illustrate our results on the infinite mode Dicke model and on various energy-conserving models.
Fictive impurity approach to dynamical mean field theory
International Nuclear Information System (INIS)
Fuhrmann, A.
2006-10-01
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.)
First-order, stationary mean-field games with congestion
Evangelista, David; Ferreira, Rita; Gomes, Diogo A.; Nurbekyan, Levon; Voskanyan, Vardan K.
2018-01-01
Mean-field games (MFGs) are models for large populations of competing rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas. Here, we study stationary MFGs with congestion with quadratic or power-like Hamiltonians. First, using explicit examples, we illustrate two main difficulties: the lack of classical solutions and the existence of areas with vanishing densities. Our main contribution is a new variational formulation for MFGs with congestion. With this formulation, we prove the existence and uniqueness of solutions. Finally, we consider applications to numerical methods.
Mean-field theory of differential rotation in density stratified turbulent convection
Rogachevskii, I.
2018-04-01
A mean-field theory of differential rotation in a density stratified turbulent convection has been developed. This theory is based on the combined effects of the turbulent heat flux and anisotropy of turbulent convection on the Reynolds stress. A coupled system of dynamical budget equations consisting in the equations for the Reynolds stress, the entropy fluctuations and the turbulent heat flux has been solved. To close the system of these equations, the spectral approach, which is valid for large Reynolds and Péclet numbers, has been applied. The adopted model of the background turbulent convection takes into account an increase of the turbulence anisotropy and a decrease of the turbulent correlation time with the rotation rate. This theory yields the radial profile of the differential rotation which is in agreement with that for the solar differential rotation.
International Nuclear Information System (INIS)
Niksic, T.; Vretenar, D.; Ring, P.
2006-01-01
The framework of relativistic self-consistent mean-field models is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum and particle-number projected relativistic wave functions. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the relativistic mean-field+Lipkin-Nogami BCS equations, with a constraint on the mass quadrupole moment. The model employs a relativistic point-coupling (contact) nucleon-nucleon effective interaction in the particle-hole channel, and a density-independent δ-interaction in the pairing channel. Illustrative calculations are performed for 24 Mg, 32 S, and 36 Ar, and compared with results obtained employing the model developed in the first part of this work, i.e., without particle-number projection, as well as with the corresponding nonrelativistic models based on Skyrme and Gogny effective interactions
Sums over geometries and improvements on the mean field approximation
International Nuclear Information System (INIS)
Sacksteder, Vincent E. IV
2007-01-01
The saddle points of a Lagrangian due to Efetov are analyzed. This Lagrangian was originally proposed as a tool for calculating systematic corrections to the Bethe approximation, a mean-field approximation which is important in statistical mechanics, glasses, coding theory, and combinatorial optimization. Detailed analysis shows that the trivial saddle point generates a sum over geometries reminiscent of dynamically triangulated quantum gravity, which suggests new possibilities to design sums over geometries for the specific purpose of obtaining improved mean-field approximations to D-dimensional theories. In the case of the Efetov theory, the dominant geometries are locally treelike, and the sum over geometries diverges in a way that is similar to quantum gravity's divergence when all topologies are included. Expertise from the field of dynamically triangulated quantum gravity about sums over geometries may be able to remedy these defects and fulfill the Efetov theory's original promise. The other saddle points of the Efetov Lagrangian are also analyzed; the Hessian at these points is nonnormal and pseudo-Hermitian, which is unusual for bosonic theories. The standard formula for Gaussian integrals is generalized to nonnormal kernels
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.)
The application of mean field theory to image motion estimation.
Zhang, J; Hanauer, G G
1995-01-01
Previously, Markov random field (MRF) model-based techniques have been proposed for image motion estimation. Since motion estimation is usually an ill-posed problem, various constraints are needed to obtain a unique and stable solution. The main advantage of the MRF approach is its capacity to incorporate such constraints, for instance, motion continuity within an object and motion discontinuity at the boundaries between objects. In the MRF approach, motion estimation is often formulated as an optimization problem, and two frequently used optimization methods are simulated annealing (SA) and iterative-conditional mode (ICM). Although the SA is theoretically optimal in the sense of finding the global optimum, it usually takes many iterations to converge. The ICM, on the other hand, converges quickly, but its results are often unsatisfactory due to its "hard decision" nature. Previously, the authors have applied the mean field theory to image segmentation and image restoration problems. It provides results nearly as good as SA but with much faster convergence. The present paper shows how the mean field theory can be applied to MRF model-based motion estimation. This approach is demonstrated on both synthetic and real-world images, where it produced good motion estimates.
Relativistic Chiral Mean Field Model for Finite Nuclei
Ogawa, Y.; Toki, H.; Tamenaga, S.; Haga, A.
2009-08-01
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^{π}. 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^{π} = 0^{-} (spherical ansatz). We extend the CPPRMF model by taking 2p-2h states with higher spin quantum numbers, J^{π} = 1^{+}, 2^{-}, 3^{+}, ... to describe the full strength of the pionic correlation in the intermediate range (r > 0.5 fm). We apply the RCMF model to the ^{4}He nucleus as a pilot calculation for the study of medium and heavy nuclei. We study the behavior of energy convergence with the pionic quantum number, J^{π}, and find convergence around J^{π}_{max} = 6^{-}. We include further the effect of the short-range repulsion in terms of the unitary correlation operator method (UCOM) for the central part of the pion-exchange interaction. The energy contribution of about 50% of the net two-body interaction comes from the tensor part and 20% comes from the spin-spin central part of the pion-exchange interaction.}
Non-local correlations within dynamical mean field theory
International Nuclear Information System (INIS)
Li, Gang
2009-03-01
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.)
Monotone numerical methods for finite-state mean-field games
Gomes, Diogo A.; Saude, Joao
2017-01-01
Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.
Neutron fraction and neutrino mean free path predictions in relativistic mean field models
International Nuclear Information System (INIS)
Hutauruk, P.T.P.; Williams, C.K.; Sulaksono, A.; Mart, T.
2004-01-01
The equation of state (EOS) of dense matter and neutrino mean free path (NMFP) in a neutron star have been studied by using relativistic mean field models motivated by effective field theory. It is found that the models predict too large proton fractions, although one of the models (G2) predicts an acceptable EOS. This is caused by the isovector terms. Except G2, the other two models predict anomalous NMFP's. In order to minimize the anomaly, besides an acceptable EOS, a large M* is favorable. A model with large M* retains the regularity in the NMFP even for a small neutron fraction
A new nonlinear mean-field model of neutron star matter
Miyazaki, K
2005-01-01
A new relativistic mean-field model of neutron star matter is developed. It is a generalization of the Zimanyi-Moszkowski (ZM) model based on the constituent quark picture of baryons. The renormalized meson-hyperon coupling constants in medium are uniquely determined in contrast to the naive extention of ZM model and so the application of the model to high-density neutron star (NS) matter is possible. Our results of the particle composition and the mass-radius relation of NSs agree well with those obtained from the phenomenologically-determined realistic equation-of-state.
Existence of weak solutions to first-order stationary mean-field games with Dirichlet conditions
Ferreira, Rita; Gomes, Diogo A.; Tada, Teruo
2018-01-01
In this paper, we study first-order stationary monotone mean-field games (MFGs) with Dirichlet boundary conditions. While for Hamilton--Jacobi equations Dirichlet conditions may not be satisfied, here, we establish the existence of solutions of MFGs that satisfy those conditions. To construct these solutions, we introduce a monotone regularized problem. Applying Schaefer's fixed-point theorem and using the monotonicity of the MFG, we verify that there exists a unique weak solution to the regularized problem. Finally, we take the limit of the solutions of the regularized problem and using Minty's method, we show the existence of weak solutions to the original MFG.
Existence of weak solutions to first-order stationary mean-field games with Dirichlet conditions
Ferreira, Rita
2018-04-19
In this paper, we study first-order stationary monotone mean-field games (MFGs) with Dirichlet boundary conditions. While for Hamilton--Jacobi equations Dirichlet conditions may not be satisfied, here, we establish the existence of solutions of MFGs that satisfy those conditions. To construct these solutions, we introduce a monotone regularized problem. Applying Schaefer\\'s fixed-point theorem and using the monotonicity of the MFG, we verify that there exists a unique weak solution to the regularized problem. Finally, we take the limit of the solutions of the regularized problem and using Minty\\'s method, we show the existence of weak solutions to the original MFG.
Monotone numerical methods for finite-state mean-field games
Gomes, Diogo A.
2017-04-29
Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.
Quantum Critical Point revisited by the Dynamical Mean Field Theory
Xu, Wenhu; Kotliar, Gabriel; Tsvelik, Alexei
Dynamical mean field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. The QCP is characterized by a universal scaling form of the self energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low energy kink and the high energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high energy antiferromagnetic paramagnons. We use the frequency dependent four-point correlation function of spin operators to calculate the momentum dependent correction to the electron self energy. Our results reveal a substantial difference with the calculations based on the Spin-Fermion model which indicates that the frequency dependence of the the quasiparitcle-paramagnon vertices is an important factor. The authors are supported by Center for Computational Design of Functional Strongly Correlated Materials and Theoretical Spectroscopy under DOE Grant DE-FOA-0001276.
Quantum critical point revisited by dynamical mean-field theory
Xu, Wenhu; Kotliar, Gabriel; Tsvelik, Alexei M.
2017-03-01
Dynamical mean-field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. The QCP is characterized by a universal scaling form of the self-energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low-energy kink and the high-energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high-energy antiferromagnetic paramagnons. We use the frequency-dependent four-point correlation function of spin operators to calculate the momentum-dependent correction to the electron self-energy. By comparing with the calculations based on the spin-fermion model, our results indicate the frequency dependence of the quasiparticle-paramagnon vertices is an important factor to capture the momentum dependence in quasiparticle scattering.
Quantum critical point revisited by dynamical mean-field theory
International Nuclear Information System (INIS)
Xu, Wenhu; Kotliar, Gabriel; Rutgers University, Piscataway, NJ; Tsvelik, Alexei M.
2017-01-01
Dynamical mean-field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. We characterize the QCP by a universal scaling form of the self-energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low-energy kink and the high-energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high-energy antiferromagnetic paramagnons. Here, we use the frequency-dependent four-point correlation function of spin operators to calculate the momentum-dependent correction to the electron self-energy. Furthermore, by comparing with the calculations based on the spin-fermion model, our results indicate the frequency dependence of the quasiparticle-paramagnon vertices is an important factor to capture the momentum dependence in quasiparticle scattering.
Mean field theory of dynamic phase transitions in ferromagnets
International Nuclear Information System (INIS)
Idigoras, O.; Vavassori, P.; Berger, A.
2012-01-01
We have studied the second order dynamic phase transition (DPT) of the two-dimensional kinetic Ising model by means of numerical calculations. While it is well established that the order parameter Q of the DPT is the average magnetization per external field oscillation cycle, the possible identity of the conjugate field has been addressed only recently. In this work, we demonstrate that our entire set of numerical data is fully consistent with the applied bias field H b being the conjugate field of order parameter Q. For this purpose, we have analyzed the Q(H b )-dependence and we have found that it follows the expected power law behavior with the same critical exponent as the mean field equilibrium case.
Relativistic mean field theory for deformed nuclei with pairing correlations
International Nuclear Information System (INIS)
Geng, Lisheng; Toki, Hiroshi; Sugimoto, Satoru; Meng, Jie
2003-01-01
We develop a relativistic mean field (RMF) description of deformed nuclei with pairing correlations in the BCS approximation. The treatment of the pairing correlations for nuclei whose Fermi surfaces are close to the threshold of unbound states needs special attention. With this in mind, we use a delta function interaction for the pairing interaction to pick up those states whose wave functions are concentrated in the nuclear region and employ the standard BCS approximation for the single-particle states obtained from the BMF theory with deformation. We apply the RMF + BCS method to the Zr isotopes and obtain a good description of the binding energies and the nuclear radii of nuclei from the proton drip line to the neutron drip line. (author)
Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
Rohringer, G.; Hafermann, H.; Toschi, A.; Katanin, A. A.; Antipov, A. E.; Katsnelson, M. I.; Lichtenstein, A. I.; Rubtsov, A. N.; Held, K.
2018-04-01
Strong electronic correlations pose one of the biggest challenges to solid state theory. Recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field theory (DMFT) are reviewed. In addition, nonlocal correlations on all length scales are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. With these diagrammatic extensions of DMFT long-range charge, magnetic, and superconducting fluctuations as well as (quantum) criticality can be addressed in strongly correlated electron systems. An overview is provided of the successes and results achieved, mainly for model Hamiltonians, and an outline is given of future prospects for realistic material calculations.
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.
Mean field games with nonlinear mobilities in pedestrian dynamics
Burger, Martin; Di Francesco, Marco; Markowich, Peter A.; Wolfram, Marie Therese
2014-01-01
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.
Mean field instabilities in dissipative heavy ion collisions
International Nuclear Information System (INIS)
Colonna, M.; Guarnera, A.; Istituto Nazionale di Fisica Nucleare, Bologna; Catania Univ.; Di Torro, M.; Catania Univ.
1995-01-01
We discuss new reaction mechanisms that may occur in semi-peripheral heavy ion collisions at intermediate energies. In particular we focus on the dynamics of the overlapping zone, showing the development of neck instabilities, coupled with the possibility of an increasing amount amount of dynamical fluctuations. In a very selected beam energy range between 40 and 70 MeV/u we observe an important interplay between stochastic nucleon exchange and the random nature of nucleon-nucleon collisions. Expected consequences are intermediate mass fragment emissions from the neck region and large variances in the projectile-like and target-like observables. The crucial importance of a time matching between the growth of mean field instabilities and the separation of the interacting system is stressed. Some hints towards the observation of relatively large instability effects in deep inelastic collisions at lower energy are finally suggested. (authors). 29 refs., 5 figs., 2 tabs
Conserving gapless mean-field theory for weakly interacting Bose gases
International Nuclear Information System (INIS)
Kita, Takafumi
2006-01-01
This paper presents a conserving gapless mean-field theory for weakly interacting Bose gases. We first construct a mean-field Luttinger-Ward thermodynamic functional in terms of the condensate wave function Ψ and the Nambu Green's function G for the quasiparticle field. Imposing its stationarity respect to Ψ and G yields a set of equations to determine the equilibrium for general non-uniform systems. They have a plausible property of satisfying the Hugenholtz-Pines theorem to provide a gapless excitation spectrum. Also, the corresponding dynamical equations of motion obey various conservation laws. Thus, the present mean-field theory shares two important properties with the exact theory: 'conserving' and 'gapless'. The theory is then applied to a homogeneous weakly interacting Bose gas with s-wave scattering length a and particle mass m to clarify its basic thermodynamic properties under two complementary conditions of constant density n and constant pressure p. The superfluid transition is predicted to be first-order because of the non-analytic nature of the order-parameter expansion near T c inherent in Bose systems, i.e., the Landau-Ginzburg expansion is not possible here. The transition temperature T c shows quite a different interaction dependence between the n-fixed and p-fixed cases. In the former case T c increases from the ideal gas value T 0 as T c /T 0 =1+2.33an 1/3 , whereas it decreases in the latter as T c /T 0 =1-3.84a(mp/2πℎ 2 ) 1/5 . Temperature dependences of basic thermodynamic quantities are clarified explicitly. (author)
Variational extension of the time-dependent mean field approach
International Nuclear Information System (INIS)
Flocard, H.
1989-01-01
We investigate an application of the variational principle of Balian and Veneroni for density operators and observables. Our choice for the trial spaces incorporates correlations in the density operator. It allows one to calculate the expectation values of both one-body and two-body observables. We derive a set of coupled equations which extends the TDHF formalism, and determines the evolution of the partition function, the one-body density and the second cumulant (it corresponds also to a truncation of the quantal counterpart of the BBKGY equations). By restricting further the trial space for the two-body observables, the variational principle generates simpler equations which still include the effects of a selected class of correlations on the evolution of the one-body density
Multiagent model and mean field theory of complex auction dynamics
Chen, Qinghua; Huang, Zi-Gang; Wang, Yougui; Lai, Ying-Cheng
2015-09-01
Recent years have witnessed a growing interest in analyzing a variety of socio-economic phenomena using methods from statistical and nonlinear physics. We study a class of complex systems arising from economics, the lowest unique bid auction (LUBA) systems, which is a recently emerged class of online auction game systems. Through analyzing large, empirical data sets of LUBA, we identify a general feature of the bid price distribution: an inverted J-shaped function with exponential decay in the large bid price region. To account for the distribution, we propose a multi-agent model in which each agent bids stochastically in the field of winner’s attractiveness, and develop a theoretical framework to obtain analytic solutions of the model based on mean field analysis. The theory produces bid-price distributions that are in excellent agreement with those from the real data. Our model and theory capture the essential features of human behaviors in the competitive environment as exemplified by LUBA, and may provide significant quantitative insights into complex socio-economic phenomena.
Multiagent model and mean field theory of complex auction dynamics
International Nuclear Information System (INIS)
Chen, Qinghua; Wang, Yougui; Huang, Zi-Gang; Lai, Ying-Cheng
2015-01-01
Recent years have witnessed a growing interest in analyzing a variety of socio-economic phenomena using methods from statistical and nonlinear physics. We study a class of complex systems arising from economics, the lowest unique bid auction (LUBA) systems, which is a recently emerged class of online auction game systems. Through analyzing large, empirical data sets of LUBA, we identify a general feature of the bid price distribution: an inverted J-shaped function with exponential decay in the large bid price region. To account for the distribution, we propose a multi-agent model in which each agent bids stochastically in the field of winner’s attractiveness, and develop a theoretical framework to obtain analytic solutions of the model based on mean field analysis. The theory produces bid-price distributions that are in excellent agreement with those from the real data. Our model and theory capture the essential features of human behaviors in the competitive environment as exemplified by LUBA, and may provide significant quantitative insights into complex socio-economic phenomena. (paper)
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.
Phase diagram of the mean field model of simplicial gravity
International Nuclear Information System (INIS)
Bialas, P.; Burda, Z.; Johnston, D.
1999-01-01
We discuss the phase diagram of the balls in boxes model, with a varying number of boxes. The model can be regarded as a mean-field model of simplicial gravity. We analyse in detail the case of weights of the form p(q) = q -β , which correspond to the measure term introduced in the simplicial quantum gravity simulations. The system has two phases: elongated (fluid) and crumpled. For β ε (2, ∞) the transition between these two phases is first-order, while for β ε (1, 2) it is continuous. The transition becomes softer when β approaches unity and eventually disappears at β = 1. We then generalise the discussion to an arbitrary set of weights. Finally, we show that if one introduces an additional kinematic bound on the average density of balls per box then a new condensed phase appears in the phase diagram. It bears some similarity to the crinkled phase of simplicial gravity discussed recently in models of gravity interacting with matter fields
Superheavy nuclei in the relativistic mean-field theory
International Nuclear Information System (INIS)
Lalazissis, G.A.; Ring, P.; Gambhir, Y.K.
1996-01-01
We have carried out a study of superheavy nuclei in the framework of the relativistic mean-field theory. Relativistic Hartree-Bogoliubov (RHB) calculations have been performed for nuclei with large proton and neutron numbers. A finite-range pairing force of Gogny type has been used in the RHB calculations. The ground-state properties of very heavy nuclei with atomic numbers Z=100-114 and neutron numbers N=154-190 have been obtained. The results show that in addition to N=184 the neutron numbers N=160 and N=166 exhibit an extra stability as compared to their neighbors. For the case of protons the atomic number Z=106 is shown to demonstrate a closed-shell behavior in the region of well deformed nuclei about N=160. The proton number Z=114 also indicates a shell closure. Indications for a doubly magic character at Z=106 and N=160 are observed. Implications of shell closures on a possible synthesis of superheavy nuclei are discussed. (orig.)
Individual based and mean-field modeling of direct aggregation
Burger, Martin; Haskovec, Jan; Wolfram, Marie-Therese
2013-01-01
We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighborhood. In the 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 Gap Estimates in Mean Field Spin Glasses
Ben Arous, Gérard; Jagannath, Aukosh
2018-05-01
We show that mixing for local, reversible dynamics of mean field spin glasses is exponentially slow in the low temperature regime. We introduce a notion of free energy barriers for the overlap, and prove that their existence imply that the spectral gap is exponentially small, and thus that mixing is exponentially slow. We then exhibit sufficient conditions on the equilibrium Gibbs measure which guarantee the existence of these barriers, using the notion of replicon eigenvalue and 2D Guerra Talagrand bounds. We show how these sufficient conditions cover large classes of Ising spin models for reversible nearest-neighbor dynamics and spherical models for Langevin dynamics. Finally, in the case of Ising spins, Panchenko's recent rigorous calculation (Panchenko in Ann Probab 46(2):865-896, 2018) of the free energy for a system of "two real replica" enables us to prove a quenched LDP for the overlap distribution, which gives us a wider criterion for slow mixing directly related to the Franz-Parisi-Virasoro approach (Franz et al. in J Phys I 2(10):1869-1880, 1992; Kurchan et al. J Phys I 3(8):1819-1838, 1993). This condition holds in a wider range of temperatures.
Antiferromagnetic and topological states in silicene: A mean field study
Liu, Feng; Liu, Cheng-Cheng; Yao, Yu-Gui
2015-08-01
It has been widely accepted that silicene is a topological insulator, and its gap closes first and then opens again with increasing electric field, which indicates a topological phase transition from the quantum spin Hall state to the band insulator state. However, due to the relatively large atomic spacing of silicene, which reduces the bandwidth, the electron-electron interaction in this system is considerably strong and cannot be ignored. The Hubbard interaction, intrinsic spin orbital coupling (SOC), and electric field are taken into consideration in our tight-binding model, with which the phase diagram of silicene is carefully investigated on the mean field level. We have found that when the magnitudes of the two mass terms produced by the Hubbard interaction and electric potential are close to each other, the intrinsic SOC flips the sign of the mass term at either K or K‧ for one spin and leads to the emergence of the spin-polarized quantum anomalous Hall state. Project supported by the National Key Basic Research Program of China (Grant Nos. 2014CB920903, 2013CB921903, 2011CBA00108, and 2012CB937500), the National Natural Science Foundation of China (Grant Nos. 11021262, 11172303, 11404022, 11225418, and 11174337), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20121101110046), the Excellent Young Scholars Research Fund of Beijing Institute of Technology (Grant No. 2014CX04028), and the Basic Research Funds of Beijing Institute of Technology (Grant No. 20141842001).
Mean-field inference of Hawkes point processes
International Nuclear Information System (INIS)
Bacry, Emmanuel; Gaïffas, Stéphane; Mastromatteo, Iacopo; Muzy, Jean-François
2016-01-01
We propose a fast and efficient estimation method that is able to accurately recover the parameters of a d-dimensional Hawkes point-process from a set of observations. We exploit a mean-field approximation that is valid when the fluctuations of the stochastic intensity are small. We show that this is notably the case in situations when interactions are sufficiently weak, when the dimension of the system is high or when the fluctuations are self-averaging due to the large number of past events they involve. In such a regime the estimation of a Hawkes process can be mapped on a least-squares problem for which we provide an analytic solution. Though this estimator is biased, we show that its precision can be comparable to the one of the maximum likelihood estimator while its computation speed is shown to be improved considerably. We give a theoretical control on the accuracy of our new approach and illustrate its efficiency using synthetic datasets, in order to assess the statistical estimation error of the parameters. (paper)
Mean-field theory of meta-learning
International Nuclear Information System (INIS)
Plewczynski, Dariusz
2009-01-01
We discuss here the mean-field theory for a cellular automata model of meta-learning. Meta-learning is the process of combining outcomes of individual learning procedures in order to determine the final decision with higher accuracy than any single learning method. Our method is constructed from an ensemble of interacting, learning agents that acquire and process incoming information using various types, or different versions, of machine learning algorithms. The abstract learning space, where all agents are located, is constructed here using a fully connected model that couples all agents with random strength values. The cellular automata network simulates the higher level integration of information acquired from the independent learning trials. The final classification of incoming input data is therefore defined as the stationary state of the meta-learning system using simple majority rule, yet the minority clusters that share the opposite classification outcome can be observed in the system. Therefore, the probability of selecting a proper class for a given input data, can be estimated even without the prior knowledge of its affiliation. The fuzzy logic can be easily introduced into the system, even if learning agents are built from simple binary classification machine learning algorithms by calculating the percentage of agreeing agents
Particle Production and Effective Thermalization in Inhomogeneous Mean Field Theory
Aarts, G.; Smit, J.
2000-01-01
As a toy model for dynamics in nonequilibrium quantum field theory we consider the abelian Higgs model in 1+1 dimensions with fermions. In the approximate dynamical equations, inhomogeneous classical (mean) Bose fields are coupled to quantized fermion fields, which are treated with a mode function
Sine-Gordon mean field theory of a Coulomb gas
Energy Technology Data Exchange (ETDEWEB)
Diehl, Alexandre; Barbosa, Marcia C.; Levin, Yan
1997-12-31
Full text. The Coulomb gas provides a paradigm for the study of various models of critical phenomena. In particular, it is well known that the two dimensional (2 D). Coulomb gas can be directly used to study the superfluidity transition in {sup 4} He films, arrays of Josephson junctions, roughening transition, etc. Not withstanding its versatility, our full understanding of the most basic model of Coulomb gas, namely an ensemble of hard spheres carrying either positive or negative charges at their center, is still lacking. It is now well accepted that at low density the two dimensional plasma of equal number of positive and negative particles undergoes a Kosterlitz-Thouless (KT) metal insulator transition. This transition is of an infinite order and is characterized by a diverging Debye screening length. As the density of particles increases, the validity of the KT theory becomes questionable and the possibility of the KT transition being replaced by some kind of first order discontinuity has been speculated for a long time. In this work sine-Gordon field theory is used to investigate the phase diagram of a neutral Coulomb gas. A variational mean-field free energy is constructed and the corresponding phase diagrams in two and three dimensions are obtained. When analyzed in terms of chemical potential, the sine-Gordon theory predicts the phase diagram topologically identical to the Monte Carlo simulations and a recently developed Debye-Huckel-Bjerrum theory. In 2D, we find that the infinite-order Kosterlitz-Thouless line terminates in a tricritical point, after which the metal-insulator transition becomes first order. However, when the transformation from chemical potential to the density is made the whole insulating phase is mapped onto zero density. (author)
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.
Mean field effects for counterpropagating traveling wave solutions of reaction-diffusion systems
International Nuclear Information System (INIS)
Bernoff, A.J.; Kuske, R.; Matkowsky, B.J.; Volpert, V.
1995-01-01
In many problems, one observes traveling waves that propagate with constant velocity and shape in the χ direction, say, are independent of y, and z and describe transitions between two equilibrium states. As parameters of the system are varied, these traveling waves can become unstable and give rise to waves having additional structure, such as traveling waves in the y and z directions, which can themselves be subject to instabilities as parameters are further varied. To investigate this scenario the authors consider a system of reaction-diffusion equations with a traveling wave solution as a basic state. They determine solutions bifurcating from the basic state that describe counterpropagating traveling wave in directions orthogonal to the direction of propagation of the basic state and determine their stability. Specifically, they derive long wave modulation equations for the amplitudes of the counterpropagating traveling waves that are coupled to an equation for a mean field, generated by the translation of the basic state in the direction of its propagation. The modulation equations are then employed to determine stability boundaries to long wave perturbations for both unidirectional and counterpropagating traveling waves. The stability analysis is delicate because the results depend on the order in which transverse and longitudinal perturbation wavenumbers are taken to zero. For the unidirectional wave they demonstrate that it is sufficient to consider the cases of (1) purely transverse perturbations, (2) purely longitudinal perturbations, and (3) longitudinal perturbations with a small transverse component. These yield Eckhaus type, zigzag type, and skew type instabilities, respectively
Quark mean field theory and consistency with nuclear matter
International Nuclear Information System (INIS)
Dey, J.; Tomio, L.; Dey, M.; Frederico, T.
1989-01-01
1/N c expansion in QCD (with N c the number of colours) suggests using a potential from meson sector (e.g. Richardson) for baryons. For light quarks a σ field has to be introduced to ensure chiral symmetry breaking ( χ SB). It is found that nuclear matter properties can be used to pin down the χ SB-modelling. All masses, M Ν , m σ , m ω are found to scale with density. The equations are solved self consistently. (author)
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.
Quark mean field theory and consistency with nuclear matter
International Nuclear Information System (INIS)
Dey, J.; Dey, M.; Frederico, T.; Tomio, L.
1990-09-01
1/N c expansion in QCD (with N c the number of colours) suggests using a potential from meson sector (e.g. Richardson) for baryons. For light quarks a σ field has to be introduced to ensure chiral symmetry breaking ( χ SB). It is found that nuclear matter properties can be used to pin down the χ SB-modelling. All masses, M N , m σ , m ω are found to scale with density. The equations are solved self consistently. (author). 29 refs, 2 tabs
Energy Technology Data Exchange (ETDEWEB)
Keller, G. (Max-Planck-Institut fuer Physik, Muenchen (Germany). Werner-Heisenberg-Institut); Kopper, C. (Goettingen Univ. (Germany). Inst. fuer Theoretische Physik)
1993-04-01
We give a rigorous and very detailed derivation of the short distance expansion for a product of two arbitrary composite operators in the framework of the perturbative Euclidean massive [Phi][sub 4][sup 4]. The technically almost trivial proof rests on an extension of the differential flow equation method to Green functions with bilocal insertions, for which we also establish a set of generalized Zimmermann identities and Lowenstein rules. (orig.).
Mean Field Type Control with Congestion (II): An Augmented Lagrangian Method
Energy Technology Data Exchange (ETDEWEB)
Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr; Laurière, Mathieu [Univ. Paris Diderot, Sorbonne Paris Cité, Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRS (France)
2016-12-15
This work deals with a numerical method for solving a mean-field type control problem with congestion. It is the continuation of an article by the same authors, in which suitably defined weak solutions of the system of partial differential equations arising from the model were discussed and existence and uniqueness were proved. Here, the focus is put on numerical methods: a monotone finite difference scheme is proposed and shown to have a variational interpretation. Then an Alternating Direction Method of Multipliers for solving the variational problem is addressed. It is based on an augmented Lagrangian. Two kinds of boundary conditions are considered: periodic conditions and more realistic boundary conditions associated to state constrained problems. Various test cases and numerical results are presented.
Antikaon condensation in neutron stars by a new nonlinear mean-field model
Miyazaki, K
2005-01-01
We have investigated both the K^- and \\bar{K}^0 condensations in beta-equilibrated neutron star (NS) matter using the relativistic mean-field model with the renormalized meson-baryon coupling constants. Adopting the antikaon optical potential of -120MeV, our model predicts the K^- condensation as the second-order phase transition inside the neutron star of maximum mass, while the deeper potential than -160MeV is ruled out. This is in contrast to the result of the density-dependent hadron field theory. Our model also predicts remarkable softening of the equation of state by the \\bar{K}^0 condensation at high densities. Although this is contrasted with the result of the nonlinear Walecka model, only the K^- condensation can be formed in NSs.
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.
A Fractional Micro-Macro Model for Crowds of Pedestrians Based on Fractional Mean Field Games
Institute of Scientific and Technical Information of China (English)
Kecai Cao; Yang Quan Chen; Daniel Stuart
2016-01-01
Modeling a crowd 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 micromacro 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.
Elementary methods for statistical systems, mean field, large-n, and duality
International Nuclear Information System (INIS)
Itzykson, C.
1983-01-01
Renormalizable field theories are singled out by such precise restraints that regularization schemes must be used to break these invariances. Statistical methods can be adapted to these problems where asymptotically free models fail. This lecture surveys approximation schemes developed in the context of statistical mechanics. The confluence point of statistical mechanics and field theory is the use of discretized path integrals, where continuous space time has been replaced by a regular lattice. Dynamic variables, a Boltzman weight factor, and boundary conditions are the ingredients. Mean field approximations --field equations, Random field transform, and gauge invariant systems--are surveyed. Under Large-N limits vector models are found to simplify tremendously. The reasons why matrix models drawn from SU (n) gauge theories do not simplify are discussed. In the epilogue, random curves versus random surfaces are offered as an example where global and local symmetries are not alike
On the binding energy of double Λ hypernuclei in the relativistic mean field theory
International Nuclear Information System (INIS)
Marcos, S.; Lombard, R.J.
1997-01-01
The binding energy of two Λ hyperons bound to a nuclear core is calculated within the relativistic mean field theory. The starting point is a two body relativistic equation of the Breit type suggested by the RMFT, and corrected for the two-particle interaction. The 2 Λ correlation energy is evaluated and the contribution of the δ and φ mesons, acting solely between hyperons, to the bond energy σB ΛΛ of ( ΛΛ ) 6 He, ( ΛΛ ) 10 Be and ( ΛΛ ) 13 B is calculated. Predictions of the ΔB ΛΛ A dependence are made for heavier Λ-hypernuclei. (K.A.)
Relativistic mean-field theory for unstable nuclei with non-linear σ and ω terms
International Nuclear Information System (INIS)
Sugahara, Y.; Toki, H.
1994-01-01
We search for a new parameter set for the description of stable as well as unstable nuclei in the wide mass range within the relativistic mean-field theory. We include a non-linear ω self-coupling term in addition to the non-linear σ self-coupling terms, the necessity of which is suggested by the relativistic Brueckner-Hartree-Fock (RBHF) theory of nuclear matter. We find two parameter sets, one of which is for nuclei above Z=20 and the other for nuclei below that. The calculated results agree very well with the existing data for finite nuclei. The parameter set for the heavy nuclei provides the equation of state of nuclear matter similar to the one of the RBHF theory. ((orig.))
Correlations and fluctuations in static and dynamic mean-field approaches
International Nuclear Information System (INIS)
Balian, R.; Veneroni, M.
1991-01-01
Let the state of a many-body system at an initial time be specified, completely or partly; find the expectation values, correlations and fluctuations of single-particle observables at a later time. The characteristic function of these observables is optimized within a general variational scheme. The expansion of the optimal characteristic function provides the same results as the conventional mean-field approaches for the thermodynamic potentials and the expectation values: for fermions the best initial state is then the Hartree-Fock (HF) solution and the evolution is described by the time-dependent Hartree-Fock (TDHF) equation. Two special cases are investigated as preliminary steps. The first case deals with the evaluation of correlations for static problems, where the initial and final times coincide. In the second special case, the exact initial state is assumed to be an independent-particle one. (K.A.) 23 refs.; 1 fig
Aymerich-Franch, Laura; Petit, Damien; Ganesh, Gowrishankar; Kheddar, Abderrahmane
2016-11-01
Whole-body embodiment studies have shown that synchronized multi-sensory cues can trick a healthy human mind to perceive self-location outside the bodily borders, producing an illusion that resembles an out-of-body experience (OBE). But can a healthy mind also perceive the sense of self in more than one body at the same time? To answer this question, we created a novel artificial reduplication of one's body using a humanoid robot embodiment system. We first enabled individuals to embody the humanoid robot by providing them with audio-visual feedback and control of the robot head movements and walk, and then explored the self-location and self-identification perceived by them when they observed themselves through the embodied robot. Our results reveal that, when individuals are exposed to the humanoid body reduplication, they experience an illusion that strongly resembles heautoscopy, suggesting that a healthy human mind is able to bi-locate in two different bodies simultaneously. Copyright © 2016 Elsevier Inc. All rights reserved.
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.
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.
A self-consistent mean field theory for diffusion in alloys
International Nuclear Information System (INIS)
Nastar, M.; Barbe, V.
2007-01-01
Starting from a microscopic model of the atomic transport via vacancies and interstitials in alloys, a self-consistent mean field (SCMF) kinetic theory yields the phenomenological coefficients L ij . In this theory, kinetic correlations are accounted for through a set of effective interactions within a non-equilibrium distribution function of the system. The introduction of a master equation describing the evolution with time of the distribution function and its moments leads to general self-consistent kinetic equations. The L ij of a face centered cubic alloy are calculated using the kinetic equations of Nastar (M. Nastar, Philos. Mag., 2005, 85, 3767, ref. 1) derived from a microscopic broken bond model of the vacancy jump frequency. A first approximation leads to an analytical expression of the L ij and a second approximation to a better agreement with the Monte Carlo simulations. A change of sign of the L ij is studied as a function of the microscopic parameters of the jump frequency. The L ij of a cubic centered alloy obtained for the complex diffusion mechanism of the dumbbell configuration of the interstitial are used to study the effect of an on-site rotation of the dumbbell on the transport. (authors)
Exact mean-field theory of ionic solutions: non-Debye screening
International Nuclear Information System (INIS)
Varela, L.M.; Garcia, Manuel; Mosquera, Victor
2003-01-01
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
International Nuclear Information System (INIS)
Grasso, M.
2009-10-01
This document is a summary of the author's research activities whose common topic is the N-body problem. The first chapter introduces the N-body issue through models based on the mean-field theory and on the Hartree-Fock-Bogoliubov equations. The second chapter presents the understanding of exotic nuclei features within the mean-field approach. Exotic phenomena like nuclear bubble structure, pairing correlations and pairing violations, giant neutron halos, non-standard terms in the Skyrme interactions are reviewed. The chapter 3 is dedicated to some extensions of the RPA (random phase approximation). For instance the computation of the shell structure far from the stability valley requires a more accurate assessment of the energy of the individual states through the introduction of a particle-vibration coupling. Different RPA extensions are described: first the self-consistent extension enlarged beyond particle-hole configurations, then the boson-mapping-based extension in a 3-level Lipkin model and also the second random-phase approximation. The chapter 4 gathers some studies concerning ultra-cold gases of trapped atoms. These systems are the only structures that allow the study of the correlations associated to superfluidity in terms of interaction intensity, temperature or system size. The mean-field approach is adequate for these studies. The last chapter draws a perspective for the mean-field-based models, their limits are assessed and ways of improvement are proposed. (A.C.)
Stochastic modeling of catalytic processes in nanoporous materials: Beyond mean-field approach
Energy Technology Data Exchange (ETDEWEB)
Garcia, Andres [Iowa State Univ., Ames, IA (United States)
2017-08-05
Transport and reaction in zeolites and other porous materials, such as mesoporous silica particles, has been a focus of interest in recent years. This is in part due to the possibility of anomalous transport effects (e.g. single-file diffusion) and its impact in the reaction yield in catalytic processes. Computational simulations are often used to study these complex nonequilibrium systems. Computer simulations using Molecular Dynamics (MD) techniques are prohibitive, so instead coarse grained one-dimensional models with the aid of Kinetic Monte Carlo (KMC) simulations are used. Both techniques can be computationally expensive, both time and resource wise. These coarse-grained systems can be exactly described by a set of coupled stochastic master equations, that describe the reaction-diffusion kinetics of the system. The equations can be written exactly, however, coupling between the equations and terms within the equations make it impossible to solve them exactly; approximations must be made. One of the most common methods to obtain approximate solutions is to use Mean Field (MF) theory. MF treatments yield reasonable results at high ratios of reaction rate k to hop rate h of the particles, but fail completely at low k=h due to the over-estimation of fluxes of particles within the pore. We develop a method to estimate fluxes and intrapore diffusivity in simple one- dimensional reaction-diffusion models at high and low k=h, where the pores are coupled to an equilibrated three-dimensional fluid. We thus successfully describe analytically these simple reaction-diffusion one-dimensional systems. Extensions to models considering behavior with long range steric interactions and wider pores require determination of multiple boundary conditions. We give a prescription to estimate the required parameters for these simulations. For one dimensional systems, if single-file diffusion is relaxed, additional parameters to describe particle exchange have to be introduced. We use
Transport in simple liquids and dense gases: kinetic mean-field theory and the KAC limit
International Nuclear Information System (INIS)
Karkheck, J.; Stell, G.; Martina, E.
1982-01-01
Maximization of entropy is used in conjunction with the BBGKY hierarchy to obtain a closed one-particle kinetic equation. For an interparticle potential of hard-sphere core plus smooth attractive tail, this equation contains a hard-core collision integral, identical to that of the revised Enskog theory, plus a mean-field term which is linear in the tail strength. The thermodynamics contained therein leads directly to the now-standard statistical-mechanical methods to construct a state-dependent effective hard-core potential in relation to a more realistic potential. These methods induce an extension of the transport coefficients to the Lennard-Jones potential. Predictions of the resulting transport theory compare very favorably with thermal conductivity and shear viscosity experimental results for real simple liquids and dense gases, and also with molecular dynamics simulation results. Poor agreement between theory and experiment is found for moderately dense and dilute gases. The kinetic theory also contains an entropy functional and an H-theorem is proven. Extension to mixtures is straightforward and the Kac-limit is discussed in detail
Mean-field approach to evolving spatial networks, with an application to osteocyte network formation
Taylor-King, Jake P.; Basanta, David; Chapman, S. Jonathan; Porter, Mason A.
2017-07-01
We consider evolving networks in which each node can have various associated properties (a state) in addition to those that arise from network structure. For example, each node can have a spatial location and a velocity, or it can have some more abstract internal property that describes something like a social trait. Edges between nodes are created and destroyed, and new nodes enter the system. We introduce a "local state degree distribution" (LSDD) as the degree distribution at a particular point in state space. We then make a mean-field assumption and thereby derive an integro-partial differential equation that is satisfied by the LSDD. We perform numerical experiments and find good agreement between solutions of the integro-differential equation and the LSDD from stochastic simulations of the full model. To illustrate our theory, we apply it to a simple model for osteocyte network formation within bones, with a view to understanding changes that may take place during cancer. Our results suggest that increased rates of differentiation lead to higher densities of osteocytes, but with a smaller number of dendrites. To help provide biological context, we also include an introduction to osteocytes, the formation of osteocyte networks, and the role of osteocytes in bone metastasis.
Mean-field analysis of an inductive reasoning game: application to influenza vaccination.
Breban, Romulus; Vardavas, Raffaele; Blower, Sally
2007-09-01
Recently we have introduced an inductive reasoning game of voluntary yearly vaccination to establish whether or not a population of individuals acting in their own self-interest would be able to prevent influenza epidemics. Here, we analyze our model to describe the dynamics of the collective yearly vaccination uptake. We discuss the mean-field equations of our model and first order effects of fluctuations. We explain why our model predicts that severe epidemics are periodically expected even without the introduction of pandemic strains. We find that fluctuations in the collective yearly vaccination uptake induce severe epidemics with an expected periodicity that depends on the number of independent decision makers in the population. The mean-field dynamics also reveal that there are conditions for which the dynamics become robust to the fluctuations. However, the transition between fluctuation-sensitive and fluctuation-robust dynamics occurs for biologically implausible parameters. We also analyze our model when incentive-based vaccination programs are offered. When a family-based incentive is offered, the expected periodicity of severe epidemics is increased. This results from the fact that the number of independent decision makers is reduced, increasing the effect of the fluctuations. However, incentives based on the number of years of prepayment of vaccination may yield fluctuation-robust dynamics where severe epidemics are prevented. In this case, depending on prepayment, the transition between fluctuation-sensitive and fluctuation-robust dynamics may occur for biologically plausible parameters. Our analysis provides a practical method for identifying how many years of free vaccination should be provided in order to successfully ameliorate influenza epidemics.
Haji Ali, Abdul Lateef
2016-01-01
I discuss using single level and multilevel Monte Carlo methods to compute quantities of interests of a stochastic particle system in the mean-field. In this context, the stochastic particles follow a coupled system of Ito stochastic differential equations (SDEs). Moreover, this stochastic particle system converges to a stochastic mean-field limit as the number of particles tends to infinity. I start by recalling the results of applying different versions of Multilevel Monte Carlo (MLMC) for particle systems, both with respect to time steps and the number of particles and using a partitioning estimator. Next, I expand on these results by proposing the use of our recent Multi-index Monte Carlo method to obtain improved convergence rates.
Haji Ali, Abdul Lateef
2016-01-08
I discuss using single level and multilevel Monte Carlo methods to compute quantities of interests of a stochastic particle system in the mean-field. In this context, the stochastic particles follow a coupled system of Ito stochastic differential equations (SDEs). Moreover, this stochastic particle system converges to a stochastic mean-field limit as the number of particles tends to infinity. I start by recalling the results of applying different versions of Multilevel Monte Carlo (MLMC) for particle systems, both with respect to time steps and the number of particles and using a partitioning estimator. Next, I expand on these results by proposing the use of our recent Multi-index Monte Carlo method to obtain improved convergence rates.
Virtual-site correlation mean field approach to criticality in spin systems
International Nuclear Information System (INIS)
Sen, Aditi; Sen, Ujjwal
2013-01-01
We propose a virtual-site correlation mean field theory for dealing with interacting many-body systems. It involves a coarse-graining technique that terminates a step before the mean field theory: While mean field theory deals with only single-body physical parameters, the virtual-site correlation mean field theory deals with single- as well as two-body ones, and involves a virtual site for every interaction term in the Hamiltonian. We generalize the theory to a cluster virtual-site correlation mean field, that works with a fundamental unit of the lattice of the many-body system. We apply these methods to interacting Ising spin systems in several lattice geometries and dimensions, and show that the predictions of the onset of criticality of these models are generally much better in the proposed theories as compared to the corresponding ones in mean field theories
International Nuclear Information System (INIS)
Hayasaka, Kiyoshi; Nakayama, Ryuichi
2002-01-01
We point out that when a D-brane is placed in an NS-NS B field background with nonvanishing field strength (H=dB) along the D-brane worldvolume, the coordinate of one end of the open string does not commute with that of the other in the low energy limit. The degrees of the freedom associated with both ends are not decoupled and accordingly, the effective action must be quite different from that of the ordinary noncommutative gauge theory for a constant B background. We construct an associative and noncommutative product * which operates on the coordinates of both ends of the string and propose a new type of noncommutative gauge action for the low energy effective theory of a Dp-brane. This effective theory is bi-local and lives in twice as large dimensions (2D=2(p+1)) as in the H=0 case. When viewed as a theory in the D-dimensional space, this theory is nonlocal and we must force the two ends of the string to coincide. We will then propose a prescription for reducing this bi-local effective action to that in D dimensions and obtaining a local effective action
Wieser, R
2017-05-04
A self-consistent mean field theory is introduced and used to investigate the thermodynamics and spin dynamics of an S = 1 quantum spin system with a magnetic Skyrmion. The temperature dependence of the Skyrmion profile as well as the phase diagram are calculated. In addition, the spin dynamics of a magnetic Skyrmion is described by solving the time dependent Schrödinger equation with additional damping term. The Skyrmion annihilation process driven by an electric field is used to compare the trajectories of the quantum mechanical simulation with a semi-classical description for the spin expectation values using a differential equation similar to the classical Landau-Lifshitz-Gilbert equation.
Relativistic mean field model for entrainment in general relativistic superfluid neutron stars
International Nuclear Information System (INIS)
Comer, G.L.; Joynt, R.
2003-01-01
General relativistic superfluid neutron stars have a significantly more intricate dynamics than their ordinary fluid counterparts. Superfluidity allows different superfluid (and superconducting) species of particles to have independent fluid flows, a consequence of which is that the fluid equations of motion contain as many fluid element velocities as superfluid species. Whenever the particles of one superfluid interact with those of another, the momentum of each superfluid will be a linear combination of both superfluid velocities. This leads to the so-called entrainment effect whereby the motion of one superfluid will induce a momentum in the other superfluid. We have constructed a fully relativistic model for entrainment between superfluid neutrons and superconducting protons using a relativistic σ-ω mean field model for the nucleons and their interactions. In this context there are two notions of 'relativistic': relativistic motion of the individual nucleons with respect to a local region of the star (i.e. a fluid element containing, say, an Avogadro's number of particles), and the motion of fluid elements with respect to the rest of the star. While it is the case that the fluid elements will typically maintain average speeds at a fraction of that of light, the supranuclear densities in the core of a neutron star can make the nucleons themselves have quite high average speeds within each fluid element. The formalism is applied to the problem of slowly rotating superfluid neutron star configurations, a distinguishing characteristic being that the neutrons can rotate at a rate different from that of the protons
Temperature dependence of magnetic anisotropy and magnetostriction: Beyond the mean-field theory
International Nuclear Information System (INIS)
Millev, Y.; Faehnle, M.
1994-05-01
The first nonvanishing magnetic anisotropy coefficient is calculated as a function of temperature for any spin quantum number and all temperatures below the Curie temperature for the case of face-centred cubic symmetry within the random-phase approximation (RPA). A detailed and instructive comparison between the mean-field and the RPA predictions is carried out. The RPA magnetization curves are also given for the first time for spins S>1/2. Most of the theoretical considerations are quite general as regard lattice type and even decoupling scheme and can thus be applied straightforwardly to other cases of interest. The progress reported here has been attained with the help of a new simplified and improved parametric approach and of a recent calculation of the average occupation number of magnons within the RPA. In particular, the new approach makes unnecessary the solving of integral equations so that the proposed procedure is especially simple and practically versatile in applications to any particular anisotropic material. (author). Refs, 6 figs
Mean field analysis of exchange coupling in amorphous DyFe2-B alloy ribbons
International Nuclear Information System (INIS)
Lee, J.M.; Jung, J.K.; Lim, S.H.
2001-01-01
Experimental magnetization-temperature curves for melt-spun ribbons of amorphous alloys (Dy 0.33 Fe 0.67 ) 1-x B x with x=0, 0.05, 0.1 and 0.15 (in atomic fraction) are fitted with theoretical equations based on the mean field theory in order to investigate exchange couplings between constituent elements as a function of the B content. The sign of the exchange coupling between Dy and Fe is negative, indicating that the magnetization direction of Dy is antiparallel to that of Fe. The sign of the other two couplings are positive. The exchange coupling between Fe ions are greatest, while that between Dy ions is negligible. The exchange couplings between Fe ions, and between Dy and Fe increase with increasing B content, the increase of the latter being much greater than the former. Resulting, the exchange coupling between Dy and Fe becomes about one half of that between Fe ions at the highest B content. The increase of the exchange coupling between Fe ions may be explained by the increase of the Fe-Fe separation with the increase of the B content. The total magnetization is dominated by the Dy sublattice magnetization. As the B content increases, the magnetization decreases over the whole temperature range, and the Curie temperature also decreases
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.
Generating functional of the mean field in quantum electrodynamics with non-stable vacuum
International Nuclear Information System (INIS)
Gitman, D.M.; Kuchin, V.A.
1981-01-01
Generating functional for calculating a mean field, in the case of unstable vacuum, in quantum field theory has been suggested. Continual representation for the generating functional of the mean field has been found in the case of quantum electrodynamics with an external field. Generating electron-positron pairs from vacuum [ru
Continuous spin mean-field models : Limiting kernels and Gibbs properties of local transforms
Kulske, Christof; Opoku, Alex A.
2008-01-01
We extend the notion of Gibbsianness for mean-field systems to the setup of general (possibly continuous) local state spaces. We investigate the Gibbs properties of systems arising from an initial mean-field Gibbs measure by application of given local transition kernels. This generalizes previous
International Nuclear Information System (INIS)
Schlichting, H.
1985-01-01
We do a linearised mean field calculation in axial gauge for the four dimensional mixed fundamental adjoint SU(2) lattice gauge theory and extract the gluon condensate parameter from the expectation values of the plaquette and the action by subtracting mean field perturbation theory from Monte Carlo data. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Speck, Thomas [Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz (Germany); Menzel, Andreas M.; Bialké, Julian; Löwen, Hartmut [Institut für Theoretische Physik II, Heinrich-Heine-Universität, D-40225 Düsseldorf (Germany)
2015-06-14
Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.
Faugeras, Olivier; Touboul, Jonathan; Cessac, Bruno
2009-01-01
We deal with the problem of bridging the gap between two scales in neuronal modeling. At the first (microscopic) scale, neurons are considered individually and their behavior described by stochastic differential equations that govern the time variations of their membrane potentials. They are coupled by synaptic connections acting on their resulting activity, a nonlinear function of their membrane potential. At the second (mesoscopic) scale, interacting populations of neurons are described individually by similar equations. The equations describing the dynamical and the stationary mean-field behaviors are considered as functional equations on a set of stochastic processes. Using this new point of view allows us to prove that these equations are well-posed on any finite time interval and to provide a constructive method for effectively computing their unique solution. This method is proved to converge to the unique solution and we characterize its complexity and convergence rate. We also provide partial results for the stationary problem on infinite time intervals. These results shed some new light on such neural mass models as the one of Jansen and Rit (1995): their dynamics appears as a coarse approximation of the much richer dynamics that emerges from our analysis. Our numerical experiments confirm that the framework we propose and the numerical methods we derive from it provide a new and powerful tool for the exploration of neural behaviors at different scales.
Mean-field theory of active electrolytes: Dynamic adsorption and overscreening
Frydel, Derek; Podgornik, Rudolf
2018-05-01
We investigate active electrolytes within the mean-field level of description. The focus is on how the double-layer structure of passive, thermalized charges is affected by active dynamics of constituting ions. One feature of active dynamics is that particles adhere to hard surfaces, regardless of chemical properties of a surface and specifically in complete absence of any chemisorption or physisorption. To carry out the mean-field analysis of the system that is out of equilibrium, we develop the "mean-field simulation" technique, where the simulated system consists of charged parallel sheets moving on a line and obeying active dynamics, with the interaction strength rescaled by the number of sheets. The mean-field limit becomes exact in the limit of an infinite number of movable sheets.
Noisy mean field game model for malware propagation in opportunistic networks
Tembine, Hamidou; Vilanova, Pedro; Debbah, Mé roú ane
2012-01-01
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
Semiclassical approximations in a mean-field theory with collision terms
International Nuclear Information System (INIS)
Galetti, D.
1986-01-01
Semiclassical approximations in a mean-field theory with collision terms are discussed taking the time dependent Hartree-Fock method as framework in the obtainment of the relevant parameters.(L.C.) [pt
On the existence of classical solutions for stationary extended mean field games
Gomes, Diogo A.; Patrizi, Stefania; Voskanyan, Vardan
2014-01-01
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.
Explicit solutions of one-dimensional, first-order, stationary mean-field games with congestion
Gomes, Diogo A.; Nurbekyan, Levon; Prazeres, Mariana
2017-01-01
Here, we consider one-dimensional first-order stationary mean-field games with congestion. These games arise when crowds face difficulty moving in high-density regions. We look at both monotone decreasing and increasing interactions and construct
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.
Stochastic mean-field dynamics for fermions in the weak coupling limit
Energy Technology Data Exchange (ETDEWEB)
Lacroix, D
2005-09-15
Assuming that the effect of the residual interaction beyond mean-field is weak and can be treated as a statistical ensemble of two-body interactions, a Markovian quantum jump theory is developed for fermionic systems. In this theory, jumps occur between many-body densities formed of pairs of states D |{phi}{sub a}> <|{phi}{sub b}| / <|{phi}{sub b} | |{phi} {sub a}> where |{phi}{sub a}> and |{phi}{sub b}> are anti-symmetrized products of single-particle states. The underlying Stochastic Mean-Field (SMF) theory is discussed and applied to the monopole vibration of a spherical {sup 40}Ca nucleus under the influence of a statistical ensemble of two-body contact interactions. In this example, the mean-field evolution of one-body observables is recovered by averaging over different stochastic trajectories while fluctuations beyond mean-field are observed. Finally, the nature of the fluctuations is discussed. (author)
Stochastic mean-field dynamics for fermions in the weak coupling limit
International Nuclear Information System (INIS)
Lacroix, D.
2005-09-01
Assuming that the effect of the residual interaction beyond mean-field is weak and can be treated as a statistical ensemble of two-body interactions, a Markovian quantum jump theory is developed for fermionic systems. In this theory, jumps occur between many-body densities formed of pairs of states D |Φ a > b | / b | |Φ a > where |Φ a > and |Φ b > are anti-symmetrized products of single-particle states. The underlying Stochastic Mean-Field (SMF) theory is discussed and applied to the monopole vibration of a spherical 40 Ca nucleus under the influence of a statistical ensemble of two-body contact interactions. In this example, the mean-field evolution of one-body observables is recovered by averaging over different stochastic trajectories while fluctuations beyond mean-field are observed. Finally, the nature of the fluctuations is discussed. (author)
Magnetic moments in present relativistic nuclear theories: a mean-field problem
International Nuclear Information System (INIS)
Desplanques, B.
1986-07-01
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
Isospin-dependent properties of asymmetric nuclear matter in relativistic mean-field models
Chen, Lie-Wen; Ko, Che Ming; Li, Bao-An
2007-01-01
Using various relativistic mean-field models, including the nonlinear ones with meson field self-interactions, those with density-dependent meson-nucleon couplings, and the point-coupling models without meson fields, we have studied the isospin-dependent bulk and single-particle properties of asymmetric nuclear matter. In particular, we have determined the density dependence of nuclear symmetry energy from these different relativistic mean-field models and compare the results with the constra...
Rädler, K.-H.
This article elucidates the basic ideas of electrodynamics and magnetohydrodynamics of mean fields in turbulently moving conducting fluids. It is stressed that the connection of the mean electromotive force with the mean magnetic field and its first spatial derivatives is in general neither local nor instantaneous and that quite a few claims concerning pretended failures of the mean-field concept result from ignoring this aspect. In addition to the mean-field dynamo mechanisms of α2 and α Ω type several others are considered. Much progress in mean-field electrodynamics and magnetohydrodynamics results from the test-field method for calculating the coefficients that determine the connection of the mean electromotive force with the mean magnetic field. As an important example the memory effect in homogeneous isotropic turbulence is explained. In magnetohydrodynamic turbulence there is the possibility of a mean electromotive force that is primarily independent of the mean magnetic field and labeled as Yoshizawa effect. Despite of many efforts there is so far no convincing comprehensive theory of α quenching, that is, the reduction of the α effect with growing mean magnetic field, and of the saturation of mean-field dynamos. Steps toward such a theory are explained. Finally, some remarks on laboratory experiments with dynamos are made.
Time-odd mean fields in covariant density functional theory: Rotating systems
International Nuclear Information System (INIS)
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 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.
Hubbard interaction in the arbitrary Chern number insulator: A mean-field study
Energy Technology Data Exchange (ETDEWEB)
Wang, Yi-Xiang, E-mail: wangyixiang@jiangnan.edu.cn [School of Science, Jiangnan University, Wuxi 214122 (China); Cao, Jie [College of Science, Hohai University, Nanjing 210098 (China)
2017-05-10
The low-dimensional electron gas owing topological property has attracted many interests recently. In this work, we study the influence of the electron-electron interaction on the arbitrary Chern number insulator. Using the mean-field method, we approximately solve the Hubbard model in the half-filling case and obtain the phase diagrams in different parametric spaces. We further verify the results by calculating the entanglement spectrum, which contains C chiral modes and corresponds to a real space partitioning. - Highlights: • In this work, we made a mean-field study of the Hubbard interaction in the arbitrary Chern number insulator. • We point out that how the Zeeman splitting, the local magnetization and the Hubbard interaction are intimately related. • The mean-field phase diagrams are obtained in different parametric spaces. • The Chern number phase is demonstrated by calculating the entanglement spectrum.
Bent dark soliton dynamics in two spatial dimensions beyond the mean field approximation
Mistakidis, Simeon; Katsimiga, Garyfallia; Koutentakis, Georgios; Kevrekidis, Panagiotis; Schmelcher, Peter; Theory Group of Fundamental Processes in Quantum Physics Team
2017-04-01
The dynamics of a bented dark soliton embedded in two spatial dimensions beyond the mean-field approximation is explored. We examine the case of a single bented dark soliton comparing the mean-field approximation to a correlated approach that involves multiple orbitals. Fragmentation is generally present and significantly affects the dynamics, especially in the case of stronger interparticle interactions and in that of lower atom numbers. It is shown that the presence of fragmentation allows for the appearance of solitonic and vortex structures in the higher-orbital dynamics. In particular, a variety of excitations including dark solitons in multiple orbitals and vortex-antidark complexes is observed to arise spontaneously within the beyond mean-field dynamics. Deutsche Forschungsgemeinschaft (DFG) in the framework of the SFB 925 ``Light induced dynamics and control of correlated quantum systems''.
Directory of Open Access Journals (Sweden)
Mauro Regi
2017-01-01
Full Text Available The magnetic field satellite data are usually referred to geocentric coordinate reference frame. Conversely, the magnetohydrodynamic waves modes in magnetized plasma depend on the ambient magnetic field, and is then useful to rotate the magnetic field measurements into the mean field aligned (MFA coordinate system. This reference frame is useful to study the ultra low frequency magnetic field variations along the direction of the mean field and perpendicularly to it. In order to identify the mean magnetic field the classical moving average (MAVG approach is usually adopted but, under particular conditions, this procedure induces undesired features, such as spectral alteration in the rotated components. We discuss these aspects promoting an alternative and more efficient method for mean field aligned projection, based on the empirical mode decomposition (EMD.
Quantum mean-field approximations for nuclear bound states and tunneling
International Nuclear Information System (INIS)
Negele, J.W.; Levit, S.; Paltiel, Z.; Massachusetts Inst. of Tech., Cambridge
1979-01-01
A conceptual framework has been presented in which observables are approximated in terms of a self-consistent quantum mean-field theory. Since the SPA (Stationary Phase Approximation) determines the optimal mean field to approximate a given observable, it is natural that when one changes the observable, the best mean field to describe it changes as well. Although the theory superficially appears applicable to any observable expressible in terms of an evolution operator, for example an S-matrix element, one would have to go far beyond the SPA to adequately approximate the overlap of two many-body wave functions. The most salient open problems thus concern quantitative assessment of the accuracy of the SPA, reformulation of the theory to accomodate hard cores, and selection of sensible expectation values of few-body operators to address in scattering problems
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.)
Energy Technology Data Exchange (ETDEWEB)
Dreyer, Wolfgang [Weierstrass-Institut fuer Angewandte Analysis und Stochastik (WIAS) im Forschungsverbund Berlin e.V. (Germany); Kimmerle, Sven-Joachim [Humboldt-Univ. Berlin (Germany). Dept. of Mathematics
2009-07-01
Based on a thermodynamically consistent model for precipitation in gallium arsenide crystals including surface tension and bulk stresses by Dreyer and Duderstadt, we propose different mathematical models to describe the size evolution of liquid droplets in a crystalline solid. The first class of models treats the diffusion-controlled regime of interface motion, while the second class is concerned with the interface-controlled regime of interface motion. Our models take care of conservation of mass and substance. We consider homogenised models, where different length scales of the experimental situation have been exploited in order to simplify the equations. These homogenised models generalise the well-known Lifshitz-Slyozov-Wagner model for Ostwald ripening. Mean field models capture the main properties of our system and are well adapted for numerics and further analysis. Numerical evidence suggests in which case which one of the two regimes might be appropriate to the experimental situation. (orig.)
International Nuclear Information System (INIS)
Frank, T D; Mongkolsakulvong, S
2015-01-01
In a previous study strongly nonlinear autoregressive (SNAR) models have been introduced as a generalization of the widely-used time-discrete autoregressive models that are known to apply both to Markov and non-Markovian systems. In contrast to conventional autoregressive models, SNAR models depend on process mean values. So far, only linear dependences have been studied. We consider the case in which process mean values can have a nonlinear impact on the processes under consideration. It is shown that such models describe Markov and non-Markovian many-body systems with mean field forces that exhibit a nonlinear impact on single subsystems. We exemplify that such nonlinear dependences can describe order-disorder phase transitions of time-discrete Markovian and non-Markovian many-body systems. The relevant order parameter equations are derived and issues of stability and stationarity are studied. (paper)
International Nuclear Information System (INIS)
Adam, G.; Adam, S.
2007-01-01
The Green function (GF) equation of motion technique for solving the effective two-band Hubbard model of high-T c superconductivity in cuprates rests on the Hubbard operator (HO) algebra. We show that, if we take into account the invariance to translations and spin reversal, the HO algebra results in invariance properties of several specific correlation functions. The use of these properties allows rigorous derivation and simplification of the expressions of the frequency matrix (FM) and of the generalized mean-field approximation (GMFA) Green functions (GFs) of the model. For the normal singlet hopping and anomalous exchange pairing correlation functions which enter the FM and GMFA-GFs, the use of spectral representations allows the identification and elimination of exponentially small quantities. This procedure secures the reduction of the correlation order to the GMFA-GF expressions
Mean-field model for the interference of matter-waves from a three-dimensional optical trap
International Nuclear Information System (INIS)
Adhikari, Sadhan K.; Muruganandam, Paulsamy
2003-01-01
Using the mean-field time-dependent Gross-Pitaevskii equation we study the formation of a repulsive Bose-Einstein condensate on a combined optical and harmonic traps in two and three dimensions and subsequent generation of the interference pattern upon the removal of the combined traps as in the experiment by Greiner et al. [Nature (London) 415 (2002) 39]. For optical traps of moderate strength, interference pattern of 27 (9) prominent bright spots is found to be formed in three (two) dimensions on a cubic (square) lattice in agreement with experiment. Similar interference pattern can also be formed upon removal of the optical lattice trap only. The pattern so formed can oscillate for a long time in the harmonic trap which can be observed experimentally
Mean Field Theory, Ginzburg Criterion, and Marginal Dimensionality of Phase-Transitions
DEFF Research Database (Denmark)
Als-Nielsen, Jens Aage; Birgenau, R. J.
1977-01-01
By applying a real space version of the Ginzburg criterion, the role of fluctuations and thence the self‐consistency of mean field theory are assessed in a simple fashion for a variety of phase transitions. It is shown that in using this approach the concept of ’’marginal dimensionality’’ emerges...... in a natural way. For example, it is shown that for many homogeneous structural transformations the marginal dimensionality is two, so that mean field theory will be valid for real three‐dimensional systems. It is suggested that this simple self‐consistent approach to Landau theory should be incorporated...
The quantum N-body problem in the mean-field and semiclassical regime.
Golse, François
2018-04-28
The present work discusses the mean-field limit for the quantum N -body problem in the semiclassical regime. More precisely, we establish a convergence rate for the mean-field limit which is uniform as the ratio of Planck constant to the action of the typical single particle tends to zero. This convergence rate is formulated in terms of a quantum analogue of the quadratic Monge-Kantorovich or Wasserstein distance. This paper is an account of some recent collaboration with C. Mouhot, T. Paul and M. Pulvirenti.This article is part of the themed issue 'Hilbert's sixth problem'. © 2018 The Author(s).
Comment on the presence of chaos in mean field dynamics inside the spinodal region
International Nuclear Information System (INIS)
Jacquot, B.; Colonna, M.; Chomaz, Ph.; Guarnera, A.
1995-01-01
The role of chaos in the mean field simulations of spinodal decomposition is analysed. It is demonstrated that, conversely to recent publications, the RPA unstable modes are only weakly non-linear and weakly coupled. The Lyapunov exponents are shown to be nothing by the largest imaginary RPA frequencies and the early mean field evolution, even of a randomly initialized trajectory, is shown to be mostly understandable within the framework of simple linear instabilities. Finally, it is recalled how the time scales are related to the use of a reasonable range for the nuclear force. (author)
Real-Space Application of the Mean-Field Description of Spin-Glass Dynamics
International Nuclear Information System (INIS)
Barrat, Alain; Berthier, Ludovic
2001-01-01
The out of equilibrium dynamics of finite dimensional spin glasses is considered from a point of view going beyond the standard 'mean-field theory' versus 'droplet picture' debate of the past decades. The main predictions of both theories concerning the spin-glass dynamics are discussed. It is shown, in particular, that predictions originating from mean-field ideas concerning the violations of the fluctuation-dissipation theorem apply quantitatively, provided one properly takes into account the role of a spin-glass coherence length, which plays a central role in the droplet picture. Dynamics in a uniform magnetic field is also briefly discussed
Coexistence of Cluster Structure and Mean-field-type Structure in Medium-weight Nuclei
International Nuclear Information System (INIS)
Taniguchi, Yasutaka; Horiuchi, Hisashi; Kimura, Masaaki
2006-01-01
We have studied the coexistence of cluster structure and mean-field-type structure in 20Ne and 40Ca using Antisymmetrized Molecular Dynamics (AMD) + Generator Coordinate Method (GCM). By energy variation with new constraint for clustering, we calculate cluster structure wave function. Superposing cluster structure wave functions and mean-field-type structure wave function, we found that 8Be-12C, α-36Ar and 12C-28Si cluster structure are important components of K π = 0 3 + band of 20Ne, that of normal deformed band of 40Ca and that of super deformed band of 40Ca, respectively
Ponomarenko, V I; Kulminskiy, D D; Prokhorov, M D
2017-08-01
We study the collective dynamics of oscillators in a network of identical bistable time-delayed feedback systems globally coupled via the mean field. The influence of delay and inertial properties of the mean field on the collective behavior of globally coupled oscillators is investigated. A variety of oscillation regimes in the network results from the presence of bistable states with substantially different frequencies in coupled oscillators. In the physical experiment and numerical simulation we demonstrate the existence of chimeralike states, in which some of the oscillators in the network exhibit synchronous oscillations, while all other oscillators remain asynchronous.
Quark number density and susceptibility calculation with one correction in mean field potential
International Nuclear Information System (INIS)
Singh, S. Somorendro
2016-01-01
We calculate quark number density and susceptibility of a model which has one loop correction in mean field potential. The calculation shows continuous increasing in the number density and susceptibility up to the temperature T = 0.4 GeV. Then the value of number density and susceptibility approach to the lattice result for higher value of temperature. The result indicates that the calculated values of the model fit well and the result increase the temperature to reach the lattice data with the one loop correction in the mean field potential. (author)
Epidemic spreading in weighted networks: an edge-based mean-field solution.
Yang, Zimo; Zhou, Tao
2012-05-01
Weight distribution greatly impacts the epidemic spreading taking place on top of networks. This paper presents a study of a susceptible-infected-susceptible model on regular random networks with different kinds of weight distributions. Simulation results show that the more homogeneous weight distribution leads to higher epidemic prevalence, which, unfortunately, could not be captured by the traditional mean-field approximation. This paper gives an edge-based mean-field solution for general weight distribution, which can quantitatively reproduce the simulation results. This method could be applied to characterize the nonequilibrium steady states of dynamical processes on weighted networks.
Mean field theory of nuclei and shell model. Present status and future outlook
International Nuclear Information System (INIS)
Nakada, Hitoshi
2003-01-01
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
Mean-Field Scenario for the Athermal Creep Dynamics of Yield-Stress Fluids
Liu, Chen; Martens, Kirsten; Barrat, Jean-Louis
2018-01-01
We develop a theoretical description based on an existent mean-field model for the transient dynamics prior to the steady flow of yielding materials. The mean-field model not only reproduces the experimentally observed nonlinear time dependence of the shear-rate response to an external stress, but also allows for the determination of the different physical processes involved in the onset of the reacceleration phase after the initial slowing down and a distinct fluidization phase. The fluidization time displays a power-law dependence on the distance of the applied stress to an age-dependent yield stress, which is not universal but strongly dependent on initial conditions.
Generator coordinate representation of the time independent mean field theory of collisions
International Nuclear Information System (INIS)
Giraud, B.G.; Lemm, J.; Weiguny, A.; Wierling, A.
1991-01-01
We show how matrix elements of the T-matrix can be easily estimated on a basis of Slater determinants, with a mean field approximation. Linear superpositions of these Slater determinants then generate plane waves, or distorted (Coulomb) waves. This provides physical matrix elements of T
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.
New a priori estimates for mean-field games with congestion
Evangelista, David; Gomes, Diogo A.
2016-01-01
We present recent developments in crowd dynamics models (e.g. pedestrian flow problems). Our formulation is given by a mean-field game (MFG) with congestion. We start by reviewing earlier models and results. Next, we develop our model. We establish new a priori estimates that give partial regularity of the solutions. Finally, we discuss numerical results.
Dark-Bright Soliton Dynamics Beyond the Mean-Field Approximation
Katsimiga, Garyfallia; Koutentakis, Georgios; Mistakidis, Simeon; Kevrekidis, Panagiotis; Schmelcher, Peter; Theory Group of Fundamental Processes in Quantum Physics Team
2017-04-01
The dynamics of dark bright solitons beyond the mean-field approximation is investigated. We first examine the case of a single dark-bright soliton and its oscillations within a parabolic trap. Subsequently, we move to the setting of collisions, comparing the mean-field approximation to that involving multiple orbitals in both the dark and the bright component. Fragmentation is present and significantly affects the dynamics, especially in the case of slower solitons and in that of lower atom numbers. It is shown that the presence of fragmentation allows for bipartite entanglement between the distinguishable species. Most importantly the interplay between fragmentation and entanglement leads to the decay of each of the initial mean-field dark-bright solitons into fast and slow fragmented dark-bright structures. A variety of excitations including dark-bright solitons in multiple (concurrently populated) orbitals is observed. Dark-antidark states and domain-wall-bright soliton complexes can also be observed to arise spontaneously in the beyond mean-field dynamics. Deutsche Forschungsgemeinschaft (DFG) in the framework of the SFB 925 ``Light induced dynamics and control of correlated quantum systems''.
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...
Constitutive modeling of two phase materials using the Mean Field method for homogenization
Perdahcioglu, Emin Semih; Geijselaers, Hubertus J.M.
2010-01-01
A Mean-Field homogenization framework for constitutive modeling of materials involving two distinct elastic-plastic phases is presented. With this approach it is possible to compute the macroscopic mechanical behavior of this type of materials based on the constitutive models of the constituent
A simplified BBGKY hierarchy for correlated fermions from a stochastic mean-field approach
International Nuclear Information System (INIS)
Lacroix, Denis; Tanimura, Yusuke; Ayik, Sakir; Yilmaz, Bulent
2016-01-01
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 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.)
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.
Existence for stationary mean-field games with congestion and quadratic Hamiltonians
Gomes, Diogo A.; Mitake, Hiroyoshi
2015-01-01
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
Automating the mean-field method for large dynamic gossip networks
Bakhshi, Rena; Endrullis, Jörg; Endrullis, Stefan; Fokkink, Wan; Haverkort, Boudewijn R.H.M.
We investigate an abstraction method, called mean- field method, for the performance evaluation of dynamic net- works with pairwise communication between nodes. It allows us to evaluate systems with very large numbers of nodes, that is, systems of a size where traditional performance evaluation
New a priori estimates for mean-field games with congestion
Evangelista, David
2016-01-06
We present recent developments in crowd dynamics models (e.g. pedestrian flow problems). Our formulation is given by a mean-field game (MFG) with congestion. We start by reviewing earlier models and results. Next, we develop our model. We establish new a priori estimates that give partial regularity of the solutions. Finally, we discuss numerical results.
Explicit solutions of one-dimensional, first-order, stationary mean-field games with congestion
Gomes, Diogo A.
2017-01-05
Here, we consider one-dimensional first-order stationary mean-field games with congestion. These games arise when crowds face difficulty moving in high-density regions. We look at both monotone decreasing and increasing interactions and construct explicit solutions using the current formulation. We observe new phenomena such as discontinuities, unhappiness traps and the non-existence of solutions.
Mean field dynamics of networks of delay-coupled noisy excitable units
Energy Technology Data Exchange (ETDEWEB)
Franović, Igor, E-mail: franovic@ipb.ac.rs [Scientific Computing Laboratory, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade (Serbia); Todorović, Kristina; Burić, Nikola [Department of Physics and Mathematics, Faculty of Pharmacy, University of Belgrade, Vojvode Stepe 450, Belgrade (Serbia); Vasović, Nebojša [Department of Applied Mathematics, Faculty of Mining and Geology, University of Belgrade, PO Box 162, Belgrade (Serbia)
2016-06-08
We use the mean-field approach to analyze the collective dynamics in macroscopic networks of stochastic Fitzhugh-Nagumo units with delayed couplings. The conditions for validity of the two main approximations behind the model, called the Gaussian approximation and the Quasi-independence approximation, are examined. It is shown that the dynamics of the mean-field model may indicate in a self-consistent fashion the parameter domains where the Quasi-independence approximation fails. Apart from a network of globally coupled units, we also consider the paradigmatic setup of two interacting assemblies to demonstrate how our framework may be extended to hierarchical and modular networks. In both cases, the mean-field model can be used to qualitatively analyze the stability of the system, as well as the scenarios for the onset and the suppression of the collective mode. In quantitative terms, the mean-field model is capable of predicting the average oscillation frequency corresponding to the global variables of the exact system.
Should the coupling constants be mass dependent in the relativistic mean field models
International Nuclear Information System (INIS)
Levai, P.; Lukacs, B.
1986-05-01
Mass dependent coupling constants are proposed for baryonic resonances in the relativistic mean field model, according to the mass splitting of the SU-6 multiplet. With this choice the negative effective masses are avoided and the system remains nucleon dominated with moderate antidelta abundance. (author)
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...
Covariant density functional theory beyond mean field and applications for nuclei far from stability
International Nuclear Information System (INIS)
Ring, P
2010-01-01
Density functional theory provides a very powerful tool for a unified microscopic description of nuclei all over the periodic table. It is not only successful in reproducing bulk properties of nuclear ground states such as binding energies, radii, or deformation parameters, but it also allows the investigation of collective phenomena, such as giant resonances and rotational excitations. However, it is based on the mean field concept and therefore it has its limits. We discuss here two methods based based on covariant density functional theory going beyond the mean field concept, (i) models with an energy dependent self energy allowing the coupling to complex configurations and a quantitative description of the width of giant resonances and (ii) methods of configuration mixing between Slater determinants with different deformation and orientation providing are very successful description of transitional nuclei and quantum phase transitions.
International Nuclear Information System (INIS)
Lesinski, Th.
2008-09-01
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)
The relativistic mean-field description of nuclei and nuclear dynamics
International Nuclear Information System (INIS)
Reinhard, P.G.
1989-01-01
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.)
Nuclear matter in relativistic mean field theory with isovector scalar meson.
Energy Technology Data Exchange (ETDEWEB)
Kubis, S.; Kutschera, M. [Institute of Nuclear Physics, Cracow (Poland)
1996-12-01
Relativistic mean field (RMF) theory of nuclear matter with the isovector scalar mean field corresponding to the {delta}-meson [a{sub 0}(980)] is studied. While the {delta}-meson 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{sub s}{approx}30 MeV, a stronger {rho}-meson coupling is required than in absence of the {delta}-field. The energy per particle of neutron star matter is than 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. (author). 4 refs, 6 figs.
Nuclear matter in relativistic mean field theory with isovector scalar meson
International Nuclear Information System (INIS)
Kubis, S.; Kutschera, M.
1996-12-01
Relativistic mean field (RMF) theory of nuclear matter with the isovector scalar mean field corresponding to the δ-meson [a 0 (980)] is studied. While the δ-meson field vanishes in symmetric nuclear matter, it can influence properties of asymmetric nuclear matter in neutron stars. The RMF contribution due to δ-field to the nuclear symmetry energy is negative. To fit the empirical value, E s ∼30 MeV, a stronger ρ-meson coupling is required than in absence of the δ-field. The energy per particle of neutron star matter is than larger at high densities than the one with no δ-field included. Also, the proton fraction of β-stable matter increases. Splitting of proton and neutron effective masses due to the δ-field can affect transport properties of neutron star matter. (author). 4 refs, 6 figs
A mean-field approach for an intercarrier interference canceller for OFDM
International Nuclear Information System (INIS)
Sakata, A; Kabashima, Y; Peleg, Y
2012-01-01
The similarity of the mathematical description of random-field spin systems to the orthogonal frequency-division multiplexing (OFDM) scheme for wireless communication is exploited in an intercarrier interference (ICI) canceller used in the demodulation of OFDM. The translational symmetry in the Fourier domain generically concentrates the major contribution of ICI from each subcarrier in the subcarrier’s neighbourhood. This observation in conjunction with the mean-field approach leads to the development of an ICI canceller whose necessary cost of computation scales linearly with respect to the number of subcarriers. It is also shown that the dynamics of the mean-field canceller are well captured by a discrete map of a single macroscopic variable, without taking the spatial and time correlations of estimated variables into account. (paper)
International Nuclear Information System (INIS)
Bellonzi, Nicole; Jain, Amber; Subotnik, Joseph E.
2016-01-01
We study several recent mean-field semiclassical dynamics methods, focusing on the ability to recover detailed balance for long time (equilibrium) populations. We focus especially on Miller and Cotton’s [J. Phys. Chem. A 117, 7190 (2013)] suggestion to include both zero point electronic energy and windowing on top of Ehrenfest dynamics. We investigate three regimes: harmonic surfaces with weak electronic coupling, harmonic surfaces with strong electronic coupling, and anharmonic surfaces with weak electronic coupling. In most cases, recent additions to Ehrenfest dynamics are a strong improvement upon mean-field theory. However, for methods that include zero point electronic energy, we show that anharmonic potential energy surfaces often lead to numerical instabilities, as caused by negative populations and forces. We also show that, though the effect of negative forces can appear hidden in harmonic systems, the resulting equilibrium limits do remain dependent on any windowing and zero point energy parameters.
Mean-field dynamics of a population of stochastic map neurons
Franović, Igor; Maslennikov, Oleg V.; Bačić, Iva; Nekorkin, Vladimir I.
2017-07-01
We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant approach complemented by the Gaussian closure hypothesis. It is demonstrated that the mean-field model can qualitatively account for stability and bifurcations of the exact system, capturing all the generic forms of collective behavior, including macroscopic excitability, subthreshold oscillations, periodic or chaotic spiking, and chaotic bursting dynamics. Apart from qualitative analogies, we find a substantial quantitative agreement between the exact and the approximate system, as reflected in matching of the parameter domains admitting the different dynamical regimes, as well as the characteristic properties of the associated time series. The effective model is further shown to reproduce with sufficient accuracy the phase response curves of the exact system and the assembly's response to external stimulation of finite amplitude and duration.
Skyrme-Hartree-Fock in the realm of nuclear mean field models
International Nuclear Information System (INIS)
Reinhard, P.G.; Reiss, C.; Maruhn, J.; Bender, M.; Buervenich, T.; Greiner, W.
2000-01-01
We discuss and compare two brands of nuclear mean field models, the Skyrme-Hartree-Fock scheme (SHF) and the relativistic mean field model (RMF). Similarities and differences are worked out on a formal basis and with respect to the models performance in describing nuclear data. The bulk observables of stable nuclei are all described very well. Differences come up when extrapolating to exotic nuclei. The typically larger asymmetry energy in RMF leads to a larger neutron skin. Superheavy nuclei are found to be very sensitive on the single particle levels particularly on the spin orbit splitting. Ground state correlations from collective surface vibrations can have a significant effect on difference observables, as two-nucleon separation energy and two-nucleon shell gap. (author)
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.
Mean-field approximations of fixation time distributions of evolutionary game dynamics on graphs
Ying, Li-Min; Zhou, Jie; Tang, Ming; Guan, Shu-Guang; Zou, Yong
2018-02-01
The mean fixation time is often not accurate for describing the timescales of fixation probabilities of evolutionary games taking place on complex networks. We simulate the game dynamics on top of complex network topologies and approximate the fixation time distributions using a mean-field approach. We assume that there are two absorbing states. Numerically, we show that the mean fixation time is sufficient in characterizing the evolutionary timescales when network structures are close to the well-mixing condition. In contrast, the mean fixation time shows large inaccuracies when networks become sparse. The approximation accuracy is determined by the network structure, and hence by the suitability of the mean-field approach. The numerical results show good agreement with the theoretical predictions.
International Nuclear Information System (INIS)
Sun, Baoxi; Lu, Xiaofu; Shen, Pengnian; Zhao, Enguang
2003-01-01
The Debye screening masses of the σ, ω and neutral ρ 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. A different result with Brown–Rho scaling is shown, 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 the Walecka-1 model, five saturation properties of the nuclear matter are fixed reasonably, and then a density-dependent relativistic mean-field model is proposed without introducing the nonlinear self-coupling terms of mesons. (author)
Quantum mean-field decoding algorithm for error-correcting codes
International Nuclear Information System (INIS)
Inoue, Jun-ichi; Saika, Yohei; Okada, Masato
2009-01-01
We numerically examine a quantum version of TAP (Thouless-Anderson-Palmer)-like mean-field algorithm for the problem of error-correcting codes. For a class of the so-called Sourlas error-correcting codes, we check the usefulness to retrieve the original bit-sequence (message) with a finite length. The decoding dynamics is derived explicitly and we evaluate the average-case performance through the bit-error rate (BER).
An RVB state with fermionic charges and bosonic spins: Mean field theory
International Nuclear Information System (INIS)
Flensberg, K.; Hedegard, P.; Brix Pedersen, M.
1989-01-01
We consider a representation of the Hubbard model, in which the charge carriers are fermions and the spin carriers are bosons. We show that there exist a mean-field solution with a condensate of spin-singlets and we characterize the low temperature behavior of the quasiparticles. Finally we calculate the tunneling spectrum for a normal metal-RVB state tunnel junction and suggest the tunneling experiment as a probe of the statistics of the RVB quasiparticles. (orig.)
Higgs and confinement phases in the fundamental SU(2) Higgs model: Mean field analysis
International Nuclear Information System (INIS)
Damgaard, P.H.; Heller, U.M.
1985-01-01
The phase diagram of the four-dimensional SU(2) gauge-Higgs model with Higgs field in the fundamental representation is derived by mean field techniques. When the Higgs field is allowed to fluctuate in. Magnitude, the analytic connection between Higgs and confinement phases breaks down for sufficiently small values of the quark Higgs coupling, indicating that the Higgs and confinement phases for these couplings are strictly distinct phases. (orig.)
Mean-field behavior for the survival probability and the point-to-surface connectivity
Sakai, A
2003-01-01
We consider the critical survival probability for oriented percolation and the contact process, and the point-to-surface connectivity for critical percolation. By similarity, let \\rho denote the critical expoents for both quantities. We prove in a unified fashion that, if \\rho exists and if both two-point function and its certain restricted version exhibit the same mean-field behavior, then \\rho=2 for percolation with d>7 and \\rho=1 for the time-oriented models with d>4.
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
Double giant resonances in time-dependent relativistic mean-field theory
International Nuclear Information System (INIS)
Ring, P.; Podobnik, B.
1996-01-01
Collective vibrations in spherical nuclei are described in the framework of time-dependent relativistic mean-field theory (RMFT). Isoscalar quadrupole and isovector dipole oscillations that correspond to giant resonances are studied, and possible excitations of higher modes are investigated. We find evidence for modes which can be interpreted as double resonances. In a quantized RMFT they correspond to two-phonon states. (orig.)
Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach
Chenavaz, Régis; Paraschiv, Corina; Turinici, Gabriel
2017-01-01
Dynamic pricing of new products has been extensively studied in monopolistic and oligopolistic markets. But, the optimal control and differential game tools used to investigate the pricing behavior on markets with a finite number of firms are not well-suited to model competitive markets with an infinity of firms. Using a mean-field games approach, this paper examines dynamic pricing policies in competitive markets, where no firm exerts market power. The theoretical setting is based on a diffu...
Mean-field energy-level shifts and dielectric properties of strongly polarized Rydberg gases
Zhelyazkova, V.; Jirschik, R.; Hogan, S. D.
2016-01-01
Mean-field energy-level shifts arising as a result of strong electrostatic dipole interactions within dilute gases of polarized helium Rydberg atoms have been probed by microwave spectroscopy. The Rydberg states studied had principal quantum numbers n=70 and 72, and electric dipole moments of up to 14 050 D, and were prepared in pulsed supersonic beams at particle number densities on the order of 108 cm−3. Comparisons of the experimental data with the results of Monte Carlo calculations highl...
Energy Technology Data Exchange (ETDEWEB)
Peru, S. [CEA, DAM, DIF, Arpajon (France); Martini, M. [Ghent University, Department of Physics and Astronomy, Gent (Belgium); CEA, DAM, DIF, Arpajon (France); Universite Libre de Bruxelles, Institut d' Astronomie et d' Astrophysique, CP-226, Brussels (Belgium)
2014-05-15
We present a review of several works using the finite-range Gogny interaction in mean field approaches and beyond to explore the most striking nuclear structure features. Shell evolution along the N = 16, 20, 28, 40 isotopic chains is investigated. The static deformation obtained in the mean field description are shown to be often in disagreement with the one experimentally determined. Dynamics is addressed in a GCM-like method, including rotational degrees of freedom, namely the five-dimension collective Hamiltonian (5DCH). This framework allows the description of the low-energy collective excitations. Nevertheless, some data cannot be reproduced with the collective Hamiltonian approach. Thus the QRPA formalism is introduced and used to simultaneously describe high- and low-energy spectroscopy as well as collective and individual excitations. After the description of giant resonances in doubly magic exotic nuclei, the role of the intrinsic deformation in giant resonances is presented. The appearance of low-energy dipole resonances in light nuclei is also discussed. In particular the isoscalar or isovector nature of Pygmy states is debated. Then, the first microscopic fully coherent description of the multipole spectrum of heavy deformed nucleus {sup 238}U is presented. Finally, a comparison of the low-energy spectrum obtained within the two extensions of the static mean field, namely QRPA and 5DCH, is performed for 2{sup +} states in N = 16 isotones, nickel and tin isotopes. For the first time the different static and dynamic factors involved in the generation of the 2{sup +} states in the nickel isotopic chain, from drip line to drip line, can be analysed in only one set of coherent approaches, free of adjustable parameters, using the same two-body interaction D1S and the resulting HFB mean field. (orig.)
Isospin-dependent properties of asymmetric nuclear matter in relativistic mean field models
Chen, Lie-Wen; Ko, Che Ming; Li, Bao-An
2007-11-01
Using various relativistic mean-field models, including nonlinear ones with meson field self-interactions, models with density-dependent meson-nucleon couplings, and point-coupling models without meson fields, we have studied the isospin-dependent bulk and single-particle properties of asymmetric nuclear matter. In particular, we have determined the density dependence of nuclear symmetry energy from these different relativistic mean-field models and compared the results with the constraints recently extracted from analyses of experimental data on isospin diffusion and isotopic scaling in intermediate energy heavy-ion collisions as well as from measured isotopic dependence of the giant monopole resonances in even-A Sn isotopes. Among the 23 parameter sets in the relativistic mean-field model that are commonly used for nuclear structure studies, only a few are found to give symmetry energies that are consistent with the empirical constraints. We have also studied the nuclear symmetry potential and the isospin splitting of the nucleon effective mass in isospin asymmetric nuclear matter. We find that both the momentum dependence of the nuclear symmetry potential at fixed baryon density and the isospin splitting of the nucleon effective mass in neutron-rich nuclear matter depend not only on the nuclear interactions but also on the definition of the nucleon optical potential.
On the Existence of Solutions for Stationary Mean-Field Games with Congestion
Evangelista, David
2017-09-11
Mean-field games (MFGs) are models of large populations of rational agents who seek to optimize an objective function that takes into account their location and the distribution of the remaining agents. Here, we consider stationary MFGs with congestion and prove the existence of stationary solutions. Because moving in congested areas is difficult, agents prefer to move in non-congested areas. As a consequence, the model becomes singular near the zero density. The existence of stationary solutions was previously obtained for MFGs with quadratic Hamiltonians thanks to a very particular identity. Here, we develop robust estimates that give the existence of a solution for general subquadratic Hamiltonians.
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.
Inverse problem for the mean-field monomer-dimer model with attractive interaction
International Nuclear Information System (INIS)
Contucci, Pierluigi; Luzi, Rachele; Vernia, Cecilia
2017-01-01
The inverse problem method is tested for a class of monomer-dimer statistical mechanics models that contain also an attractive potential and display a mean-field critical point at a boundary of a coexistence line. The inversion is obtained by analytically identifying the parameters in terms of the correlation functions and via the maximum-likelihood method. The precision is tested in the whole phase space and, when close to the coexistence line, the algorithm is used together with a clustering method to take care of the underlying possible ambiguity of the inversion. (paper)
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.
Fission barriers and asymmetric ground states in the relativistic mean-field theory
International Nuclear Information System (INIS)
Rutz, K.; Reinhard, P.G.; Greiner, W.
1995-01-01
The symmetric and asymmetric fission path for 240 Pu, 232 Th and 226 Ra is investigated within the relativistic mean-field model. Standard parametrizations which are well fitted to nuclear ground-state properties are found to deliver reasonable qualitative and quantitative features of fission, comparable to similar nonrelativistic calculations. Furthermore, stable octupole deformations in the ground states of radium isotopes are investigated. They are found in a series of isotopes, qualitatively in agreement with nonrelativistic models. But the quantitative details differ amongst the models and between the various relativistic parametrizations. (orig.)
Quark self-energy beyond the mean field at finite temperature
International Nuclear Information System (INIS)
Zhuang, P.
1995-01-01
The Nambu--Jona-Lasinio model, an effective low-energy model of QCD, is extended to the next to the leading order in the 1/N c expansion at finite temperature and density. The contributions to the quark self-energy and the constituent quark mass from the meson dressing are considered in a perturbative approach about the mean field. In particular, the temperature dependence of the quark mass is shown numerically at zero chemical potential. The correction to the quark mass from the meson dressing amounts to 20% compared to the result of the leading order at low temperature, and rapidly approaches zero at high temperature
Fission properties of odd-A nuclei in a mean field framework
International Nuclear Information System (INIS)
Perez-Martin, S.; Robledo, L.M.
2009-01-01
Theoretical tools at the level of the mean field approximation are used to explore the spontaneous fission properties of odd-A nuclei. The tools rely on the equal (or uniform) filling approximation to deal with the unpaired nucleon in a time-reversal preserving manner. Realistic calculations have been carried out with the finite range Gogny force D1S, which was tailored to reasonably reproduce fission properties in the actinides. The preliminary results obtained for the nucleus 235 U are analyzed and the physical origin for the hindrance factor for the spontaneous fission half life is discussed. (author)
On the Existence of Solutions for Stationary Mean-Field Games with Congestion
Evangelista, David; Gomes, Diogo A.
2017-01-01
Mean-field games (MFGs) are models of large populations of rational agents who seek to optimize an objective function that takes into account their location and the distribution of the remaining agents. Here, we consider stationary MFGs with congestion and prove the existence of stationary solutions. Because moving in congested areas is difficult, agents prefer to move in non-congested areas. As a consequence, the model becomes singular near the zero density. The existence of stationary solutions was previously obtained for MFGs with quadratic Hamiltonians thanks to a very particular identity. Here, we develop robust estimates that give the existence of a solution for general subquadratic Hamiltonians.
Time dependent mean field approximation to the many-body S-matrix
International Nuclear Information System (INIS)
Alhassid, Y.; Koonin, S.E.
1980-01-01
Time-dependent Hartree-Fock (TDHF) calculations are a good description of some inclusive properties of deep inelastic heavy-ion collisions. The first steps toward a mean-field theory that approximates specific elements of the many-body S matrix are presented. A many-body system with pairwise interactions excited by an external, time-dependent one-body field is considered. The methods are used to solve the forced Lipkin model. The moduli of elastic and excitation amplitudes are plotted. 3 figures
Naturalness of Nonlinear Scalar Self-Couplings in a Relativistic Mean Field Theory for Neutron Stars
International Nuclear Information System (INIS)
Maekawa, Claudio; Razeira, Moises; Vasconcellos, Cesar A. Z.; Dillig, Manfred; Bodmann, Bardo E. J.
2004-01-01
We investigate the role of naturalness in effective field theory. We focus on dense hadronic matter using a generalized relativistic multi-baryon lagrangian density mean field approach which contains nonlinear self-couplings of the σ, δ meson fields and the fundamental baryon octet. We adjust the model parameters to describe bulk static properties of ordinary nuclear matter. Then, we show that our approach represents a natural modelling of nuclear matter under the extreme conditions of density as the ones found in the interior of neutron stars
One-pion exchange current corrections for nuclear magnetic moments in relativistic mean field theory
International Nuclear Information System (INIS)
Li Jian; Yao, J.M.; Meng Jie; Arima, Akito
2011-01-01
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 enhances the isovector magnetic moments further and does not improve the corresponding description for the concerned nuclei in the present work. (author)
Mass dispersions in a time-dependent mean-field approach
International Nuclear Information System (INIS)
Balian, R.; Bonche, P.; Flocard, H.; Veneroni, M.
1984-05-01
Characteristic functions for single-particle (s.p.) observables are evaluated by means of a time-dependent variational principle, which involves a state and an observable as conjugate variables. This provides a mean-field expression for fluctuations of s.p. observables, such as mass dispersions. The result differs from TDHF, it requires only the use of existing codes, and it presents attractive theoretical features. First numerical tests are encouraging. In particular, a calculation for 16 O + 16 O provides a significant increase of the predicted mass dispersion
Giant halos in medium nuclei within modified relativistic mean field (MRMF) model
Energy Technology Data Exchange (ETDEWEB)
Nugraha, A. M., E-mail: alpi.mahisha@gmail.com; Sulaksono, A. [Departemen Fisika, FMIPA, Universitas Indonesia, Kampus UI Depok (Indonesia); Sumaryada, T. [Department of Physics, Bogor Agricultural University, Jalan Meranti Kampus IPB Dramaga Bogor 16680 (Indonesia)
2016-04-19
The large number of neutrons in a region beyond a closed shell core indicates the presence of giant halos in nuclei. In this work, by using the Rotival method within a modified relativistic mean field (MRMF) model, we predict theoretically the formation of giant halos in Cr and Zr isotopes. The MRMF model is a modification of standard RMF model augmented with isoscalar and isovector tensor terms, isovector-isoscalar vector cross coupling term and electromagnetic exchange term for Coulomb interaction in local density approximation (LDA).
Pionic atoms, the relativistic mean-field theory and the pion-nucleon scattering lenghts
International Nuclear Information System (INIS)
Goudsmit, P.F.A.; Leisi, H.J.; Matsinos, E.
1991-01-01
Analysing pionic-atom data of isoscalar nuclei within the relativistic mean-field (RMF) theory, we determine the pseudoscalar πNN mixing parameter x=0.24±0.06 (syst.) and the strength of the nuclear scalar meson field for pions, S π =-34±14 (syst.) MeV. We show that these values are compatible with the elementary π-N interaction. Our RMF model provides a solution to the long-standing problem of the s-wave repulsion. (orig.)
New mean-field calculations for the phase diagram of the Annni model
International Nuclear Information System (INIS)
Tome, T.; Salinas, S.R.A.
1987-01-01
A variational procedure, with the inclusion of some spin fluctuations, to go beyond the standard layer-by-layer mean-field calculations for the T-p phase diagram of the ANNNI model is used. The high temperature region is studied analytically. The transition lines meet smoothly at the Lifshitz point, which is an inflection point of the second-order paramagnetic border. At low temperature, these numerical resuls confirm the stability of the main commensurate phases and show a quantitative trend towards the preductions f the Monte Carlo analyses. (author) [pt
A mean field study of the quasi-one-dimensional antiferromagnetic anisotropic Heisenberg model
International Nuclear Information System (INIS)
Benyoussef, A.
1996-10-01
The effect of the chain and the dimer anisotropies on the ground state energy and the energy gap of the spin-1/2 quasi-one-dimensional antiferromagnetic Heisenberg model is investigated using a mean field theory. The dependence of the magnetization and the effective hopping parameters on the anisotropy α xy (=J xy perpendicular /J xy parallel ) are presented for several values of the chain anisotropy. However, such a system exhibits a transition from antiferromagnetic ordered to disordered phases for arbitrary chain anisotropy and dimer anisotropy. (author). 22 refs, 11 figs
Identical bands at normal deformation: Necessity of going beyond the mean-field approach
International Nuclear Information System (INIS)
Sun, Y.; Wu, C.; Feng, D.H.; Egido, J.L.; Guidry, M.
1996-01-01
The validity of BCS theory has been questioned because the appearance of normally deformed identical bands in odd and even nuclei seems to contradict the conventional understanding of the blocking effect. This problem is examined with the projected shell model (PSM), which projects good angular momentum states and includes many-body correlations in both deformation and pairing channels. Satisfactory reproduction of identical band data by the PSM suggests that it may be necessary to go beyond the mean field to obtain a quantitative account of identical bands. copyright 1996 The American Physical Society
DEFF Research Database (Denmark)
Pedersen, T.G.; Johansen, P.M.
1997-01-01
. The theory provides an explanation for the high long-term stability of the photoinduced anisotropy as well as a theoretical prediction of the temporal behavior of photoinduced birefringence. The theoretical results agree favorably with measurements in the entire range of writing intensities used......A novel mean-field theory of photoinduced reorientation and optical anisotropy in liquid crystalline side-chain polymers is presented and compared with experiments, The reorientation mechanism is based on photoinduced trans cis isomerization and a multidomain model of the material is introduced...
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 approach to the Ising chain in a transverse magnetic field
Osácar, C.; Pacheco, A. F.
2017-07-01
We evaluate a mean field method to describe the properties of the ground state of the Ising chain in a transverse magnetic field. Specifically, a method of the Bethe-Peierls type is used by solving spin blocks with a self-consistency condition at the borders. The computations include the critical point for the phase transition, exponent of magnetisation and energy density. All results are obtained using basic quantum mechanics at an undergraduate level. The advantages and the limitations of the approach are emphasised.
International Nuclear Information System (INIS)
Backes, Steffen
2017-04-01
The study of the electronic properties of correlated systems is a very diverse field and has lead to valuable insight into the physics of real materials. In these systems, the decisive factor that governs the physical properties is the ratio between the electronic kinetic energy, which promotes delocalization over the lattice, and the Coulomb interaction, which instead favours localized electronic states. Due to this competition, correlated electronic systems can show unique and interesting properties like the Metal-Insulator transition, diverse phase diagrams, strong temperature dependence and in general a high sensitivity to the environmental conditions. A theoretical description of these systems is not an easy task, since perturbative approaches that do not preserve the competition between the kinetic and interaction terms can only be applied in special limiting cases. One of the most famous approaches to obtain the electronic properties of a real material is the ab initio density functional theory (DFT) method. It allows one to obtain the ground state density of the system under investigation by mapping onto an effective non-interacting system that has to be found self-consistently. While being an exact theory, in practical implementations certain approximations have to be made to the exchange-correlation potential. The local density approximation (LDA), which approximates the exchange-correlation contribution to the total energy by that of a homogeneous electron gas with the corresponding density, has proven quite successful in many cases. Though, this approximation in general leads to an underestimation of electronic correlations and is not able to describe a metal-insulator transition due to electronic localization in the presence of strong Coulomb interaction. A different approach to the interacting electronic problem is the dynamical mean-field theory (DMFT), which is non-perturbative in the kinetic and interaction term but neglects all non
Energy Technology Data Exchange (ETDEWEB)
Backes, Steffen
2017-04-15
The study of the electronic properties of correlated systems is a very diverse field and has lead to valuable insight into the physics of real materials. In these systems, the decisive factor that governs the physical properties is the ratio between the electronic kinetic energy, which promotes delocalization over the lattice, and the Coulomb interaction, which instead favours localized electronic states. Due to this competition, correlated electronic systems can show unique and interesting properties like the Metal-Insulator transition, diverse phase diagrams, strong temperature dependence and in general a high sensitivity to the environmental conditions. A theoretical description of these systems is not an easy task, since perturbative approaches that do not preserve the competition between the kinetic and interaction terms can only be applied in special limiting cases. One of the most famous approaches to obtain the electronic properties of a real material is the ab initio density functional theory (DFT) method. It allows one to obtain the ground state density of the system under investigation by mapping onto an effective non-interacting system that has to be found self-consistently. While being an exact theory, in practical implementations certain approximations have to be made to the exchange-correlation potential. The local density approximation (LDA), which approximates the exchange-correlation contribution to the total energy by that of a homogeneous electron gas with the corresponding density, has proven quite successful in many cases. Though, this approximation in general leads to an underestimation of electronic correlations and is not able to describe a metal-insulator transition due to electronic localization in the presence of strong Coulomb interaction. A different approach to the interacting electronic problem is the dynamical mean-field theory (DMFT), which is non-perturbative in the kinetic and interaction term but neglects all non
Nonlinear many-body reaction theories from nuclear mean field approximations
International Nuclear Information System (INIS)
Griffin, J.J.
1983-01-01
Several methods of utilizing nonlinear mean field propagation in time to describe nuclear reaction have been studied. The property of physical asymptoticity is analyzed in this paper, which guarantees that the prediction by a reaction theory for the physical measurement of internal fragment properties shall not depend upon the precise location of the measuring apparatus. The physical asymptoticity is guaranteed in the Schroedinger collision theory of a scuttering system with translationally invariant interaction by the constancy of the S-matrix elements and by the translational invariance of the internal motion for well-separated fragments. Both conditions are necessary for the physical asymptoticity. The channel asymptotic single-determinantal propagation can be described by the Dirac-TDHF (time dependent Hartree-Fock) time evolution. A new asymptotic Hartree-Fock stationary phase (AHFSP) description together with the S-matrix time-dependent Hartree-Fock (TD-S-HF) theory constitute the second example of a physically asymptotic nonlinear many-body reaction theory. A review of nonlinear mean field many-body reaction theories shows that initial value TDHF is non-asymptotic. The TD-S-HF theory is asymptotic by the construction. The gauge invariant periodic quantized solution of the exact Schroedinger problem has been considered to test whether it includes all of the exact eigenfunctions as it ought to. It did, but included as well an infinity of all spurions solutions. (Kato, T.)
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.
Atomically flat superconducting nanofilms: multiband properties and mean-field theory
International Nuclear Information System (INIS)
Shanenko, A A; Aguiar, J Albino; Vagov, A; Croitoru, M D; Milošević, M V
2015-01-01
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. (paper)
Cluster Mean-Field Approach to the Steady-State Phase Diagram of Dissipative Spin Systems
Directory of Open Access Journals (Sweden)
Jiasen Jin
2016-07-01
Full Text Available 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 XYZ 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.
Mean field approximation for biased diffusion on Japanese inter-firm trading network.
Watanabe, Hayafumi
2014-01-01
By analysing the financial data of firms across Japan, a nonlinear power law with an exponent of 1.3 was observed between the number of business partners (i.e. the degree of the inter-firm trading network) and sales. In a previous study using numerical simulations, we found that this scaling can be explained by both the money-transport model, where a firm (i.e. customer) distributes money to its out-edges (suppliers) in proportion to the in-degree of destinations, and by the correlations among the Japanese inter-firm trading network. However, in this previous study, we could not specifically identify what types of structure properties (or correlations) of the network determine the 1.3 exponent. In the present study, we more clearly elucidate the relationship between this nonlinear scaling and the network structure by applying mean-field approximation of the diffusion in a complex network to this money-transport model. Using theoretical analysis, we obtained the mean-field solution of the model and found that, in the case of the Japanese firms, the scaling exponent of 1.3 can be determined from the power law of the average degree of the nearest neighbours of the network with an exponent of -0.7.
Mean-field Theory for Some Bus Transport Networks with Random Overlapping Clique Structure
International Nuclear Information System (INIS)
Yang Xuhua; Sun Bao; Wang Bo; Sun Youxian
2010-01-01
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)
On a mean field game optimal control approach modeling fast exit scenarios in human crowds
Burger, Martin; Di Francesco, Marco; Markowich, Peter A.; Wolfram, Marie Therese
2013-01-01
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.
Gomes, Diogo A.
2016-01-06
We present recent developments in the theory of first-order mean-field games (MFGs). A standard assumption in MFGs is that the cost function of the agents is monotone in the density of the distribution. This assumption leads to a comprehensive existence theory and to the uniqueness of smooth solutions. Here, our goals are to understand the role of local monotonicity in the small perturbation regime and the properties of solutions for problems without monotonicity. Under a local monotonicity assumption, we show that small perturbations of MFGs have unique smooth solutions. In addition, we explore the connection between first-order MFGs and classical mechanics and KAM theory. Next, for non-monotone problems, we construct non-unique explicit solutions for a broad class of first-order mean-field games. We provide an alternative formulation of MFGs in terms of a new current variable. These examples illustrate two new phenomena: the non-uniqueness of solutions and the breakdown of regularity.
Edge-Corrected Mean-Field Hubbard Model: Principle and Applications in 2D Materials
Directory of Open Access Journals (Sweden)
Xi Zhang
2017-05-01
Full Text Available This work reviews the current progress of tight-binding methods and the recent edge-modified mean-field Hubbard model. Undercoordinated atoms (atoms not fully coordinated exist at a high rate in nanomaterials with their impact overlooked. A quantum theory was proposed to calculate electronic structure of nanomaterials by incorporating bond order-length-strength (BOLS correlation to mean-field Hubbard model, i.e., BOLS-HM. Consistency between the BOLS-HM calculation and density functional theory (DFT calculation on 2D materials verified that (i bond contractions and potential well depression occur at the edge of graphene, phosphorene, and antimonene nanoribbons; (ii the physical origin of the band gap opening of graphene, phosphorene, and antimonene nanoribbons lays in the enhancement of edge potentials and hopping integrals due to the shorter and stronger bonds between undercoordinated atoms; (iii the band gap of 2D material nanoribbons expand as the width decreases due to the increasing under-coordination effects of edges which modulates the conductive behaviors; and (iv non-bond electrons at the edges and atomic vacancies of 2D material accompanied with the broken bond contribute to the Dirac-Fermi polaron (DFP with a local magnetic moment.
Gomes, Diogo A.; Nurbekyan, Levon; Prazeres, Mariana
2016-01-01
We present recent developments in the theory of first-order mean-field games (MFGs). A standard assumption in MFGs is that the cost function of the agents is monotone in the density of the distribution. This assumption leads to a comprehensive existence theory and to the uniqueness of smooth solutions. Here, our goals are to understand the role of local monotonicity in the small perturbation regime and the properties of solutions for problems without monotonicity. Under a local monotonicity assumption, we show that small perturbations of MFGs have unique smooth solutions. In addition, we explore the connection between first-order MFGs and classical mechanics and KAM theory. Next, for non-monotone problems, we construct non-unique explicit solutions for a broad class of first-order mean-field games. We provide an alternative formulation of MFGs in terms of a new current variable. These examples illustrate two new phenomena: the non-uniqueness of solutions and the breakdown of regularity.
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.
Autonomously responsive pumping by a bacterial flagellar forest: A mean-field approach
Martindale, James D.; Fu, Henry C.
2017-09-01
This study is motivated by a microfluidic device that imparts a magnetic torque on an array of bacterial flagella. Bacterial flagella can transform their helical geometry autonomously in response to properties of the background fluid, which provides an intriguing mechanism allowing their use as an engineered element for the regulation or transport of chemicals in microscale applications. The synchronization of flagellar phase has been widely studied in biological contexts, but here we examine the synchronization of flagellar tilt, which is necessary for effective pumping. We first examine the effects of helical geometry and tilt on the pumping flows generated by a single rotating flagellum. Next, we explore a mean-field model for an array of helical flagella to understand how collective tilt arises and influences pumping. The mean-field methodology allows us to take into account possible phase differences through a time-averaging procedure and to model an infinite array of flagella. We find array separation distances, magnetic field strengths, and rotation frequencies that produce nontrivial self-consistent pumping solutions. For individual flagella, pumping is reversed when helicity or rotation is reversed; in contrast, when collective effects are included, self-consistent tilted pumping solutions become untilted nonpumping solutions when helicity or rotation is reversed.
Realization of the mean-field universality class in spin-crossover materials
Miyashita, Seiji; Konishi, Yusuké; Nishino, Masamichi; Tokoro, Hiroko; Rikvold, Per Arne
2008-01-01
In spin-crossover materials, the volume of a molecule changes depending on whether it is in the high-spin (HS) or low-spin (LS) state. This change causes distortion of the lattice. Elastic interactions among these distortions play an important role for the cooperative properties of spin-transition phenomena. We find that the critical behavior caused by this elastic interaction belongs to the mean-field universality class, in which the critical exponents for the spontaneous magnetization and the susceptibility are β=1/2 and γ=1 , respectively. Furthermore, the spin-spin correlation function is a constant at long distances, and it does not show an exponential decay in contrast to short-range models. The value of the correlation function at long distances shows different size dependences: O(1/N) , O(1/N) , and constant for temperatures above, at, and below the critical temperature, respectively. The model does not exhibit clusters, even near the critical point. We also found that cluster growth is suppressed in the present model and that there is no critical opalescence in the coexistence region. During the relaxation process from a metastable state at the end of a hysteresis loop, nucleation phenomena are not observed, and spatially uniform configurations are maintained during the change of the fraction of HS and LS. These characteristics of the mean-field model are expected to be found not only in spin-crossover materials, but also generally in systems where elastic distortion mediates the interaction among local states.
Baró, Jordi; Davidsen, Jörn
2018-03-01
The hypothesis of critical failure relates the presence of an ultimate stability point in the structural constitutive equation of materials to a divergence of characteristic scales in the microscopic dynamics responsible for deformation. Avalanche models involving critical failure have determined common universality classes for stick-slip processes and fracture. However, not all empirical failure processes exhibit the trademarks of criticality. The rheological properties of materials introduce dissipation, usually reproduced in conceptual models as a hardening of the coarse grained elements of the system. Here, we investigate the effects of transient hardening on (i) the activity rate and (ii) the statistical properties of avalanches. We find the explicit representation of transient hardening in the presence of generalized viscoelasticity and solve the corresponding mean-field model of fracture. In the quasistatic limit, the accelerated energy release is invariant with respect to rheology and the avalanche propagation can be reinterpreted in terms of a stochastic counting process. A single universality class can be defined from such analogy, and all statistical properties depend only on the distance to criticality. We also prove that interevent correlations emerge due to the hardening—even in the quasistatic limit—that can be interpreted as "aftershocks" and "foreshocks."
International Nuclear Information System (INIS)
Hasegawa, Hideo
2003-01-01
A dynamical mean-field approximation (DMA) previously proposed by the present author [H. Hasegawa, Phys. Rev E 67, 041903 (2003)] has been extended to ensembles described by a general noisy spiking neuron model. Ensembles of N-unit neurons, each of which is expressed by coupled K-dimensional differential equations (DEs), are assumed to be subject to spatially correlated white noises. The original KN-dimensional stochastic DEs have been replaced by K(K+2)-dimensional deterministic DEs expressed in terms of means and the second-order moments of local and global variables: the fourth-order contributions are taken into account by the Gaussian decoupling approximation. Our DMA has been applied to an ensemble of Hodgkin-Huxley (HH) neurons (K=4), for which effects of the noise, the coupling strength, and the ensemble size on the response to a single-spike input have been investigated. Numerical results calculated by the DMA theory are in good agreement with those obtained by direct simulations, although the former computation is about a thousand times faster than the latter for a typical HH neuron ensemble with N=100
Klaiman, S.; Streltsov, A. I.; Alon, O. E.
2018-04-01
A solvable model of a generic trapped bosonic mixture, N 1 bosons of mass m 1 and N 2 bosons of mass m 2 trapped in an harmonic potential of frequency ω and interacting by harmonic inter-particle interactions of strengths λ 1, λ 2, and λ 12, is discussed. It has recently been shown for the ground state [J. Phys. A 50, 295002 (2017)] that in the infinite-particle limit, when the interaction parameters λ 1(N 1 ‑ 1), λ 2(N 2 ‑ 1), λ 12 N 1, λ 12 N 2 are held fixed, each of the species is 100% condensed and its density per particle as well as the total energy per particle are given by the solution of the coupled Gross-Pitaevskii equations of the mixture. In the present work we investigate properties of the trapped generic mixture at the infinite-particle limit, and find differences between the many-body and mean-field descriptions of the mixture, despite each species being 100%. We compute analytically and analyze, both for the mixture and for each species, the center-of-mass position and momentum variances, their uncertainty product, the angular-momentum variance, as well as the overlap of the exact and Gross-Pitaevskii wavefunctions of the mixture. The results obtained in this work can be considered as a step forward in characterizing how important are many-body effects in a fully condensed trapped bosonic mixture at the infinite-particle limit.
Baro Urbea, J.; Davidsen, J.
2017-12-01
The hypothesis of critical failure relates the presence of an ultimate stability point in the structural constitutive equation of materials to a divergence of characteristic scales in the microscopic dynamics responsible of deformation. Avalanche models involving critical failure have determined universality classes in different systems: from slip events in crystalline and amorphous materials to the jamming of granular media or the fracture of brittle materials. However, not all empirical failure processes exhibit the trademarks of critical failure. As an example, the statistical properties of ultrasonic acoustic events recorded during the failure of porous brittle materials are stationary, except for variations in the activity rate that can be interpreted in terms of aftershock and foreshock activity (J. Baró et al., PRL 2013).The rheological properties of materials introduce dissipation, usually reproduced in atomistic models as a hardening of the coarse-grained elements of the system. If the hardening is associated to a relaxation process the same mechanism is able to generate temporal correlations. We report the analytic solution of a mean field fracture model exemplifying how criticality and temporal correlations are tuned by transient hardening. We provide a physical meaning to the conceptual model by deriving the constitutive equation from the explicit representation of the transient hardening in terms of a generalized viscoelasticity model. The rate of 'aftershocks' is controlled by the temporal evolution of the viscoelastic creep. At the quasistatic limit, the moment release is invariant to rheology. Therefore, the lack of criticality is explained by the increase of the activity rate close to failure, i.e. 'foreshocks'. Finally, the avalanche propagation can be reinterpreted as a pure mathematical problem in terms of a stochastic counting process. The statistical properties depend only on the distance to a critical point, which is universal for any
Malpetti, Daniele; Roscilde, Tommaso
2017-02-01
The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical
Magnetic cluster mean-field description of spin glasses in amorphous La-Gd-Au alloys
International Nuclear Information System (INIS)
Poon, S.J.; Durand, J.
1978-03-01
Bulk magnetic properties of splat-cooled amorphous alloys of composition La/sub 80-x/Gd/sub x/Au 20 (0 less than or equal to x less than or equal to 80) were studied. Zero-field susceptibility, high-field magnetization (up to 75 kOe) and saturated remanence were measured between 1.8 and 290 0 K. Data were analyzed using a cluster mean-field approximation for the spin-glass and mictomagnetic alloys (x less than or equal to 56). Mean-field theories can account for the experimental freezing-temperatures of dilute spin-glasses in which the Ruderman-Kittel-Kasuya-Yosida interaction is dominant. For the dilute alloys, the role of amorphousness on the magnetic interactions is discussed. By extending the mean-field approximation, the concentrated spin-glasses are represented by rigid ferromagnetic clusters as individual spin-entities interacting via random forces. Scaling laws for the magnetization M and saturation remanent magnetization M/sub rs/ are obtained and presented graphically for the x less than or equal to 32 alloys in which M/x = g(H/x*, T/x), M/sub rs/(T)/x = M/sub rs/(0)/x/ exp (-α*T/x/sup p/) where x* is the concentration of clusters, α* is a constant, and p is the freezing-temperature exponent given by T/sub M/ infinity x/sup p/. It is found that p = 1 and 1.3 for the regions 4 less than or equal to x less than or equal to 40 respectively. An attempt is also made to account for the freezing temperatures of concentrated spin glasses. The strength of the interaction among clusters is determined from high-field magnetization measurements using the Larkin-Smith method modified for clusters. It is shown that for the x < 24 alloys, the size of the clusters can be correlated to the structural short-range order in the amorphous state. More concentrated alloys are marked by the emergence of cluster percolation
Microscopic mean-field boson approach to the shape transition in Sm isotopes
International Nuclear Information System (INIS)
Kuchta, R.
1988-01-01
The phase transition from spherical to deformed shape in Sm 146-156 nuclei is analyzed within the mean-field approximation applied to the Dyson image of the shell-model Hamiltonian. No quasiparticle transformation is involved in the present approach and the Pauli principle in the physical boson subspace is properly taken into account. The low-lying spectra, B(E2; O 1 + →2 + ) probabilities and the corresponding densities of electromagnetic transitions are calculated. The results provide a reasonable explanation of the phase transition in the Sm isotopes. The role of bosons with different multipolarity is investigated and it is found that g-bosons (J=4) cannot be neglected in the transition region. Comparison of the present results with those of other approaches is given as well
High-conductance states in a mean-field cortical network model
DEFF Research Database (Denmark)
Lerchner, Alexander; Ahmadi, Mandana; Hertz, John
2004-01-01
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......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...... of cortical neurons in their natural environment, and variable non-Poissonian spike statistics with Fano factors greater than 1. (C) 2004 Elsevier B.V. All rights reserved....
Mean field theory of EM algorithm for Bayesian grey scale image restoration
International Nuclear Information System (INIS)
Inoue, Jun-ichi; Tanaka, Kazuyuki
2003-01-01
The EM algorithm for the Bayesian grey scale image restoration is investigated in the framework of the mean field theory. Our model system is identical to the infinite range random field Q-Ising model. The maximum marginal likelihood method is applied to the determination of hyper-parameters. We calculate both the data-averaged mean square error between the original image and its maximizer of posterior marginal estimate, and the data-averaged marginal likelihood function exactly. After evaluating the hyper-parameter dependence of the data-averaged marginal likelihood function, we derive the EM algorithm which updates the hyper-parameters to obtain the maximum likelihood estimate analytically. The time evolutions of the hyper-parameters and so-called Q function are obtained. The relation between the speed of convergence of the hyper-parameters and the shape of the Q function is explained from the viewpoint of dynamics
Simple Theory for the Dynamics of Mean-Field-Like Models of Glass-Forming Fluids
Szamel, Grzegorz
2017-10-01
We propose a simple theory for the dynamics of model glass-forming fluids, which should be solvable using a mean-field-like approach. The theory is based on transparent physical assumptions, which can be tested in computer simulations. The theory predicts an ergodicity-breaking transition that is identical to the so-called dynamic transition predicted within the replica approach. Thus, it can provide the missing dynamic component of the random first order transition framework. In the large-dimensional limit the theory reproduces the result of a recent exact calculation of Maimbourg et al. [Phys. Rev. Lett. 116, 015902 (2016), 10.1103/PhysRevLett.116.015902]. Our approach provides an alternative, physically motivated derivation of this result.
Finite nucleus Dirac mean field theory and random phase approximation using finite B splines
International Nuclear Information System (INIS)
McNeil, J.A.; Furnstahl, R.J.; Rost, E.; Shepard, J.R.; Department of Physics, University of Maryland, College Park, Maryland 20742; Department of Physics, University of Colorado, Boulder, Colorado 80309)
1989-01-01
We calculate the finite nucleus Dirac mean field spectrum in a Galerkin approach using finite basis splines. We review the method and present results for the relativistic σ-ω model for the closed-shell nuclei 16 O and 40 Ca. We study the convergence of the method as a function of the size of the basis and the closure properties of the spectrum using an energy-weighted dipole sum rule. We apply the method to the Dirac random-phase-approximation response and present results for the isoscalar 1/sup -/ and 3/sup -/ longitudinal form factors of 16 O and 40 Ca. We also use a B-spline spectral representation of the positive-energy projector to evaluate partial energy-weighted sum rules and compare with nonrelativistic sum rule results
Critical behavior of mean-field hadronic models for warm nuclear matter
International Nuclear Information System (INIS)
Silva, J.B.; Lourenco, O.; Delfino, A.; Martins, J.S. Sa; Dutra, M.
2008-01-01
We study a set of hadronic mean-field models in the liquid-gas phase transition regime and calculate their critical parameters. The discussion is unified by scaling the coexistence curves in terms of these critical parameters. We study the models close to spinodal points, where they also present critical behavior. Inspired by signals of criticality shown in fragmentation experiments, we analyze two different scenarios in which such behavior would be expected: (i) the stability limits of a metastable system with vanishing external pressure; and (ii) the critical point of a gas-liquid phase equilibrium system for which the Maxwell construction applies. Spinodal and coexistence curves show the regions in which model dependence arises. Unexpectedly, this model dependence does not manifest if one calculates the thermal incompressibility of the models
Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth
Burger, Martin
2016-11-18
In this paper we study balanced growth path solutions of a Boltzmann mean field game model proposed by Lucas and Moll [15] to model knowledge growth in an economy. Agents can either increase their knowledge level by exchanging ideas in learning events or by producing goods with the knowledge they already have. The existence of balanced growth path solutions implies exponential growth of the overall production in time. We prove existence of balanced growth path solutions if the initial distribution of individuals with respect to their knowledge level satisfies a Pareto-tail condition. Furthermore we give first insights into the existence of such solutions if in addition to production and knowledge exchange the knowledge level evolves by geometric Brownian motion.
One-dimensional, forward-forward mean-field games with congestion
Gomes, Diogo A.
2017-03-29
Here, we consider one-dimensional forward-forward mean-field games (MFGs) with congestion, which were introduced to approximate stationary MFGs. We use methods from the theory of conservation laws to examine the qualitative properties of these games. First, by computing Riemann invariants and corresponding invariant regions, we develop a method to prove lower bounds for the density. Next, by combining the lower bound with an entropy function, we prove the existence of global solutions for parabolic forward-forward MFGs. Finally, we construct traveling-wave solutions, which settles in a negative way the convergence problem for forward-forward MFGs. A similar technique gives the existence of time-periodic solutions for non-monotonic MFGs.
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 distribution of couplings between the random variables is required, our method adapts to the concrete set of couplings. We show the significance of the approach in two ways: Our approach reproduces replica symmetric results for a wide class of toy models (assuming a nonglassy phase) with given disorder...... distributions in the thermodynamic limit. On the other hand, simulations on a real data model demonstrate that the method achieves more accurate predictions as compared to conventional TAP approaches....
Parity doubling structure of nucleon at non-zero density in the holographic mean field theory
Directory of Open Access Journals (Sweden)
He Bing-Ran
2014-06-01
Full Text Available We summarize our recent work in which we develope the holographic mean field approach to study the dense baryonic matter in a bottom-up holographic QCD model including baryons and scalar mesons in addition to vector mesons. We first show that, at zero density, the rate of the chiral invariant mass of nucleon is controlled by the ratio of the infrared boundary values of two baryon fields included in the model. Then, at non-zero density, we find that the chiral condensate decreases with the increasing density indicating the partial restoration of the chiral symmetry. Our result shows that the more amount of the proton mass comes from the chiral symmetry breaking, the faster the effective nucleon mass decrease with density.
The surface compression of nuclei in relativistic mean-field approach
International Nuclear Information System (INIS)
Sharma, M.M.
1991-01-01
The surface compression properties of nuclei have been studied in the framework of the relativistic non-linear σ-ω model. Using the Thomas-Fermi approximation for semi-infinite nuclear matter, it is shown that by varying the σ-meson mass one can change the surface compression as relative to the bulk compression. This fact is in contrast with the known properties of the phenomenological Skyrme interactions, where the ratio of the surface to the bulk incompressibility (-K S /K V ) is nearly 1 in the scaling mode of compression. The results suggest that the relativistic mean-field model may provide an interaction with the essential ingredients different from those of the Skyrme interactions. (author) 23 refs., 2 figs., 1 tab
The mean field theory in EM procedures for blind Markov random field image restoration.
Zhang, J
1993-01-01
A Markov random field (MRF) model-based EM (expectation-maximization) procedure for simultaneously estimating the degradation model and restoring the image is described. The MRF is a coupled one which provides continuity (inside regions of smooth gray tones) and discontinuity (at region boundaries) constraints for the restoration problem which is, in general, ill posed. The computational difficulty associated with the EM procedure for MRFs is resolved by using the mean field theory from statistical mechanics. An orthonormal blur decomposition is used to reduce the chances of undesirable locally optimal estimates. Experimental results on synthetic and real-world images show that this approach provides good blur estimates and restored images. The restored images are comparable to those obtained by a Wiener filter in mean-square error, but are most visually pleasing.
Regular and chaotic dynamics in time-dependent relativistic mean-field theory
International Nuclear Information System (INIS)
Vretenar, D.; Ring, P.; Lalazissis, G.A.; Poeschl, W.
1997-01-01
Isoscalar and isovector monopole oscillations that correspond to giant resonances in spherical nuclei are described in the framework of time-dependent relativistic mean-field theory. Time-dependent and self-consistent calculations that reproduce experimental data on monopole resonances in 208 Pb show that the motion of the collective coordinate is regular for isoscalar oscillations, and that it becomes chaotic when initial conditions correspond to the isovector mode. Regular collective dynamics coexists with chaotic oscillations on the microscopic level. Time histories, Fourier spectra, state-space plots, Poincare sections, autocorrelation functions, and Lyapunov exponents are used to characterize the nonlinear system and to identify chaotic oscillations. Analogous considerations apply to higher multipolarities. copyright 1997 The American Physical Society
Consequences of the center-of-mass correction in nuclear mean-field models
International Nuclear Information System (INIS)
Bender, M.; Rutz, K.; Reinhard, P.G.; Maruhn, J.A.
2000-01-01
We study the influence of the scheme for the correction for spurious center-of-mass motion on the fit of effective interactions for self-consistent nuclear mean-field calculations. We find that interactions with very simple center-of-mass correction have significantly larger surface coefficients than interactions for which the center-of-mass correction was calculated for the actual many-body state during the fit. The reason for that is that the effective interaction has to counteract the wrong trends with nucleon number of all simplified schemes for center-of-mass correction which puts a wrong trend with mass number into the effective interaction itself. The effect becomes clearly visible when looking at the deformation energy of largely deformed systems, e.g. superdeformed states or fission barriers of heavy nuclei. (orig.)
Mean-field analysis of orientation selectivity in inhibition-dominated networks of spiking neurons.
Sadeh, Sadra; Cardanobile, Stefano; Rotter, Stefan
2014-01-01
Mechanisms underlying the emergence of orientation selectivity in the primary visual cortex are highly debated. Here we study the contribution of inhibition-dominated random recurrent networks to orientation selectivity, and more generally to sensory processing. By simulating and analyzing large-scale networks of spiking neurons, we investigate tuning amplification and contrast invariance of orientation selectivity in these networks. In particular, we show how selective attenuation of the common mode and amplification of the modulation component take place in these networks. Selective attenuation of the baseline, which is governed by the exceptional eigenvalue of the connectivity matrix, removes the unspecific, redundant signal component and ensures the invariance of selectivity across different contrasts. Selective amplification of modulation, which is governed by the operating regime of the network and depends on the strength of coupling, amplifies the informative signal component and thus increases the signal-to-noise ratio. Here, we perform a mean-field analysis which accounts for this process.
Orbital effect of the magnetic field in dynamical mean-field theory
Acheche, S.; Arsenault, L.-F.; Tremblay, A.-M. S.
2017-12-01
The availability of large magnetic fields at international facilities and of simulated magnetic fields that can reach the flux-quantum-per-unit-area level in cold atoms calls for systematic studies of orbital effects of the magnetic field on the self-energy of interacting systems. Here we demonstrate theoretically that orbital effects of magnetic fields can be treated within single-site dynamical mean-field theory with a translationally invariant quantum impurity problem. As an example, we study the one-band Hubbard model on the square lattice using iterated perturbation theory as an impurity solver. We recover the expected quantum oscillations in the scattering rate, and we show that the magnetic fields allow the interaction-induced effective mass to be measured through the single-particle density of states accessible in tunneling experiments. The orbital effect of magnetic fields on scattering becomes particularly important in the Hofstadter butterfly regime.
Small traveling clusters in attractive and repulsive Hamiltonian mean-field models.
Barré, Julien; Yamaguchi, Yoshiyuki Y
2009-03-01
Long-lasting small traveling clusters are studied in the Hamiltonian mean-field model by comparing between attractive and repulsive interactions. Nonlinear Landau damping theory predicts that a Gaussian momentum distribution on a spatially homogeneous background permits the existence of traveling clusters in the repulsive case, as in plasma systems, but not in the attractive case. Nevertheless, extending the analysis to a two-parameter family of momentum distributions of Fermi-Dirac type, we theoretically predict the existence of traveling clusters in the attractive case; these findings are confirmed by direct N -body numerical simulations. The parameter region with the traveling clusters is much reduced in the attractive case with respect to the repulsive case.
A network of spiking neurons that can represent interval timing: mean field analysis.
Gavornik, Jeffrey P; Shouval, Harel Z
2011-04-01
Despite the vital importance of our ability to accurately process and encode temporal information, the underlying neural mechanisms are largely unknown. We have previously described a theoretical framework that explains how temporal representations, similar to those reported in the visual cortex, can form in locally recurrent cortical networks as a function of reward modulated synaptic plasticity. This framework allows networks of both linear and spiking neurons to learn the temporal interval between a stimulus and paired reward signal presented during training. Here we use a mean field approach to analyze the dynamics of non-linear stochastic spiking neurons in a network trained to encode specific time intervals. This analysis explains how recurrent excitatory feedback allows a network structure to encode temporal representations.
Mean-Field-Game Model for Botnet Defense in Cyber-Security
Energy Technology Data Exchange (ETDEWEB)
Kolokoltsov, V. N., E-mail: v.kolokoltsov@warwick.ac.uk [University of Warwick, Department of Statistics (United Kingdom); Bensoussan, A. [The University of Texas at Dallas, School of Management (United States)
2016-12-15
We initiate the analysis of the response of computer owners to various offers of defence systems against a cyber-hacker (for instance, a botnet attack), as a stochastic game of a large number of interacting agents. We introduce a simple mean-field game that models their behavior. It takes into account both the random process of the propagation of the infection (controlled by the botner herder) and the decision making process of customers. Its stationary version turns out to be exactly solvable (but not at all trivial) under an additional natural assumption that the execution time of the decisions of the customers (say, switch on or out the defence system) is much faster that the infection rates.
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.
Mean field theory of epidemic spreading with effective contacts on networks
International Nuclear Information System (INIS)
Wu, Qingchu; Chen, Shufang
2015-01-01
We present a general approach to the analysis of the susceptible-infected-susceptible model with effective contacts on networks, where each susceptible node will be infected with a certain probability only for effective contacts. In the network, each node has a given effective contact number. By using the one-vertex heterogenous mean-field (HMF) approximation and the pair HMF approximation, we obtain conditions for epidemic outbreak on degree-uncorrelated networks. Our results suggest that the epidemic threshold is closely related to the effective contact and its distribution. However, when the effective contact is only dependent of node degree, the epidemic threshold can be established by the degree distribution of networks.
Dependence of synchronization transitions on mean field approach in two-way coupled neural system
Shi, J. C.; Luo, M.; Huang, C. S.
2018-03-01
This work investigates the synchronization transitions in two-way coupled neural system by mean field approach. Results show that, there exists a critical noise intensity for the synchronization transitions, i.e., above (or below) the critical noise intensity, the synchronization transitions are decreased (or hardly change) with increasing the noise intensity. Meanwhile, the heterogeneity effect plays a negative role for the synchronization transitions, and above critical coupling strength, the heterogeneity effect on synchronization transitions can be negligible. Furthermore, when an external signal is introduced into the coupled system, the novel frequency-induced and amplitude-induced synchronization transitions are found, and there exist an optimal frequency and an optimal amplitude of external signal which makes the system to display the best synchronization transitions. In particular, it is observed that the synchronization transitions can not be further affected above critical frequency of external signal.
Relativistic deformed mean-field calculation of binding energy differences of mirror nuclei
International Nuclear Information System (INIS)
Koepf, W.; Barreiro, L.A.
1996-01-01
Binding energy differences of mirror nuclei for A=15, 17, 27, 29, 31, 33, 39 and 41 are calculated in the framework of relativistic deformed mean-field theory. The spatial components of the vector meson fields and the photon are fully taken into account in a self-consistent manner. The calculated binding energy differences are systematically smaller than the experimental values and lend support to the existence of the Okamoto-Nolen-Schiffer anomaly found decades ago in nonrelativistic calculations. For the majority of the nuclei studied, however, the results are such that the anomaly is significantly smaller than the one obtained within state-of-the-art nonrelativistic calculations. (author). 35 refs
Mean-Field-Game Model for Botnet Defense in Cyber-Security
International Nuclear Information System (INIS)
Kolokoltsov, V. N.; Bensoussan, A.
2016-01-01
We initiate the analysis of the response of computer owners to various offers of defence systems against a cyber-hacker (for instance, a botnet attack), as a stochastic game of a large number of interacting agents. We introduce a simple mean-field game that models their behavior. It takes into account both the random process of the propagation of the infection (controlled by the botner herder) and the decision making process of customers. Its stationary version turns out to be exactly solvable (but not at all trivial) under an additional natural assumption that the execution time of the decisions of the customers (say, switch on or out the defence system) is much faster that the infection rates.
International Nuclear Information System (INIS)
Kuchinskii, E. Z.; Nekrasov, I. A.; Sadovskii, M. V.
2008-01-01
The DOS, the dynamic (optical) conductivity, and the phase diagram of a strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are taken into account by the DMFT, and disorder is taken into account via an appropriate generalization of the self-consistent theory of localization. The DMFT effective single-impurity problem is solved by a numerical renormalization group (NRG); we consider the three-dimensional system with a semielliptic DOS. The correlated metal, Mott insulator, and correlated Anderson insulator phases are identified via the evolution of the DOS and dynamic conductivity, demonstrating both the Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of the complete zero-temperature phase diagram of the Anderson-Hubbard model. Rather unusual is the possibility of a disorder-induced Mott insulator-to-metal transition
Multichain Mean-Field Theory of Quasi-One-Dimensional Quantum Spin Systems
International Nuclear Information System (INIS)
Sandvik, A.W.
1999-01-01
A multichain mean-field theory is developed and applied to a two-dimensional system of weakly coupled S=1/2 Heisenberg chains. The environment of a chain C 0 is modeled by a number of neighboring chains C δ , δ=±1, hor-ellipsis,± , with the edge chains C ±n coupled to a staggered field. Using a quantum Monte Carlo method, the effective (2n+1) -chain Hamiltonian is solved self-consistently for n up to 4 . The results are compared with simulation results for the original Hamiltonian on large rectangular lattices. Both methods show that the staggered magnetization M for small interchain couplings α behaves as M∼√(α) enhanced by a multiplicative logarithmic correction. copyright 1999 The American Physical Society
Skyrme's interaction beyond the mean-field. The DGCM+GOA Hamiltonian of nuclear quadrupole motion
International Nuclear Information System (INIS)
Kluepfel, Peter
2008-01-01
This work focuses on the microscopic description of nuclear collective quadrupole motion within the framework of the dynamic Generator-Coordinate-Method(DGCM)+Gaussian-Overlap-Approximation(GOA). Skyrme-type effective interactions are used as the fundamental many-particle interaction. Starting from a rotational invariant, polynomial and topologic consistent formulation of the GCM+GOA Hamiltonian an interpolation scheme for the collective masses and potential is developed. It allows to define the collective Hamiltonian of fully triaxial collective quadrupole dynamics from a purely axial symmetric configuration space. The substantial gain in performance allows the self-consistent evaluation of the dynamic quadrupole mass within the ATDHF-cranking model. This work presents the first large-scale analysis of quadrupole correlation energies and lowlying collective states within the DGCM+GOA model. Different Skyrme- and pairing interactions are compared from old standards up to more recent parameterizations. After checking the validity of several approximations to the DGCM+GOA model - both on the mean-field and the collective level - we proceed with a detailed investigation of correlation effects along the chains of semi-magic isotopes and isotones. This finally allows to define a set of observables which are hardly affected by collective correlations. Those observables were used for a refit of a Skyrme-type effective interaction which is expected to cure most of the problems of the recent parameterizations. Preparing further work, estimates for the correlated ground state energy are proposed which can be evaluated directly from the mean-field model. (orig.)
Skyrme's interaction beyond the mean-field. The DGCM+GOA Hamiltonian of nuclear quadrupole motion
Energy Technology Data Exchange (ETDEWEB)
Kluepfel, Peter
2008-07-29
This work focuses on the microscopic description of nuclear collective quadrupole motion within the framework of the dynamic Generator-Coordinate-Method(DGCM)+Gaussian-Overlap-Approximation(GOA). Skyrme-type effective interactions are used as the fundamental many-particle interaction. Starting from a rotational invariant, polynomial and topologic consistent formulation of the GCM+GOA Hamiltonian an interpolation scheme for the collective masses and potential is developed. It allows to define the collective Hamiltonian of fully triaxial collective quadrupole dynamics from a purely axial symmetric configuration space. The substantial gain in performance allows the self-consistent evaluation of the dynamic quadrupole mass within the ATDHF-cranking model. This work presents the first large-scale analysis of quadrupole correlation energies and lowlying collective states within the DGCM+GOA model. Different Skyrme- and pairing interactions are compared from old standards up to more recent parameterizations. After checking the validity of several approximations to the DGCM+GOA model - both on the mean-field and the collective level - we proceed with a detailed investigation of correlation effects along the chains of semi-magic isotopes and isotones. This finally allows to define a set of observables which are hardly affected by collective correlations. Those observables were used for a refit of a Skyrme-type effective interaction which is expected to cure most of the problems of the recent parameterizations. Preparing further work, estimates for the correlated ground state energy are proposed which can be evaluated directly from the mean-field model. (orig.)
Saggar, Manish; Zanesco, Anthony P; King, Brandon G; Bridwell, David A; MacLean, Katherine A; Aichele, Stephen R; Jacobs, Tonya L; Wallace, B Alan; Saron, Clifford D; Miikkulainen, Risto
2015-07-01
Meditation training has been shown to enhance attention and improve emotion regulation. However, the brain processes associated with such training are poorly understood and a computational modeling framework is lacking. Modeling approaches that can realistically simulate neurophysiological data while conforming to basic anatomical and physiological constraints can provide a unique opportunity to generate concrete and testable hypotheses about the mechanisms supporting complex cognitive tasks such as meditation. Here we applied the mean-field computational modeling approach using the scalp-recorded electroencephalogram (EEG) collected at three assessment points from meditating participants during two separate 3-month-long shamatha meditation retreats. We modeled cortical, corticothalamic, and intrathalamic interactions to generate a simulation of EEG signals recorded across the scalp. We also present two novel extensions to the mean-field approach that allow for: (a) non-parametric analysis of changes in model parameter values across all channels and assessments; and (b) examination of variation in modeled thalamic reticular nucleus (TRN) connectivity over the retreat period. After successfully fitting whole-brain EEG data across three assessment points within each retreat, two model parameters were found to replicably change across both meditation retreats. First, after training, we observed an increased temporal delay between modeled cortical and thalamic cells. This increase provides a putative neural mechanism for a previously observed reduction in individual alpha frequency in these same participants. Second, we found decreased inhibitory connection strength between the TRN and secondary relay nuclei (SRN) of the modeled thalamus after training. This reduction in inhibitory strength was found to be associated with increased dynamical stability of the model. Altogether, this paper presents the first computational approach, taking core aspects of physiology and
Effects of anisotropies in turbulent magnetic diffusion in mean-field solar dynamo models
Energy Technology Data Exchange (ETDEWEB)
Pipin, V. V. [Institute of Solar-Terrestrial Physics, Russian Academy of Sciences, Irkutsk 664033 (Russian Federation); Kosovichev, A. G. [Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305 (United States)
2014-04-10
We study how anisotropies of turbulent diffusion affect the evolution of large-scale magnetic fields and the dynamo process on the Sun. The effect of anisotropy is calculated in a mean-field magnetohydrodynamics framework assuming that triple correlations provide relaxation to the turbulent electromotive force (so-called the 'minimal τ-approximation'). We examine two types of mean-field dynamo models: the well-known benchmark flux-transport model and a distributed-dynamo model with a subsurface rotational shear layer. For both models, we investigate effects of the double- and triple-cell meridional circulation, recently suggested by helioseismology and numerical simulations. To characterize the anisotropy effects, we introduce a parameter of anisotropy as a ratio of the radial and horizontal intensities of turbulent mixing. It is found that the anisotropy affects the distribution of magnetic fields inside the convection zone. The concentration of the magnetic flux near the bottom and top boundaries of the convection zone is greater when the anisotropy is stronger. It is shown that the critical dynamo number and the dynamo period approach to constant values for large values of the anisotropy parameter. The anisotropy reduces the overlap of toroidal magnetic fields generated in subsequent dynamo cycles, in the time-latitude 'butterfly' diagram. If we assume that sunspots are formed in the vicinity of the subsurface shear layer, then the distributed dynamo model with the anisotropic diffusivity satisfies the observational constraints from helioseismology and is consistent with the value of effective turbulent diffusion estimated from the dynamics of surface magnetic fields.
σ-SCF: A direct energy-targeting method to mean-field excited states.
Ye, Hong-Zhou; Welborn, Matthew; Ricke, Nathan D; Van Voorhis, Troy
2017-12-07
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 Δ-SCF (self-consistent field), 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, σ-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 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 Δ-SCF solutions that are otherwise hardly accessible by the usual non-aufbau configuration initial guess. We present results for this new method for small atoms (He, Be) and molecules (H 2 , HF). We find that σ-SCF is very effective at locating excited states, including individual, high energy excitations within a dense manifold of excited states. Like all single determinant methods, σ-SCF shows prominent spin-symmetry breaking for open shell states and our results suggest that this method could be further improved with spin projection.
σ-SCF: A direct energy-targeting method to mean-field excited states
Ye, Hong-Zhou; Welborn, Matthew; Ricke, Nathan D.; Van Voorhis, Troy
2017-12-01
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 Δ-SCF (self-consistent field), 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, σ-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 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 Δ-SCF solutions that are otherwise hardly accessible by the usual non-aufbau configuration initial guess. We present results for this new method for small atoms (He, Be) and molecules (H2, HF). We find that σ-SCF is very effective at locating excited states, including individual, high energy excitations within a dense manifold of excited states. Like all single determinant methods, σ-SCF shows prominent spin-symmetry breaking for open shell states and our results suggest that this method could be further improved with spin projection.
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)
Mean-field modeling approach for understanding epidemic dynamics in interconnected networks
International Nuclear Information System (INIS)
Zhu, Guanghu; Fu, Xinchu; Tang, Qinggan; Li, Kezan
2015-01-01
Modern systems (e.g., social, communicant, biological networks) are increasingly interconnected each other formed as ‘networks of networks’. Such complex systems usually possess inconsistent topologies and permit agents distributed in different subnetworks to interact directly/indirectly. Corresponding dynamics phenomena, such as the transmission of information, power, computer virus and disease, would exhibit complicated and heterogeneous tempo-spatial patterns. In this paper, we focus on the scenario of epidemic spreading in interconnected networks. We intend to provide a typical mean-field modeling framework to describe the time-evolution dynamics, and offer some mathematical skills to study the spreading threshold and the global stability of the model. Integrating the research with numerical analysis, we are able to quantify the effects of networks structure and epidemiology parameters on the transmission dynamics. Interestingly, we find that the diffusion transition in the whole network is governed by a unique threshold, which mainly depends on the most heterogenous connection patterns of network substructures. Further, the dynamics is highly sensitive to the critical values of cross infectivity with switchable phases.
Mean-field behavior in coupled oscillators with attractive and repulsive interactions.
Hong, Hyunsuk; Strogatz, Steven H
2012-05-01
We consider a variant of the Kuramoto model of coupled oscillators in which both attractive and repulsive pairwise interactions are allowed. The sign of the coupling is assumed to be a characteristic of a given oscillator. Specifically, some oscillators repel all the others, thus favoring an antiphase relationship with them. Other oscillators attract all the others, thus favoring an in-phase relationship. The Ott-Antonsen ansatz is used to derive the exact low-dimensional dynamics governing the system's long-term macroscopic behavior. The resulting analytical predictions agree with simulations of the full system. We explore the effects of changing various parameters, such as the width of the distribution of natural frequencies and the relative strengths and proportions of the positive and negative interactions. For the particular model studied here we find, unexpectedly, that the mixed interactions produce no new effects. The system exhibits conventional mean-field behavior and displays a second-order phase transition like that found in the original Kuramoto model. In contrast to our recent study of a different model with mixed interactions [Phys. Rev. Lett. 106, 054102 (2011)], the π state and traveling-wave state do not appear for the coupling type considered here.
Dispersive versus constant-geometry models of the neutron-208Pb mean field
International Nuclear Information System (INIS)
Mahaux, C.; Sartor, R.
1990-01-01
Phenomenological optical-model analyses of differential elastic scattering cross sections of neutrons by 208 Pb indicate that the radius of the real part of the potential decreases with increasing energy in the domain 4< E<40 MeV. On the other hand, the experimental total cross section is compatible with a real potential whose radial shape is energy independent. In order to clarify this situation, we compare a 'constant geometry' model whose real part has an energy-independent radial shape with a 'dispersive model' whose real part has an energy-dependent radial shape calculated from the dispersion relation which connects the real and imaginary parts of the field. The following three main features are considered. (i) The junction of the optical-model potential with the shell-model potential at negative energy. (ii) The agreement between the calculated total and differential cross sections and their experimental values. (iii) The extent to which the real part of the optical-model potential can be accurately determined by analyzing the total cross section only. It is concluded that the presently available experimental data support the existence of an energy dependence of the radial shape of the real potential, in keeping with the dispersion relation. A new parametrization of a 'dispersive' mean field is also presented. It does not involve more parameters than the previously published one but takes better account of the physical properties of the spectral functions; it is shown to improve the agreement between predicted and experimental scattering data. (orig.)
THE MEAN-FIELD SOLAR DYNAMO WITH A DOUBLE CELL MERIDIONAL CIRCULATION PATTERN
Energy Technology Data Exchange (ETDEWEB)
Pipin, V. V. [Institute of Solar-Terrestrial Physics, Russian Academy of Sciences, Irkutsk, 664033 (Russian Federation); Kosovichev, A. G. [Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305 (United States)
2013-10-10
Recent helioseismology findings, as well as advances in direct numerical simulations of global dynamics of the Sun, have indicated that in each solar hemisphere meridional circulation may form more than one cell along the radius in the convection zone. In particular, recent helioseismology results revealed a double-cell structure of the meridional circulation. We investigate properties of a mean-field solar dynamo with such double-cell meridional circulation. The dynamo model also includes the realistic profile of solar differential rotation (including the tachocline and subsurface shear layer) and takes into account effects of turbulent pumping, anisotropic turbulent diffusivity, and conservation of magnetic helicity. Contrary to previous flux-transport dynamo models, we find that the dynamo model can robustly reproduce the basic properties of the solar magnetic cycles for a wide range of model parameters and circulation speeds. The best agreement with observations is achieved when the surface meridional circulation speed is about 12 m s{sup –1}. For this circulation speed, the simulated sunspot activity shows good synchronization with the polar magnetic fields. Such synchronization was indeed observed during previous sunspot Cycles 21 and 22. We compare theoretical and observed phase diagrams of the sunspot number and the polar field strength and discuss the peculiar properties of Cycle 23.
International Nuclear Information System (INIS)
Singh, BirBikram; Patra, S. K.; Gupta, Raj K.
2010-01-01
We have studied the (ground-state) cluster radioactive decays within the preformed cluster model (PCM) of Gupta and collaborators [R. K. Gupta, in Proceedings of the 5th International Conference on Nuclear Reaction Mechanisms, Varenna, edited by E. Gadioli (Ricerca Scientifica ed Educazione Permanente, Milano, 1988), p. 416; S. S. Malik and R. K. Gupta, Phys. Rev. C 39, 1992 (1989)]. The relativistic mean-field (RMF) theory is used to obtain the nuclear matter densities for the double folding procedure used to construct the cluster-daughter potential with M3Y nucleon-nucleon interaction including exchange effects. Following the PCM approach, we have deduced empirically the preformation probability P 0 emp from the experimental data on both the α- and exotic cluster-decays, specifically of parents in the trans-lead region having doubly magic 208 Pb or its neighboring nuclei as daughters. Interestingly, the RMF-densities-based nuclear potential supports the concept of preformation for both the α and heavier clusters in radioactive nuclei. P 0 α(emp) for α decays is almost constant (∼10 -2 -10 -3 ) for all the parent nuclei considered here, and P 0 c(emp) for cluster decays of the same parents decrease with the size of clusters emitted from different parents. The results obtained for P 0 c(emp) are reasonable and are within two to three orders of magnitude of the well-accepted phenomenological model of Blendowske-Walliser for light clusters.
Nuclear sub-structure in 112–122Ba nuclei within relativistic mean field theory
International Nuclear Information System (INIS)
Bhuyan, M.; Patra, S.K.; Arumugam, P.; Gupta, Raj K.
2011-01-01
Working within the framework of relativistic mean field theory, we study for the first time the clustering structure (nuclear sub-structure) of 112–122 Ba nuclei in an axially deformed cylindrical coordinate. We calculate the individual neutrons and protons density distributions for Ba-isotopes. From the analysis of the clustering configurations in total (neutrons-plus-protons) density distributions for various shapes of both the ground and excited states, we find different sub-structures inside the Ba nuclei considered here. The important step, carried out here for the first time, is the counting of number of protons and neutrons present in the clustering region(s). 12 C is shown to constitute the cluster configuration in prolate-deformed ground-states of 112–116 Ba and oblate-deformed first excited states of 118–122 Ba nuclei. Presence of other lighter clusters such as 2 H, 3 H and nuclei in the neighborhood of N = Z, 14 N, 34–36 Cl, 36 Ar and 42 Ca are also indicated in the ground and excited states of these nuclei. Cases with no cluster configuration are shown for 112–116 Ba in their first and second excited states. All these results are of interest for the observed intermediate-mass-fragments and fusion–fission processes, and the so far unobserved evaporation residues from the decaying Ba* compound nuclei formed in heavy ion reactions. (author)
A mean-field theory on the differential capacitance of asymmetric ionic liquid electrolytes
International Nuclear Information System (INIS)
Han, Yining; Huang, Shanghui; Yan, Tianying
2014-01-01
The size of ions significantly influences the electric double layer structure of room temperature ionic liquid (IL) electrolytes and their differential capacitance (C d ). 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 C d , with the higher peak in C d occurring at positive polarization for the smaller anionic size. At high potential, C d 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 C d , which exceeds that of Gouy–Chapman theory. (paper)
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.)
Study of two-proton radioactivity within the relativistic mean-field plus BCS approach
International Nuclear Information System (INIS)
Singh, D.; Saxena, G.
2012-01-01
Inspired by recent experimental studies of two-proton radioactivity in the light-medium mass region, we have employed relativistic mean-field plus state-dependent BCS approach (RMF+BCS) to study the ground state properties of selected even-Z nuclei in the region 20 ≤ Z ≤ 40. It is found that the effective potential barrier provided by the Coulomb interaction and that due to centrifugal force may cause a long delay in the decay of some of the nuclei even with small negative proton separation energy. This may cause the existence of proton-rich nuclei beyond the proton drip-line. Nuclei 38 Ti, 42 Cr, 45 Fe, 48 Ni, 55 Zn, 60 Ge, 63, 64 Se, 68 Kr, 72 Sr and 76 Zr are found to be the potential candidates for exhibiting two-proton radioactivity in the region 20 ≤ Z ≤ 40. The reliability of these predictions is further strengthened by the agreement of the calculated results for the ground state properties such as binding energy, one- and two-proton separation energy, proton and neutron radii, and deformation with the available experimental data for the entire chain of the isotopes of the nuclei in the region 20 ≤ Z ≤ 40. (author)
A self-consistent mean-field approach to the dynamical symmetry breaking
International Nuclear Information System (INIS)
Kunihiro, Teiji; Hatsuda, Tetsuo.
1984-01-01
The dynamical symmetry breaking phenomena in the Nambu and Jona-Lasimio model are reexamined in the framework of a self-consistent mean-field (SCMF) theory. First, we formulate the SCMF theory in a lucid manner based on a successful decomposition of the Lagrangian into semiclassical and residual interaction parts by imposing a condition that ''the dangerous term'' in Bogoliubov's sense should vanish. Then, we show that the difference of the energy density between the super and normal phases, the correct expression of which the original authors failed to give, can be readily obtained by applying the SCMF theory. Futhermore, it is shown that the expression thus obtained is identical to that of the effective potential (E.P.) given by the path-integral method with an auxiliary field up to the one loop order in the loop expansion, then one finds a new and simple way to get the E.P. Some numerical results of the E.P. and the dynamically generated mass of fermion are also shown. As another demonstration of the powerfulness of the SCMF theory, we derive, in the Appendix, the energy density of the O(N)-phi 4 model including the higher order corrections in the sense of large N expansion. (author)
Mean-field potential approach for thermodynamic properties of lanthanide: Europium as a prototype
Kumar, Priyank; Bhatt, N. K.; Vyas, P. R.; Gohel, V. B.
2018-03-01
In the present paper, a simple conjunction scheme [mean-field potential (MFP) + local pseudopotential] is used to study the thermodynamic properties of divalent lanthanide europium (Eu) at extreme environment. Present study has been carried out due to the fact that divalent nature of Eu arises because of stable half-filled 4f-shell at ambient condition, which has great influence on the thermodynamic properties at extreme environment. Due to such electronic structure, it is different from remaining lanthanides having incomplete 4f-shell. The presently computed results of thermodynamic properties of Eu are in good agreement with the experimental results. Looking to such success, it seems that the concept of MFP approach is successful to account contribution due to nuclear motion to the total Helmholtz free energy at finite temperatures and pressure-induced inter-band transfer of electrons for condensed state of matter. The local pseudopotential is used to evaluate cold energy and hence MFP accounts the s-p-d-f hybridization properly. Looking to the reliability and transferability along with its computational and conceptual simplicity, we would like to extend the present scheme for the study of thermodynamic properties of remaining lanthanides and actinides at extreme environment.
Haule, Kristjan
2018-04-01
The Dynamical Mean Field Theory (DMFT) in combination with the band structure methods has been able to address reach physics of correlated materials, such as the fluctuating local moments, spin and orbital fluctuations, atomic multiplet physics and band formation on equal footing. Recently it is getting increasingly recognized that more predictive ab-initio theory of correlated systems needs to also address the feedback effect of the correlated electronic structure on the ionic positions, as the metal-insulator transition is almost always accompanied with considerable structural distortions. We will review recently developed extension of merger between the Density Functional Theory (DFT) and DMFT method, dubbed DFT+ embedded DMFT (DFT+eDMFT), whichsuccessfully addresses this challenge. It is based on the stationary Luttinger-Ward functional to minimize the numerical error, it subtracts the exact double-counting of DFT and DMFT, and implements self-consistent forces on all atoms in the unit cell. In a few examples, we will also show how the method elucidated the important feedback effect of correlations on crystal structure in rare earth nickelates to explain the mechanism of the metal-insulator transition. The method showed that such feedback effect is also essential to understand the dynamic stability of the high-temperature body-centered cubic phase of elemental iron, and in particular it predicted strong enhancement of the electron-phonon coupling over DFT values in FeSe, which was very recently verified by pioneering time-domain experiment.
Rigorous study of the mean field approximation of Debye and Hueckel for Coulomb systems
International Nuclear Information System (INIS)
Kennedy, T.G.
1984-01-01
The statistical mechanics of a classical charge symmetric Coulomb system is studied in three dimensions in the limit that the plasma parameter (the inverse temperature divided by the Debye length) goes to zero. To make the system stable, a short range interaction, e.g., hard cores is included. This short range interaction is allowed to go to zero as the plasma parameter goes to zero. Debye and Hueckel used a mean field approximation to give a nonrigorous study of Coulomb systems in his limit. For a system with no external charge distribution, it is shown that the pressure, density, and correlation functions are asymptotic to their Debye-Hueckel approximations. These approximations consist of the ideal gas term plus a term of one lower order in the plasma parameter. The main tools are the Sine-Gordon transformation, the Mayer expansion, and some new correlation inequalities. The sine-Gordon transformation and the Mayer expansion are used to express the observables as functional integrals with respect to a Gaussian measure. The correlation inequalities help control these functional integrals
International Nuclear Information System (INIS)
Heilmann, D.B.
2007-02-01
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.)
Dedes, I.; Dudek, J.
2018-03-01
We examine the effects of the parametric correlations on the predictive capacities of the theoretical modelling keeping in mind the nuclear structure applications. The main purpose of this work is to illustrate the method of establishing the presence and determining the form of parametric correlations within a model as well as an algorithm of elimination by substitution (see text) of parametric correlations. We examine the effects of the elimination of the parametric correlations on the stabilisation of the model predictions further and further away from the fitting zone. It follows that the choice of the physics case and the selection of the associated model are of secondary importance in this case. Under these circumstances we give priority to the relative simplicity of the underlying mathematical algorithm, provided the model is realistic. Following such criteria, we focus specifically on an important but relatively simple case of doubly magic spherical nuclei. To profit from the algorithmic simplicity we chose working with the phenomenological spherically symmetric Woods–Saxon mean-field. We employ two variants of the underlying Hamiltonian, the traditional one involving both the central and the spin orbit potential in the Woods–Saxon form and the more advanced version with the self-consistent density-dependent spin–orbit interaction. We compare the effects of eliminating of various types of correlations and discuss the improvement of the quality of predictions (‘predictive power’) under realistic parameter adjustment conditions.
Magnetic properties of mixed Ni–Cu ferrites calculated using mean field approach
Energy Technology Data Exchange (ETDEWEB)
Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, 63, 46000 Safi (Morocco); LMPHE, URAC 12, Faculté des Sciences, Université Mohamed V-Agdal, Rabat (Morocco); Hamedoun, M. [Institute for Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Benyoussef, A. [LMPHE, URAC 12, Faculté des Sciences, Université Mohamed V-Agdal, Rabat (Morocco); Institute for Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Academie Hassan II des Sciences et Techniques, Rabat (Morocco); Hlil, E.K. [Institut Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble cedex 9 (France)
2014-08-01
The magnetic properties of spinel ferrites [Fe{sub 1−(1−x)y}{sup 3+}Cu{sub (1−x)y}{sup 2+}]{sub A}[Ni{sub x}{sup 2+}Cu{sub (1−x)(1−y)}{sup 2+}Fe{sub 1+(1−x)y}{sup 3+}]{sub B}O{sub 4} have been studied by the mean field theory (MFT) and high temperature series expansions (HTSEs) combined with the Padé approximants. The critical temperature, the saturation magnetisation (M{sub S}) and the intra-sublattice exchanges interactions (J{sub AA}(x,y), J{sub BB}(x,y) and J{sub AB}(x,y)) are obtained by using a probability distribution law. The critical exponents associate with the magnetic susceptibility have been obtained. The effect of copper doping on the magnetic properties of nickel ferrites has been examined. - Highlights: • The exchange and constants interactions of CuFe{sub 2}O{sub 4} material are obtained. • The saturation magnetisation, the critical temperature, the Curie Weiss temperature and the Curie constant of CuFe{sub 2}O{sub 4} are obtained. • The critical exponent associated with the magnetic susceptibility is given.
Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy*
Directory of Open Access Journals (Sweden)
Kostyantyn Kechedzhi
2016-05-01
Full Text Available 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.
Site-disorder driven superconductor–insulator transition: a dynamical mean field study
International Nuclear Information System (INIS)
Kamar, Naushad Ahmad; Vidhyadhiraja, N S
2014-01-01
We investigate the effect of site disorder on the superconducting state in the attractive Hubbard model within the framework of dynamical mean field theory. For a fixed interaction strength (U), the superconducting order parameter decreases monotonically with increasing disorder (x), while the single-particle spectral gap decreases for small x, reaches a minimum and keeps increasing for larger x. Thus, the system remains gapped beyond the destruction of the superconducting state, indicating a disorder-driven superconductor–insulator transition. We investigate this transition in depth considering the effects of weak and strong disorder for a range of interaction strengths. In the clean case, the order parameter is known to increase monotonically with increasing interaction, saturating at a finite value asymptotically for U→∞. The presence of disorder results in destruction of superconductivity at large U, thus drastically modifying the clean case behaviour. A physical understanding of our findings is obtained by invoking particle–hole asymmetry and the probability distributions of the order parameter and spectral gap. (paper)
Effective interactions and mean field theory: from nuclear matter to nuclei
International Nuclear Information System (INIS)
Cochet, B.
2005-07-01
The Skyrme force is a zero-range force that allows the construction of the mean field inside the nucleus in a simple way. Skyrme forces are reasonably predictive but some features of the infinite nuclear matter or the mass of heavy nuclei are not well computed. The aim of this work is to propose an expanded parametrization of the Skyrme force in order to improve its predictive power. The first part is dedicated to the construction of the expansion of the parametrization. We recall how the effective forces are linked to the nucleon-nucleon interaction then we show the limits of the standard Skyrme forces and we propose a relatively natural improvements based on the integration of spin and isospin instabilities. The second part deals with the validation of the model, first by describing infinite nuclear matter then by studying β-balanced nuclear matter which has enabled us to reproduce some features of neutron stars like mass and radius. The computation of properties of nuclei like binding energy, mass, radii depends strongly on the adjustment procedure. (A.C.)
Stable oscillations of a predator-prey probabilistic cellular automaton: a mean-field approach
International Nuclear Information System (INIS)
Tome, Tania; Carvalho, Kelly C de
2007-01-01
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
International Nuclear Information System (INIS)
Nisha, M R; Philip, J
2013-01-01
Polymeric nanofluids of TiO 2 /PVA (polyvinyl alcohol) and Cu/PVA have been prepared by dispersing nanoparticles of TiO 2 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 TiO 2 /PVA. (paper)
The time-dependent relativistic mean-field theory and the random phase approximation
International Nuclear Information System (INIS)
Ring, P.; Ma, Zhong-yu; Van Giai, Nguyen; Vretenar, D.; Wandelt, A.; Cao, Li-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 αh-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 116 Sn. It is shown that, because the matrix elements of the time-like component of the vector-meson fields which couple the αh-configurations with the ph-configurations are strongly reduced with respect to the corresponding matrix elements of the isoscalar scalar meson field, the inclusion of states with unperturbed energies more than 1.2 GeV below the Fermi energy has a pronounced effect on giant resonances with excitation energies in the MeV region. The influence of nuclear magnetism, i.e. the effect of the spatial components of the vector fields is examined, and the difference between the nonrelativistic and relativistic RPA predictions for the nuclear matter compression modulus is explained
Higgs-Yukawa model with higher dimension operators via extended mean field theory
Akerlund, Oscar
2016-01-01
Using Extended Mean Field Theory (EMFT) on the lattice, we study properties of the Higgs-Yukawa model as an approximation of the Standard Model Higgs sector, and the effect of higher dimension operators. We note that the discussion of vacuum stability is completely modified in the presence of a $\\phi^6$ term, and that the Higgs mass no longer appears fine tuned. We also study the finite temperature transition. Without higher dimension operators the transition is found to be second order (crossover with gauge fields) for the experimental value of the Higgs mass $M_h=125$ GeV. By taking a $\\phi^6$ interaction in the Higgs potential as a proxy for a UV completion of the Standard Model, the transition becomes stronger and turns first order if the scale of new physics, i.e. the mass of the lightest mediator particle, is around $1.5$ TeV. This implies that electroweak baryogenesis may be viable in models which introduce new particles around that scale.
A mean-field theory on the differential capacitance of asymmetric ionic liquid electrolytes.
Han, Yining; Huang, Shanghui; Yan, Tianying
2014-07-16
The size of ions significantly influences the electric double layer structure of room temperature ionic liquid (IL) electrolytes and their differential capacitance (Cd). In this study, we extended the mean-field theory (MFT) developed independently by Kornyshev (2007J. Phys. Chem. B 111 5545-57) and Kilic, Bazant, and Ajdari (2007 Phys. Rev. E 75 021502) (the KKBA MFT) to take into account the asymmetric 1:1 IL electrolytes by introducing an additional parameter ξ for the anion/cation volume ratio, besides the ionic compressibility γ in the KKBA MFT. The MFT of asymmetric ions becomes KKBA MFT upon ξ = 1, and further reduces to Gouy-Chapman theory in the γ → 0 limit. The result of the extended MFT demonstrates that the asymmetric ILs give rise to an asymmetric Cd, with the higher peak in Cd occurring at positive polarization for the smaller anionic size. At high potential, Cd decays asymptotically toward KKBA MFT characterized by γ for the negative polarization, and characterized by ξγ for the positive polarization, with inverse-square-root behavior. At low potential, around the potential of zero charge, the asymmetric ions cause a higher Cd, which exceeds that of Gouy-Chapman theory.
Quest of halo in 31Ne using Glauber model formalism with deformed relativistic mean field density
International Nuclear Information System (INIS)
Sharma, Mahesh K.; Patra, S.K.
2012-01-01
The advancement of radio active ion beam (RIB) explored the structure of exotic nuclei, which are away from the β stability line. Such nuclei with weak binding lie at the limit of stability and exhibit some fascinating phenomena. One of them is the formation of one or more nucleon halo structure. It is well established that the interaction cross section of halo nuclei like 11 Li, 11 Be and 19 C show anomalously large interaction cross sections and matter radius than that of their neighboring nuclei. Some recent investigations for 31 Ne predict that has a halo nature. The first experimental evidence also suggests 31 Ne as a halo candidate. The isotope 31 Ne having N=21, which breaks the shell closer structure as a consequence of deformation associated with the strong intruder configuration and having special interest, because it lie at island of inversion. Here we apply the well known Glauber approach with conjunction of deformed relativistic mean field densities of projectile and target nuclei. It is to be noted that Panda et al has done the similar calculation using a spherical density
Dynamic mean field theory for lattice gas models of fluid mixtures confined in mesoporous materials.
Edison, J R; Monson, P A
2013-11-12
We present the extension of dynamic mean field theory (DMFT) for fluids in porous materials (Monson, P. A. J. Chem. Phys. 2008, 128, 084701) to the case of mixtures. The theory can be used to describe the relaxation processes in the approach to equilibrium or metastable equilibrium states for fluids in pores after a change in the bulk pressure or composition. It is especially useful for studying systems where there are capillary condensation or evaporation transitions. Nucleation processes associated with these transitions are emergent features of the theory and can be visualized via the time dependence of the density distribution and composition distribution in the system. For mixtures an important component of the dynamics is relaxation of the composition distribution in the system, especially in the neighborhood of vapor-liquid interfaces. We consider two different types of mixtures, modeling hydrocarbon adsorption in carbon-like slit pores. We first present results on bulk phase equilibria of the mixtures and then the equilibrium (stable/metastable) behavior of these mixtures in a finite slit pore and an inkbottle pore. We then use DMFT to describe the evolution of the density and composition in the pore in the approach to equilibrium after changing the state of the bulk fluid via composition or pressure changes.
Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model
Erban, Radek; Chapman, S. Jonathan; Kevrekidis, Ioannis G.; Vejchodský , Tomá š
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
Existence of optimal controls for systems governed by mean-field ...
African Journals Online (AJOL)
In this paper, we study the existence of an optimal control for systems, governed by stochastic dierential equations of mean-eld type. For non linear systems, we prove the existence of an optimal relaxed control, by using tightness techniques and Skorokhod selection theorem. The optimal control is a measure valued process ...
Bipolar Jets Launched by a Mean-field Accretion Disk Dynamo
Fendt, Christian; Gaßmann, Dennis
2018-03-01
By applying magnetohydrodynamic simulations, we investigate the launching of jets driven by a disk magnetic field generated by a mean-field disk dynamo. Extending our earlier studies, we explore the bipolar evolution of the disk α 2Ω-dynamo and the outflow. We confirm that a negative dynamo-α leads to a dipolar field geometry, whereas positive values generate quadrupolar fields. The latter remain mainly confined to the disk and cannot launch outflows. We investigate a parameter range for the dynamo-α ranging from a critical value below which field generation is negligible, {α }0,{crit}=-0.0005, to α 0 = ‑1.0. For weak | {α }0| ≤slant 0.07, two magnetic loop structures with opposite polarity may arise, which leads to reconnection and disturbs the field evolution and accretion-ejection process. For a strong dynamo-α, a higher poloidal magnetic energy is reached, roughly scaling with {E}mag}∼ | {α }0| , which also leads to higher accretion and ejection rates. The terminal jet speed is governed by the available magnetic energy and increases with the dynamo-α. We find jet velocities on the order of the inner disk Keplerian velocity. For a strong dynamo-α, oscillating dynamo modes may occur that can lead to a pulsed ejection. This is triggered by an oscillating mode in the toroidal field component. The oscillation period is comparable to the Keplerian timescale in the launching region, thus too short to be associated with the knots in observed jets. We find a hemispherically asymmetric evolution for the jet and counter-jet in the mass flux and field structure.
DOUBLE DYNAMO SIGNATURES IN A GLOBAL MHD SIMULATION AND MEAN-FIELD DYNAMOS
Energy Technology Data Exchange (ETDEWEB)
Beaudoin, Patrice; Simard, Corinne; Cossette, Jean-François; Charbonneau, Paul [Département de Physique, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, Québec, H3C 3J7 (Canada)
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 {sup 2}Ω 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.
Single-chain-in-mean-field simulations of weak polyelectrolyte brushes
Léonforte, F.; Welling, U.; Müller, M.
2016-12-01
Structural properties of brushes which are composed of weak acidic and basic polyelectrolytes are studied in the framework of a particle-based approach that implicitly accounts for the solvent quality. Using a semi-grandcanonical partition function in the framework of the Single-Chain-in-Mean-Field (SCMF) algorithm, the weak polyelectrolyte is conceived as a supramolecular mixture of polymers in different dissociation states, which are explicitly treated in the partition function and sampled by the SCMF procedure. One obtains a local expression for the equilibrium acid-base reaction responsible for the regulation of the charged groups that is also incorporated to the SCMF sampling. Coupled to a simultaneous treatment of the electrostatics, the approach is shown to capture the main features of weak polyelectrolyte brushes as a function of the bulk pH in the solution, the salt concentration, and the grafting density. Results are compared to experimental and theoretical works from the literature using coarse-grained representations of poly(acrylic acid) (PAA) and poly(2-vinyl pyridine) (P2VP) polymer-based brushes. As the Born self-energy of ions can be straightforwardly included in the numerical approach, we also study its effect on the local charge regulation mechanism of the brush. We find that its effect becomes significant when the brush is dense and exposed to high salt concentrations. The numerical methodology is then applied (1) to the study of the kinetics of collapse/swelling of a P2VP brush and (2) to the ability of an applied voltage to induce collapse/swelling of a PAA brush in a pH range close to the pKa value of the polymer.
Study of bubble structure in N = 20 isotones within relativistic mean-field plus BCS approach
International Nuclear Information System (INIS)
Kumawat, M.; Singh, U.K.; Jain, S.K.; Saxena, G.; Aggarwal, Mamta; Singh, S. Somorendro; Kaushik, M.
2017-01-01
Guided by various theoretical studies and encouraged with recent first experimental evidence of proton density depletion in "3"4Si, we have applied relativistic mean field plus BCS approach for systematic study of bubble structure in magic nuclei with N = 20 isotones. Our present investigations include single particle energies, deformations, separation energies as well as neutron and proton densities etc. It is found that proton sd shells (1d_5_/_2,2s_1_/_2,1d_3_/_2) in N = 20 isotones play very important role in the formation of bubble structure. The unoccupied 2s_1_/_2 state gives rise to bubble since this 2s_1_/_2 state does not have any centrifugal barrier, therefore for Z = 8 - 14 in the isotonic chain radial distributions of such state is found with peak in the interior of the nucleus with corresponding wave functions extending into the surface region. Consequently, in these nuclei with unoccupied s-state the central density found depleted as compared to the nucleus wherein this state is fully occupied. It is important to note here that in these nuclei depletion in proton density for "3"4Si is found with most significance which is in accord with the recent experiment. Moving further for higher Z value, Z = 16 and Z = 18 the 2s_1_/_2 state remains semi-occupied and contributing partially in the depletion of central density resulting semi-bubble structure for Z = 16 and 18. For Z≥20, 2s_1_/_2 state get fully occupied and no sign of bubble structures are seen for higher isotones
Real-space, mean-field algorithm to numerically calculate long-range interactions
Cadilhe, A.; Costa, B. V.
2016-02-01
Long-range interactions are known to be of difficult treatment in statistical mechanics models. There are some approaches that introduce a cutoff in the interactions or make use of reaction field approaches. However, those treatments suffer the illness of being of limited use, in particular close to phase transitions. The use of open boundary conditions allows the sum of the long-range interactions over the entire system to be done, however, this approach demands a sum over all degrees of freedom in the system, which makes a numerical treatment prohibitive. Techniques like the Ewald summation or fast multipole expansion account for the exact interactions but are still limited to a few thousands of particles. In this paper we introduce a novel mean-field approach to treat long-range interactions. The method is based in the division of the system in cells. In the inner cell, that contains the particle in sight, the 'local' interactions are computed exactly, the 'far' contributions are then computed as the average over the particles inside a given cell with the particle in sight for each of the remaining cells. Using this approach, the large and small cells limits are exact. At a fixed cell size, the method also becomes exact in the limit of large lattices. We have applied the procedure to the two-dimensional anisotropic dipolar Heisenberg model. A detailed comparison between our method, the exact calculation and the cutoff radius approximation were done. Our results show that the cutoff-cell approach outperforms any cutoff radius approach as it maintains the long-range memory present in these interactions, contrary to the cutoff radius approximation. Besides that, we calculated the critical temperature and the critical behavior of the specific heat of the anisotropic Heisenberg model using our method. The results are in excellent agreement with extensive Monte Carlo simulations using Ewald summation.
General model of phospholipid bilayers in fluid phase within the single chain mean field theory
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Guo, Yachong; Baulin, Vladimir A. [Departament d’Enginyeria Química, Universitat Rovira i Virgili, Av. dels Paisos Catalans 26, 43007 Tarragona (Spain); Pogodin, Sergey [Institute of Chemical Research of Catalonia, ICIQ, Av. Paisos Catalans 16, 43007 Tarragona (Spain)
2014-05-07
Coarse-grained model for saturated phospholipids: 1,2-didecanoyl-sn-glycero-3-phosphocholine (DCPC), 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC), 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) and unsaturated phospholipids: 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1,2- dioleoyl-sn-glycero-3-phosphocholine (DOPC) is introduced within the single chain mean field theory. A single set of parameters adjusted for DMPC bilayers gives an adequate description of equilibrium and mechanical properties of a range of saturated lipid molecules that differ only in length of their hydrophobic tails and unsaturated (POPC, DOPC) phospholipids which have double bonds in the tails. A double bond is modeled with a fixed angle of 120°, while the rest of the parameters are kept the same as saturated lipids. The thickness of the bilayer and its hydrophobic core, the compressibility, and the equilibrium area per lipid correspond to experimentally measured values for each lipid, changing linearly with the length of the tail. The model for unsaturated phospholipids also fetches main thermodynamical properties of the bilayers. This model is used for an accurate estimation of the free energies of the compressed or stretched bilayers in stacks or multilayers and gives reasonable estimates for free energies. The proposed model may further be used for studies of mixtures of lipids, small molecule inclusions, interactions of bilayers with embedded proteins.
A two-site mean field model of discontinuous dynamic recrystallization
International Nuclear Information System (INIS)
Bernard, P.; Bag, S.; Huang, K.; Loge, R.E.
2011-01-01
Highlights: → Discontinuous dynamic recrystallization (DDRX) is modelled at the grain scale. → The two-site mean field approach allows introducing topological information. → DDRX kinetics, flow stress curves and recrystallized grain size are well predicted. → Temperature, strain rate and initial grain size effects are successfully described. → Grain size dependence naturally emerges from the model and agrees with experiment. - Abstract: The paper describes a new model of discontinuous dynamic recrystallization (DDRX) which can operate in constant or variable thermomechanical conditions. The model considers the elementary physical phenomena at the grain scale such as strain hardening, recovery, grain boundary migration, and nucleation. The microstructure is represented through a set of representative grains defined by their size and dislocation density. It is linked to a constitutive law giving access to the polycrystal flow stress. Interaction between representative grains and the surrounding material is idealized using a two-site approach whereby two homogeneous equivalent media with different dislocation densities are considered. Topological information is incorporated into the model by prescribing the relative weight of these two equivalent media as a function of their volume fractions. This procedure allows accounting for the well-known necklace structures. The model is applied to the prediction of DDRX in 304 L stainless steel, with parameters identified using an inverse methodology based on a genetic algorithm. Results show good agreement with experimental data at different temperatures and strain rates, predicting recrystallization kinetics, recrystallized grain size and stress-strain curve. Parameters identified with one initial grain size lead to accurate results for another initial grain size without introducing any additional parameter.
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
Relationship between Feshbach's and Green's function theories of the nucleon-nucleus mean field
International Nuclear Information System (INIS)
Capuzzi, F.; Mahaux, C.
1995-01-01
We clarify the relationship and difference between theories of the optical-model potential which had previously been developed in the framework of Feshbach's projection operator approach to nuclear reactions and of Green's function theory, respectively. For definiteness, we consider the nucleon-nucleus system but all results can readily be adapted to the atomic case. The effects of antisymmetrization are properly taken into account. It is shown that one can develop along closely parallel lines the theories of open-quotes holeclose quotes and open-quotes particleclose quotes mean fields. The open-quotes holeclose quotes one-body Hamiltonians describe the single-particle properties of the system formed when one nucleon is taken away from the target ground state, for instance in knockout of pickup processes. The particle one-body Hamiltonians are associated with the system formed when one nucleon is elastically scattered from the ground state, or is added to it by means of stripping reactions. An infinite number of particle, as well as of hole, Hamiltonians are constructed which all yield exactly the same single-particle wave functions. Many open-quotes equivalentclose quotes one-body Hamiltonians can coexist because these operators have a complicated structure: they are nonlocal, complex, and energy-dependent. They do not have the same analytic properties in the complex energy plane. Their real and imaginary parts fulfill dispersion relations which may be different. It is shown that hole and particle Hamiltonians can also be constructed by decomposing any vector of the Hilbert space into two parts which are not orthogonal to one another, in contrast to Feshbach's original theory; one interest of this procedure is that the construction and properties of the corresponding hole Hamiltonian can be justified in a mathematically rigorous way. We exhibit the relationship between the hole and particle Hamiltonians and the open-quotes mass operator.close quotes
The symmetry energy {\\boldsymbol{\\gamma }} parameter of relativistic mean-field models
Dutra, Mariana; Lourenço, Odilon; Hen, Or; Piasetzky, Eliezer; Menezes, Débora P.
2018-05-01
The relativistic mean-field models tested in previous works against nuclear matter experimental values, critical parameters and macroscopic stellar properties are revisited and used in the evaluation of the symmetry energy γ parameter obtained in three different ways. We have checked that, independent of the choice made to calculate the γ values, a trend of linear correlation is observed between γ and the symmetry energy ({{\\mathscr{S}}}0) and a more clear linear relationship is established between γ and the slope of the symmetry energy (L 0). These results directly contribute to the arising of other linear correlations between γ and the neutron star radii of {R}1.0 and {R}1.4, in agreement with recent findings. Finally, we have found that short-range correlations induce two specific parametrizations, namely, IU-FSU and DD-MEδ, simultaneously compatible with the neutron star mass constraint of 1.93≤slant {M}{{\\max }}/{M}ȯ ≤slant 2.05 and with the overlap band for the {L}0× {{\\mathscr{S}}}0 region, to present γ in the range of γ =0.25+/- 0.05. This work is a part of the project INCT-FNA Proc. No. 464898/2014-5 and was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil under grants 300602/2009-0 and 306786/2014-1. E. P. acknowledges support from the Israel Science Foundation. O. H. acknowledges the U.S. Department of Energy Office of Science, Office of Nuclear Physics program under award number DE-FG02-94ER40818
Nonlinear cloudy bag model in the meson mean-field approximation
International Nuclear Information System (INIS)
Bunatyan, G.G.
1989-01-01
We investigate the cloudy bag model for the nucleon, including the essentially nonlinear interaction of the quarks with the meson field. From the boundary conditions, which guarantee the stability of the bag, we obtain equations for the size R of the bag, for the momentum p of the quarks, and for the mean pion field var-phi. We obtain an expression for the total energy E of the bag nucleon. By taking the appropriate averages of all the relations the calculations reduce to the case of a spherically symmetric bag. We show that in the general nonlinear cloudy bag model in question the equations for R, p, and var-phi have a simultaneous solution which corresponds to the absolute minimum of the bag energy E and, consequently, that there exists a stable equilibrium state of the bag nucleon
Microbunching instability in a chicane: Two-dimensional mean field treatment
Directory of Open Access Journals (Sweden)
Gabriele Bassi
2009-08-01
Full Text Available We study the microbunching instability in a bunch compressor by a parallel code with some improved numerical algorithms. The two-dimensional charge/current distribution is represented by a Fourier series, with coefficients determined through Monte Carlo sampling over an ensemble of tracked points. This gives a globally smooth distribution with low noise. The field equations are solved accurately in the lab frame using retarded potentials and a novel choice of integration variables that eliminates singularities. We apply the scheme with parameters for the first bunch compressor system of FERMI@Elettra, with emphasis on the amplification of a perturbation at a particular wavelength and the associated longitudinal bunch spectrum. Gain curves are in rough agreement with those of the linearized Vlasov system at intermediate wavelengths, but show some deviation at the smallest wavelengths treated and show the breakdown of a coasting beam assumption at long wavelengths. The linearized Vlasov system is discussed in some detail. A new 2D integral equation is derived which reduces to a well-known 1D integral equation in the coasting beam case.
A Study of Multi-Λ Hypernuclei Within Spherical Relativistic Mean-Field Approach
Rather, Asloob A.; Ikram, M.; Usmani, A. A.; Kumar, B.; Patra, S. K.
2017-12-01
This research article is a follow up of an earlier work by M. Ikram et al., reported in Int. J. Mod. Phys. E 25, 1650103 (2016) where we searched for Λ magic numbers in experimentally confirmed doubly magic nucleonic cores in light to heavy mass region (i.e., 16 O-208 P b) by injecting Λ's into them. In the present manuscript, working within the state of the art relativistic mean field theory with the inclusion of Λ N and ΛΛ interaction in addition to nucleon-meson NL 3∗ effective force, we extend the search of lambda magic numbers in multi- Λ hypernuclei using the predicted doubly magic nucleonic cores 292120, 304120, 360132, 370132, 336138, 396138 of the elusive superheavy mass regime. In analogy to well established signatures of magicity in conventional nuclear theory, the prediction of hypernuclear magicities is made on the basis of one-, two- Λ separation energy ( S Λ, S 2Λ) and two lambda shell gaps ( δ 2Λ) in multi- Λ hypernuclei. The calculations suggest that the Λ numbers 92, 106, 126, 138, 184, 198, 240, and 258 might be the Λ shell closures after introducing the Λ's in the elusive superheavy nucleonic cores. The appearance of new lambda shell closures apart from the nucleonic ones predicted by various relativistic and non-relativistic theoretical investigations can be attributed to the relatively weak strength of the spin-orbit coupling in hypernuclei compared to normal nuclei. Further, the predictions made in multi- Λ hypernuclei under study resembles closely the magic numbers in conventional nuclear theory suggested by various relativistic and non-relativistic theoretical models. Moreover, in support of the Λ shell closure, the investigation of Λ pairing energy and effective Λ pairing gap has been made. We noticed a very close agreement of the predicted Λ shell closures with the survey made on the pretext of S Λ, S 2Λ, and δ 2Λ except for the appearance of magic numbers corresponding to Λ = 156 which manifest in Λ effective
Cattes, Stefanie M.; Gubbins, Keith E.; Schoen, Martin
2016-05-01
In this work, we employ classical density functional theory (DFT) to investigate for the first time equilibrium properties of a Heisenberg fluid confined to nanoscopic slit pores of variable width. Within DFT pair correlations are treated at modified mean-field level. We consider three types of walls: hard ones, where the fluid-wall potential becomes infinite upon molecular contact but vanishes otherwise, and hard walls with superimposed short-range attraction with and without explicit orientation dependence. To model the distance dependence of the attractions, we employ a Yukawa potential. The orientation dependence is realized through anchoring of molecules at the substrates, i.e., an energetic discrimination of specific molecular orientations. If the walls are hard or attractive without specific anchoring, the results are "quasi-bulk"-like in that they can be linked to a confinement-induced reduction of the bulk mean field. In these cases, the precise nature of the walls is completely irrelevant at coexistence. Only for specific anchoring nontrivial features arise, because then the fluid-wall interaction potential affects the orientation distribution function in a nontrivial way and thus appears explicitly in the Euler-Lagrange equations to be solved for minima of the grand potential of coexisting phases.
Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy
2016-08-25
dissipative relaxation within a domain of attraction of a local minima due to the hardware noise introduces a lifetime or level widthW. This fast local...equation gives the location of the turning points qð1ÞTP ðk; EÞ and qð2ÞTP ðk; EÞ, which limit the classically allowed region. Inverting the secular...condition Eq. (17) [requiring the period of motion in the inverted potential TðEÞ to match the inverse temperature β [39
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.
International Nuclear Information System (INIS)
Rodrigues, Serafim; Terry, John R.; Breakspear, Michael
2006-01-01
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)
Liu, Shuanglong; Feng, Yuan Ping; Zhang, Chun
2013-01-01
We show that when a molecular junction is under an external bias, its properties cannot be uniquely determined by the total electron density in the same manner as the density functional theory for ground state properties. In order to correctly incorporate bias-induced nonequilibrium effects, we present a dual mean field (DMF) approach. The key idea is that the total electron density together with the density of current-carrying electrons are sufficient to determine the properties of the system. Two mean fields, one for current-carrying electrons and the other one for equilibrium electrons can then be derived. Calculations for a graphene nanoribbon junction show that compared with the commonly used ab initio transport theory, the DMF approach could significantly reduce the electric current at low biases due to the non-equilibrium corrections to the mean field potential in the scattering region
Grabska-Barwińska, Agnieszka; Latham, Peter E
2014-06-01
We use mean field techniques to compute the distribution of excitatory and inhibitory firing rates in large networks of randomly connected spiking quadratic integrate and fire neurons. These techniques are based on the assumption that activity is asynchronous and Poisson. For most parameter settings these assumptions are strongly violated; nevertheless, so long as the networks are not too synchronous, we find good agreement between mean field prediction and network simulations. Thus, much of the intuition developed for randomly connected networks in the asynchronous regime applies to mildly synchronous networks.
Mean-field kinetic theory approach to evaporation of a binary liquid into vacuum
Frezzotti, A.; Gibelli, L.; Lockerby, D. A.; Sprittles, J. E.
2018-05-01
Evaporation of a binary liquid into near-vacuum conditions has been studied using numerical solutions of a system of two coupled Enskog-Vlasov equations. Liquid-vapor coexistence curves have been mapped out for different liquid compositions. The evaporation process has been investigated at a range of liquid temperatures sufficiently lower than the critical one for the vapor not to significantly deviate from the ideal behavior. It is found that the shape of the distribution functions of evaporating atoms is well approximated by an anisotropic Maxwellian distribution with different characteristic temperatures for velocity components normal and parallel to the liquid-vapor interface. The anisotropy reduces as the evaporation temperature decreases. Evaporation coefficients are computed based on the separation temperature and the maximum concentration of the less volatile component close to the liquid-vapor interface. This choice leads to values which are almost constant in the simulation conditions.