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Sample records for relativistic mean-field models

  1. Parametrization of light clusters within relativistic mean field models

    SciTech Connect

    Ferreira, Marcio; Providencia, Constanca

    2013-06-10

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

  2. Relativistic mean-field models and nuclear matter constraints

    SciTech Connect

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

    2013-05-06

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

  3. Relativistic mean field model based on realistic nuclear forces

    SciTech Connect

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

    2007-02-15

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-11-01

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

  6. Relativistic mean field model for entrainment in general relativistic superfluid neutron stars

    NASA Astrophysics Data System (ADS)

    Comer, G. L.; Joynt, R.

    2003-07-01

    General relativistic superfluid neutron stars have a significantly more intricate dynamics than their ordinary fluid counterparts. Superfluidity allows different superfluid (and superconducting) species of particles to have independent fluid flows, a consequence of which is that the fluid equations of motion contain as many fluid element velocities as superfluid species. Whenever the particles of one superfluid interact with those of another, the momentum of each superfluid will be a linear combination of both superfluid velocities. This leads to the so-called entrainment effect whereby the motion of one superfluid will induce a momentum in the other superfluid. We have constructed a fully relativistic model for entrainment between superfluid neutrons and superconducting protons using a relativistic σ-ω mean field model for the nucleons and their interactions. In this context there are two notions of “relativistic”: relativistic motion of the individual nucleons with respect to a local region of the star (i.e. a fluid element containing, say, an Avogadro’s number of particles), and the motion of fluid elements with respect to the rest of the star. While it is the case that the fluid elements will typically maintain average speeds at a fraction of that of light, the supranuclear densities in the core of a neutron star can make the nucleons themselves have quite high average speeds within each fluid element. The formalism is applied to the problem of slowly rotating superfluid neutron star configurations, a distinguishing characteristic being that the neutrons can rotate at a rate different from that of the protons.

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

    SciTech Connect

    Jiang Weizhou; Li Baoan; Chen Liewen

    2007-11-15

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

  8. Comparative study of nuclear masses in the relativistic mean-field model

    NASA Astrophysics Data System (ADS)

    Hua, XueMin; Heng, TaiHua; Niu, ZhongMing; Sun, BaoHua; Guo, JianYou

    2012-12-01

    With experimental masses updated from AME11, the predictive power of relativistic mean-field (RMF) mass model is carefully examined and compared with HFB-17, FRDM, WS*, and DZ28 mass models. In the relativistic mean-field model, the calculation with the PC-PK1 has improved significantly in describing masses compared to the TMA, especially for the neutron-deficient nuclei. The corresponding rms deviation with respect to the known masses falls to 1.4 MeV. Furthermore, it is found that the RMF mass model better describes the nuclei with large deformations. The rms deviation for nuclei with the absolute value of quadrupole deformation parameter greater than 0.25 falls to 0.93, crossing the 1 MeV accuracy threshold for the PC-PK1, which may indicate the new model is more suitable for those largely-deformed nuclei. In addition, the necessity of new high-precision experimental data to evaluate and develop the nuclear mass models is emphasized as well.

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

    SciTech Connect

    Antic, S.; Typel, S.

    2015-02-24

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

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

    SciTech Connect

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

    2009-12-15

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

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

    SciTech Connect

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

    2010-07-15

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

  12. Relativistic mean-field theory

    NASA Astrophysics Data System (ADS)

    Meng, Jie; Ring, Peter; Zhao, Pengwei

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

  13. Relativistic Mean Field description of exotic nuclei

    NASA Astrophysics Data System (ADS)

    Gambhir, Y. K.

    1994-03-01

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

  14. Vlasov formalism for extended relativistic mean field models: The crust-core transition and the stellar matter equation of state

    NASA Astrophysics Data System (ADS)

    Pais, Helena; Providência, Constança

    2016-07-01

    The Vlasov formalism is extended to relativistic mean field hadron models with nonlinear terms up to fourth order and applied to the calculation of the crust-core transition density. The effect of the nonlinear ω ρ and σ ρ coupling terms on the crust-core transition density and pressure and on the macroscopic properties of some families of hadronic stars is investigated. For that purpose, six families of relativistic mean field models are considered. Within each family, the members differ in the symmetry energy behavior. For all the models, the dynamical spinodals are calculated, and the crust-core transition density and pressure and the neutron star mass-radius relations are obtained. The effect on the star radius of the inclusion of a pasta calculation in the inner crust is discussed. The set of six models that best satisfy terrestrial and observational constraints predicts a radius of 13.6 ±0.3 km and a crust thickness of 1.36 ±0.06 km for a 1.4 M⊙ star.

  15. Relativistic mean-field models with scaled hadron masses and couplings: Hyperons and maximum neutron star mass

    NASA Astrophysics Data System (ADS)

    Maslov, K. A.; Kolomeitsev, E. E.; Voskresensky, D. N.

    2016-06-01

    An equation of state of cold nuclear matter with an arbitrary isotopic composition is studied within a relativistic mean-field approach with hadron masses and coupling constants depending self-consistently on the scalar mean-field. All hadron masses decrease universally with the scalar field growth, whereas meson-nucleon coupling constants can vary differently. More specifically we focus on two modifications of the KVOR model studied previously. One extension of the model (KVORcut) demonstrates that the equation of state stiffens if the increase of the scalar-field magnitude with the density is bounded from above at some value for baryon densities above the saturation nuclear density. This can be realized if the nucleon vector-meson coupling constant changes rapidly as a function of the scalar field slightly above the desired value. The other version of the model (MKVOR) utilizes a smaller value of the nucleon effective mass at the nuclear saturation density and a saturation of the scalar field in the isospin asymmetric matter induced by a strong variation of the nucleon isovector-meson coupling constant as function of the scalar field. A possibility of hyperonization of the matter in neutron star interiors is incorporated. Our equations of state fulfill majority of known empirical constraints including the pressure-density constraint from heavy-ion collisions, direct Urca constraint, gravitational-baryon mass constraint for the pulsar J0737-3039B, and the constraint on the maximum mass of the neutron stars.

  16. Stochastic kinetic mean field model

    NASA Astrophysics Data System (ADS)

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

    2016-07-01

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

  17. The Brownian mean field model

    NASA Astrophysics Data System (ADS)

    Chavanis, Pierre-Henri

    2014-05-01

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

  18. Relativistic mean field calculations in neutron-rich nuclei

    SciTech Connect

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

    2014-08-14

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

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

    SciTech Connect

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

    2008-03-15

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-08-01

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

  1. Effects of δ mesons in relativistic mean field theory

    NASA Astrophysics Data System (ADS)

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

    2014-04-01

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

  2. Hot and dense matter beyond relativistic mean field theory

    NASA Astrophysics Data System (ADS)

    Zhang, Xilin; Prakash, Madappa

    2016-05-01

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

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

    NASA Astrophysics Data System (ADS)

    Gaitanos, T.; Kaskulov, M.

    2015-08-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  5. Systematic study of Bh isotopes in a relativistic mean field formalism

    NASA Astrophysics Data System (ADS)

    Mehta, M. S.; Raj, B. K.; Patra, S. K.; Gupta, Raj K.

    2002-10-01

    The binding energy, charge radius, and quadrupole deformation parameter for the isotopic chain of the superheavy element bohrium (107Bh), from proton to neutron drip line, are calculated by using an axially deformed relativistic mean field model. The potential energy surfaces for some of the selected nuclei are plotted and the various possible shapes are investigated. The rms radii, density distributions, and two-neutron separation energies are also evaluated and the single-particle energies for some illustrative cases are analyzed to see the magic structures. Furthermore, the α-decay rates are calculated and compared with the available experimental data for the recently observed new isotopes 266,267Bh.

  6. Invisible dynamo in mean-field models

    NASA Astrophysics Data System (ADS)

    Reshetnyak, M. Yu.

    2016-07-01

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

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

    SciTech Connect

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

    2010-05-21

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

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

    PubMed

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

    2014-03-01

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

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

    SciTech Connect

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

    2011-03-15

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-08-01

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

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

    NASA Astrophysics Data System (ADS)

    Karim, Afaque; Ahmad, Shakeb

    2015-12-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2010-12-01

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

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

    SciTech Connect

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

    2010-12-15

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

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

    SciTech Connect

    Uechi, Schun T.; Uechi, Hiroshi

    2011-10-21

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

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

    SciTech Connect

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

    2014-05-02

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

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

    NASA Astrophysics Data System (ADS)

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

    2004-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-01-01

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

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

    SciTech Connect

    Wu Chen; Ren Zhongzhou

    2011-02-15

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-11-01

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

  20. MEAN FIELD AND MONTE CARLO MODELING OF MULTIBLOCK COPOLYMERS

    SciTech Connect

    K. RASMUSSEN; ET AL

    2001-01-01

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

  1. Incorporating spatial correlations into multispecies mean-field models

    NASA Astrophysics Data System (ADS)

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

    2013-11-01

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

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

    SciTech Connect

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

    2005-02-24

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

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

    PubMed

    Nagy, Viktor

    2009-06-01

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

  4. Mean-field theory of a recurrent epidemiological model

    NASA Astrophysics Data System (ADS)

    Nagy, Viktor

    2009-06-01

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

  5. Disorder Chaos in the Spherical Mean-Field Model

    NASA Astrophysics Data System (ADS)

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

    2015-07-01

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

  6. Mean-field approach in the multi-component gas of interacting particles applied to relativistic heavy-ion collisions

    NASA Astrophysics Data System (ADS)

    Anchishkin, D.; Vovchenko, V.

    2015-10-01

    A generalized mean-field approach for the thermodynamic description of relativistic single- and multi-component gas in the grand canonical ensemble is formulated. In the framework of the proposed approach, different phenomenological excluded-volume procedures are presented and compared to the existing ones. The mean-field approach is then used to effectively include hard-core repulsion in hadron-resonance gas model for description of chemical freeze-out in heavy-ion collisions. We calculate the collision energy dependence of several quantities for different values of hard-core hadron radius and for different excluded-volume procedures such as the van der Waals and Carnahan-Starling models. It is shown that a choice of the excluded-volume model becomes important for large particle densities. For large enough values of hadron radii (r≳ 0.9 fm) there can be a sizable difference between different excluded-volume procedures used to describe the chemical freeze-out in heavy-ion collisions. At the same time, for the smaller and more commonly used values of hard-core hadron radii (r≲ 0.5 fm), the precision of the van der Waals excluded-volume procedure is shown to be sufficient.

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

    NASA Astrophysics Data System (ADS)

    Ieda, Masashi; Shiino, Masatoshi

    2011-12-01

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

  8. A mechanical approach to mean field spin models

    NASA Astrophysics Data System (ADS)

    Genovese, Giuseppe; Barra, Adriano

    2009-05-01

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

  9. Second relativistic mean field and virial equation of state for astrophysical simulations

    SciTech Connect

    Shen, G.; Horowitz, C. J.; O'Connor, E.

    2011-06-15

    We generate a second equation of state (EOS) of nuclear matter for a wide range of temperatures, densities, and proton fractions for use in supernovae, neutron star mergers, and black hole formation simulations. We employ full relativistic mean field (RMF) calculations for matter at intermediate density and high density, and the virial expansion of a nonideal gas for matter at low density. For this EOS we use the RMF effective interaction FSUGold, whereas our earlier EOS was based on the RMF effective interaction NL3. The FSUGold interaction has a lower pressure at high densities compared to the NL3 interaction. We calculate the resulting EOS at over 100 000 grid points in the temperature range T=0 to 80 MeV, the density range n{sub B}=10{sup -8} to 1.6 fm{sup -3}, and the proton fraction range Y{sub p}=0 to 0.56. We then interpolate these data points using a suitable scheme to generate a thermodynamically consistent equation of state table on a finer grid. We discuss differences between this EOS, our NL3-based EOS, and previous EOSs by Lattimer-Swesty and H. Shen et al. for the thermodynamic properties, composition, and neutron star structure. The original FSUGold interaction produces an EOS, which we call FSU1.7, that has a maximum neutron star mass of 1.7 solar masses. A modification in the high-density EOS is introduced to increase the maximum neutron star mass to 2.1 solar masses and results in a slightly different EOS that we call FSU2.1. The EOS tables for FSU1.7 and FSU2.1 are available for download.

  10. Mean field linear response within the elimination of the small component formalism to evaluate relativistic effects on magnetic properties

    NASA Astrophysics Data System (ADS)

    Roura, P. G.; Melo, J. I.; Ruiz de Azúa, M. C.; Giribet, C. G.

    2006-08-01

    The linear response within the elimination of the small component formalism is aimed at obtaining the leading order relativistic corrections to magnetic molecular properties in the context of the elimination of the small component approximation. In the present work we extend the method in order to include two-body effects in the form of a mean field one-body operator. To this end we consider the four-component Dirac-Hartree-Fock operator as the starting point in the evaluation of the second order relativistic expression of magnetic properties. The approach thus obtained is the fully consistent leading order approximation of the random phase approximation four-component formalism. The mean field effect on the relativistic corrections to both the diamagnetic and paramagnetic terms of magnetic properties taking into account both the Coulomb and Breit two-body interactions is considered.

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

    SciTech Connect

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

    2010-06-15

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

  12. Simulated Tempering and Swapping on Mean-Field Models

    NASA Astrophysics Data System (ADS)

    Bhatnagar, Nayantara; Randall, Dana

    2016-08-01

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

  13. Mean field bipartite spin models treated with mechanical techniques

    NASA Astrophysics Data System (ADS)

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

    2014-03-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-11-01

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

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

    NASA Astrophysics Data System (ADS)

    Alba, Vincenzo; Inglis, Stephen; Pollet, Lode

    2016-03-01

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

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

    SciTech Connect

    Afanasjev, A. V.; Abusara, H.

    2008-07-15

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

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

    PubMed Central

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

    2013-01-01

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

  18. Multidimensionally-constrained relativistic mean-field study of spontaneous fission: Coupling between shape and pairing degrees of freedom

    NASA Astrophysics Data System (ADS)

    Zhao, Jie; Lu, Bing-Nan; Nikšić, Tamara; Vretenar, Dario; Zhou, Shan-Gui

    2016-04-01

    Background: Studies of fission dynamics, based on nuclear energy density functionals, have shown that the coupling between shape and pairing degrees of freedom has a pronounced effect on the nonperturbative collective inertia and, therefore, on dynamic (least-action) spontaneous fission paths and half-lives. Purpose: The aim is to analyze the effects of particle-number fluctuation degrees of freedom on symmetric and asymmetric spontaneous fission (SF) dynamics, and to compare the findings with the results of recent studies based on the self-consistent Hartree-Fock-Bogoliubov (HFB) method. Methods: Collective potentials and nonperturbative cranking collective inertia tensors are calculated using the multidimensionally-constrained relativistic-mean-field (MDC-RMF) model. Pairing correlations are treated in the BCS approximation using a separable pairing force of finite range. Pairing fluctuations are included as a collective variable using a constraint on particle-number dispersion. Fission paths are determined with the dynamic programming method by minimizing the action in multidimensional collective spaces. Results: The dynamics of spontaneous fission of 264Fm and 250Fm are explored. Fission paths, action integrals, and corresponding half-lives computed in the three-dimensional collective space of shape and pairing coordinates, using the relativistic functional DD-PC1 and a separable pairing force of finite range, are compared with results obtained without pairing fluctuations. Results for 264Fm are also discussed in relation with those recently obtained using the HFB model. Conclusions: The inclusion of pairing correlations in the space of collective coordinates favors axially symmetric shapes along the dynamic path of the fissioning system, amplifies pairing as the path traverses the fission barriers, significantly reduces the action integral, and shortens the

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

    PubMed

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

    2011-12-21

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-09-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2008-11-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2011-05-01

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

  3. Relativistic Energy Density Functionals: beyond mean-field description of exotic structures

    SciTech Connect

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

    2009-01-28

    The framework of relativistic energy density functionals 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. This approach enables a quantitative description of the evolution of shell-structure, deformation and shape coexistence phenomena in nuclei with soft potential energy surfaces, and singular properties of excitation spectra and transition rates at critical points of quantum shape phase transitions.

  4. Relativistic mean-field study of the properties of Z=117 nuclei and the decay chains of the {sup 293,294}117 isotopes

    SciTech Connect

    Bhuyan, M.; Patra, S. K.; Gupta, Raj K.

    2011-07-15

    We have calculated the binding energy, root-mean-square radius, and quadrupole deformation parameter for the recently synthesized superheavy element Z=117, using the axially deformed relativistic mean-field (RMF) model. The calculation is extended to various isotopes of the Z=117 element, starting from A=286 till A=310. We predict almost spherical structures in the ground state for almost all the isotopes. A shape transition appears at about A=292 from a prolate to an oblate shape structure of the Z=117 nucleus in our mean-field approach. The most stable isotope (largest binding energy per nucleon) is found to be the {sup 288}117 nucleus. Also, the Q{sub {alpha}} values and the half-life T{sub 1/2}{sup {alpha}} for the {alpha}-decay chains of {sup 293}117 and {sup 294}117 are calculated, supporting the magic numbers at N=172 and/or 184.

  5. Neural Population Dynamics Modeled by Mean-Field Graphs

    NASA Astrophysics Data System (ADS)

    Kozma, Robert; Puljic, Marko

    2011-09-01

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

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

    NASA Astrophysics Data System (ADS)

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

    1997-09-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-08-01

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

  8. Origin of the neutron skin thickness of {sup 208}Pb in nuclear mean-field models

    SciTech Connect

    Centelles, M.; Roca-Maza, X.; Vinas, X.; Warda, M.

    2010-11-15

    We study whether the neutron skin thickness {Delta}r{sub np} of {sup 208}Pb originates from the bulk or from the surface of the nucleon density distributions, according to the mean-field models of nuclear structure, and find that it depends on the stiffness of the nuclear symmetry energy. The bulk contribution to {Delta}r{sub np} arises from an extended sharp radius of neutrons, whereas the surface contribution arises from different widths of the neutron and proton surfaces. Nuclear models where the symmetry energy is stiff, as typical of relativistic models, predict a bulk contribution in {Delta}r{sub np} of {sup 208}Pb about twice as large as the surface contribution. In contrast, models with a soft symmetry energy like common nonrelativistic models predict that {Delta}r{sub np} of {sup 208}Pb is divided similarly into bulk and surface parts. Indeed, if the symmetry energy is supersoft, the surface contribution becomes dominant. We note that the linear correlation of {Delta}r{sub np} of {sup 208}Pb with the density derivative of the nuclear symmetry energy arises from the bulk part of {Delta}r{sub np}. We also note that most models predict a mixed-type (between halo and skin) neutron distribution for {sup 208}Pb. Although the halo-type limit is actually found in the models with a supersoft symmetry energy, the skin-type limit is not supported by any mean-field model. Finally, we compute parity-violating electron scattering in the conditions of the {sup 208}Pb parity radius experiment (PREX) and obtain a pocket formula for the parity-violating asymmetry in terms of the parameters that characterize the shape of the {sup 208}Pb nucleon densities.

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

    SciTech Connect

    Uechi, Schun T.; Uechi, Hiroshi

    2011-05-06

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

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

    NASA Astrophysics Data System (ADS)

    Simpson, Matthew J.; Baker, Ruth E.

    2011-05-01

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

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

    NASA Astrophysics Data System (ADS)

    Go, Ara; Millis, Andrew J.

    2013-03-01

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

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

    SciTech Connect

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

    2005-05-01

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

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

    NASA Astrophysics Data System (ADS)

    Gaeta, Giuseppe

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

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

    PubMed Central

    Nicola, Wilten; Campbell, Sue Ann

    2013-01-01

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

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

    SciTech Connect

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

    2013-05-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2002-11-01

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

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

    NASA Astrophysics Data System (ADS)

    Simard, Corinne; Charbonneau, Paul; Bouchat, Amélie

    2013-05-01

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

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

    NASA Astrophysics Data System (ADS)

    Chamberlin, Ralph V.

    2000-11-01

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

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

    PubMed

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

    2016-04-01

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

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

    SciTech Connect

    Kahana, S.; Ripka, G.

    1983-01-01

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

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

    SciTech Connect

    Liang Haozhao; Zhao Pengwei; Li Lulu; Meng Jie

    2011-01-15

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

  2. Modeling of coherent ultrafast magneto-optical experiments: Light-induced molecular mean-field model

    SciTech Connect

    Hinschberger, Y.; Hervieux, P.-A.

    2015-12-28

    We present calculations which aim to describe coherent ultrafast magneto-optical effects observed in time-resolved pump-probe experiments. Our approach is based on a nonlinear semi-classical Drude-Voigt model and is used to interpret experiments performed on nickel ferromagnetic thin film. Within this framework, a phenomenological light-induced coherent molecular mean-field depending on the polarizations of the pump and probe pulses is proposed whose microscopic origin is related to a spin-orbit coupling involving the electron spins of the material sample and the electric field of the laser pulses. Theoretical predictions are compared to available experimental data. The model successfully reproduces the observed experimental trends and gives meaningful insight into the understanding of magneto-optical rotation behavior in the ultrafast regime. Theoretical predictions for further experimental studies are also proposed.

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

    PubMed

    Jagla, E A

    2015-10-01

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

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

    NASA Astrophysics Data System (ADS)

    Konishi, Eiji

    2016-04-01

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

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

    NASA Astrophysics Data System (ADS)

    Collet, Francesca; Ruszel, Wioletta

    2016-08-01

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

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

    NASA Astrophysics Data System (ADS)

    Mao, Shijun

    2016-07-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-03-01

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

  8. Dynamical Aspects of Mean Field Plane Rotators and the Kuramoto Model

    NASA Astrophysics Data System (ADS)

    Bertini, Lorenzo; Giacomin, Giambattista; Pakdaman, Khashayar

    2010-02-01

    The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc. We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N oscillators, each driven by an independent Brownian motion with a constant drift, that is each oscillator has its own frequency, which, in general, changes from one oscillator to another (these frequencies are usually taken to be random and they may be viewed as a quenched disorder). The interactions between oscillators are of long range type (mean field). We review some results on the Kuramoto model from a statistical mechanics standpoint: we give in particular necessary and sufficient conditions for reversibility and we point out a formal analogy, in the N→∞ limit, with local mean field models with conservative dynamics (an analogy that is exploited to identify in particular a Lyapunov functional in the reversible set-up). We then focus on the reversible Kuramoto model with sinusoidal interactions in the N→∞ limit and analyze the stability of the non-trivial stationary profiles arising when the interaction parameter K is larger than its critical value K c . We provide an analysis of the linear operator describing the time evolution in a neighborhood of the synchronized profile: we exhibit a Hilbert space in which this operator has a self-adjoint extension and we establish, as our main result, a spectral gap inequality for every K> K c .

  9. Mean-field approximation for a limit order driven market model.

    PubMed

    Slanina, F

    2001-11-01

    A mean-field variant of the model of limit order driven market introduced recently by Maslov is formulated and solved. The agents do not have any strategies and the memory of the system is kept within the order book. We show that the evolution of the order book is governed by a matrix multiplicative process. The resulting stationary distribution of step-to-step price changes is calculated. It exhibits a power-law tail with exponent 2. We obtain also the price autocorrelation function, which agrees qualitatively with the experimentally observed negative autocorrelation for short times. PMID:11736043

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

    NASA Astrophysics Data System (ADS)

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

    2012-06-01

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

  11. Mean-field thalamocortical modeling of longitudinal EEG acquired during intensive meditation training.

    PubMed

    Saggar, Manish; Zanesco, Anthony P; King, Brandon G; Bridwell, David A; MacLean, Katherine A; Aichele, Stephen R; Jacobs, Tonya L; Wallace, B Alan; Saron, Clifford D; Miikkulainen, Risto

    2015-07-01

    Meditation training has been shown to enhance attention and improve emotion regulation. However, the brain processes associated with such training are poorly understood and a computational modeling framework is lacking. Modeling approaches that can realistically simulate neurophysiological data while conforming to basic anatomical and physiological constraints can provide a unique opportunity to generate concrete and testable hypotheses about the mechanisms supporting complex cognitive tasks such as meditation. Here we applied the mean-field computational modeling approach using the scalp-recorded electroencephalogram (EEG) collected at three assessment points from meditating participants during two separate 3-month-long shamatha meditation retreats. We modeled cortical, corticothalamic, and intrathalamic interactions to generate a simulation of EEG signals recorded across the scalp. We also present two novel extensions to the mean-field approach that allow for: (a) non-parametric analysis of changes in model parameter values across all channels and assessments; and (b) examination of variation in modeled thalamic reticular nucleus (TRN) connectivity over the retreat period. After successfully fitting whole-brain EEG data across three assessment points within each retreat, two model parameters were found to replicably change across both meditation retreats. First, after training, we observed an increased temporal delay between modeled cortical and thalamic cells. This increase provides a putative neural mechanism for a previously observed reduction in individual alpha frequency in these same participants. Second, we found decreased inhibitory connection strength between the TRN and secondary relay nuclei (SRN) of the modeled thalamus after training. This reduction in inhibitory strength was found to be associated with increased dynamical stability of the model. Altogether, this paper presents the first computational approach, taking core aspects of physiology and

  12. Economic dynamics with financial fragility and mean-field interaction: A model

    NASA Astrophysics Data System (ADS)

    Di Guilmi, C.; Gallegati, M.; Landini, S.

    2008-06-01

    Following Aoki’s statistical mechanics methodology [Masanao Aoki, New Approaches to Macroeconomic Modeling, Cambridge University Press, 1996; Masanao Aoki, Modeling Aggregate Behaviour and Fluctuations in Economics, Cambridge University Press, 2002; Masanao Aoki, and Hiroshi Yoshikawa, Reconstructing Macroeconomics, Cambridge University Press, 2006], we provide some insights into the well-known works of [Bruce Greenwald, Joseph Stiglitz, Macroeconomic models with equity and credit rationing, in: R. Hubbard (Ed.), Information, Capital Markets and Investment, Chicago University Press, Chicago, 1990; Bruce Greenwald, Joseph Stiglitz, Financial markets imperfections and business cycles, Quarterly journal of Economics (1993)]. Specifically, we reach analytically a closed form solution of their models overcoming the aggregation problem. The key idea is to represent the economy as an evolving complex system, composed by heterogeneous interacting agents, that can be partitioned into a space of macroscopic states. This meso level of aggregation permits to adopt mean-field interaction modeling and master equation techniques.

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

    NASA Astrophysics Data System (ADS)

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

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

  14. Octupole degree of freedom for the critical-point candidate nucleus {sup 152}Sm in a reflection-asymmetric relativistic mean-field approach

    SciTech Connect

    Zhang, W.; Li, Z. P.; Zhang, S. Q.; Meng, J.

    2010-03-15

    The potential energy surfaces of even-even {sup 146-156}Sm are investigated in the constrained reflection-asymmetric relativistic mean-field approach with parameter set PK1. It is shown that the critical-point candidate nucleus {sup 152}Sm marks the shape/phase transition not only from U(5) to SU(3) symmetry, but also from the octupole-deformed ground state in {sup 150}Sm to the quadrupole-deformed ground state in {sup 154}Sm. By including the octupole degree of freedom, an energy gap near the Fermi surface for single-particle levels in {sup 152}Sm with beta{sub 2}=0.14approx0.26 is found and the important role of the octupole deformation driving pair nu2f{sub 7/2} and nu1i{sub 13/2} is demonstrated.

  15. Structural Properties of the Disordered Spherical and Other Mean Field Spin Models

    NASA Astrophysics Data System (ADS)

    Sanctis, Luca De

    2007-03-01

    We extend the approach of Aizenman, Sims and Starr for the SK-type models to their spherical versions. Such an extension has already been performed for diluted spin glasses. The factorization property of the optimal structures found by Guerra for the SK model, which holds for diluted models as well, is verified also in the case of spherical systems, with the due modifications. Hence we show that there are some common structural features in various mean field spin models. These similarities seem to be quite paradigmatic, and we summarize the various techniques typically used to prove the structural analogies and to tackle the computation of the free energy per spin in the thermodynamic limit.

  16. Bayesian Learning in Sparse Graphical Factor Models via Variational Mean-Field Annealing

    PubMed Central

    Yoshida, Ryo; West, Mike

    2010-01-01

    We describe a class of sparse latent factor models, called graphical factor models (GFMs), and relevant sparse learning algorithms for posterior mode estimation. Linear, Gaussian GFMs have sparse, orthogonal factor loadings matrices, that, in addition to sparsity of the implied covariance matrices, also induce conditional independence structures via zeros in the implied precision matrices. We describe the models and their use for robust estimation of sparse latent factor structure and data/signal reconstruction. We develop computational algorithms for model exploration and posterior mode search, addressing the hard combinatorial optimization involved in the search over a huge space of potential sparse configurations. A mean-field variational technique coupled with annealing is developed to successively generate “artificial” posterior distributions that, at the limiting temperature in the annealing schedule, define required posterior modes in the GFM parameter space. Several detailed empirical studies and comparisons to related approaches are discussed, including analyses of handwritten digit image and cancer gene expression data. PMID:20890391

  17. Mean-field approximation for the Sznajd model in complex networks

    NASA Astrophysics Data System (ADS)

    Araújo, Maycon S.; Vannucchi, Fabio S.; Timpanaro, André M.; Prado, Carmen P. C.

    2015-02-01

    This paper studies the Sznajd model for opinion formation in a population connected through a general network. A master equation describing the time evolution of opinions is presented and solved in a mean-field approximation. Although quite simple, this approximation allows us to capture the most important features regarding the steady states of the model. When spontaneous opinion changes are included, a discontinuous transition from consensus to polarization can be found as the rate of spontaneous change is increased. In this case we show that a hybrid mean-field approach including interactions between second nearest neighbors is necessary to estimate correctly the critical point of the transition. The analytical prediction of the critical point is also compared with numerical simulations in a wide variety of networks, in particular Barabási-Albert networks, finding reasonable agreement despite the strong approximations involved. The same hybrid approach that made it possible to deal with second-order neighbors could just as well be adapted to treat other problems such as epidemic spreading or predator-prey systems.

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

    PubMed

    Bogoyavlenskiy, V A

    2001-12-01

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

  19. Modeling and computation of mean field equilibria in producers' game with emission permits trading

    NASA Astrophysics Data System (ADS)

    Zhang, Shuhua; Wang, Xinyu; Shanain, Aleksandr

    2016-08-01

    In this paper, we present a mean field game to model the production behaviors of a very large number of producers, whose carbon emissions are regulated by government. Especially, an emission permits trading scheme is considered in our model, in which each enterprise can trade its own permits flexibly. By means of the mean field equilibrium, we obtain a Hamilton-Jacobi-Bellman (HJB) equation coupled with a Kolmogorov equation, which are satisfied by the adjoint state and the density of producers (agents), respectively. Then, we propose a so-called fitted finite volume method to solve the HJB equation and the Kolmogorov equation. The efficiency and the usefulness of this method are illustrated by the numerical experiments. Under different conditions, the equilibrium states as well as the effects of the emission permits price are examined, which demonstrates that the emission permits trading scheme influences the producers' behaviors, that is, more populations would like to choose a lower rather than a higher emission level when the emission permits are expensive.

  20. Ground state phase transition in the Nilsson mean-field plus standard pairing model

    NASA Astrophysics Data System (ADS)

    Guan, Xin; Xu, Haocheng; Zhang, Yu; Pan, Feng; Draayer, Jerry P.

    2016-08-01

    The ground state phase transition in Nd, Sm, and Gd isotopes is investigated by using the Nilsson mean-field plus standard pairing model based on the exact solutions obtained from the extended Heine-Stieltjes correspondence. The results of the model calculations successfully reproduce the critical phenomena observed experimentally in the odd-even mass differences, odd-even differences of two-neutron separation energy, and the α -decay and double β--decay energies of these isotopes. Since the odd-even effects are the most important signatures of pairing interactions in nuclei, the model calculations yield microscopic insight into the nature of the ground state phase transition manifested by the standard pairing interaction.

  1. Mean-field model for the growth and coarsening of stoichiometric precipitates at grain boundaries

    NASA Astrophysics Data System (ADS)

    Kozeschnik, E.; Svoboda, J.; Radis, R.; Fischer, F. D.

    2010-01-01

    In this paper, a model for growth and coarsening of precipitates at grain boundaries is developed. The concept takes into account that the evolution of grain boundary precipitates involves fast short-circuit diffusion along grain boundaries as well as slow bulk diffusion of atoms from the grain interior to the grain boundaries. The mathematical formalism is based on a mean-field approximation, utilizing the thermodynamic extremal principle. The model is applied to the precipitation of aluminum nitrides in microalloyed steel in austenite, where precipitation occurs predominately at the austenite grain boundaries. It is shown that the kinetics of precipitation predicted by the proposed model differs significantly from that calculated for randomly distributed precipitates with spherical diffusion fields. Good agreement of the numerical solution is found with experimental observations as well as theoretical treatment of precipitate coarsening.

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  3. Effects of anisotropies in turbulent magnetic diffusion in mean-field solar dynamo models

    SciTech Connect

    Pipin, V. V.; Kosovichev, A. G.

    2014-04-10

    We study how anisotropies of turbulent diffusion affect the evolution of large-scale magnetic fields and the dynamo process on the Sun. The effect of anisotropy is calculated in a mean-field magnetohydrodynamics framework assuming that triple correlations provide relaxation to the turbulent electromotive force (so-called the 'minimal τ-approximation'). We examine two types of mean-field dynamo models: the well-known benchmark flux-transport model and a distributed-dynamo model with a subsurface rotational shear layer. For both models, we investigate effects of the double- and triple-cell meridional circulation, recently suggested by helioseismology and numerical simulations. To characterize the anisotropy effects, we introduce a parameter of anisotropy as a ratio of the radial and horizontal intensities of turbulent mixing. It is found that the anisotropy affects the distribution of magnetic fields inside the convection zone. The concentration of the magnetic flux near the bottom and top boundaries of the convection zone is greater when the anisotropy is stronger. It is shown that the critical dynamo number and the dynamo period approach to constant values for large values of the anisotropy parameter. The anisotropy reduces the overlap of toroidal magnetic fields generated in subsequent dynamo cycles, in the time-latitude 'butterfly' diagram. If we assume that sunspots are formed in the vicinity of the subsurface shear layer, then the distributed dynamo model with the anisotropic diffusivity satisfies the observational constraints from helioseismology and is consistent with the value of effective turbulent diffusion estimated from the dynamics of surface magnetic fields.

  4. Thermodynamics of the one-dimensional parallel Kawasaki model: Exact solution and mean-field approximations

    NASA Astrophysics Data System (ADS)

    Pazzona, Federico G.; Demontis, Pierfranco; Suffritti, Giuseppe B.

    2014-08-01

    The adsorption isotherm for the recently proposed parallel Kawasaki (PK) lattice-gas model [Phys. Rev. E 88, 062144 (2013), 10.1103/PhysRevE.88.062144] is calculated exactly in one dimension. To do so, a third-order difference equation for the grand-canonical partition function is derived and solved analytically. In the present version of the PK model, the attraction and repulsion effects between two neighboring particles and between a particle and a neighboring empty site are ruled, respectively, by the dimensionless parameters ϕ and θ. We discuss the inflections induced in the isotherms by situations of high repulsion, the role played by finite lattice sizes in the emergence of substeps, and the adequacy of the two most widely used mean-field approximations in lattice gases, namely, the Bragg-Williams and the Bethe-Peierls approximations.

  5. Angular momentum projection for a Nilsson mean-field plus pairing model

    NASA Astrophysics Data System (ADS)

    Wang, Yin; Pan, Feng; Launey, Kristina D.; Luo, Yan-An; Draayer, J. P.

    2016-06-01

    The angular momentum projection for the axially deformed Nilsson mean-field plus a modified standard pairing (MSP) or the nearest-level pairing (NLP) model is proposed. Both the exact projection, in which all intrinsic states are taken into consideration, and the approximate projection, in which only intrinsic states with K = 0 are taken in the projection, are considered. The analysis shows that the approximate projection with only K = 0 intrinsic states seems reasonable, of which the configuration subspace considered is greatly reduced. As simple examples for the model application, low-lying spectra and electromagnetic properties of 18O and 18Ne are described by using both the exact and approximate angular momentum projection of the MSP or the NLP, while those of 20Ne and 24Mg are described by using the approximate angular momentum projection of the MSP or NLP.

  6. Dynamics and Self-consistent Chaos in a Mean Field Hamiltonian Model

    NASA Astrophysics Data System (ADS)

    del-Castillo-Negrete, Diego

    We study a mean field Hamiltonian model that describes the collective dynamics of marginally stable fluids and plasmas in the finite N and N-> infty kinetic limit (where N is the number of particles). The linear stability of equilibria in the kinetic model is studied as well as the initial value problem including Landau damping . Numerical simulations show the existence of coherent, rotating dipole states. We approximate the dipole as two macroparticles and show that the N=2 limit has a family of rotating integrable solutions that provide an accurate description of the dynamics. We discuss the role of self-consistent Hamiltonian chaos in the formation of coherent structures, and discuss a mechanism of "violent" mixing caused by a self-consistent elliptic-hyperbolic bifurcation in phase space.

  7. Mean-field behavior of the negative-weight percolation model on random regular graphs.

    PubMed

    Melchert, Oliver; Hartmann, Alexander K; Mézard, Marc

    2011-10-01

    We investigate both analytically and numerically the ensemble of minimum-weight loops in the negative-weight percolation model on random graphs with fixed connectivity and bimodal weight distribution. This allows us to study the mean-field behavior of this model. The analytical study is based on a conjectured equivalence with the problem of self-avoiding walks in a random medium. The numerical study is based on a mapping to a standard minimum-weight matching problem for which fast algorithms exist. Both approaches yield results that are in agreement on the location of the phase transition, on the value of critical exponents, and on the absence of any sizable indications of a glass phase. By these results, the previously conjectured upper critical dimension of d(u)=6 is confirmed. PMID:22181086

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

    NASA Astrophysics Data System (ADS)

    Coslovich, Daniele; Ikeda, Atsushi; Miyazaki, Kunimasa

    2016-04-01

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

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

    PubMed

    Coslovich, Daniele; Ikeda, Atsushi; Miyazaki, Kunimasa

    2016-04-01

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

  10. Metastates in Mean-Field Models with Random External Fields Generated by Markov Chains

    NASA Astrophysics Data System (ADS)

    Formentin, M.; Külske, C.; Reichenbachs, A.

    2012-01-01

    We extend the construction by Külske and Iacobelli of metastates in finite-state mean-field models in independent disorder to situations where the local disorder terms are a sample of an external ergodic Markov chain in equilibrium. We show that for non-degenerate Markov chains, the structure of the theorems is analogous to the case of i.i.d. variables when the limiting weights in the metastate are expressed with the aid of a CLT for the occupation time measure of the chain. As a new phenomenon we also show in a Potts example that for a degenerate non-reversible chain this CLT approximation is not enough, and that the metastate can have less symmetry than the symmetry of the interaction and a Gaussian approximation of disorder fluctuations would suggest.

  11. Improving Solar Cycle Prediction Using Variational Data Assimilation in a Mean-Field Dynamo Model

    NASA Astrophysics Data System (ADS)

    Fournier, A.; Hung, C. P.; Jouve, L.; Brun, S.

    2014-12-01

    We present our recent effort to implement modern variational data assimilation techniques into a mean field solar dynamo code. This work extends the work of (Jouve et al. 2011, ApJ) to take into account the correct spherical geometry and meridional circulation into so-called Babcock-Leigthon flux transport dynamo models. Based on twin-experiments, in which we observe our dynamo simulations, and on a well defined cost function using toroidal and poloidal field observations we are able to recover the main attributes of the dynamo solution used to test our data assimilation algorithm. By assimilating solar data (such as Wolf number or butterfly diagram) we are starting to deduce the profile and temporal variations of key ingredients of the solar dynamo. We find that the data sampling and the temporal window are key to get reliable results. We show how such a powerful technique can be used to improve our ability to predict the solar magnetic activity.

  12. Mean field study of the topological Haldane-Hubbard model of spin-1/2 fermions

    NASA Astrophysics Data System (ADS)

    Arun, V. S.; Sohal, R.; Hickey, C.; Paramekanti, A.

    2016-03-01

    Motivated by exploring the effect of interactions on Chern insulators, and by recent experiments realizing topological bands for ultracold atoms in synthetic gauge fields, we study the honeycomb lattice Haldane-Hubbard model of spin-1/2 fermions. Using an unrestricted mean field approach, we map out the instability of the topological band insulator towards magnetically ordered insulators which emerge with increasing Hubbard repulsion. In addition to the topological Néel phase, we recover various chiral noncoplanar magnetic orders previously identified within a strong-coupling approach. We compute the band structure of these ordered phases, showing that the triple-Q tetrahedral phase harbors topological Chern bands with large Chern numbers.

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

    NASA Astrophysics Data System (ADS)

    Poilblanc, Didier

    2005-08-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-08-01

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

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

    PubMed

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

    2015-08-01

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

  16. Algebraic Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Dankova, T. S.; Rosensteel, G.

    1998-10-01

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

  17. Self-consistent mean-field model for palmitoyloleoylphosphatidylcholine-palmitoyl sphingomyelin-cholesterol lipid bilayers

    NASA Astrophysics Data System (ADS)

    Tumaneng, Paul W.; Pandit, Sagar A.; Zhao, Guijun; Scott, H. L.

    2011-03-01

    The connection between membrane inhomogeneity and the structural basis of lipid rafts has sparked interest in the lateral organization of model lipid bilayers of two and three components. In an effort to investigate anisotropic lipid distribution in mixed bilayers, a self-consistent mean-field theoretical model is applied to palmitoyloleoylphosphatidylcholine (POPC)-palmitoyl sphingomyelin (PSM)-cholesterol mixtures. The compositional dependence of lateral organization in these mixtures is mapped onto a ternary plot. The model utilizes molecular dynamics simulations to estimate interaction parameters and to construct chain conformation libraries. We find that at some concentration ratios the bilayers separate spatially into regions of higher and lower chain order coinciding with areas enriched with PSM and POPC, respectively. To examine the effect of the asymmetric chain structure of POPC on bilayer lateral inhomogeneity, we consider POPC-lipid interactions with and without angular dependence. Results are compared with experimental data and with results from a similar model for mixtures of dioleoylphosphatidylcholine, steroyl sphingomyelin, and cholesterol.

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

    NASA Astrophysics Data System (ADS)

    Akerlund, Oscar; de Forcrand, Philippe

    2016-02-01

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

  19. A stochastic mean field model for an excitatory and inhibitory synaptic drive cortical neuronal network.

    PubMed

    Hui, Qing; Haddad, Wassim M; Bailey, James M; Hayakawa, Tomohisa

    2014-04-01

    With the advances in biochemistry, molecular biology, and neurochemistry there has been impressive progress in understanding the molecular properties of anesthetic agents. However, there has been little focus on how the molecular properties of anesthetic agents lead to the observed macroscopic property that defines the anesthetic state, that is, lack of responsiveness to noxious stimuli. In this paper, we develop a mean field synaptic drive firing rate cortical neuronal model and demonstrate how the induction of general anesthesia can be explained using multistability; the property whereby the solutions of a dynamical system exhibit multiple attracting equilibria under asymptotically slowly changing inputs or system parameters. In particular, we demonstrate multistability in the mean when the system initial conditions or the system coefficients of the neuronal connectivity matrix are random variables. Uncertainty in the system coefficients is captured by representing system uncertain parameters by a multiplicative white noise model wherein stochastic integration is interpreted in the sense of Itô. Modeling a priori system parameter uncertainty using a multiplicative white noise model is motivated by means of the maximum entropy principle of Jaynes and statistical analysis. PMID:24807952

  20. Novel dynamics and thermodynamics of a new Hamiltonian mean field model

    NASA Astrophysics Data System (ADS)

    Curilef, Sergio; Atenas, Boris

    Statistical systems are idealized by the hypothesis that the particles do not interact among them, or the range of interactions is short enough, reaching very fast the statistical state that we know as equilibrium. However, systems with long-range interactions are common in nature because of they are observed from the atomic scale to the astronomical scale, exhibiting some anomalies as inequivalence of ensembles, negative heat capacity, ergodicity breaking, non equilibrium phase transitions, quasi-stationarity, anomalous diffusion, etc. We present in this contribution a new Hamiltonian mean field model whose potential is inspired in the dipole-dipole interactions. The equilibrium is analytically studied in the canonical ensemble and coincides with the one obtained from molecular dynamics simulations (microcanonical ensemble). We notice, this model presents a kind of inequivalence of ensembles in long-standing states before arriving at equilibrium. However, the novelty, compared to other models presented in recent literature, is that two quasi-stationary states appear in the behavior of this system. The first quasi-stationary state decays to a second one, which is different to the first, before going to the equilibrium.We characterize them by its dynamics and thermodynamics. We acknowledge partial financial support by Anillo ACT-1204, VRIDT-UCN105/2015. We appreciate the computational assistance of A. Pluchino.

  1. Critical behavior of a tumor growth model: directed percolation with a mean-field flavor.

    PubMed

    Lipowski, Adam; Ferreira, António Luis; Wendykier, Jacek

    2012-10-01

    We examine the critical behavior of a lattice model of tumor growth where supplied nutrients are correlated with the distribution of tumor cells. Our results support the previous report [Ferreira et al., Phys. Rev. E 85, 010901(R) (2012)], which suggested that the critical behavior of the model differs from the expected directed percolation (DP) universality class. Surprisingly, only some of the critical exponents (β, α, ν([perpendicular]), and z) take non-DP values while some others (β', ν(||), and spreading-dynamics exponents Θ, δ, z') remain very close to their DP counterparts. The obtained exponents satisfy the scaling relations β=αν(||), β'=δν(||), and the generalized hyperscaling relation Θ+α+δ=d/z, where the dynamical exponent z is, however, used instead of the spreading exponent z'. Both in d=1 and d=2 versions of our model, the exponent β most likely takes the mean-field value β=1, and we speculate that it might be due to the roulette-wheel selection, which is used to choose the site to supply a nutrient. PMID:23214560

  2. Spin-orbit interaction in relativistic nuclear structure models

    NASA Astrophysics Data System (ADS)

    Ebran, J.-P.; Mutschler, A.; Khan, E.; Vretenar, D.

    2016-08-01

    Relativistic self-consistent mean-field (SCMF) models naturally account for the coupling of the nucleon spin to its orbital motion, whereas nonrelativistic SCMF methods necessitate a phenomenological ansatz for the effective spin-orbit potential. Recent experimental studies aim to explore the isospin properties of the effective spin-orbit interaction in nuclei. SCMF models are very useful in the interpretation of the corresponding data; however, standard relativistic mean-field and nonrelativistic Hartree-Fock models use effective spin-orbit potentials with different isovector properties, mainly because exchange contributions are not treated explicitly in the former. The impact of exchange terms on the effective spin-orbit potential in relativistic mean-field models is analyzed, and it is shown that it leads to an isovector structure similar to the one used in standard nonrelativistic Hartree-Fock models. Data on the isospin dependence of spin-orbit splittings in spherical nuclei could be used to constrain the isovector-scalar channel of relativistic mean-field models. The reproduction of the empirical kink in the isotope shifts of even Pb nuclei by relativistic effective interactions points to the occurrence of pseudospin symmetry in the single-neutron spectra in these nuclei.

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

    SciTech Connect

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

    2007-01-15

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

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

    SciTech Connect

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

    2014-05-07

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

  5. Correlation patterns of NIKKEI index constituents. Towards a mean-field model

    NASA Astrophysics Data System (ADS)

    Hayashi, Katsuhiko; Kaizoji, Taisei; Pichl, Lukáš

    2007-09-01

    An analysis of minute-tick data from the Japanese stock index market is reported for a three-year period of 2000/7/4-2003/6/30. Correlation patterns and principal component distributions were determined for 180 constituents of the NIKKEI 225 index, excluding the effects of after-hours trading and constituent revisions. The first principal component describes about 30% of the total variance in constituent log returns (subject to slow decrease with the size of the correlation window), suggesting that a small number of physical parameters may describe the internal dynamics of the index, allowing for an adiabatic representation of index dynamics, and a self-consistent mean-field model of its constituents. Finally, it is shown that the introduction of a time gap into minute-tick data significantly improves the correlations of the price-weighed index with its constituents, even when such gap inserts are strictly penalized. This phenomenon corresponds to a heterogenous response time of index constituents to the adiabatic collective motion and also demonstrates the inhomogeneous nature of equidistant time ticks in financial trading.

  6. Hamiltonian mean field model: Effect of network structure on synchronization dynamics.

    PubMed

    Virkar, Yogesh S; Restrepo, Juan G; Meiss, James D

    2015-11-01

    The Hamiltonian mean field model of coupled inertial Hamiltonian rotors is a prototype for conservative dynamics in systems with long-range interactions. We consider the case where the interactions between the rotors are governed by a network described by a weighted adjacency matrix. By studying the linear stability of the incoherent state, we find that the transition to synchrony begins when the coupling constant K is inversely proportional to the largest eigenvalue of the adjacency matrix. We derive a closed system of equations for a set of local order parameters to study the effect of network heterogeneity on the synchronization of the rotors. When K is just beyond the transition to synchronization, we find that the degree of synchronization is highly dependent on the network's heterogeneity, but that for large K the degree of synchronization is robust to changes in the degree distribution. Our results are illustrated with numerical simulations on Erdös-Renyi networks and networks with power-law degree distributions. PMID:26651739

  7. Structural versus dynamical origins of mean-field behavior in a self-organized critical model of neuronal avalanches.

    PubMed

    Moosavi, S Amin; Montakhab, Afshin

    2015-11-01

    Critical dynamics of cortical neurons have been intensively studied over the past decade. Neuronal avalanches provide the main experimental as well as theoretical tools to consider criticality in such systems. Experimental studies show that critical neuronal avalanches show mean-field behavior. There are structural as well as recently proposed [Phys. Rev. E 89, 052139 (2014)] dynamical mechanisms that can lead to mean-field behavior. In this work we consider a simple model of neuronal dynamics based on threshold self-organized critical models with synaptic noise. We investigate the role of high-average connectivity, random long-range connections, as well as synaptic noise in achieving mean-field behavior. We employ finite-size scaling in order to extract critical exponents with good accuracy. We conclude that relevant structural mechanisms responsible for mean-field behavior cannot be justified in realistic models of the cortex. However, strong dynamical noise, which can have realistic justifications, always leads to mean-field behavior regardless of the underlying structure. Our work provides a different (dynamical) origin than the conventionally accepted (structural) mechanisms for mean-field behavior in neuronal avalanches. PMID:26651741

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

    NASA Astrophysics Data System (ADS)

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

    2015-08-01

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

  9. Structural versus dynamical origins of mean-field behavior in a self-organized critical model of neuronal avalanches

    NASA Astrophysics Data System (ADS)

    Moosavi, S. Amin; Montakhab, Afshin

    2015-11-01

    Critical dynamics of cortical neurons have been intensively studied over the past decade. Neuronal avalanches provide the main experimental as well as theoretical tools to consider criticality in such systems. Experimental studies show that critical neuronal avalanches show mean-field behavior. There are structural as well as recently proposed [Phys. Rev. E 89, 052139 (2014), 10.1103/PhysRevE.89.052139] dynamical mechanisms that can lead to mean-field behavior. In this work we consider a simple model of neuronal dynamics based on threshold self-organized critical models with synaptic noise. We investigate the role of high-average connectivity, random long-range connections, as well as synaptic noise in achieving mean-field behavior. We employ finite-size scaling in order to extract critical exponents with good accuracy. We conclude that relevant structural mechanisms responsible for mean-field behavior cannot be justified in realistic models of the cortex. However, strong dynamical noise, which can have realistic justifications, always leads to mean-field behavior regardless of the underlying structure. Our work provides a different (dynamical) origin than the conventionally accepted (structural) mechanisms for mean-field behavior in neuronal avalanches.

  10. Modeling relativistic nuclear collisions.

    SciTech Connect

    Anderlik, C.; Magas, V.; Strottman, D.; Csernai, L. P.

    2001-01-01

    Modeling Ultra-Relativistic Heavy Ion Collisioiis at RHIC and LHC energies using a Multi Module Model is presented. The first Module is the Effective String Rope Model for the calculation of the initial stages of the reaction; the output of this module is used as the initial state for the subsequent one-fluid hydrodynainical calculation module. It is shown that such an initial state leads to the creation of the third flow component. The hydrodynamical evolution of the energy density distribution is presented for RHIC energies. The final module describing the Freeze Out; and Hadronization is also discussed.

  11. Dynamical instabilities in density-dependent hadronic relativistic models

    SciTech Connect

    Santos, A. M.; Brito, L.; Providencia, C.

    2008-04-15

    Unstable modes in asymmetric nuclear matter (ANM) at subsaturation densities are studied in the framework of relativistic mean-field density-dependent hadron models. The size of the instabilities that drive the system are calculated and a comparison with results obtained within the nonlinear Walecka model is presented. The distillation and antidistillation effects are discussed.

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

    NASA Astrophysics Data System (ADS)

    Tsuda, Junichi; Nishimori, Hidetoshi

    2014-07-01

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

  13. Mean-field plus various types of pairing models and an exact boson mapping of the standard pairing model

    SciTech Connect

    Pan Feng; Wang Yin; Guan Xin; Jia Lu; Chen Xiangrong; Draayer, J. P.

    2011-06-28

    Exact solutions of Nilsson mean-field with various pairing interactions are reviewed. Some even-odd mass differences and moments of inertia of low-lying states for rare earth and actinide nuclei are calculated for the nearest-orbit pairing approximation as well as for the extended pairing model and compared to available experimental data. An exact boson mapping of the standard pairing Hamiltonian is also reported. Under the mapping, fermion pair operators are mapped exactly onto corresponding bosons. The image of the mapping is a Bose-Hubbard model with orbit-dependent hopping.

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

    NASA Astrophysics Data System (ADS)

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

    2016-05-01

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

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

    NASA Astrophysics Data System (ADS)

    LeSher, Daniel

    2015-10-01

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

  16. Mean Field Analysis of Stochastic Neural Network Models with Synaptic Depression

    NASA Astrophysics Data System (ADS)

    Yasuhiko Igarashi,; Masafumi Oizumi,; Masato Okada,

    2010-08-01

    We investigated the effects of synaptic depression on the macroscopic behavior of stochastic neural networks. Dynamical mean field equations were derived for such networks by taking the average of two stochastic variables: a firing-state variable and a synaptic variable. In these equations, the average product of thesevariables is decoupled as the product of their averages because the two stochastic variables are independent. We proved the independence of these two stochastic variables assuming that the synaptic weight Jij is of the order of 1/N with respect to the number of neurons N. Using these equations, we derived macroscopic steady-state equations for a network with uniform connections and for a ring attractor network with Mexican hat type connectivity and investigated the stability of the steady-state solutions. An oscillatory uniform state was observed in the network with uniform connections owing to a Hopf instability. For the ring network, high-frequency perturbations were shown not to affect system stability. Two mechanisms destabilize the inhomogeneous steady state, leading to two oscillatory states. A Turing instability leads to a rotating bump state, while a Hopf instability leads to an oscillatory bump state, which was previously unreported. Various oscillatory states take place in a network with synaptic depression depending on the strength of the interneuron connections.

  17. MEAN-FIELD MODELING OF AN α{sup 2} DYNAMO COUPLED WITH DIRECT NUMERICAL SIMULATIONS OF RIGIDLY ROTATING CONVECTION

    SciTech Connect

    Masada, Youhei; Sano, Takayoshi E-mail: sano@ile.osaka-u.ac.jp

    2014-10-10

    The mechanism of large-scale dynamos in rigidly rotating stratified convection is explored by direct numerical simulations (DNS) in Cartesian geometry. A mean-field dynamo model is also constructed using turbulent velocity profiles consistently extracted from the corresponding DNS results. By quantitative comparison between the DNS and our mean-field model, it is demonstrated that the oscillatory α{sup 2} dynamo wave, excited and sustained in the convection zone, is responsible for large-scale magnetic activities such as cyclic polarity reversal and spatiotemporal migration. The results provide strong evidence that a nonuniformity of the α-effect, which is a natural outcome of rotating stratified convection, can be an important prerequisite for large-scale stellar dynamos, even without the Ω-effect.

  18. Brownian regime of finite-N corrections to particle motion in the XY Hamiltonian mean field model

    NASA Astrophysics Data System (ADS)

    Ribeiro, Bruno V.; Amato, Marco A.; Elskens, Yves

    2016-08-01

    We study the dynamics of the N-particle system evolving in the XY Hamiltonian mean field (HMF) model for a repulsive potential, when no phase transition occurs. Starting from a homogeneous distribution, particles evolve in a mean field created by the interaction with all others. This interaction does not change the homogeneous state of the system, and particle motion is approximately ballistic with small corrections. For initial particle data approaching a waterbag, it is explicitly proved that corrections to the ballistic velocities are in the form of independent Brownian noises over a time scale diverging not slower than {N}2/5 as N\\to ∞ , which proves the propagation of molecular chaos. Molecular dynamics simulations of the XY-HMF model confirm our analytical findings.

  19. Relativistic dynamical collapse model

    NASA Astrophysics Data System (ADS)

    Pearle, Philip

    2015-05-01

    A model is discussed where all operators are constructed from a quantum scalar field whose energy spectrum takes on all real values. The Schrödinger picture wave function depends upon space and time coordinates for each particle, as well as an inexorably increasing evolution parameter s which labels a foliation of spacelike hypersurfaces. The model is constructed to be manifestly Lorentz invariant in the interaction picture. Free particle states and interactions are discussed in this framework. Then, the formalism of the continuous spontaneous localization (CSL) theory of dynamical collapse is applied. The collapse-generating operator is chosen to be the particle number space-time density. Unlike previous relativistically invariant models, the vacuum state is not excited. The collapse dynamics depends upon two parameters, a parameter Λ which represents the collapse rate/volume and a scale factor ℓ. A common example of collapse dynamics, involving a clump of matter in a superposition of two locations, is analyzed. The collapse rate is shown to be identical to that of nonrelativistic CSL when the GRW-CSL choice of ℓ=a =1 0-5 cm , is made, along with Λ =λ /a3 (GRW-CSL choice λ =1 0-16s-1). The collapse rate is also satisfactory with the choice ℓ as the size of the Universe, with Λ =λ /ℓa2. Because the collapse narrows wave functions in space and time, it increases a particle's momentum and energy, altering its mass. It is shown that, with ℓ=a , the change of mass of a nucleon is unacceptably large but, when ℓ is the size of the Universe, the change of mass over the age of the Universe is acceptably small.

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

    SciTech Connect

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

    2015-03-21

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

  1. Microstructure for ferroelastic transitions from strain pseudo-spin clock models in two and three dimensions: a mean field analysis

    SciTech Connect

    Lookman, Turab; Vasseur, Romain

    2009-01-01

    We obtain the microstructure of ferroelastic transitions in two and three dimensions from the solution of their corresponding discrete pseudo-spin models. In two dimensions we consider two transitions each from the high symmetry square and triangle symmetries: square-to-rectangle (SR), square-to-oblique (SO), triangle-to-centered rectangle (TR) and triangle-to-oblique (TO). In three dimensions we study the corresponding spin model for the cubic to tetragonal transition. The Landau free energies for these transitions result in N+ I states clock models (Z{sub N}) with long range interactions and we derive mean-field self-consistency equations for the clock model Hamiltonians. The microstructures from the mean-field solutions of the models are very similar to those obtained from the original continuum models or Monte Carlo simulations on the spin models (in the SR case), illustrating that these discrete models capture the salient physics. The models, in the presence of disorder, provide the basis for the study of the strain glass phase observed in martensitic alloys.

  2. A Mean-Field Photoreaction Model for the Pretilt Generation of a Liquid Crystal on Photopolymer Layers upon Ultraviolet Exposure

    NASA Astrophysics Data System (ADS)

    Na, Jun-Hee; Pae, Hyungwu; Kim, Jinyool; Yu, Chang-Jae; Lee, Sin-Doo

    2011-03-01

    We present a mean-field photoreaction model for the pretilt generation of a nematic liquid crystal (NLC) on the surfaces of photopolymers upon the exposure of ultraviolet (UV) light. The angular distribution function of photopolymer side chains, calculated in the photoreaction model, is used for determining the surface anchoring energy within the Rapini-Papoular approximation. The pretilt angle transition from the homeotropic alignment to the planar alignment of the NLC is demonstrated in two photopolymers with different alkyl chain lengths as a function of the UV exposure time. The main features of the experimental results agree well with theoretical predictions.

  3. About a solvable mean field model of a Gaussian spin glass

    NASA Astrophysics Data System (ADS)

    Barra, Adriano; Genovese, Giuseppe; Guerra, Francesco; Tantari, Daniele

    2014-04-01

    In a series of papers, we have studied a modified Hopfield model of a neural network, with learned words characterized by a Gaussian distribution. The model can be represented as a bipartite spin glass, with one party described by dichotomic Ising spins, and the other party by continuous spin variables, with an a priori Gaussian distribution. By application of standard interpolation methods, we have found it useful to compare the neural network model (bipartite) from one side, with two spin glass models, each monopartite, from the other side. Of these, the first is the usual Sherrington-Kirkpatrick model, the second is a spin glass model, with continuous spins and inbuilt highly nonlinear smooth cut-off interactions. This model is an invaluable laboratory for testing all techniques which have been useful in the study of spin glasses. The purpose of this paper is to give a synthetic description of the most peculiar aspects, by stressing the necessary novelties in the treatment. In particular, it will be shown that the control of the infinite volume limit, according to the well-known Guerra-Toninelli strategy, requires in addition one to consider the involvement of the cut-off interaction in the interpolation procedure. Moreover, the control of the ergodic region, the annealed case, cannot be directly achieved through the standard application of the Borel-Cantelli lemma, but requires previous modification of the interaction. This remark could find useful application in other cases. The replica symmetric expression for the free energy can be easily reached through a suitable version of the doubly stochastic interpolation technique. However, this model shares the unique property that the fully broken replica symmetry ansatz can be explicitly calculated. A very simple sum rule connects the general expression of the fully broken free energy trial function with the replica symmetric one. The definite sign of the error term shows that the replica solution is optimal. Then

  4. MEAN-FIELD SOLAR DYNAMO MODELS WITH A STRONG MERIDIONAL FLOW AT THE BOTTOM OF THE CONVECTION ZONE

    SciTech Connect

    Pipin, V. V.; Kosovichev, A. G.

    2011-09-01

    This paper presents a study of kinematic axisymmetric mean-field dynamo models for the case of meridional circulation with a deep-seated stagnation point and a strong return flow at the bottom of the convection zone. This kind of circulation follows from mean-field models of the angular momentum balance in the solar convection zone. The dynamo models include turbulent sources of the large-scale poloidal magnetic field production due to kinetic helicity and a combined effect due to the Coriolis force and large-scale electric current. In these models the toroidal magnetic field, which is responsible for sunspot production, is concentrated at the bottom of the convection zone and is transported to low-latitude regions by a meridional flow. The meridional component of the poloidal field is also concentrated at the bottom of the convection zone, while the radial component is concentrated in near-polar regions. We show that it is possible for this type of meridional circulation to construct kinematic dynamo models that resemble in some aspects the sunspot magnetic activity cycle. However, in the near-equatorial regions the phase relation between the toroidal and poloidal components disagrees with observations. We also show that the period of the magnetic cycle may not always monotonically decrease with the increase of the meridional flow speed. Thus, for further progress it is important to determine the structure of the meridional circulation, which is one of the critical properties, from helioseismology observations.

  5. Limit theorems in the imitative monomer-dimer mean-field model via Stein's method

    NASA Astrophysics Data System (ADS)

    Chen, Wei-Kuo

    2016-08-01

    We consider the imitative monomer-dimer model on the complete graph introduced in the work of Alberici et al. [J. Math. Phys. 55, 063301-1-063301-27 (2014)]. It was shown that this model is described by the monomer density and has a phase transition along certain coexistence curve, where the monomer and dimer phases coexist. More recently, it was understood [D. Alberici et al., Commun. Math. Phys. (published online, 2016)] that the monomer density exhibits the central limit theorem away from the coexistence curve and enjoys a non-normal limit theorem at criticality with normalized exponent 3/4. By reverting the model to a weighted Curie-Weiss model with hard core interaction, we establish the complete description of the fluctuation properties of the monomer density on the full parameter space via Stein's method of exchangeable pairs. Our approach recovers what were established in the work of Alberici et al. [Commun. Math. Phys. (published online, 2016)] and furthermore allows to obtain the conditional central limit theorems along the coexistence curve. In all these results, the Berry-Esseen inequalities for the Kolmogorov-Smirnov distance are given.

  6. Microstructure from ferroelastic transitions using strain pseudospin clock models in two and three dimensions: A local mean-field analysis

    NASA Astrophysics Data System (ADS)

    Vasseur, Romain; Lookman, Turab; Shenoy, Subodh R.

    2010-09-01

    We show how microstructure can arise in first-order ferroelastic structural transitions, in two and three spatial dimensions, through a local mean-field approximation of their pseudospin Hamiltonians, that include anisotropic elastic interactions. Such transitions have symmetry-selected physical strains as their NOP -component order parameters, with Landau free energies that have a single zero-strain “austenite” minimum at high temperatures, and spontaneous-strain “martensite” minima of NV structural variants at low temperatures. The total free energy also has gradient terms, and power-law anisotropic effective interactions, induced by “no-dislocation” St Venant compatibility constraints. In a reduced description, the strains at Landau minima induce temperature dependent, clocklike ZNV+1 Hamiltonians, with NOP -component strain-pseudospin vectors S⃗ pointing to NV+1 discrete values (including zero). We study elastic texturing in five such first-order structural transitions through a local mean-field approximation of their pseudospin Hamiltonians, that include the power-law interactions. As a prototype, we consider the two-variant square/rectangle transition, with a one-component pseudospin taking NV+1=3 values of S=0,±1 , as in a generalized Blume-Capel model. We then consider transitions with two-component (NOP=2) pseudospins: the equilateral to centered rectangle (NV=3) ; the square to oblique polygon (NV=4) ; the triangle to oblique (NV=6) transitions; and finally the three-dimensional (3D) cubic to tetragonal transition (NV=3) . The local mean-field solutions in two-dimensional and 3D yield oriented domain-wall patterns as from continuous-variable strain dynamics, showing the discrete-variable models capture the essential ferroelastic texturings. Other related Hamiltonians illustrate that structural transitions in materials science can be the source of interesting spin models in statistical mechanics.

  7. Dynamics and termination cost of spatially coupled mean-field models

    NASA Astrophysics Data System (ADS)

    Caltagirone, Francesco; Franz, Silvio; Morris, Richard G.; Zdeborová, Lenka

    2014-01-01

    This work is motivated by recent progress in information theory and signal processing where the so-called spatially coupled design of systems leads to considerably better performance. We address relevant open questions about spatially coupled systems through the study of a simple Ising model. In particular, we consider a chain of Curie-Weiss models that are coupled by interactions up to a certain range. Indeed, it is well known that the pure (uncoupled) Curie-Weiss model undergoes a first-order phase transition driven by the magnetic field, and furthermore in the spinodal region such systems are unable to reach equilibrium in subexponential time if initialized in the metastable state. In contrast, the spatially coupled system is instead able to reach the equilibrium even when initialized to the metastable state. The equilibrium phase propagates along the chain in the form of a traveling wave. Here we study the speed of the wave front and the so-called termination cost—i.e., the conditions necessary for the propagation to occur. We reach several interesting conclusions about optimization of the speed and the cost.

  8. Periodic solutions to a mean-field model for electrocortical activity

    NASA Astrophysics Data System (ADS)

    van Veen, L.; Green, K. R.

    2014-12-01

    We consider a continuum model of electrical signals in the human cortex, which takes the form of a system of semilinear, hyperbolic partial differential equations for the inhibitory and excitatory membrane potentials and the synaptic inputs. The coupling of these components is represented by sigmoidal and quadratic nonlinearities. We consider these equations on a square domain with periodic boundary conditions, in the vicinity of the primary transition from a stable equilibrium to time-periodic motion through an equivariant Hopf bifurcation. We compute part of a family of standing wave solutions, emanating from this point.

  9. Analytical approaches to modelling panspermia - beyond the mean-field paradigm

    NASA Astrophysics Data System (ADS)

    Lingam, Manasvi

    2016-01-01

    We model the process of panspermia by adopting two different approaches. The first method conceives it as a self-replication process, endowed with non-local creation and extinction. We show that some features suggestive of universal behaviour emerge, such as exponential decay or growth, and a power spectral density that displays a power-law behaviour in a particular regime. We also present a special case wherein the number density of the planets seeded through panspermia approaches a finite asymptotic distribution. The power spectral density for the independent and spontaneous emergence of life is investigated in conjunction with its counterpart for panspermia. The former exhibits attributes characteristic of a noise spectrum, including the resemblance to white noise in a certain regime. These features are absent in panspermia, suggesting that the power spectral density could be utilized as a future tool for differentiating between the two processes. Our second approach adopts the machinery of Markov processes and diffusion, and we show that the power spectral density exhibits a power-law tail in some domains, as earlier, suggesting that this behaviour may be fairly robust. We comment on a generalization of the diffusive model, and also indicate how the methods and results developed herein could be used to analyse other phenomena.

  10. Folding of small knotted proteins: Insights from a mean field coarse-grained model

    SciTech Connect

    Najafi, Saeed; Potestio, Raffaello

    2015-12-28

    A small but relevant number of proteins whose native structure is known features nontrivial topology, i.e., they are knotted. Understanding the process of folding from a swollen unknotted state to the biologically relevant native conformation is, for these proteins, particularly difficult, due to their rate-limiting topological entanglement. To shed some light into this conundrum, we introduced a structure-based coarse-grained model of the protein, where the information about the folded conformation is encoded in bonded angular interactions only, which do not favor the formation of native contacts. A stochastic search scheme in parameter space is employed to identify a set of interactions that maximizes the probability to attain the knotted state. The optimal knotting pathways of the two smallest knotted proteins, obtained through this approach, are consistent with the results derived by means of coarse-grained as well as full atomistic simulations.

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

    NASA Astrophysics Data System (ADS)

    Le, Duc-Anh; Tran, Minh-Tien

    2015-05-01

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

  12. Mean-field dispersion-induced spatial synchrony, oscillation and amplitude death, and temporal stability in an ecological model.

    PubMed

    Banerjee, Tanmoy; Dutta, Partha Sharathi; Gupta, Anubhav

    2015-05-01

    One of the most important issues in spatial ecology is to understand how spatial synchrony and dispersal-induced stability interact. In the existing studies it is shown that dispersion among identical patches results in spatial synchrony; on the other hand, the combination of spatial heterogeneity and dispersion is necessary for dispersal-induced stability (or temporal stability). Population synchrony and temporal stability are thus often thought of as conflicting outcomes of dispersion. In contrast to the general belief, in this present study we show that mean-field dispersion is conducive to both spatial synchrony and dispersal-induced stability even in identical patches. This simultaneous occurrence of rather conflicting phenomena is governed by the suppression of oscillation states, namely amplitude death (AD) and oscillation death (OD). These states emerge through spatial synchrony of the oscillating patches in the strong-coupling strength. We present an interpretation of the mean-field diffusive coupling in the context of ecology and identify that, with increasing mean-field density, an open ecosystem transforms into a closed ecosystem. We report on the occurrence of OD in an ecological model and explain its significance. Using a detailed bifurcation analysis we show that, depending on the mortality rate and carrying capacity, the system shows either AD or both AD and OD. We also show that the results remain qualitatively the same for a network of oscillators. We identify a new transition scenario between the same type of oscillation suppression states whose geneses differ. In the parameter-mismatched case, we further report on the direct transition from OD to AD through a transcritical bifurcation. We believe that this study will lead to a proper interpretation of AD and OD in ecology, which may be important for the conservation and management of several communities in ecosystems. PMID:26066241

  13. Mean-field dispersion-induced spatial synchrony, oscillation and amplitude death, and temporal stability in an ecological model

    NASA Astrophysics Data System (ADS)

    Banerjee, Tanmoy; Dutta, Partha Sharathi; Gupta, Anubhav

    2015-05-01

    One of the most important issues in spatial ecology is to understand how spatial synchrony and dispersal-induced stability interact. In the existing studies it is shown that dispersion among identical patches results in spatial synchrony; on the other hand, the combination of spatial heterogeneity and dispersion is necessary for dispersal-induced stability (or temporal stability). Population synchrony and temporal stability are thus often thought of as conflicting outcomes of dispersion. In contrast to the general belief, in this present study we show that mean-field dispersion is conducive to both spatial synchrony and dispersal-induced stability even in identical patches. This simultaneous occurrence of rather conflicting phenomena is governed by the suppression of oscillation states, namely amplitude death (AD) and oscillation death (OD). These states emerge through spatial synchrony of the oscillating patches in the strong-coupling strength. We present an interpretation of the mean-field diffusive coupling in the context of ecology and identify that, with increasing mean-field density, an open ecosystem transforms into a closed ecosystem. We report on the occurrence of OD in an ecological model and explain its significance. Using a detailed bifurcation analysis we show that, depending on the mortality rate and carrying capacity, the system shows either AD or both AD and OD. We also show that the results remain qualitatively the same for a network of oscillators. We identify a new transition scenario between the same type of oscillation suppression states whose geneses differ. In the parameter-mismatched case, we further report on the direct transition from OD to AD through a transcritical bifurcation. We believe that this study will lead to a proper interpretation of AD and OD in ecology, which may be important for the conservation and management of several communities in ecosystems.

  14. Relativistic Continuum Shell Model

    NASA Astrophysics Data System (ADS)

    Grineviciute, Janina; Halderson, Dean

    2011-04-01

    The R-matrix formalism of Lane and Thomas has been extended to the relativistic case so that the many-coupled channels problem may be solved for systems in which binary breakup channels satisfy a relative Dirac equation. The formalism was previously applied to the relativistic impulse approximation RIA and now we applied it to Quantum Hadrodynamics QHD in the continuum Tamm-Dancoff approximation TDA with the classical meson fields replaced by one-meson exchange potentials. None of the published QHD parameters provide a decent fit to the 15 N + p elastic cross section. The deficiency is also evident in inability of the QHD parameters with the one meson exchange potentials to reproduce the QHD single particle energies. Results with alternate parameters sets are presented. A. M. Lane and R. G. Thomas, R-Matrix Theory of Nuclear Reactions, Reviews of Modern Physics, 30 (1958) 257

  15. Approximate analytical solution for nuclear matter in a mean-field Walecka model and Coester line behavior

    SciTech Connect

    Delfino, A.; Silva, J.B.; Malheiro, M.

    2006-03-15

    We study nuclear matter, at the mean-field approximation, by considering as equal the values of the scalar and the vector density in the Walecka model, which is a very reasonable approximation up to the nuclear matter saturation density. It turns out that the model has an analytical solution for the scalar and vector couplings as functions only of the nuclear matter density and binding energy. The nuclear matter properties are very close to the original version of the model. This solution allows us to show that the correlation between the binding energy and the saturation density is Coester line like. The liquid-gas phase transition is also studied and the critical and flash temperatures are again very similar to the original ones.

  16. Modeling MHD accretion-ejection: episodic ejections of jets triggered by a mean-field disk dynamo

    SciTech Connect

    Stepanovs, Deniss; Fendt, Christian; Sheikhnezami, Somayeh E-mail: fendt@mpia.de

    2014-11-20

    We present MHD simulations exploring the launching, acceleration, and collimation of jets and disk winds. The evolution of the disk structure is consistently taken into account. Extending our earlier studies, we now consider the self-generation of the magnetic field by an α{sup 2}Ω mean-field dynamo. The disk magnetization remains on a rather low level, which helps to evolve the simulations for T > 10, 000 dynamical time steps on a domain extending 1500 inner disk radii. We find the magnetic field of the inner disk to be similar to the commonly found open field structure, favoring magneto-centrifugal launching. The outer disk field is highly inclined and predominantly radial. Here, differential rotation induces a strong toroidal component, which plays a key role in outflow launching. These outflows from the outer disk are slower, denser, and less collimated. If the dynamo action is not quenched, magnetic flux is continuously generated, diffuses outward through the disk, and fills the entire disk. We have invented a toy model triggering a time-dependent mean-field dynamo. The duty cycles of this dynamo lead to episodic ejections on similar timescales. When the dynamo is suppressed as the magnetization falls below a critical value, the generation of the outflows and also accretion is inhibited. The general result is that we can steer episodic ejection and large-scale jet knots by a disk-intrinsic dynamo that is time-dependent and regenerates the jet-launching magnetic field.

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

    NASA Astrophysics Data System (ADS)

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

    2009-04-01

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

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

    NASA Astrophysics Data System (ADS)

    Franz, Silvio; Tria, Francesca

    2006-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2009-08-01

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

  20. Flocking dynamics and mean-field limit in the Cucker-Smale-type model with topological interactions

    NASA Astrophysics Data System (ADS)

    Haskovec, Jan

    2013-10-01

    We introduce a Cucker-Smale-type model for flocking, where the strength of interaction between two agents depends on their relative separation (called “topological distance” in previous works), which is the number of intermediate individuals separating them. This makes the model scale-free and is motivated by recent extensive observations of starling flocks, suggesting that the interaction ruling animal collective behavior depends on topological rather than the metric distance. We study the conditions leading to asymptotic flocking in the topological model, defined as the convergence of the agents’ velocities to a common vector. The shift from metric to topological interactions requires development of new analytical methods, taking into account the graph-theoretical nature of the problem. Moreover, we provide a rigorous derivation of the mean-field limit of large populations, recovering kinetic and hydrodynamic descriptions. In particular, we introduce the novel concept of relative separation in continuum descriptions, which is applicable to a broad variety of models of collective behavior. As an example, we shortly discuss a topological modification of the attraction-repulsion model and illustrate with numerical simulations that the modified model produces interesting new pattern dynamics.

  1. Continuum random-phase approximation for relativistic point coupling models

    SciTech Connect

    Daoutidis, J.; Ring, P.

    2009-08-15

    Continuum relativistic random-phase approximation (CRPA) is used to investigate collective excitation phenomena in several spherical nuclei along the periodic table. We start from relativistic mean-field calculations based on a covariant density functional with density-dependent zero-range forces. From the same functional an effective interaction is obtained as the second derivative with respect to the density. This interaction is used in relativistic CRPA calculations for the investigation of isoscalar monopole, isovector dipole, and isoscalar quadrupole resonances of spherical nuclei. In particular we study the low-lying E1 strength in the vicinity of the neutron evaporation threshold. The properties of the resonances, such as centroid energies and strengths distributions are compared with results of discrete RPA calculations for the same model as well as with experimental data.

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

    NASA Astrophysics Data System (ADS)

    Koehl, Patrice; Orland, Henri; Delarue, Marc

    2011-08-01

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

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

    NASA Astrophysics Data System (ADS)

    Ayral, Thomas; Biermann, Silke; Werner, Philipp

    2013-03-01

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

  4. Exact chiral spin liquids and mean-field perturbations of gamma matrix models on the ruby lattice

    NASA Astrophysics Data System (ADS)

    Whitsitt, Seth; Chua, Victor; Fiete, Gregory A.

    2012-11-01

    We theoretically studied an exactly solvable gamma matrix generalization of the Kitaev spin model on the ruby lattice, which is a honeycomb lattice with ‘expanded’ vertices and links. We find that this model displays an exceptionally rich phase diagram that includes (i) gapless phases with stable spin Fermi surfaces, (ii) gapless phases with low-energy Dirac cones and quadratic band touching points and (iii) gapped phases with finite Chern numbers possessing the values ±4,±3,±2 and ±1. The model is then generalized to include Ising-like interactions that break the exact solvability of the model in a controlled manner. When these terms are dominant, they lead to a trivial Ising ordered phase which is shown to be adiabatically connected to a large coupling limit of the exactly solvable phase. In the limit where these interactions are weak, we treat them within mean-field theory and present the resulting phase diagrams. We discuss the nature of the transitions between various phases. Our results show the richness of possible ground states in closely related magnetic systems.

  5. Large pseudocounts and L2-norm penalties are necessary for the mean-field inference of Ising and Potts models

    NASA Astrophysics Data System (ADS)

    Barton, J. P.; Cocco, S.; De Leonardis, E.; Monasson, R.

    2014-07-01

    The mean-field (MF) approximation offers a simple, fast way to infer direct interactions between elements in a network of correlated variables, a common, computationally challenging problem with practical applications in fields ranging from physics and biology to the social sciences. However, MF methods achieve their best performance with strong regularization, well beyond Bayesian expectations, an empirical fact that is poorly understood. In this work, we study the influence of pseudocount and L2-norm regularization schemes on the quality of inferred Ising or Potts interaction networks from correlation data within the MF approximation. We argue, based on the analysis of small systems, that the optimal value of the regularization strength remains finite even if the sampling noise tends to zero, in order to correct for systematic biases introduced by the MF approximation. Our claim is corroborated by extensive numerical studies of diverse model systems and by the analytical study of the m-component spin model for large but finite m. Additionally, we find that pseudocount regularization is robust against sampling noise and often outperforms L2-norm regularization, particularly when the underlying network of interactions is strongly heterogeneous. Much better performances are generally obtained for the Ising model than for the Potts model, for which only couplings incoming onto medium-frequency symbols are reliably inferred.

  6. Mean-field model of the von Kármán sodium dynamo experiment using soft iron impellers.

    PubMed

    Nore, C; Léorat, J; Guermond, J-L; Giesecke, A

    2015-01-01

    It has been observed that dynamo action occurs in the von-Kármán-Sodium (VKS) experiment only when the rotating disks and the blades are made of soft iron. The purpose of this paper is to numerically investigate the role of soft iron in the VKS dynamo scenario. This is done by using a mean-field model based on an axisymmetric mean flow, a localized permeability distribution, and a localized α effect modeling the action of the small velocity scales between the blades. The action of the rotating blades is modeled by an axisymmetric effective permeability field. Key properties of the flow giving to the numerical magnetic field a geometric structure similar to that observed experimentally are identified. Depending on the permeability of the disks and the effective permeability of the blades, the dynamo that is obtained is either oscillatory or stationary. Our numerical results confirm the leading role played by the ferromagnetic impellers. A scenario for the VKS dynamo is proposed. PMID:25679709

  7. Mean-field model of the von Kármán sodium dynamo experiment using soft iron impellers

    NASA Astrophysics Data System (ADS)

    Nore, C.; Léorat, J.; Guermond, J.-L.; Giesecke, A.

    2015-01-01

    It has been observed that dynamo action occurs in the von-Kármán-Sodium (VKS) experiment only when the rotating disks and the blades are made of soft iron. The purpose of this paper is to numerically investigate the role of soft iron in the VKS dynamo scenario. This is done by using a mean-field model based on an axisymmetric mean flow, a localized permeability distribution, and a localized α effect modeling the action of the small velocity scales between the blades. The action of the rotating blades is modeled by an axisymmetric effective permeability field. Key properties of the flow giving to the numerical magnetic field a geometric structure similar to that observed experimentally are identified. Depending on the permeability of the disks and the effective permeability of the blades, the dynamo that is obtained is either oscillatory or stationary. Our numerical results confirm the leading role played by the ferromagnetic impellers. A scenario for the VKS dynamo is proposed.

  8. Primitive-path statistics of entangled polymers: mapping multi-chain simulations onto single-chain mean-field models

    NASA Astrophysics Data System (ADS)

    Steenbakkers, Rudi J. A.; Tzoumanekas, Christos; Li, Ying; Liu, Wing Kam; Kröger, Martin; Schieber, Jay D.

    2014-01-01

    We present a method to map the full equilibrium distribution of the primitive-path (PP) length, obtained from multi-chain simulations of polymer melts, onto a single-chain mean-field ‘target’ model. Most previous works used the Doi-Edwards tube model as a target. However, the average number of monomers per PP segment, obtained from multi-chain PP networks, has consistently shown a discrepancy of a factor of two with respect to tube-model estimates. Part of the problem is that the tube model neglects fluctuations in the lengths of PP segments, the number of entanglements per chain and the distribution of monomers among PP segments, while all these fluctuations are observed in multi-chain simulations. Here we use a recently proposed slip-link model, which includes fluctuations in all these variables as well as in the spatial positions of the entanglements. This turns out to be essential to obtain qualitative and quantitative agreement with the equilibrium PP-length distribution obtained from multi-chain simulations. By fitting this distribution, we are able to determine two of the three parameters of the model, which govern its equilibrium properties. This mapping is executed for four different linear polymers and for different molecular weights. The two parameters are found to depend on chemistry, but not on molecular weight. The model predicts a constant plateau modulus minus a correction inversely proportional to molecular weight. The value for well-entangled chains, with the parameters determined ab initio, lies in the range of experimental data for the materials investigated.

  9. Majority-vote model on spatially embedded networks: Crossover from mean-field to Ising universality classes

    NASA Astrophysics Data System (ADS)

    Sampaio Filho, C. I. N.; dos Santos, T. B.; Moreira, A. A.; Moreira, F. G. B.; Andrade, J. S.

    2016-05-01

    We study through Monte Carlo simulations and finite-size scaling analysis the nonequilibrium phase transitions of the majority-vote model taking place on spatially embedded networks. These structures are built from an underlying regular lattice over which directed long-range connections are randomly added according to the probability Pi j˜r-α , where ri j is the Manhattan distance between nodes i and j , and the exponent α is a controlling parameter [J. M. Kleinberg, Nature (London) 406, 845 (2000), 10.1038/35022643]. Our results show that the collective behavior of this system exhibits a continuous order-disorder phase transition at a critical parameter, which is a decreasing function of the exponent α . Precisely, considering the scaling functions and the critical exponents calculated, we conclude that the system undergoes a crossover among distinct universality classes. For α ≤3 the critical behavior is described by mean-field exponents, while for α ≥4 it belongs to the Ising universality class. Finally, in the region where the crossover occurs, 3 <α <4 , the critical exponents are dependent on α .

  10. Dispersal-induced synchrony, temporal stability, and clustering in a mean-field coupled Rosenzweig-MacArthur model

    NASA Astrophysics Data System (ADS)

    Arumugam, Ramesh; Dutta, Partha Sharathi; Banerjee, Tanmoy

    2015-10-01

    In spatial ecology, dispersal among a set of spatially separated habitats, named as metapopulation, preserves the diversity and persistence by interconnecting the local populations. Understanding the effects of several variants of dispersion in metapopulation dynamics and to identify the factors which promote population synchrony and population stability are important in ecology. In this paper, we consider the mean-field dispersion among the habitats in a network and study the collective dynamics of the spatially extended system. Using the Rosenzweig-MacArthur model for individual patches, we show that the population synchrony and temporal stability, which are believed to be of conflicting outcomes of dispersion, can be simultaneously achieved by oscillation quenching mechanisms. Particularly, we explore the more natural coupling configuration where the rates of dispersal of different habitats are disparate. We show that asymmetry in dispersal rate plays a crucial role in determining inhomogeneity in an otherwise homogeneous metapopulation. We further identify an unusual emergent state in the network, namely, a multi-branch clustered inhomogeneous steady state, which arises due to the intrinsic parameter mismatch among the patches. We believe that the present study will shed light on the cooperative behavior of spatially structured ecosystems.

  11. Dispersal-induced synchrony, temporal stability, and clustering in a mean-field coupled Rosenzweig-MacArthur model.

    PubMed

    Arumugam, Ramesh; Dutta, Partha Sharathi; Banerjee, Tanmoy

    2015-10-01

    In spatial ecology, dispersal among a set of spatially separated habitats, named as metapopulation, preserves the diversity and persistence by interconnecting the local populations. Understanding the effects of several variants of dispersion in metapopulation dynamics and to identify the factors which promote population synchrony and population stability are important in ecology. In this paper, we consider the mean-field dispersion among the habitats in a network and study the collective dynamics of the spatially extended system. Using the Rosenzweig-MacArthur model for individual patches, we show that the population synchrony and temporal stability, which are believed to be of conflicting outcomes of dispersion, can be simultaneously achieved by oscillation quenching mechanisms. Particularly, we explore the more natural coupling configuration where the rates of dispersal of different habitats are disparate. We show that asymmetry in dispersal rate plays a crucial role in determining inhomogeneity in an otherwise homogeneous metapopulation. We further identify an unusual emergent state in the network, namely, a multi-branch clustered inhomogeneous steady state, which arises due to the intrinsic parameter mismatch among the patches. We believe that the present study will shed light on the cooperative behavior of spatially structured ecosystems. PMID:26520087

  12. Improving solar 11yr magnetic cycle prediction by using variational data assimilation in a mean field dynamo model

    NASA Astrophysics Data System (ADS)

    Hung, Ching Pui; Jouve, Laurène; Brun, Allan-Sacha; Fournier, Alexandre; Talagrand, Olivier

    2015-04-01

    We present our recent effort to implement modern variational data assimilation techniques into a 2.5 D mean field solar dynamo code. This work extend the work of (Jouve et al. 2011, ApJ) to take into account the correct spherical geometry and meridional circulation into so-called Babccok-Leigthon flux transport dynamo models. Based on twin-experiments, in which we observe our dynamo simulations, and on a well defined cost function using toroidal and poloidal field observations we are able to recover the main attributes of the dynamo solution used to test our data assimilation algorithm. By assimilating solar data (such as Wolf number or butterfly diagram) we are starting to deduce the profile and temporal variations of key ingredients of the solar dynamo. We find that the data sampling and the temporal window are key to get reliable results. We show how such powerful technique can be used to improve our ability to predict the solar magnetic activity. This work is supported by Idex Sorbonne Paris Cite via the DAMSE project.

  13. Stochastic multi-scale models of competition within heterogeneous cellular populations: Simulation methods and mean-field analysis.

    PubMed

    Cruz, Roberto de la; Guerrero, Pilar; Spill, Fabian; Alarcón, Tomás

    2016-10-21

    We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age (i.e. time elapsed since they were born). The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. Once the birth rate is determined, we formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size (carrying capacity): cells consume oxygen which in turn fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. Besides the fact that this simple behaviour emerges from a rather complex model, this allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance

  14. Hierarchical mean-field approach to the J1-J2 Heisenberg model on a square lattice

    NASA Astrophysics Data System (ADS)

    Isaev, Leonid; Ortiz, Gerardo; Dukelsky, Jorge

    2009-03-01

    We study the quantum phase diagram and excitation spectrum of the frustrated J1-J2 spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field approach, at the heart of which lies the idea of identifying relevant degrees of freedom, is developed. Thus, by performing educated, manifestly symmetry preserving mean-field approximations, we unveil fundamental properties of the system. We then compare various coverings of the square lattice with plaquettes, dimers and other degrees of freedom, and show that only the symmetric plaquette covering, which reproduces the original Bravais lattice, leads to the known phase diagram. The intermediate quantum paramagnetic phase is shown to be a (singlet) plaquette crystal, connected with the neighbouring N'eel phase by a continuous phase transition. We also introduce fluctuations around the hierarchical mean-field solutions, and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap, which closes in the N'eel and columnar phases. Our results suggest that the quantum phase transition between N'eel and paramagnetic phases can be properly described within the Ginzburg-Landau-Wilson paradigm.

  15. Hierarchical mean-field approach to the J1-J2 Heisenberg model on a square lattice

    NASA Astrophysics Data System (ADS)

    Isaev, L.; Ortiz, G.; Dukelsky, J.

    2009-01-01

    We study the quantum phase diagram and excitation spectrum of the frustrated J1-J2 spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field approach, at the heart of which lies the idea of identifying relevant degrees of freedom, is developed. Thus, by performing educated, manifestly symmetry-preserving mean-field approximations, we unveil fundamental properties of the system. We then compare various coverings of the square lattice with plaquettes, dimers, and other degrees of freedom, and show that only the symmetric plaquette covering, which reproduces the original Bravais lattice, leads to the known phase diagram. The intermediate quantum paramagnetic phase is shown to be a (singlet) plaquette crystal, connected with the neighboring Néel phase by a continuous phase transition. We also introduce fluctuations around the hierarchical mean-field solutions, and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap, which closes in the Néel and columnar phases. Our results suggest that the quantum phase transition between Néel and paramagnetic phases can be properly described within the Ginzburg-Landau-Wilson paradigm.

  16. Continuous Time Finite State Mean Field Games

    SciTech Connect

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

    2013-08-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2012-08-01

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

  18. Periodic mean-field solutions and the spectra of discrete bosonic fields: Trace formula for Bose-Hubbard models.

    PubMed

    Engl, Thomas; Urbina, Juan Diego; Richter, Klaus

    2015-12-01

    We consider the many-body spectra of interacting bosonic quantum fields on a lattice in the semiclassical limit of large particle number N. We show that the many-body density of states can be expressed as a coherent sum over oscillating long-wavelength contributions given by periodic, nonperturbative solutions of the, typically nonlinear, wave equation of the classical (mean-field) limit. To this end, we construct the semiclassical approximation for both the smooth and oscillatory parts of the many-body density of states in terms of a trace formula starting from the exact path integral form of the propagator between many-body quadrature states. We therefore avoid the use of a complexified classical limit characteristic of the coherent state representation. While quantum effects such as vacuum fluctuations and gauge invariance are exactly accounted for, our semiclassical approach captures quantum interference and therefore is valid well beyond the Ehrenfest time where naive quantum-classical correspondence breaks down. Remarkably, due to a special feature of harmonic systems with incommensurable frequencies, our formulas are generically valid also in the free-field case of noninteracting bosons. PMID:26764774

  19. Three-site Bose-Hubbard model subject to atom losses: Boson-pair dissipation channel and failure of the mean-field approach

    SciTech Connect

    Shchesnovich, V. S.; Mogilevtsev, D. S.

    2010-10-15

    We employ the perturbation series expansion for derivation of the reduced master equations for the three-site Bose-Hubbard model subject to strong atom losses from the central site. The model describes a condensate trapped in a triple-well potential subject to externally controlled removal of atoms. We find that the {pi}-phase state of the coherent superposition between the side wells decays via two dissipation channels, the single-boson channel (similar to the externally applied dissipation) and the boson-pair channel. The quantum derivation is compared to the classical adiabatic elimination within the mean-field approximation. We find that the boson-pair dissipation channel is not captured by the mean-field model, whereas the single-boson channel is described by it. Moreover, there is a matching condition between the zero-point energy bias of the side wells and the nonlinear interaction parameter which separates the regions where either the single-boson or the boson-pair dissipation channel dominate. Our results indicate that the M-site Bose-Hubbard models, for M>2, subject to atom losses may require an analysis which goes beyond the usual mean-field approximation for correct description of their dissipative features. This is an important result in view of the recent experimental works on the single-site addressability of condensates trapped in optical lattices.

  20. Information geometry of mean-field approximation.

    PubMed

    Tanaka, T

    2000-08-01

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

  1. Superconductivity in the single-band Hubbard model: Mean-field treatment of slave-boson pairing

    SciTech Connect

    Kopp, T.; Seco, F.J.; Schiller, S.; Woelfle, P.

    1988-12-01

    We investigate the possibility of superconductivity in the large-U limit of the Hubbard model near half filling, using a slave-boson representation. The local constraint is treated in a novel way, incorporating short-range fluctuations in addition to the global constraint. We find slave-boson pairing and a superconducting extended s-wave phase at hole concentrations delta above 4% and below 32%.

  2. Equivalence between the semirelativistic limit of the Dirac-Maxwell equations and the Breit-Pauli model in the mean-field approximation

    NASA Astrophysics Data System (ADS)

    Hinschberger, Y.; Dixit, A.; Manfredi, G.; Hervieux, P.-A.

    2015-01-01

    We demonstrate the equivalence between (i) the semirelativistic limit (up to second order in the inverse of the speed of light) of the self-consistent Dirac-Maxwell equations and (ii) the Breit-Pauli equations in the mean-field (Hartree-like) approximation. We explain how the charge and current densities that act as sources in the Dirac-Maxwell equations are related to the microscopic two-electron interactions of the Breit-Pauli model (spin orbit, spin-other-orbit, and spin-spin). The key role played by the second-order corrections to the charge density is clarified.

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

    PubMed

    Yamaguchi, Yoshiyuki Y

    2011-07-01

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

  4. Statics and dynamics of the ten-state mean-field Potts glass model: a Monte Carlo study

    NASA Astrophysics Data System (ADS)

    Brangian, Claudio; Kob, Walter; Binder, Kurt

    2002-01-01

    We investigate by means of Monte Carlo simulations the fully connected p-state Potts model for different system sizes in order to see how the static and dynamic properties of a finite model compare with the, exactly known, behaviour of the system in the thermodynamic limit. Using p = 10 we are able to study the equilibrium dynamics for system sizes as large as N = 2560. We find that the static quantities, such as the energy, the entropy, the spin glass susceptibility as well as the distribution of the order parameter P(q) show very strong finite-size effects. From P(q) we calculate the fourth-order cumulant g4(N,T) and the Guerra parameter G(N,T) and show that these quantities cannot be used to locate the static transition temperature for the system sizes investigated. Also the spin-autocorrelation function C(t) shows strong finite-size effects in that it does not show a plateau even for temperatures around the dynamical critical temperature TD. We show that the dependence on N and T of the α-relaxation time can be understood by means of a dynamical finite-size scaling ansatz. C(t) does not obey the time-temperature superposition principle for temperatures around TD, but does so for significantly lower T. Finally we study the relaxation dynamics of the individual spins and show that their dependence on time depends strongly on the chosen spin, i.e. that the system is dynamically very heterogeneous, which explains the non-exponentiality of C(t).

  5. Scale-free memory model for multiagent reinforcement learning. Mean field approximation and rock-paper-scissors dynamics

    NASA Astrophysics Data System (ADS)

    Lubashevsky, I.; Kanemoto, S.

    2010-07-01

    A continuous time model for multiagent systems governed by reinforcement learning with scale-free memory is developed. The agents are assumed to act independently of one another in optimizing their choice of possible actions via trial-and-error search. To gain awareness about the action value the agents accumulate in their memory the rewards obtained from taking a specific action at each moment of time. The contribution of the rewards in the past to the agent current perception of action value is described by an integral operator with a power-law kernel. Finally a fractional differential equation governing the system dynamics is obtained. The agents are considered to interact with one another implicitly via the reward of one agent depending on the choice of the other agents. The pairwise interaction model is adopted to describe this effect. As a specific example of systems with non-transitive interactions, a two agent and three agent systems of the rock-paper-scissors type are analyzed in detail, including the stability analysis and numerical simulation. Scale-free memory is demonstrated to cause complex dynamics of the systems at hand. In particular, it is shown that there can be simultaneously two modes of the system instability undergoing subcritical and supercritical bifurcation, with the latter one exhibiting anomalous oscillations with the amplitude and period growing with time. Besides, the instability onset via this supercritical mode may be regarded as “altruism self-organization”. For the three agent system the instability dynamics is found to be rather irregular and can be composed of alternate fragments of oscillations different in their properties.

  6. Constraining relativistic models through heavy ion collisions

    SciTech Connect

    Menezes, D. P.; Providencia, C.; Chiapparini, M.; Bracco, M. E.; Delfino, A.; Malheiro, M.

    2007-12-15

    Relativistic models can be successfully applied to the description of compact star properties in nuclear astrophysics as well as to nuclear matter and finite nuclei properties, these studies taking place at low and moderate temperatures. Nevertheless, all results are model dependent, and so far it is unclear whether some of them should be discarded. Moreover, in the regime of hot hadronic matter, very few calculations exist using these relativistic models, in particular when applied to particle yields in heavy ion collisions. A very important investigation is the simulation of a supernova explosion that is based on the construction of an adequate equation of state that needs to be valid within very large ranges of temperatures (0 to 100 MeV at least) and densities (very low to ten times the nuclear saturation density at least). In the present work, we comment on the known constraints that can help the selection of adequate models in this wide regime and investigate the main differences that arise when the particle production during a Au+Au collision at the BNL Relativistic Heavy Ion Collider is calculated with different relativistic models. We conclude that most of the models investigated in the present work give a very good overall description of the data and make predictions for not yet measured particle ratios.

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

    NASA Astrophysics Data System (ADS)

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

    2015-01-01

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

  8. Anomalous diffusion in the evolution of soccer championship scores: Real data, mean-field analysis, and an agent-based model

    NASA Astrophysics Data System (ADS)

    da Silva, Roberto; Vainstein, Mendeli H.; Gonçalves, Sebastián; Paula, Felipe S. F.

    2013-08-01

    Statistics of soccer tournament scores based on the double round robin system of several countries are studied. Exploring the dynamics of team scoring during tournament seasons from recent years we find evidences of superdiffusion. A mean-field analysis results in a drift velocity equal to that of real data but in a different diffusion coefficient. Along with the analysis of real data we present the results of simulations of soccer tournaments obtained by an agent-based model which successfully describes the final scoring distribution [da Silva , Comput. Phys. Commun.CPHCBZ0010-465510.1016/j.cpc.2012.10.030 184, 661 (2013)]. Such model yields random walks of scores over time with the same anomalous diffusion as observed in real data.

  9. A stochastically forced time delay solar dynamo model: Self-consistent recovery from a maunder-like grand minimum necessitates a mean-field alpha effect

    SciTech Connect

    Hazra, Soumitra; Nandy, Dibyendu; Passos, Dário E-mail: dariopassos@ist.utl.pt

    2014-07-01

    Fluctuations in the Sun's magnetic activity, including episodes of grand minima such as the Maunder minimum have important consequences for space and planetary environments. However, the underlying dynamics of such extreme fluctuations remain ill-understood. Here, we use a novel mathematical model based on stochastically forced, non-linear delay differential equations to study solar cycle fluctuations in which time delays capture the physics of magnetic flux transport between spatially segregated dynamo source regions in the solar interior. Using this model, we explicitly demonstrate that the Babcock-Leighton poloidal field source based on dispersal of tilted bipolar sunspot flux, alone, cannot recover the sunspot cycle from a grand minimum. We find that an additional poloidal field source effective on weak fields—e.g., the mean-field α effect driven by helical turbulence—is necessary for self-consistent recovery of the sunspot cycle from grand minima episodes.

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

    SciTech Connect

    Hoang Sy Than; Nguyen Van Giai

    2009-12-15

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

  11. Spatial Correlation in the Three-band Copper Oxide Model: Dynamical Mean-field Study with Configuration Interaction Based Impurity Solver

    NASA Astrophysics Data System (ADS)

    Go, Ara; Millis, Andrew J.

    2014-03-01

    The three-band copper oxide model is studied using the single-site and four-site dynamical mean-field theory with configuration interaction based impurity solver. Comparison of the single and four site approximations shows that short ranged antiferromagnetic correlations are crucial to the physics. In the undoped case, they increase the gap size, shift the metal-insulator phase boundary and enhance the conductivity at the gap edge. The relation of antiferromagnetism and the pseudogap is discussed for the doped case. The new solver permits the inclusion of more bath orbitals which are crucial for accurate studies of spectral properties near the gap edge. This work was supported by the US Department of Energy under Grants No. DOE FG02-04ER46169 and DE-SC0006613.

  12. Spinodal instabilities and the distillation effect in relativistic hadronic models

    SciTech Connect

    Avancini, S. S.; Menezes, D. P.; Brito, L.; Provide circumflex ncia, C.; Chomaz, Ph.

    2006-08-15

    Liquid-gas phase transitions in asymmetric nuclear matter give rise to a distillation effect that corresponds to the formation of droplets of high-density symmetric matter in a background of a neutron gas possibly with a very small fraction of protons. In the present work we test the model dependence of this effect. We study the spinodal instabilities of asymmetric nuclear matter within six different mean-field relativistic models with both constant and density-dependent coupling parameters. We also consider the effects of introducing the {delta} meson and the nonlinear {omega}-{rho} coupling. It is shown that the distillation effect within density-dependent models is not so efficient and is comparable to results obtained for nonrelativistic models. Thermodynamical instabilities of nuclear matter neutralized by electrons as found in stellar matter are also investigated. The high Fermi energy of electrons completely erases the instability of density-dependent models. The other models still show a small region of instability but the distillation effect completely disappears because the electron presence freezes the proton fluctuations.

  13. A mean field approach to watershed hydrology

    NASA Astrophysics Data System (ADS)

    Bartlett, Mark; Porporato, Amilcare

    2016-04-01

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

  14. Quantum phase transition in the spherical mean-field plus quadrupole-quadrupole and pairing model in a single-j shell

    NASA Astrophysics Data System (ADS)

    Li, Bo; Pan, Feng; Draayer, J. P.

    2016-04-01

    The quantum-phase-transitional behavior of the spherical shell-model mean field plus the geometric quadrupole-quadrupole and standard pairing model within a single-j shell is analyzed in detail. Various quantities, such as low-lying energy levels, some typical energy ratios, the overlaps of the excited states with those of the corresponding limiting cases, B (E 2 ) values and electric quadrupole moments of some low-lying states and their ratios, as functions of the control parameter of the model in a j =15 /2 shell are calculated as an example, in which only a crossover occurs due to the Pauli exclusion. The results show that there are noticeable changes within the crossover region of the rotation-like to the pair-excitation (superconducting) phase transition, especially in the half-filling case. As an application to realistic nuclear systems, a chain of isotones 212Rn-213Fr-214Ra-215Ac is chosen to be described by the model with valence protons in the 1 h9 /2 shell. As far as the low-lying energy levels, the experimentally observed B (E 2 ) values, and the electric quadrupole moment within the yrast band are concerned, these nuclei seem fitted reasonably well. The results indicate that these nuclei are all within the rotation-like to the pair-excitation phase transition near the crossover point.

  15. Shell corrections, magic numbers, and mean field

    SciTech Connect

    Denisov, V. Yu.

    2007-02-15

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

  16. Systematics of light nuclei in a relativistic model

    SciTech Connect

    Price, C.E.

    1988-01-01

    The results of relativistic mean field calculations for non-spherical nuclei are presented and discussed. The need for non-linear scalar meson self-couplings in order to describe the properties of s-d shell nuclei is emphasized along with the importance of self-consistency in calculations of magnetic moments of odd-mass nuclei. 16 refs., 3 figs., 2 tabs.

  17. "Phase diagram" of a mean field game

    NASA Astrophysics Data System (ADS)

    Swiecicki, Igor; Gobron, Thierry; Ullmo, Denis

    2016-01-01

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

  18. A general relativistic model for free-fall absolute gravimeters

    NASA Astrophysics Data System (ADS)

    Tan, Yu-Jie; Shao, Cheng-Gang; Li, Jia; Hu, Zhong-Kun

    2016-04-01

    Although the relativistic manifestations of gravitational fields in gravimetry were first studied 40 years ago, the relativistic effects combined with free-fall absolute gravimeters have rarely been considered. In light of this, we present a general relativistic model for free-fall absolute gravimeters in a local-Fermi coordinates system, where we focus on effects related to the measuring devices: relativistic transverse Doppler effects, gravitational redshift effects and Earth’s rotation effects. Based on this model, a general relativistic expression of the measured gravity acceleration is obtained.

  19. Finite nuclei in relativistic models with a light chiral scalar meson

    SciTech Connect

    Serot, B.D.; Furnstahl, R.J.

    1993-10-01

    Relativistic chiral models with a light scalar, meson appear to provide an economical marriage of successful relativistic mean-field theories and chiral symmetry. In these models, the scalar meson serves as both the chiral partner of the pion and the mediator of the intermediate-range nucleon-nucleon (NN) attraction. However, while some of these models can reproduce the empirical nuclear matter saturation point, they fail to reproduce observed properties of finite nuclei, such as spin-orbit splittings, shell structure, charge densities, and surface energetics. There deficiencies imply that this realization of chiral symmetry is incorrect. An alternative scenario for chiral hadronic models, which features a heavy chiral scalar and dynamical generation of the NN attraction, is discussed.

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

    SciTech Connect

    Edison, John R.; Monson, Peter A.

    2014-07-14

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

  1. Periodic ordering of clusters and stripes in a two-dimensional lattice model. I. Ground state, mean-field phase diagram and structure of the disordered phases

    SciTech Connect

    Pekalski, J.; Ciach, A.; Almarza, N. G.

    2014-03-21

    The short-range attraction and long-range repulsion between nanoparticles or macromolecules can lead to spontaneous pattern formation on solid surfaces, fluid interfaces, or membranes. In order to study the self-assembly in such systems we consider a triangular lattice model with nearest-neighbor attraction and third-neighbor repulsion. At the ground state of the model (T = 0) the lattice is empty for small values of the chemical potential μ, and fully occupied for large μ. For intermediate values of μ periodically distributed clusters, bubbles, or stripes appear if the repulsion is sufficiently strong. At the phase coexistences between the vacuum and the ordered cluster phases and between the cluster and the lamellar (stripe) phases the entropy per site does not vanish. As a consequence of this ground state degeneracy, disordered fluid phases consisting of clusters or stripes are stable, and the surface tension vanishes. For T > 0 we construct the phase diagram in the mean-field approximation and calculate the correlation function in the self-consistent Brazovskii-type field theory.

  2. A New Relativistic Jet Model of Blazars

    NASA Astrophysics Data System (ADS)

    Webb, James; Benitez, Erika; Howard, Emily

    1998-11-01

    The subclass of Active galaxies called Blazars encompass the most intrinsically luminous and rapidly variable sources known to astrophysicists. Attempts to model these sources has largely been frustrated due in part to observational difficulties, but also due to the lack of theoretical models capable of explaining the different characteristics of the observed sources. Leading candidate models all incorporate a massive, rotating black hole which is accreting galactic material, with some of this material being ejected out the ratational axis of the hole in the form of relativistically expanding jets. These jets are thought to emit energy via the synchrotron process across the entire spectrum from radio frequences all the way through the GEV (sometimes TEV) gamma-ray frequencies. Attempts to model these sources with single relativistic jets has proven difficult. We present a new model which features concentric interacting jets that do a much better job of explaining the types of Blazars we observe. We also discuss ways of testing this new model against multifreuqency observations.

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

    NASA Astrophysics Data System (ADS)

    Sato, Toshihiro; Tsunetsugu, Hirokazu

    2016-08-01

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

  4. Magnetic fluctuations and dynamics in the vicinity of quantum spin liquids: Cluster dynamical mean-field study of the Kitaev model

    NASA Astrophysics Data System (ADS)

    Yoshitake, Junki; Nasu, Joji; Motome, Yukitoshi

    The quantum spin liquid, which does not show any long-range ordering down to the lowest temperature, has attracted broad interest as a new quantum state of matter. Since the ground state of the Kitaev model was shown to be a quantum spin liquid in two dimensions, there has been an explosion in both theoretical and experimental studies. Nevertheless, dynamical properties at finite temperatures remain a challenge, despite the relevance to analysis of recent experiments for Ir and Ru compounds. In this contribution, we address this problem by using the cluster dynamical mean-field approximation, which we newly develop on the basis of the Majorana fermion representation. Using the continuous-time quantum Monte Carlo method for the impurity solver, we calculate the magnetic susceptibility, dynamical spin structure factor, and relaxation time in the nuclear magnetic resonance. We find that these quantities show peculiar temperature dependences in the paramagnetic state when approaching the quantum spin liquid by decreasing temperature, which reflects the fractionalization of quantum spins. We will discuss the results while changing the anisotropy and sign (ferro/antiferro) of the exchange interactions, in comparison with experiments.

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

    PubMed

    Ciach, A; Góźdź, W T; Stell, G

    2007-05-01

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

  6. Interacting Turing-Hopf Instabilities Drive Symmetry-Breaking Transitions in a Mean-Field Model of the Cortex: A Mechanism for the Slow Oscillation

    NASA Astrophysics Data System (ADS)

    Steyn-Ross, Moira L.; Steyn-Ross, D. A.; Sleigh, J. W.

    2013-04-01

    Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (≲1Hz) similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial) symmetry-breaking bifurcation that is modulated by a Hopf (temporal) instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from “wake” to “coma.” In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural sleep and comment on the

  7. The Mean-Field Flux Pinning Theory

    NASA Astrophysics Data System (ADS)

    Stejic, George

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

  8. Modelling of relativistic laser-plasma interactions

    NASA Astrophysics Data System (ADS)

    Berwick, Stuart James

    In order to characterise the propagation and stability of linearly polarised laser pulses of arbitrary intensity interacting with underdense plasma, a one-dimensional, fully relativistic, covariant electron fluid model is derived. As a first step, the model is Lorentz transformed into a frame moving with the group velocity of the laser pulse. A linear instability analysis is undertaken which generates an infinite hierarchy of homogeneous mode-coupling equations describing the decay of the laser pump via stimulated Raman forward scattering (SRFS), stimulated Raman back scattering (SRBS) and the relativistic modulational instability (RMI). SRFS and RMI are seen to merge into a hybrid instability at high intensities (1>1018Wcm-2) and a 6-wave analysis (rather than the conventional 3 or 4-wave) is required to accurately predict growth. Next, an Eulerian fluid code is developed in order to evolve the full non- linear equations. The method of characteristics is used to integrate the electromagnetic wave equation and a predictor-corrector algorithm is used to integrate the equations of continuity and momentum. After testing, this code is used to simulate the propagation and stability of ultra-short (<200fs), 'table-top' and cos2 modulated laser pulses of relativistic intensities in underdense plasma. Comparison is made to the predictions of the dispersion relation and growth rates obtained in each case are reconciled. The spatiotemporal behaviour is discussed with reference to the results of a 3-wave WKB model of the interaction. The importance of seeding mechanisms, pulse shape and relativity on the evolution of the instabilities is also discussed.

  9. Finite nuclei in relativistic models with a light chiral scalar meson

    SciTech Connect

    Furnstahl, R.J. ); Serot, B.D. )

    1993-05-01

    Relativistic chiral models with a light scalar meson appear to provide an economical marriage of successful relativistic mean-field theories and chiral symmetry. The scalar meson serves as both the chiral partner of the pion and the mediator of the intermediate-range nucleon-nucleon ([ital NN]) attraction. However, while some of these models can reproduce the empirical nuclear matter saturation point, they fail to reproduce observed properties of finite nuclei, such as spin-orbit splittings, shell structure, charge densities, and surface energetics. These deficiencies imply that this realization of chiral symmetry is incorrect. An alternative scenario, which features a heavy chiral scalar and dynamical generation of the [ital NN] attraction, is discussed.

  10. Relativistic interactions and realistic applications

    SciTech Connect

    Hoch, T.; Madland, D.; Manakos, P.; Mannel, T.; Nikolaus, B.A.; Strottman, D. |

    1992-12-31

    A four-fermion-coupling Lagrangian (relativistic Skyrme-type) interaction has been proposed for relativistic nuclear structure calculations. This interaction, which has the merit of simplicity, is from the outset tailored as an effective interaction for relativistic Hartree-Fock calculations. Various extensions of such a model are discussed and compared with Walecka`s meson-nucleon mean field approach. We also present results of the calculation of nuclear ground state properties with an extended (density dependent) version of the four fermion interaction in a relativistic Hartree-Fock approximation.

  11. Exact evolution of discrete relativistic cosmological models

    SciTech Connect

    Clifton, Timothy; Tavakol, Reza; Gregoris, Daniele; Rosquist, Kjell E-mail: danielegregoris@libero.it E-mail: r.tavakol@qmul.ac.uk

    2013-11-01

    We study the effects of inhomogeneities on the evolution of the Universe, by considering a range of cosmological models with discretized matter content. This is done using exact and fully relativistic methods that exploit the symmetries in and about submanifolds of spacetimes that themselves possess no continuous global symmetries. These methods allow us to follow the evolution of our models throughout their entire history, far beyond what has previously been possible. We find that while some space-like curves collapse to anisotropic singularities in finite time, others remain non-singular forever. The resulting picture is of a cosmological spacetime in which some behaviour remains close to Friedmann-like, while other behaviours deviate radically. In particular, we find that large-scale acceleration is possible without any violation of the energy conditions.

  12. Relativistic constituent quark model with infrared confinement

    SciTech Connect

    Branz, Tanja; Faessler, Amand; Gutsche, Thomas; Lyubovitskij, Valery E.; Ivanov, Mikhail A.; Koerner, Juergen G.

    2010-02-01

    We refine the relativistic constituent quark model developed in our previous papers to include the confinement of quarks. It is done, first, by introducing the scale integration in the space of {alpha} parameters, and, second, by cutting this scale integration on the upper limit which corresponds to an infrared cutoff. In this manner one removes all possible thresholds present in the initial quark diagram. The cutoff parameter is taken to be the same for all physical processes. We adjust other model parameters by fitting the calculated quantities of the basic physical processes to available experimental data. As an application, we calculate the electromagnetic form factors of the pion and the transition form factors of the {omega} and {eta} Dalitz decays.

  13. Mean-field sparse optimal control

    PubMed Central

    Fornasier, Massimo; Piccoli, Benedetto; Rossi, Francesco

    2014-01-01

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

  14. One Model of Singular Relativistic Lagrangian

    NASA Astrophysics Data System (ADS)

    Laserra, E.; Strianese, M.; Pavlotsky, I. P.

    The so-called no-interaction theorem of D.G. Currie, T.F. Jordan, E.C. Sudarshan, H. Leutwyler, G. Marmo and N. Mukunda makes it possible to construct relativistic quasiclassical particle dynamics in the post-Galilean approximation only. It is obtained that in this approximation the Lagrangians are singular on some surfaces of the phase space. These peculiarities have different physical and mathematical nature from the ones studied by P.M.A. Dirac, where Hessians vanish in the whole phase-space. The dynamical properties are essentially peculiar on the studied singular surfaces. These properties, in our opinion, can be related with some physical phenomena. In the present paper the general situation is first described. As the whole problem is large and difficult we examined in detail just typical one- and two-dimensional models in the second part of the paper.

  15. Solutions to the relativistic precession model

    NASA Astrophysics Data System (ADS)

    Ingram, Adam; Motta, Sara

    2014-11-01

    The relativistic precession model (RPM) can be used to obtain a precise measurement of the mass and spin of a black hole when the appropriate set of quasi-periodic oscillations is detected in the power-density spectrum of an accreting black hole. However, in previous studies, the solution of the RPM equations could be obtained only through numerical methods at a price of an intensive computational effort. Here, we demonstrate that the RPM system of equations can be solved analytically, drastically reducing the computational load, now limited to the Monte Carlo simulation necessary to estimate the uncertainties. The analytical method not only provides an easy solution to the RPM system when three oscillations are detected, but in all the cases where the detection of two simultaneous oscillations is coupled with an independent mass measurement. We also present a computationally inexpensive method to place limits on the black hole mass and spin when only two oscillations are observed.

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

    NASA Astrophysics Data System (ADS)

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

    2013-09-01

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

  17. Kinetic analysis of thermally relativistic flow with dissipation. II. Relativistic Boltzmann equation versus its kinetic models

    NASA Astrophysics Data System (ADS)

    Yano, Ryosuke; Matsumoto, Jun; Suzuki, Kojiro

    2011-06-01

    Thermally relativistic flow with dissipation was analyzed by solving the rarefied supersonic flow of thermally relativistic matter around a triangle prism by Yano and Suzuki [Phys. Rev. DPRVDAQ1550-7998 83, 023517 (2011)10.1103/PhysRevD.83.023517], where the Anderson-Witting (AW) model was used as a solver. In this paper, we solve the same problem, which was analyzed by Yano and Suzuki, using the relativistic Boltzmann equation (RBE). To solve the RBE, the conventional direct simulation Monte Carlo method for the nonrelativistic Boltzmann equation is extended to a new direct simulation Monte Carlo method for the RBE. Additionally, we solve the modified Marle (MM) model proposed by Yano-Suzuki-Kuroda for comparisons. The solution of the thermally relativistic shock layer around the triangle prism obtained using the relativistic Boltzmann equation is considered by focusing on profiles of macroscopic quantities, such as the density, velocity, temperature, heat flux and dynamic pressure along the stagnation streamline (SSL). Differences among profiles of the number density, velocity and temperature along the SSL obtained using the RBE, the AW and MM. models are described in the framework of the relativistic Navier-Stokes-Fourier law. Finally, distribution functions on the SSL obtained using the RBE are compared with those obtained using the AW and MM models. The distribution function inside the shock wave obtained using the RBE does not indicate a bimodal form, which is obtained using the AW and MM models, but a smooth deceleration of thermally relativistic matter inside a shock wave.

  18. Lattice Boltzmann model for resistive relativistic magnetohydrodynamics.

    PubMed

    Mohseni, F; Mendoza, M; Succi, S; Herrmann, H J

    2015-08-01

    In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1/2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere. PMID:26382548

  19. Lattice Boltzmann model for resistive relativistic magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Mohseni, F.; Mendoza, M.; Succi, S.; Herrmann, H. J.

    2015-08-01

    In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1 / 2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere.

  20. Mean Field Theory for Nonequilibrium Network Reconstruction

    NASA Astrophysics Data System (ADS)

    Roudi, Yasser; Hertz, John

    2011-01-01

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

  1. Optical-model potential in a relativistic quantum field model

    NASA Astrophysics Data System (ADS)

    Jaminon, M.; Mahaux, C.; Rochus, P.

    1980-11-01

    The average nucleon-nucleus potential at low and medium energy is investigated in the framework of a relativistic quantum field model. Using the same input parameters as Brockmann in his recent study of nuclear ground states, we calculate the self-consistent relativistic Hartree potential at positive energy in the case of infinite nuclear matter and of 16O and 40Ca. This potential is the sum of a scalar operator and of the fourth component of a vector operator. We construct its Schrödinger-equivalent potential by eliminating the small component of the Dirac spinor. The central part of this Schrödinger-equivalent potential is in fair agreement with empirical values at low and intermediate energy. Particular attention is paid to the intermediate energy domain, in which the calculated potential is repulsive in the nuclear interior and attractive at the nuclear surface. This is in keeping with some empirical evidence and is similar to results found in the framework of the nonrelativistic Brueckner-Hartree-Fock approximation. The spin-orbit potential of the relativistic Hartree model is also in good agreement with empirical values. NUCLEAR REACTIONS Calculated average nuclear field of nuclear matter, 16O and 40Ca at positive energy from relativistic Hartree approximation.

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

    SciTech Connect

    Lavagno, A.

    2010-04-15

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

  3. Chemical potential beyond the quasiparticle mean field

    SciTech Connect

    Dinh Dang, N.; Hung, N. Quang

    2010-03-15

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

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

    SciTech Connect

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

    2008-05-15

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

  5. Global relativistic folding optical potential and the relativistic Green's function model

    NASA Astrophysics Data System (ADS)

    Ivanov, M. V.; Vignote, J. R.; Álvarez-Rodríguez, R.; Meucci, A.; Giusti, C.; Udías, J. M.

    2016-07-01

    Optical potentials provide critical input for calculations on a wide variety of nuclear reactions, in particular, for neutrino-nucleus reactions, which are of great interest in the light of the new neutrino oscillation experiments. We present the global relativistic folding optical potential (GRFOP) fits to elastic proton scattering data from 12C nucleus at energies between 20 and 1040 MeV. We estimate observables, such as the differential cross section, the analyzing power, and the spin rotation parameter, in elastic proton scattering within the relativistic impulse approximation. The new GRFOP potential is employed within the relativistic Green's function model for inclusive quasielastic electron scattering and for (anti)neutrino-nucleus scattering at MiniBooNE kinematics.

  6. Machine Learning for Dynamical Mean Field Theory

    NASA Astrophysics Data System (ADS)

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

    2014-03-01

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

  7. Relativistic Landau models and generation of fuzzy spheres

    NASA Astrophysics Data System (ADS)

    Hasebe, Kazuki

    2016-07-01

    Noncommutative geometry naturally emerges in low energy physics of Landau models as a consequence of level projection. In this work, we proactively utilize the level projection as an effective tool to generate fuzzy geometry. The level projection is specifically applied to the relativistic Landau models. In the first half of the paper, a detail analysis of the relativistic Landau problems on a sphere is presented, where a concise expression of the Dirac-Landau operator eigenstates is obtained based on algebraic methods. We establish SU(2) “gauge” transformation between the relativistic Landau model and the Pauli-Schrödinger nonrelativistic quantum mechanics. After the SU(2) transformation, the Dirac operator and the angular momentum operators are found to satisfy the SO(3, 1) algebra. In the second half, the fuzzy geometries generated from the relativistic Landau levels are elucidated, where unique properties of the relativistic fuzzy geometries are clarified. We consider mass deformation of the relativistic Landau models and demonstrate its geometrical effects to fuzzy geometry. Super fuzzy geometry is also constructed from a supersymmetric quantum mechanics as the square of the Dirac-Landau operator. Finally, we apply the level projection method to real graphene system to generate valley fuzzy spheres.

  8. Fractional Relativistic Yamaleev Oscillator Model and Its Dynamical Behaviors

    NASA Astrophysics Data System (ADS)

    Luo, Shao-Kai; He, Jin-Man; Xu, Yan-Li; Zhang, Xiao-Tian

    2016-07-01

    In the paper we construct a new kind of fractional dynamical model, i.e. the fractional relativistic Yamaleev oscillator model, and explore its dynamical behaviors. We will find that the fractional relativistic Yamaleev oscillator model possesses Lie algebraic structure and satisfies generalized Poisson conservation law. We will also give the Poisson conserved quantities of the model. Further, the relation between conserved quantities and integral invariants of the model is studied and it is proved that, by using the Poisson conserved quantities, we can construct integral invariants of the model. Finally, the stability of the manifold of equilibrium states of the fractional relativistic Yamaleev oscillator model is studied. The paper provides a general method, i.e. fractional generalized Hamiltonian method, for constructing a family of fractional dynamical models of an actual dynamical system.

  9. Coulomb Glass: a Mean Field Study

    NASA Astrophysics Data System (ADS)

    Mandra, Salvatore; Palassini, Matteo

    2012-02-01

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

  10. Stochastic mean-field polycrystal plasticity methods

    NASA Astrophysics Data System (ADS)

    Tonks, Michael R.

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

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

    SciTech Connect

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

    2009-04-15

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

  12. Relativistic models for Gaia at the (cross)check-point

    NASA Astrophysics Data System (ADS)

    Bertone, S.; Le Poncin-Lafitte, C.; Crosta, M.; Vecchiato, A.; Minazzoli, O.; Angonin, M.-C.

    2013-11-01

    Given the extreme accuracy of modern space astrometry, a precise relativistic modeling of observations is required. Concerning light propagation, most approaches rely on the solution of the null-geodesic equations. However, another approach based on the Time Transfer Functions (TTF) can be used to define an astrometric observation using an integral-based method derived from the Synge World Function. The availability of several models, formulated in different and independent ways, is indeed a security against the presence of systematic errors in the analysis of future experimental results. It is the case of the forthcoming Gaia mission. In this work, we review the modeling of a Gaia-like astrometric observation using the TTF and two other approaches, namely the Gaia RElativistic Model (GREM) and the Relativistic Astrometric MODel (RAMOD), and we provide explicit relations between their characteristic quantities.

  13. Mean Field Analysis of Quantum Annealing Correction

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  14. Mean Field Analysis of Quantum Annealing Correction.

    PubMed

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

    2016-06-01

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

  15. Nonrelativistic approaches derived from point-coupling relativistic models

    SciTech Connect

    Lourenco, O.; Dutra, M.; Delfino, A.; Sa Martins, J. S.

    2010-03-15

    We construct nonrelativistic versions of relativistic nonlinear hadronic point-coupling models, based on new normalized spinor wave functions after small component reduction. These expansions give us energy density functionals that can be compared to their relativistic counterparts. We show that the agreement between the nonrelativistic limit approach and the Skyrme parametrizations becomes strongly dependent on the incompressibility of each model. We also show that the particular case A=B=0 (Walecka model) leads to the same energy density functional of the Skyrme parametrizations SV and ZR2, while the truncation scheme, up to order {rho}{sup 3}, leads to parametrizations for which {sigma}=1.

  16. Mean-Field Games for Marriage

    PubMed Central

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

    2014-01-01

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

  17. Deterministic Mean-Field Ensemble Kalman Filtering

    DOE PAGESBeta

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

    2016-05-03

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

  18. The relativistic feedback discharge model of terrestrial gamma ray flashes

    NASA Astrophysics Data System (ADS)

    Dwyer, Joseph R.

    2012-02-01

    As thunderclouds charge, the large-scale fields may approach the relativistic feedback threshold, above which the production of relativistic runaway electron avalanches becomes self-sustaining through the generation of backward propagating runaway positrons and backscattered X-rays. Positive intracloud (IC) lightning may force the large-scale electric fields inside thunderclouds above the relativistic feedback threshold, causing the number of runaway electrons, and the resulting X-ray and gamma ray emission, to grow exponentially, producing very large fluxes of energetic radiation. As the flux of runaway electrons increases, ionization eventually causes the electric field to discharge, bringing the field below the relativistic feedback threshold again and reducing the flux of runaway electrons. These processes are investigated with a new model that includes the production, propagation, diffusion, and avalanche multiplication of runaway electrons; the production and propagation of X-rays and gamma rays; and the production, propagation, and annihilation of runaway positrons. In this model, referred to as the relativistic feedback discharge model, the large-scale electric fields are calculated self-consistently from the charge motion of the drifting low-energy electrons and ions, produced from the ionization of air by the runaway electrons, including two- and three-body attachment and recombination. Simulation results show that when relativistic feedback is considered, bright gamma ray flashes are a natural consequence of upward +IC lightning propagating in large-scale thundercloud fields. Furthermore, these flashes have the same time structures, including both single and multiple pulses, intensities, angular distributions, current moments, and energy spectra as terrestrial gamma ray flashes, and produce large current moments that should be observable in radio waves.

  19. Local excitations in mean-field spin glasses

    NASA Astrophysics Data System (ADS)

    Krzakala, F.; Parisi, G.

    2004-06-01

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

  20. Relativistic reflection: Review and recent developments in modeling

    NASA Astrophysics Data System (ADS)

    Dauser, T.; García, J.; Wilms, J.

    2016-05-01

    Measuring relativistic reflection is an important tool to study the innermost regions of the an accreting black hole system. In the following we present a brief review on the different aspects contributing to the relativistic reflection. The combined approach is for the first time incorporated in the new ``relxill'' model. The advantages of this more self-consistent approach are briefly summarized. A special focus is put on the new definition of the intrinsic reflection fraction in the lamp post geometry, which allows to draw conclusions about the primary source of radiation in these system. Additionally the influence of the high energy cutoff of the primary source on the reflection spectrum is motivated, revealing the remarkable capabilities of constraining E_cut by measuring relativistic reflection spectra from NuSTAR, preferably with lower energy coverage.

  1. Modeling terrestrial gamma ray flashes produced by relativistic feedback discharges

    NASA Astrophysics Data System (ADS)

    Liu, Ningyu; Dwyer, Joseph R.

    2013-05-01

    This paper reports a modeling study of terrestrial gamma ray flashes (TGFs) produced by relativistic feedback discharges. Terrestrial gamma ray flashes are intense energetic radiation originating from the Earth's atmosphere that has been observed by spacecraft. They are produced by bremsstrahlung interactions of energetic electrons, known as runaway electrons, with air atoms. An efficient physical mechanism for producing large fluxes of the runaway electrons to make the TGFs is the relativistic feedback discharge, where seed runaway electrons are generated by positrons and X-rays, products of the discharge itself. Once the relativistic feedback discharge becomes self-sustaining, an exponentially increasing number of relativistic electron avalanches propagate through the same high-field region inside the thundercloud until the electric field is partially discharged by the ionization created by the discharge. The modeling results indicate that the durations of the TGF pulses produced by the relativistic feedback discharge vary from tens of microseconds to several milliseconds, encompassing all durations of the TGFs observed so far. In addition, when a sufficiently large potential difference is available in thunderclouds, a self-propagating discharge known as the relativistic feedback streamer can be formed, which propagates like a conventional positive streamer. For the relativistic feedback streamer, the positive feedback mechanism of runaway electron production by the positrons and X-rays plays a similar role as the photoionization for the conventional positive streamer. The simulation results of the relativistic feedback streamer show that a sequence of TGF pulses with varying durations can be produced by the streamer. The relativistic streamer may initially propagate with a pulsed manner and turn into a continuous propagation mode at a later stage. Milliseconds long TGF pulses can be produced by the feedback streamer during its continuous propagation. However

  2. Universality in bipartite mean field spin glasses

    NASA Astrophysics Data System (ADS)

    Genovese, Giuseppe

    2012-12-01

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

  3. Instabilities in the Mean Field Limit

    NASA Astrophysics Data System (ADS)

    Han-Kwan, Daniel; Nguyen, Toan T.

    2016-03-01

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

  4. Relativistic HD and MHD modelling for AGN jets

    NASA Astrophysics Data System (ADS)

    Keppens, R.; Porth, O.; Monceau-Baroux, R.; Walg, S.

    2013-12-01

    Relativistic hydro and magnetohydrodynamics (MHD) provide a continuum fluid description for plasma dynamics characterized by shock-dominated flows approaching the speed of light. Significant progress in its numerical modelling emerged in the last two decades; we highlight selected examples of modern grid-adaptive, massively parallel simulations realized by our open-source software MPI-AMRVAC (Keppens et al 2012 J. Comput. Phys. 231 718). Hydrodynamical models quantify how energy transfer from active galactic nuclei (AGN) jets to their surrounding interstellar/intergalactic medium (ISM/IGM) gets mediated through shocks and various fluid instability mechanisms (Monceau-Baroux et al 2012 Astron. Astrophys. 545 A62). With jet parameters representative for Fanaroff-Riley type-II jets with finite opening angles, we can quantify the ISM volumes affected by jet injection and distinguish the roles of mixing versus shock-heating in cocoon regions. This provides insight in energy feedback by AGN jets, usually incorporated parametrically in cosmological evolution scenarios. We discuss recent axisymmetric studies up to full 3D simulations for precessing relativistic jets, where synthetic radio maps can confront observations. While relativistic hydrodynamic models allow one to better constrain dynamical parameters like the Lorentz factor and density contrast between jets and their surroundings, the role of magnetic fields in AGN jet dynamics and propagation characteristics needs full relativistic MHD treatments. Then, we can demonstrate the collimating properties of an overal helical magnetic field backbone and study differences between poloidal versus toroidal field dominated scenarios (Keppens et al 2008 Astron. Astrophys. 486 663). Full 3D simulations allow one to consider the fate of non-axisymmetric perturbations on relativistic jet propagation from rotating magnetospheres (Porth 2013 Mon. Not. R. Astron. Soc. 429 2482). Self-stabilization mechanisms related to the detailed

  5. An Extended Magnetohydrodynamics Model for Relativistic Weakly Collisional Plasmas

    NASA Astrophysics Data System (ADS)

    Chandra, Mani; Gammie, Charles F.; Foucart, Francois; Quataert, Eliot

    2015-09-01

    Black holes that accrete far below the Eddington limit are believed to accrete through a geometrically thick, optically thin, rotationally supported plasma that we will refer to as a radiatively inefficient accretion flow (RIAF). RIAFs are typically collisionless in the sense that the Coulomb mean free path is large compared to {GM}/{c}2, and relativistically hot near the event horizon. In this paper we develop a phenomenological model for the plasma in RIAFs, motivated by the application to sources such as Sgr A* and M87. The model is derived using Israel–Stewart theory, which considers deviations up to second order from thermal equilibrium, but modified for a magnetized plasma. This leads to thermal conduction along magnetic field lines and a difference in pressure, parallel and perpendicular to the field lines (which is equivalent to anisotropic viscosity). In the non-relativistic limit, our model reduces to the widely used Braginskii theory of magnetized, weakly collisional plasmas. We compare our model to the existing literature on dissipative relativistic fluids, describe the linear theory of the plasma, and elucidate the physical meaning of the free parameters in the model. We also describe limits of the model when the conduction is saturated and when the viscosity implies a large pressure anisotropy. In future work, the formalism developed in this paper will be used in numerical models of RIAFs to assess the importance of non-ideal processes for the dynamics and radiative properties of slowly accreting black holes.

  6. Kinematic arguments against single relativistic shell models for GRBs

    NASA Technical Reports Server (NTRS)

    Fenimore, Edward E.; Ramirez, E.; Sumner, M. C.

    1997-01-01

    Two main types of models have been suggested to explain the long durations and multiple peaks of Gamma Ray Bursts (GRBs). In one, there is a very quick release of energy at a central site resulting in a single relativistic shell that produces peaks in the time history through its interactions with the ambient material. In the other, the central site sporadically releases energy over hundreds of seconds forming a peak with each burst of energy. The authors show that the average envelope of emission and the presence of gaps in GRBs are inconsistent with a single relativistic shell. They estimate that the maximum fraction of a single shell that can produce gamma-rays in a GRB with multiple peaks is 10(exp (minus)3), implying that single relativistic shells require 10(exp 3) times more energy than previously thought. They conclude that either the central site of a GRB must produce (approx)10(exp 51) erg/s(exp (minus)1) for hundreds of seconds, or the relativistic shell must have structure on a scales the order of (radical)(epsilon)(Gamma)(exp (minus)1), where (Gamma) is the bulk Lorentz factor ((approximately)10(exp 2) to 10(exp 3)) and (epsilon) is the efficiency.

  7. On Mean Field Limits for Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Boers, Niklas; Pickl, Peter

    2016-07-01

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

  8. Mean-Field Evolution of Fermionic Systems

    NASA Astrophysics Data System (ADS)

    Benedikter, Niels; Porta, Marcello; Schlein, Benjamin

    2014-11-01

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

  9. Relativistic modeling capabilities in PERSEUS extended MHD simulation code for HED plasmas

    SciTech Connect

    Hamlin, Nathaniel D.; Seyler, Charles E.

    2014-12-15

    We discuss the incorporation of relativistic modeling capabilities into the PERSEUS extended MHD simulation code for high-energy-density (HED) plasmas, and present the latest hybrid X-pinch simulation results. The use of fully relativistic equations enables the model to remain self-consistent in simulations of such relativistic phenomena as X-pinches and laser-plasma interactions. By suitable formulation of the relativistic generalized Ohm’s law as an evolution equation, we have reduced the recovery of primitive variables, a major technical challenge in relativistic codes, to a straightforward algebraic computation. Our code recovers expected results in the non-relativistic limit, and reveals new physics in the modeling of electron beam acceleration following an X-pinch. Through the use of a relaxation scheme, relativistic PERSEUS is able to handle nine orders of magnitude in density variation, making it the first fluid code, to our knowledge, that can simulate relativistic HED plasmas.

  10. Derivation of manifestly covariant quantum models for spinning relativistic particles

    NASA Astrophysics Data System (ADS)

    Marnelius, Robert; Mårtensson, Ulf

    1990-05-01

    A method to construct manifestly covariant models for relativistic spinning particles is given. The models involve manifestly covariant internal variables leading to discrete state spaces apart from the coordinate and momentum variables. The precise form of the models are extracted from the Bargmann-Wigner conditions on the Pauli-Lubanski operator, together with some consistency conditions. Several simple models are derived and analysed, some of which are new. Also manifestly conformally invariant models for particles with arbitrary spins are derived using a condition of Bracken and Jessup.

  11. Fully Relativistic Calculations for Non-LTE Modeling

    NASA Astrophysics Data System (ADS)

    Fontes, Christopher J.; Zhang, Hong Lin; Abdallah, Joseph, Jr.; Clark, Robert E. H.; Kilcrease, David P.

    1999-11-01

    A set of fully relativistic codes has been developed to calculate non-LTE, configuration-average atomic models for use in ICF simulations. The codes are based on the same architecture as that used by existing atomic data codes at Los Alamos such as CATS, ACE, GIPPER and FINE. Therefore the new codes are just as easily used in detailed configuration calculations, similar to work reported at previous meetings. In keeping with earlier work we provide sample calculations for some simple gold models. The effect of a fully relativistic treatment on quantities such as average charge state, ion fractions and emissivity will be reported. The possibility of applying the new codes to a very large number of configurations will also be discussed.

  12. Relativistic models in nuclear and particle physics

    SciTech Connect

    Coester, F.

    1988-01-01

    A comparative overview is presented of different approaches to the construction of phenomenological dynamical models that respect basic principles of quantum theory and relativity. Wave functions defined as matrix elements of products of field operators on one hand and wave functions that are defined as representatives of state vectors in model Hilbert spaces are related differently to observables and dynamical models for these wave functions have each distinct advantages and disadvantages 34 refs.

  13. Development of mean-field electrical double layer theory

    NASA Astrophysics Data System (ADS)

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

    2016-01-01

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

  14. Modelling early stages of relativistic heavy-ion collisions

    NASA Astrophysics Data System (ADS)

    Ruggieri, M.; Puglisi, A.; Oliva, L.; Plumari, S.; Scardina, F.; Greco, V.

    2016-05-01

    In this study we model early time dynamics of relativistic heavy ion collisions by an initial color-electric field which then decays to a plasma by the Schwinger mechanism. The dynamics of the many particles system produced by the decay is described by relativistic kinetic theory, taking into account the backreaction on the color field by solving self-consistently the kinetic and the field equations. Our main results concern isotropization and thermalization for a 1+1D expanding geometry. In case of small η/s (η/s ≲ 0.3) we find τisotropization ≈ 0.8 fm/c and τthermalization ≈ 1 fm/c in agreement with the common lore of hydrodynamics.

  15. Momentum dependence of the nuclear mean field

    SciTech Connect

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

    1989-08-01

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

  16. A minimax approach to mean field games

    NASA Astrophysics Data System (ADS)

    Averboukh, Yu V.

    2015-07-01

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

  17. A precessing relativistic jet model for 3C 449

    NASA Technical Reports Server (NTRS)

    Gower, A. C.; Hutchings, J. B.

    1982-01-01

    It is shown that the radio structure of 3C 449 can be matched with a model in which the jets are precessing and have relativistic (beta greater-than or equal to 0.4) velocities. The best-fit model implies a precession period of about 100,000 yr and a cone angle which increases with time. A similar model may be relevant for the radio structure of 3C 31. A brief discussion of the implications for 3C 449 is given.

  18. Exactly solvable relativistic model with the anomalous interaction

    NASA Astrophysics Data System (ADS)

    Ferraro, Elena; Messina, Antonino; Nikitin, A. G.

    2010-04-01

    A special class of Dirac-Pauli equations with time-like vector potentials of an external field is investigated. An exactly solvable relativistic model describing the anomalous interaction of a neutral Dirac fermion with a cylindrically symmetric external electromagnetic field is presented. The related external field is a superposition of the electric field generated by a charged infinite filament and the magnetic field generated by a straight line current. In the nonrelativistic approximation the considered model is reduced to the integrable Pron’ko-Stroganov model.

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

    NASA Astrophysics Data System (ADS)

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

    2015-12-01

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

  20. Relativistic static thin disks: The counterrotating model

    NASA Astrophysics Data System (ADS)

    González, Guillermo A.; Espitia, Omar A.

    2003-11-01

    A detailed study is presented of the counterrotating model (CRM) for generic finite static axially symmetric thin disks with nonzero radial pressure. A general constraint over the counterrotating tangential velocities, needed to cast the surface energy-momentum tensor of the disk as the superposition of two counterrotating perfect fluids, and expressions for the energy density and pressure of the counterrotating fluids are obtained. We show that, in general, it is not possible to take the two counterrotating fluids as circulating along geodesics nor take the two counterrotating tangential velocities as equal and opposite. A simple family of disks is studied that admits some CRMs with well defined counterrotating tangential velocities and stable against radial perturbations.

  1. Mean-field dynamics of a Bose-Einstein condensate in a time-dependent triple-well trap: Nonlinear eigenstates, Landau-Zener models, and stimulated Raman adiabatic passage

    SciTech Connect

    Graefe, E. M.; Korsch, H. J.; Witthaut, D.

    2006-01-15

    We investigate the dynamics of a Bose-Einstein condensate in a triple-well trap in a three-level approximation. The interatomic interactions are taken into account in a mean-field approximation (Gross-Pitaevskii equation), leading to a nonlinear three-level model. Additional eigenstates emerge due to the nonlinearity, depending on the system parameters. Adiabaticity breaks down if such a nonlinear eigenstate disappears when the parameters are varied. The dynamical implications of this loss of adiabaticity are analyzed for two important special cases: A three-level Landau-Zener model and the stimulated Raman adiabatic passage (STIRAP) scheme. We discuss the emergence of looped levels for an equal-slope Landau-Zener model. The Zener tunneling probability does not tend to zero in the adiabatic limit and shows pronounced oscillations as a function of the velocity of the parameter variation. Furthermore we generalize the STIRAP scheme for adiabatic coherent population transfer between atomic states to the nonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceeds the detuning.

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

    PubMed Central

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

    2015-01-01

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

  3. Heavy-light mesons in a relativistic model

    NASA Astrophysics Data System (ADS)

    Liu, Jing-Bin; Yang, Mao-Zhi

    2016-07-01

    We study the heavy-light mesons in a relativistic model, which is derived from the Bethe-Salpeter equation by applying the Foldy-Wouthuysen transformation to the heavy quark. The kernel we choose is based on scalar confinement and vector Coulomb potentials. The transverse interaction of the gluon exchange is also taken into account in this model. The spectra and wave functions of D, Ds, B, Bs meson states are obtained. The spectra are calculated up to the order of 1/m Q, and wave functions are treated to leading order. Supported by National Natural Science Foundation of China (11375088, 10975077, 10735080, 11125525)

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

    NASA Astrophysics Data System (ADS)

    Lin, Jie; Wyart, Matthieu

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

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

    NASA Astrophysics Data System (ADS)

    Lin, Jie; Wyart, Matthieu

    2016-01-01

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

  6. Mean field theory for scale-free random networks

    NASA Astrophysics Data System (ADS)

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

    1999-10-01

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

  7. Schrödinger Approach to Mean Field Games

    NASA Astrophysics Data System (ADS)

    Swiecicki, Igor; Gobron, Thierry; Ullmo, Denis

    2016-03-01

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

  8. A two-fluid model for relativistic heat conduction

    SciTech Connect

    López-Monsalvo, César S.

    2014-01-14

    Three years ago it was presented in these proceedings the relativistic dynamics of a multi-fluid system together with various applications to a set of topical problems [1]. In this talk, I will start from such dynamics and present a covariant formulation of relativistic thermodynamics which provides us with a causal constitutive equation for the propagation of heat in a relativistic setting.

  9. Gaia relativistic astrometric models. I. Proper stellar direction and aberration

    NASA Astrophysics Data System (ADS)

    Crosta, M.; Vecchiato, A.

    2010-01-01

    The high accuracy achievable by modern space astrometry requires the use of General Relativity to model the stellar light propagation through the gravitational field encountered from a source to a given observer inside the Solar System. The general relativistic definition of an astrometric measurement needs an appropriate use of the concept of reference frame, which should then be linked to the conventions of the IAU resolutions. On the other hand, a definition of the astrometric observables in the context of General Relativity is also essential for finding the stellar coordinates and proper motion uniquely, this being the main physical task of the inverse ray-tracing problem. The aim of this work is to set the level of reciprocal consistency of two relativistic models, GREM and RAMOD (Gaia, ESA mission), in order to guarantee a physically correct definition of the light's local direction to a star and deduce the star coordinates and proper motions at the level of accuracy required by these models consistently with the IAU's adopted reference systems.

  10. General Relativistic MHD Models of Sgr A* and M87

    NASA Astrophysics Data System (ADS)

    Dexter, Jason

    2011-01-01

    Ongoing high resolution observations of the Galactic center black hole provide a direct probe of the structure of its accretion flow (Sgr A*) on event-horizon scales. Due to its low luminosity, this source is uniquely suitable for modeling with relativistic MHD simulations. We perform time-dependent, relativistic radiative transfer on 3D simulation data to compute images and light curves of Sgr A* at millimeter wavelengths. Fitting the images to observations allows us to constrain the parameters of the accretion flow and black hole. Simulations with misaligned angular momentum and black hole spin axes ("tilted") are also considered. Due to the precession of these accretion flows, the inferred best fit parameters should appear to change on week timescales if Sgr A* is tilted. Light curves from all simulations exhibit flaring behavior consistent with the observations. The black hole shadow, a signature of the event horizon, is visible in all best fit models and may be detected in the next 5-10 years. Preliminary results from similar models of M87 are also discussed.

  11. Modeling quasar central engine as a relativistic radiating star

    NASA Astrophysics Data System (ADS)

    Singh, Ksh. Newton; Pant, Neeraj

    2015-01-01

    Long ago Hoyle & Fowler attempted to model the central engine of quasars as hot super-massive stars supported by radiation pressure. Whereas the model of Hoyle & Fowler was Newtonian, here we make a toy model of quasar central engines as ultra relativistic ultrahot plasma or as a ball of radiation. Accordingly, we consider general relativistic gravitational collapse including emission of radiation. More specifically, we discuss a new class of radiating fluid ball exact solution in conformally-flat metric which is quasi-static and contracting at negligible rate. The problem is solved by assuming that the metric potential is separable in to radial and time dependent parts. It is found the gravitational mass of the radiating ball M→0 as comoving time t→∞ in conformity of the idea of an "Eternally Collapsing Object" (ECO) which has been claimed to be the true nature of the so-called "Black Holes". In particular, we consider here a quasi-static radiation ball having M≈9.507×107 M ⊙, a radius of ≈2×1014 km, and a luminosity L ∞≈9.1×1046 erg/s. Prima-facie, such an ECO solution is compatible with the central compact object of a quasar having comoving lifetime of ≈107 yr and a distantly observed lifetime ( u) which could be higher by many orders of magnitude.

  12. Mean-field theory of echo state networks

    NASA Astrophysics Data System (ADS)

    Massar, Marc; Massar, Serge

    2013-04-01

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

  13. Mean-field theory of echo state networks.

    PubMed

    Massar, Marc; Massar, Serge

    2013-04-01

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

  14. Relativistic quantum model of confinement and the current quark masses

    NASA Astrophysics Data System (ADS)

    Soloviev, L. D.

    1998-08-01

    We consider a relativistic quantum model of confined massive spinning quarks and antiquarks which describes the leading Regge trajectories of mesons. The quarks are described by the Dirac equations and the gluon contribution is approximated by the Nambu-Goto straight-line string. The string tension and the current quark masses are the main parameters of the model. Additional parameters are phenomenological constants which approximate nonstring short-range contributions. A comparison of the measured meson masses with the model predictions allows one to determine the current quark masses (in MeV) to be ms=227+/-5, mc=1440+/-10, and mb=4715+/-20. The chiral SU3 model makes it possible to estimate from here the u- and d-quark masses to be mu=6.2+/-0.2 Mev and md=11.1+/-0.4 Mev.

  15. Generalized charge-screening in relativistic Thomas-Fermi model

    NASA Astrophysics Data System (ADS)

    Akbari-Moghanjoughi, M.

    2014-10-01

    In this paper, we study the charge shielding within the relativistic Thomas-Fermi model for a wide range of electron number-densities and the atomic-number of screened ions. A generalized energy-density relation is obtained using the force-balance equation and taking into account the Chandrasekhar's relativistic electron degeneracy pressure. By numerically solving a second-order nonlinear differential equation, the Thomas-Fermi screening length is investigated, and the results are compared for three distinct regimes of the solid-density, warm-dense-matter, and white-dwarfs (WDs). It is revealed that our nonlinear screening theory is compatible with the exponentially decaying Thomas-Fermi-type shielding predicted by the linear response theory. Moreover, the variation of relative Thomas-Fermi screening length shows that extremely dense quantum electron fluids are relatively poor charge shielders. Calculation of the total number of screening electrons around a nucleus shows that there is a position of maximum number of screening localized electrons around the screened nucleus, which moves closer to the point-like nucleus by increase in the plasma number density but is unaffected due to increase in the atomic-number value. It is discovered that the total number of screening electrons, ( N s ∝ r T F 3 / r d 3 where rTF and rd are the Thomas-Fermi and interparticle distance, respectively) has a distinct limit for extremely dense plasmas such as WD-cores and neutron star crusts, which is unique for all given values of the atomic-number. This is equal to saying that in an ultrarelativistic degeneracy limit of electron-ion plasma, the screening length couples with the system dimensionality and the plasma becomes spherically self-similar. Current analysis can provide useful information on the effects of relativistic correction to the charge screening for a wide range of plasma density, such as the inertial-confined plasmas and compact stellar objects.

  16. Mean field theory for long chain molecules

    NASA Astrophysics Data System (ADS)

    Pereira, Gerald G.

    1996-06-01

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

  17. RELATIVISTIC MODEL ON PULSAR RADIO EMISSION AND POLARIZATION

    SciTech Connect

    Kumar, D.; Gangadhara, R. T. E-mail: ganga@iiap.res.in

    2012-02-20

    We have developed a relativistic model for pulsar radio emission and polarization by taking into account a detailed geometry of emission region, rotation, and modulation. The sparks activity on the polar cap leads to plasma columns in the emission region and modulated emission. By considering relativistic plasma bunches streaming out along the rotating dipolar field lines as a source of curvature radiation, we have deduced the polarization state of the radiation field in terms of the Stokes parameters. We have simulated a set of typical pulse profiles and analyzed the role of viewing geometry, rotation, and modulation in the pulsar polarization profiles. Our simulations explain most of the diverse behaviors of polarization generally found in pulsar radio profiles. We show that both the 'antisymmetric' and 'symmetric' types of circular polarization are possible within the framework of curvature radiation. We also show that the 'kinky' nature in the polarization position angle traverses might be due to the rotation and modulation effects. The phase lag of the polarization position angle inflection point relative to the phase of core peak depends upon the rotationally induced asymmetry in the curvature of source trajectory and modulation.

  18. Path integral quantization of the relativistic Hopfield model

    NASA Astrophysics Data System (ADS)

    Belgiorno, F.; Cacciatori, S. L.; Dalla Piazza, F.; Doronzo, M.

    2016-03-01

    The path-integral quantization method is applied to a relativistically covariant version of the Hopfield model, which represents a very interesting mesoscopic framework for the description of the interaction between quantum light and dielectric quantum matter, with particular reference to the context of analogue gravity. In order to take into account the constraints occurring in the model, we adopt the Faddeev-Jackiw approach to constrained quantization in the path-integral formalism. In particular, we demonstrate that the propagator obtained with the Faddeev-Jackiw approach is equivalent to the one which, in the framework of Dirac canonical quantization for constrained systems, can be directly computed as the vacuum expectation value of the time-ordered product of the fields. Our analysis also provides an explicit example of quantization of the electromagnetic field in a covariant gauge and coupled with the polarization field, which is a novel contribution to the literature on the Faddeev-Jackiw procedure.

  19. Benchmarking mean-field approximations to level densities

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

  20. New charged shear-free relativistic models with heat flux

    NASA Astrophysics Data System (ADS)

    Nyonyi, Y.; Maharaj, S. D.; Govinder, K. S.

    2013-11-01

    We study shear-free spherically symmetric relativistic gravitating fluids with heat flow and electric charge. The solution to the Einstein-Maxwell system is governed by the generalised pressure isotropy condition which contains a contribution from the electric field. This condition is a highly nonlinear partial differential equation. We analyse this master equation using Lie's group theoretic approach. The Lie symmetry generators that leave the equation invariant are found. The first generator is independent of the electromagnetic field. The second generator depends critically on the form of the charge, which is determined explicitly in general. We provide exact solutions to the gravitational potentials using the symmetries admitted by the equation. Our new exact solutions contain earlier results without charge. We show that other charged solutions, related to the Lie symmetries, may be generated using the algorithm of Deng. This leads to new classes of charged Deng models which are generalisations of conformally flat metrics.

  1. Relativistic Models for the BepiColombo Radioscience Experiment

    NASA Astrophysics Data System (ADS)

    Milani, Andrea

    2009-05-01

    For the dynamics we start from the Lagrangian Post-Newtonian formulation, using a relativistic equation for the solar system barycenter to avoid rank deficiency. For the determination of the PN parameters the difficulty, already reported in (Milani et al., Phis. Rev. D 2002), in disentagling the effects of beta from the ones of the Sun's oblateness is confirmed. We have found a consistent formulation for the preferred frame effects, altough a barycenter is not well defined. For the identification of SEP violations we use a formulation containing both direct and indirect effects (through the modified position of the Sun in a barycentric frame). We report on our methods for validation tests and algorithm certification. The light-time implicit equations are solved with iterative loops, the Shapiro effect is modeled to PN order 1 but with an order 2 correction as recently computed with different methods by several authors, which is compatible with Moyer's. We have also tested the 1.5 PN order corrections due to the motion of the Sun and found they are not relevant at the required level of accuracy. The integrated range-rate observable has been smoothed by an averaging technique removing the well known numerical instability problems. To model the orbit of the probe, we use a mercurycentric reference frame with its own "Mercury Dynamical Time": this is the largest and the only relativistic correction required, taking into account the major uncertainties introduced by non-gravitational perturbations (mostly as uncertainty in accelerometer calibrations). A delicate issue is the compatibility of our solution with the ephemerides for the other planets, and for the Moon, which presumably cannot be improved by the BepiColombo data alone. On the other hand, we plan to later export the BepiColombo measurements, as normal points, to contribute with their unprecedented accuracy to the global improvement of planetary ephemerides.

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

    NASA Astrophysics Data System (ADS)

    Grabow, Carsten; Grosskinsky, Stefan; Timme, Marc

    2012-05-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

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

  4. Generalized charge-screening in relativistic Thomas–Fermi model

    SciTech Connect

    Akbari-Moghanjoughi, M.

    2014-10-15

    In this paper, we study the charge shielding within the relativistic Thomas-Fermi model for a wide range of electron number-densities and the atomic-number of screened ions. A generalized energy-density relation is obtained using the force-balance equation and taking into account the Chandrasekhar's relativistic electron degeneracy pressure. By numerically solving a second-order nonlinear differential equation, the Thomas-Fermi screening length is investigated, and the results are compared for three distinct regimes of the solid-density, warm-dense-matter, and white-dwarfs (WDs). It is revealed that our nonlinear screening theory is compatible with the exponentially decaying Thomas-Fermi-type shielding predicted by the linear response theory. Moreover, the variation of relative Thomas-Fermi screening length shows that extremely dense quantum electron fluids are relatively poor charge shielders. Calculation of the total number of screening electrons around a nucleus shows that there is a position of maximum number of screening localized electrons around the screened nucleus, which moves closer to the point-like nucleus by increase in the plasma number density but is unaffected due to increase in the atomic-number value. It is discovered that the total number of screening electrons, (N{sub s}∝r{sub TF}{sup 3}/r{sub d}{sup 3} where r{sub TF} and r{sub d} are the Thomas-Fermi and interparticle distance, respectively) has a distinct limit for extremely dense plasmas such as WD-cores and neutron star crusts, which is unique for all given values of the atomic-number. This is equal to saying that in an ultrarelativistic degeneracy limit of electron-ion plasma, the screening length couples with the system dimensionality and the plasma becomes spherically self-similar. Current analysis can provide useful information on the effects of relativistic correction to the charge screening for a wide range of plasma density, such as the inertial-confined plasmas and compact stellar

  5. A model distribution function for relativistic bi-Maxwellian with drift

    SciTech Connect

    Naito, O.

    2013-04-15

    A model distribution function for relativistic bi-Maxwellian with drift is proposed, based on the maximum entropy principle and the relativistic canonical transformation. Since the obtained expression is compatible with the existing distribution functions and has a relatively simple form as well as smoothness, it might serve as a useful tool in the research fields of space or high temperature fusion plasmas.

  6. Dynamics of low dimensional model for weakly relativistic Zakharov equations for plasmas

    SciTech Connect

    Sahu, Biswajit; Pal, Barnali; Poria, Swarup; Roychoudhury, Rajkumar

    2013-05-15

    In the present paper, the nonlinear interaction between Langmuir waves and ion acoustic waves described by the one-dimensional Zakharov equations (ZEs) for relativistic plasmas are investigated formulating a low dimensional model. Equilibrium points of the model are found and it is shown that the existence and stability conditions of the equilibrium point depend on the relativistic parameter. Computational investigations are carried out to examine the effects of relativistic parameter and other plasma parameters on the dynamics of the model. Power spectrum analysis using fast fourier transform and also construction of first return map confirm that periodic, quasi-periodic, and chaotic type solution exist for both relativistic as well as in non-relativistic case. Existence of supercritical Hopf bifurcation is noted in the system for two critical plasmon numbers.

  7. Mean field approach to fluctuations of surface line defects

    NASA Astrophysics Data System (ADS)

    Margetis, Dionisios

    2011-03-01

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

  8. Numerical modelling of the lobes of radio galaxies in cluster environments - III. Powerful relativistic and non-relativistic jets

    NASA Astrophysics Data System (ADS)

    English, W.; Hardcastle, M. J.; Krause, M. G. H.

    2016-09-01

    We present results from two suites of simulations of powerful radio galaxies in poor cluster environments, with a focus on the formation and evolution of the radio lobes. One suite of models uses relativistic hydrodynamics and the other relativistic magnetohydrodynamics; both are set up to cover a range of jet powers and velocities. The dynamics of the lobes are shown to be in good agreement with analytical models and with previous numerical models, confirming in the relativistic regime that the observed widths of radio lobes may be explained if they are driven by very light jets. The ratio of energy stored in the radio lobes to that put into the intracluster gas is seen to be the same regardless of jet power, jet velocity or simulation type, suggesting that we have a robust understanding of the work done on the ambient gas by this type of radio source. For the most powerful jets, we at times find magnetic field amplification by up to a factor of 2 in energy, but mostly the magnetic energy in the lobes is consistent with the magnetic energy injected. We confirm our earlier result that for jets with a toroidally injected magnetic field, the field in the lobes is predominantly aligned with the jet axis once the lobes are well developed, and that this leads to radio flux anisotropies of up to a factor of about two for mature sources. We reproduce the relationship between 151 MHz luminosity and jet power determined analytically in the literature.

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

    NASA Astrophysics Data System (ADS)

    Afanasjev, A. V.; Abusara, H.

    2010-09-01

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

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

    SciTech Connect

    Afanasjev, A. V.; Abusara, H.

    2010-09-15

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

  11. Two stochastic mean-field polycrystal plasticity methods

    SciTech Connect

    Tonks, Michael

    2008-01-01

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

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

    PubMed

    Zhang, J; Hanauer, G G

    1995-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Lee, Edward; Raju, Archishman; Sethna, James

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

  14. The Thomas–Fermi quark model: Non-relativistic aspects

    SciTech Connect

    Liu, Quan Wilcox, Walter

    2014-02-15

    The first numerical investigation of non-relativistic aspects of the Thomas–Fermi (TF) statistical multi-quark model is given. We begin with a review of the traditional TF model without an explicit spin interaction and find that the spin splittings are too small in this approach. An explicit spin interaction is then introduced which entails the definition of a generalized spin “flavor”. We investigate baryonic states in this approach which can be described with two inequivalent wave functions; such states can however apply to multiple degenerate flavors. We find that the model requires a spatial separation of quark flavors, even if completely degenerate. Although the TF model is designed to investigate the possibility of many-quark states, we find surprisingly that it may be used to fit the low energy spectrum of almost all ground state octet and decuplet baryons. The charge radii of such states are determined and compared with lattice calculations and other models. The low energy fit obtained allows us to extrapolate to the six-quark doubly strange H-dibaryon state, flavor symmetric strange states of higher quark content and possible six quark nucleon–nucleon resonances. The emphasis here is on the systematics revealed in this approach. We view our model as a versatile and convenient tool for quickly assessing the characteristics of new, possibly bound, particle states of higher quark number content. -- Highlights: • First application of the statistical Thomas–Fermi quark model to baryonic systems. • Novel aspects: spin as generalized flavor; spatial separation of quark flavor phases. • The model is statistical, but the low energy baryonic spectrum is successfully fit. • Numerical applications include the H-dibaryon, strange states and nucleon resonances. • The statistical point of view does not encourage the idea of bound many-quark baryons.

  15. Quasi-exactly solvable relativistic soft-core Coulomb models

    SciTech Connect

    Agboola, Davids Zhang, Yao-Zhong

    2012-09-15

    By considering a unified treatment, we present quasi exact polynomial solutions to both the Klein-Gordon and Dirac equations with the family of soft-core Coulomb potentials V{sub q}(r)=-Z/(r{sup q}+{beta}{sup q}){sup 1/q}, Z>0, {beta}>0, q{>=}1. We consider cases q=1 and q=2 and show that both cases are reducible to the same basic ordinary differential equation. A systematic and closed form solution to the basic equation is obtained using the Bethe ansatz method. For each case, the expressions for the energies and the allowed parameters are obtained analytically and the wavefunctions are derived in terms of the roots of a set of Bethe ansatz equations. - Highlights: Black-Right-Pointing-Pointer The relativistic bound-state solutions of the soft-core Coulomb models. Black-Right-Pointing-Pointer Quasi-exact treatments of the Dirac and Klein-Gordon equations for the soft-core Coulomb models. Black-Right-Pointing-Pointer Solutions obtained in terms of the roots to the Bethe ansatz equations. Black-Right-Pointing-Pointer The hidden Lie algebraic structure discussed for the models. Black-Right-Pointing-Pointer Results useful in describing mesonic atoms and interaction of intense laser fields with atom.

  16. Nuclear ρ meson transparency in a relativistic Glauber model

    NASA Astrophysics Data System (ADS)

    Cosyn, W.; Ryckebusch, J.

    2013-06-01

    Background: The recent Jefferson Laboratory data for the nuclear transparency in ρ0 electroproduction have the potential to settle the scale for the onset of color transparency (CT) in vector meson production.Purpose: To compare the data to calculations in a relativistic and quantum-mechanical Glauber model and to investigate whether they are in accordance with results including color transparency given that the computation of ρ-nucleus attenuations is subject to some uncertainties.Method: We compute the nuclear transparencies in a multiple-scattering Glauber model and account for effects stemming from color transparency, from ρ-meson decay, and from short-range correlations (SRC) in the final-state interactions (FSI).Results: The robustness of the model is tested by comparing the mass dependence and the hard-scale dependence of the A(e,e'p) nuclear transparencies with the data. The hard-scale dependence of the (e,e'ρ0) nuclear transparencies for 12C and 56Fe are only moderately affected by SRC and by ρ0 decay.Conclusions: The RMSGA calculations confirm the onset of CT at four-momentum transfers of a few (GeV/c)2 in ρ meson electroproduction data. A more precise determination of the scale for the onset of CT is hampered by the lack of precise input in the FSI and ρ-meson decay calculations.

  17. Structure of relativistic accretion disk with non-standard model

    NASA Astrophysics Data System (ADS)

    Khesali, A. R.; Salahshoor, K.

    2016-07-01

    The structure of stationary, axisymmetric advection-dominated accretion disk (ADAF) around rotating black hole, using non-standard model, was examined. In this model, the transport efficiency of the angular momentum α was dependent on the magnetic Prandtl number α ∝ Pm^{δ } . The full relativistic shear stress recently obtained by a new manner, was used. By considering black hole spin and Prandtl number instantaneously, the structure of ADAFs was changed in inner and outer region of the disk. It was discovered that the accretion flow was denser and hotter in the inner region, due to the black hole spin, and in the outer region, due to the presence of Prandtl parameter. Inasmuch as the rotation of the black hole affected the transport efficiency of angular momentum in parts of the disk very close to the even horizon, then in these regions, the viscosity depended on the rotation of black hole. Also, it was discovered that the effect of the black hole spin on the structure of the disk was related to the presence of Prandtl parameter.

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

    PubMed Central

    Buice, Michael A; Chow, Carson C

    2014-01-01

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

  19. Relativistic proton-nucleus scattering and one-boson-exchange models

    NASA Technical Reports Server (NTRS)

    Maung, Khin Maung; Gross, Franz; Tjon, J. A.; Townsend, L. W.; Wallace, S. J.

    1993-01-01

    Relativistic p-(Ca-40) elastic scattering observables are calculated using four sets of relativistic NN amplitudes obtained from different one-boson-exchange (OBE) models. The first two sets are based upon a relativistic equation in which one particle is on mass shell and the other two sets are obtained from a quasipotential reduction of the Bethe-Salpeter equation. Results at 200, 300, and 500 MeV are presented for these amplitudes. Differences between the predictions of these models provide a study of the uncertainty in constructing Dirac optical potentials from OBE-based NN amplitudes.

  20. Modeling Relativistic Jets Using the Athena Hydrodynamics Code

    NASA Astrophysics Data System (ADS)

    Pauls, David; Pollack, Maxwell; Wiita, Paul

    2014-11-01

    We used the Athena hydrodynamics code (Beckwith & Stone 2011) to model early-stage two-dimensional relativistic jets as approximations to the growth of radio-loud active galactic nuclei. We analyzed variability of the radio emission by calculating fluxes from a vertical strip of zones behind a standing shock, as discussed in the accompanying poster. We found the advance speed of the jet bow shock for various input jet velocities and jet-to-ambient density ratios. Faster jets and higher jet densities produce faster shock advances. We investigated the effects of parameters such as the Courant-Friedrichs-Lewy number, the input jet velocity, and the density ratio on the stability of the simulated jet, finding that numerical instabilities grow rapidly when the CFL number is above 0.1. We found that greater jet input velocities and higher density ratios lengthen the time the jet remains stable. We also examined the effects of the boundary conditions, the CFL number, the input jet velocity, the grid resolution, and the density ratio on the premature termination of Athena code. We found that a grid of 1200 by 1000 zones allows the code to run with minimal errors, while still maintaining an adequate resolution. This work is supported by the Mentored Undergraduate Summer Experience program at TCNJ.

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

    PubMed

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

    2006-07-01

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

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

    PubMed

    Park, H; Haule, K; Kotliar, G

    2008-10-31

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

  3. Lifting mean field degeneracies in anisotropic spin systems

    NASA Astrophysics Data System (ADS)

    Sizyuk, Yuriy; Perkins, Natalia; Wolfle, Peter

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

  4. Nonlinear Walecka models and point-coupling relativistic models

    SciTech Connect

    Lourenco, O.; Amaral, R. L. P. G.; Dutra, M.; Delfino, A.

    2009-10-15

    We study hadronic nonlinear point-coupling (NLPC) models which reproduce numerically the binding energy, the incompressibility, and the nucleon effective mass at the nuclear matter saturation obtained by different nonlinear Walecka (NLW) models. We have investigated their behaviors as functions of the nuclear matter density to observe how they deviate from known NLW models. In our study we present a meson-exchange modified nonlinear Walecka model (MNLW) which exactly underlies a nonlinear point-coupling model (NLPC) presenting third- and fourth-order scalar density self-couplings. A discussion about naive dimensional analysis (NDA) and naturalness is also provided for a large class of NLW and NLPC models. At finite temperature, critical and flash parameters of both approaches are presented.

  5. A reduced model for relativistic electron beam transport in solids and dense plasmas

    NASA Astrophysics Data System (ADS)

    Touati, M.; Feugeas, J.-L.; Nicolaï, Ph; Santos, J. J.; Gremillet, L.; Tikhonchuk, V. T.

    2014-07-01

    A hybrid reduced model for relativistic electron beam transport based on the angular moments of the relativistic kinetic equation with a special closure is presented. It takes into account collective effects with the self-generated electromagnetic fields as well as collisional effects with the slowing down of the relativistic electrons by plasmons, bound and free electrons and their angular scattering on both ions and electrons. This model allows for fast computations of relativistic electron beam transport while describing their energy distribution evolution. Despite the loss of information concerning the angular distribution of the electron beam, the model reproduces analytical estimates in the academic case of a monodirectional and monoenergetic electron beam propagating through a warm and dense plasma and hybrid particle-in-cell simulation results in a realistic laser-generated electron beam transport case.

  6. Decay constants of pseudoscalar mesons in a relativistic quark model

    SciTech Connect

    Micu, L.

    1997-04-01

    The decay constants of pseudoscalar mesons are calculated in a relativistic quark model which assumes that mesons are made of a valence quark-antiquark pair and of an effective vacuumlike component. The results are given as functions of quark masses and of some free parameters entering the expression of the internal wave functions of the mesons. Using F{sub {pi}{sup +}}=130.7 MeV, F{sub K{sup +}}=159.8 MeV to fix the parameters of the model, we predict 60MeV{le}F{sub D{sup +}}{le}185 MeV, 95MeV{le}F{sub D{sub s}}{le}230 MeV, 80MeV{le}F{sub B{sup +}}{le}205 MeV, 90MeV{le}F{sub B{sub s}}{le}235 MeV for the light quark masses m{sub u}=5.1 MeV, m{sub d}=9.3 MeV, m{sub s}=175 MeV and the heavy quark masses in the range 1GeV{le}m{sub c}{le}1.6 GeV, 4.1GeV{le}m{sub b}{le}4.5 GeV. In the case of light neutral mesons one obtains with the same set of parameters F{sub {pi}{sup 0}}{approx}138 MeV, F{sub {eta}}{approx}130 MeV, F{sub {eta}{sup {prime}}}{approx}78 MeV. The values are in agreement with the experimental data and other theoretical results. {copyright} {ital 1997} {ital The American Physical Society}

  7. Relativistic feedback models of terrestrial gamma-ray flashes and gamma-ray glows

    NASA Astrophysics Data System (ADS)

    Dwyer, J. R.

    2015-12-01

    Relativistic feedback discharges, also known as dark lightning, are capable of explaining many of the observed properties of terrestrial gamma-ray flashes (TGFs) and gamma-ray glows, both created within thunderstorms. During relativistic feedback discharges, the generation of energetic electrons is self-sustained via the production of backward propagating positrons and back-scattered x-rays, resulting in very larges fluxes of energetic radiation. In addition, ionization produces large electric currents that generate LF/VLF radio emissions and eventually discharge the electric field, terminating the gamma-ray production. In this presentation, new relativistic feedback model results will be presented and compared to recent observations.

  8. A hydrodynamical model for relativistic spin quantum plasmas

    SciTech Connect

    Asenjo, Felipe A.; Munoz, Victor; Valdivia, J. Alejandro; Mahajan, Swadesh M.

    2011-01-15

    Based on the one-body particle-antiparticle Dirac theory of electrons, a set of relativistic quantum fluid equations for a spin half plasma is derived. The particle-antiparticle nature of the relativistic particles is explicit in this fluid theory, which also includes quantum effects such as spin. The nonrelativistic limit is shown to be in agreement with previous attempts to develop a spin plasma theory derived from the Pauli Hamiltonian. Harnessing the formalism to the study of electromagnetic mode propagation, conceptually new phenomena are revealed; the particle-antiparticle effects increase the fluid opacity to these waves, while the spin effects tend to make the fluid more transparent.

  9. Derivation of the lattice Boltzmann model for relativistic hydrodynamics

    SciTech Connect

    Mendoza, M.; Herrmann, H. J.; Boghosian, B. M.; Succi, S.

    2010-11-15

    A detailed derivation of the lattice Boltzmann scheme for relativistic fluids recently proposed in M. Mendoza, B. Boghosian, H. Herrmann, and S. Succi, Phys. Rev. Lett. 105, 014502 (2010) is presented. The method is numerically validated and applied to the case of two quite different relativistic fluid-dynamic problems, namely, shock-wave propagation in quark-gluon plasmas and the impact of a supernova blast wave on massive interstellar clouds. Close to second-order convergence with the grid resolution, as well as linear dependence of computational time on the number of grid points and time steps, are reported.

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

    SciTech Connect

    Bardakci, Korkut; Bardakci, Korkut

    2007-01-10

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

  11. Pseudo-Newtonian models for the equilibrium structures of rotating relativistic stars

    NASA Astrophysics Data System (ADS)

    Kim, Jinho; Il Kim, Hee; Mok Lee, Hyung

    2009-10-01

    We obtain equilibrium solutions for rotating compact stars, including special relativistic effects. The gravity is assumed to be Newtonian, but we use the active mass density, which takes into account all energies such as the motion of the fluid, internal energy and pressure energy in addition to the rest-mass energy, in computing the gravitational potential using Poisson's equation. Such a treatment could be applicable to neutron stars with relativistic motions or a relativistic equation of state. We applied Hachisu's self-consistent field (SCF) method to find spheroidal as well as toroidal sequences of equilibrium solutions. Our solutions show better agreement with general relativistic solutions than the Newtonian relativistic hydrodynamic approach, which does not take into account the active mass. Physical quantities such as the peak density and equatorial radii in our solutions agree with the general relativistic ones to within 5 per cent. Therefore our approach can be used as a simple alternative to the fully relativistic one when a large number of model calculations is necessary, as it requires much fewer computational resources.

  12. Modelling Relativistic Astrophysics at the Large and Small Scale

    NASA Astrophysics Data System (ADS)

    Haugboelle, Troels

    2005-10-01

    In this thesis different numerical methods, as well as applications of the methods to a number of current problems in relativistic astrophysics, are presented. In the first part the theoretical foundation and numerical implementation of a new general relativistic magnetohydrodynamics code is discussed. A new form of the equations of motion using global coordinates, but evolving the dynamical variables from the point of view of a local observer is presented. No assumptions are made about the background metric and the design is ready to be coupled with methods solving the full Einstein equations. In the second part of the thesis important results concerning the understanding of collisionless shocks, obtained from experiments with a relativistic charged particle code, are presented. Relativistic collisionless shocks are important in a range of astrophysical objects; in particular in gamma ray burst afterglows and other relativistic jets. It is shown that a strong small scale, fluctuating, and predominantly transversal magnetic field is unavoidably generated by a two-stream instability. The magnetic energy density reaches a few percent of equipartition. A new acceleration mechanism for electrons in ion-electron collisionless shocks is proposed. The mechanism is capable of creating a powerlaw electron distribution in a collisionless shocked region. The non-thermal acceleration of the electrons is directly related to the ion current channels generated by the two-stream instability and is local in nature. Thus the observed radiation field may be tied directly to the local conditions of the plasma and could be a strong handle on the physical processes. (abridged)

  13. Relativistic Modeling Capabilities in PERSEUS Extended-MHD Simulation Code for HED Plasmas

    NASA Astrophysics Data System (ADS)

    Hamlin, Nathaniel; Seyler, Charles

    2015-11-01

    We discuss the incorporation of relativistic modeling capabilities into the PERSEUS extended MHD simulation code for high-energy-density (HED) plasmas, and present the latest simulation results. The use of fully relativistic equations enables the model to remain self-consistent in simulations of such relativistic phenomena as hybrid X-pinches and laser-plasma interactions. We have overcome a major challenge of a relativistic fluid implementation, namely the recovery of primitive variables (density, velocity, pressure) from conserved quantities at each time step of a simulation. Our code recovers non-relativistic results along with important features of published Particle-In-Cell simulation results for a laser penetrating a super-critical hydrogen gas with Fast Ignition applications. In particular, we recover the penetration of magnetized relativistic electron jets ahead of the laser. Our code also reveals new physics in the modeling of a laser incident on a thin foil. This work is supported by the National Nuclear Security Administration stewardship sciences academic program under Department of Energy cooperative agreements DE-FOA-0001153 and DE-NA0001836.

  14. HELICITY CONSERVATION IN NONLINEAR MEAN-FIELD SOLAR DYNAMO

    SciTech Connect

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

    2013-05-01

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

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

    NASA Astrophysics Data System (ADS)

    Ammari, Z.; Nier, F.

    2009-04-01

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

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

    SciTech Connect

    Ammari, Z.; Nier, F.

    2009-04-15

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

  17. General relativistic models of binary neutron stars in quasiequilibrium

    NASA Astrophysics Data System (ADS)

    Baumgarte, T. W.; Cook, G. B.; Scheel, M. A.; Shapiro, S. L.; Teukolsky, S. A.

    1998-06-01

    We perform fully relativistic calculations of binary neutron stars in corotating, circular orbit. While Newtonian gravity allows for a strict equilibrium, a relativistic binary system emits gravitational radiation, causing the system to lose energy and slowly spiral inwards. However, since inspiral occurs on a time scale much longer than the orbital period, we can treat the binary to be in quasiequilibrium. In this approximation, we integrate a subset of the Einstein equations coupled to the relativistic equation of hydrostatic equilibrium to solve the initial value problem for binaries of arbitrary separation. We adopt a polytropic equation of state to determine the structure and maximum mass of neutron stars in close binaries for polytropic indices n=1, 1.5 and 2. We construct sequences of constant rest-mass and locate turning points along energy equilibrium curves to identify the onset of orbital instability. In particular, we locate the innermost stable circular orbit and its angular velocity. We construct the first contact binary systems in full general relativity. These arise whenever the equation of state is sufficiently soft (n>~1.5). A radial stability analysis reveals no tendency for neutron stars in close binaries to collapse to black holes prior to merger.

  18. Relativistic fluid dynamics. Proceedings.

    NASA Astrophysics Data System (ADS)

    Anile, A. M.; Choquet-Bruhat, Y.

    Contents: 1. Covariant theory of conductivity in ideal fluid or solid media (B. Carter). 2. Hamiltonian techniques for relativistic fluid dynamics and stability theory (D. D. Holm). 3. Covariant fluid mechanics and thermodynamics: an introduction (W. Israel). 4. Relativistic plasmas (H. Weitzner). 5. An improved relativistic warm plasma model (A. M. Anile, S. Pennisi). 6. Relativistic extended thermodynamics II (I. Müller). 7. Relativistic extended thermodynamics: general assumptions and mathematical procedure (T. Ruggeri). 8. Relativistic hydrodynamics and heavy ion reactions (D. Strottman). 9. Some problems in relativistic hydrodynamics (C. G. van Weert).

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

    NASA Astrophysics Data System (ADS)

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

    2011-03-01

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

  20. Triaxially deformed relativistic point-coupling model for Λ hypernuclei: A quantitative analysis of the hyperon impurity effect on nuclear collective properties

    NASA Astrophysics Data System (ADS)

    Xue, W. X.; Yao, J. M.; Hagino, K.; Li, Z. P.; Mei, H.; Tanimura, Y.

    2015-02-01

    Background: The impurity effect of hyperons on atomic nuclei has received a renewed interest in nuclear physics since the first experimental observation of appreciable reduction of E 2 transition strength in low-lying states of the hypernucleus Λ7Li . Many more data on low-lying states of Λ hypernuclei will be measured soon for s d -shell nuclei, providing good opportunities to study the Λ impurity effect on nuclear low-energy excitations. Purpose: We carry out a quantitative analysis of the Λ hyperon impurity effect on the low-lying states of s d -shell nuclei at the beyond-mean-field level based on a relativistic point-coupling energy density functional (EDF), considering that the Λ hyperon is injected into the lowest positive-parity (Λs) and negative-parity (Λp) states. Method: We adopt a triaxially deformed relativistic mean-field (RMF) approach for hypernuclei and calculate the Λ binding energies of hypernuclei as well as the potential-energy surfaces (PESs) in the (β ,γ ) deformation plane. We also calculate the PESs for the Λ hypernuclei with good quantum numbers by using a microscopic particle rotor model (PRM) with the same relativistic EDF. The triaxially deformed RMF approach is further applied in order to determine the parameters of a five-dimensional collective Hamiltonian (5DCH) for the collective excitations of triaxially deformed core nuclei. Taking 25,27Mg Λ and Si31Λ as examples, we analyze the impurity effects of Λs and Λp on the low-lying states of the core nuclei. Results: We show that Λs increases the excitation energy of the 21+ state and decreases the E 2 transition strength from this state to the ground state by 12 %to17 % . On the other hand, Λp tends to develop pronounced energy minima with larger deformation, although it modifies the collective parameters in such a way that the collectivity of the core nucleus can be either increased or decreased. Conclusions: The quadrupole deformation significantly affects the

  1. Real-space renormalized dynamical mean field theory

    NASA Astrophysics Data System (ADS)

    Kubota, Dai; Sakai, Shiro; Imada, Masatoshi

    2016-05-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-08-01

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

  3. A finite Zitterbewegung model for relativistic quantum mechanics

    SciTech Connect

    Noyes, H.P.

    1990-02-19

    Starting from steps of length h/mc and time intervals h/mc{sup 2}, which imply a quasi-local Zitterbewegung with velocity steps {plus minus}c, we employ discrimination between bit-strings of finite length to construct a necessary 3+1 dimensional event-space for relativistic quantum mechanics. By using the combinatorial hierarchy to label the strings, we provide a successful start on constructing the coupling constants and mass ratios implied by the scheme. Agreement with experiments is surprisingly accurate. 22 refs., 1 fig.

  4. Modeling early stages of relativistic heavy ion collisions: Coupling relativistic transport theory to decaying color-electric flux tubes

    NASA Astrophysics Data System (ADS)

    Ruggieri, M.; Puglisi, A.; Oliva, L.; Plumari, S.; Scardina, F.; Greco, V.

    2015-12-01

    In this study we model early-time dynamics of relativistic heavy ion collisions by an initial color-electric field which then decays to a plasma by the Schwinger mechanism, coupling the dynamical evolution of the initial color field to the dynamics of the many particles system produced by the decay. The latter is described by relativistic kinetic theory in which we fix the ratio η /s rather than insisting on specific microscopic processes, and the backreaction on the color field is taken into account by solving self-consistently the kinetic and the field equations. We study isotropization and thermalization of the system produced by the field decay for a static box and for a 1 +1 D expanding geometry. We find that regardless of the viscosity of the produced plasma, the initial color-electric field decays within 1 fm/c ; however, in the case where η /s is large, oscillations of the field are effective along all the entire time evolution of the system, which affect the late-time evolution of the ratio between longitudinal and transverse pressure. In the case of small η /s (η /s ≲0.3 ) we find τisotropization≈0.8 fm/c and τthermalization≈1 fm/c , in agreement with the common lore of hydrodynamics. Moreover, we have investigated the effect of turning from the relaxation time approximation to the Chapman-Enskog one: We find that this improvement affects mainly the early-time evolution of the physical quantities, the effect being milder in the late-time evolution.

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

    NASA Astrophysics Data System (ADS)

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

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

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

    NASA Astrophysics Data System (ADS)

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

    2012-02-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-08-01

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

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

    SciTech Connect

    Weening, R. H.

    2011-12-15

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

  9. Avalanche shape and exponents beyond mean-field theory

    NASA Astrophysics Data System (ADS)

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

    2014-12-01

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

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

    NASA Astrophysics Data System (ADS)

    Belemuk, Alexander M.; Ryzhov, Valentin N.

    2016-04-01

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

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

    SciTech Connect

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

    1993-12-31

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

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

    PubMed

    Lee, Cathy Yuen Yi; Wand, Matt P

    2016-07-01

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

  13. Quantum-relativistic hydrodynamic model for a spin-polarized electron gas interacting with light.

    PubMed

    Morandi, Omar; Zamanian, Jens; Manfredi, Giovanni; Hervieux, Paul-Antoine

    2014-07-01

    We develop a semirelativistic quantum fluid theory based on the expansion of the Dirac Hamiltonian to second order in 1/c. By making use of the Madelung representation of the wave function, we derive a set of hydrodynamic equations that comprises a continuity equation, an Euler equation for the mean velocity, and an evolution equation for the electron spin density. This hydrodynamic model is then applied to study the dynamics of a dense and weakly relativistic electron plasma. In particular, we investigate the impact of the quantum-relativistic spin effects on the Faraday rotation in a one-dimensional plasma slab irradiated by an x-ray laser source. PMID:25122397

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

    SciTech Connect

    Lakshmi Priya, K. B.; Natesan, Baskaran

    2015-06-24

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-09-01

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

  16. Spectropolarimetric test of the relativistic disk model for the broad emission lines of active galactic nuclei

    NASA Technical Reports Server (NTRS)

    Chen, Kaiyou; Halpern, Jules P.

    1990-01-01

    Previously, it was claimed that the broad emission lines of the radio galaxy Arp 102B can be fitted by the line profile from a simple relativistic Keplerian thin disk. It was argued that the lines originating from the relativistic accretion disk could be polarized due to electron scattering, which is likely to be the dominant opacity in the line-emitting region of Arp 102B. In the present work, the expected polarization properties of these broad emission lines are calculated. The percentage of polarization depends strongly on the inclination angle. For some angles, the red peak of the polarized, double-peaked line profile can be higher than the blue peak. This is in contrast to the total line profile, in which the blue peak is always higher than the red one. Spectropolarimetric observations could, therefore, provide an independent test of the relativistic disk model for the broad emission lines of Arp 102B and other active galactic nuclei.

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

    NASA Astrophysics Data System (ADS)

    Golse, François; Mouhot, Clément; Paul, Thierry

    2016-04-01

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

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

    NASA Astrophysics Data System (ADS)

    Moon, Jun; Başar, Tamer

    2016-07-01

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

  19. On the Methods for Constructing Meson-Baryon Reaction Models within Relativistic Quantum Field Theory

    SciTech Connect

    B. Julia-Diaz, H. Kamano, T.-S. H. Lee, A. Matsuyama, T. Sato, N. Suzuki

    2009-04-01

    Within the relativistic quantum field theory, we analyze the differences between the $\\pi N$ reaction models constructed from using (1) three-dimensional reductions of Bethe-Salpeter Equation, (2) method of unitary transformation, and (3) time-ordered perturbation theory. Their relations with the approach based on the dispersion relations of S-matrix theory are dicusssed.

  20. Longitudinal and Transverse Parton Momentum Distributions for Hadrons within Relativistic Constituent Quark Models

    SciTech Connect

    Frederico, T.; Pace, E.; Pasquini, B.; Salme, G.

    2010-08-05

    Longitudinal and transverse parton distributions for pion and nucleon are calculated from hadron vertexes obtained by a study of form factors within relativistic quark models. The relevance of the one-gluon-exchange dominance at short range for the behavior of the form factors at large momentum transfer and of the parton distributions at the end points is stressed.

  1. Relativistic jet models for the BL Lacertae object Mrk 421 during three epochs of observation

    NASA Technical Reports Server (NTRS)

    Mufson, S. L.; Hutter, D. J.; Kondo, Y.; Wisniewski, W. Z.

    1988-01-01

    Coordinated observation of the nearby BL Lacertae object Mrk 421 obtained during May 1980, January 1984, and March 1984 are described. These observations give a time-frozen picture of the continuous spectrum of Mrk 421 at X-ray, ultraviolet, optical, and radio wavelengths. The observed spectra have been fitted to an inhomogeneous relativistic jet model. In general, the models reproduce the data well. Many of the observed differences during the three epochs can be attributed to variations in the opening angle of the jet and in the angle that the jet makes to the line of sight. The jet models obtained here are compared with the homogeneous, spherically symmetric, synchrotron self-Compton models for this source. The models are also compared with the relativistic jet models obtained for other active galactic nuclei.

  2. Modeling the Impenetrable Barrier to Inward Transport of Ultra-relativistic Radiation Belt Electrons

    NASA Astrophysics Data System (ADS)

    Tu, W.; Cunningham, G.; Chen, Y.; Baker, D. N.; Henderson, M. G.; Reeves, G. D.

    2014-12-01

    It has long been considered that the inner edge of the Earth's outer radiation belt is closely correlated with the minimum plasmapause location. However, recent discoveries by Baker et al. [1] show that it is not the case for ultra-relativistic electrons (2-10 MeV) in the radiation belt. Based on almost two years of Van Allen Probes/REPT data, they find that the inner edge of highly relativistic electrons is rarely collocated with the plasmapause; and more interestingly, there is a clear, persistent, and nearly impenetrable barrier to inward transport of high energy electrons, observed to locate at L~2.8. The presence of such an impenetrable barrier at this very specific location poses a significant puzzle. Using our DREAM3D diffusion model, which includes radial, pitch angle, and momentum diffusion, we are able to simulate the observed impenetrable barrier of ultra-relativistic electrons. The simulation demonstrates that during strong geomagnetic storms the plasmapause can be compressed to very low L region (sometimes as low as L~3), then strong chorus waves just outside the plasmapause can locally accelerate electrons up to multiple-MeV; when storm recovers, plasmapause moves back to large L, while the highly-relativistic electrons generated at low L continue to diffuse inward and slow decay by pitch angle diffusion from plasmaspheric hiss. The delicate balance between slow inward radial diffusion and weak pitch angle scattering creates a fixed inner boundary or barrier for ultra-relativistic electrons. The barrier is found to locate at a fixed L location, independent of the initial penetration depth of electrons that is correlated with the plasmapause location. Our simulation results quantitatively reproduce the evolution of the flux versus L profile, the L location of the barrier, and the decay rate of highly energetic electrons right outside the barrier. 1Baker, D. N., et al. (2014), Nearly Impenetrable Barrier to Inward Ultra-relativistic Magnetospheric

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

    NASA Astrophysics Data System (ADS)

    Noack, Reinhard M.; Gebhard, Florian

    1998-03-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-09-01

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

  5. Multi-module model for ultra-relativistic heavy ion collisions.

    SciTech Connect

    Magas, V.; Csernai, L. P.; Strottman, D.

    2001-01-01

    The Multi Module Model for Ultra-Relativistic Heavy Ion Collisioiis at RHIC and LHC energies is presented. It uses the Effective String Rope Model for the calculation of the initial stages of the reaction; the output of this model is used as the initial state for the subsequent one-fluid calculations. It is shown that such an initial state leads to the creation of the third flow component. The hydrodynainical evolution of the energy density distribution is also presented.

  6. Comparisons of cross-section predictions for relativistic iron and argon beams with semiempirical fragmentation models

    NASA Technical Reports Server (NTRS)

    Townsend, Lawrence W.; Tripathi, Ram K.; Khan, Ferdous

    1993-01-01

    Cross-section predictions with semi-empirical nuclear fragmentation models from the Langley Research Center and the Naval Research Laboratory are compared with experimental data for the breakup of relativistic iron and argon projectile nuclei in various targets. Both these models are commonly used to provide fragmentation cross-section inputs into galactic cosmic ray transport codes for shielding and exposure analyses. Overall, the Langley model appears to yield better agreement with the experimental data.

  7. Axisymmetric toroidal modes of general relativistic magnetized neutron star models

    SciTech Connect

    Asai, Hidetaka; Lee, Umin E-mail: lee@astr.tohoku.ac.jp

    2014-07-20

    We calculate axisymmetric toroidal modes of magnetized neutron stars with a solid crust in the general relativistic Cowling approximation. We assume that the interior of the star is threaded by a poloidal magnetic field, which is continuous at the surface with an outside dipole field. We examine the cases of the field strength B{sub S} ∼ 10{sup 16} G at the surface. Since separation of variables is not possible for the oscillations of magnetized stars, we employ finite series expansions for the perturbations using spherical harmonic functions. We find discrete normal toroidal modes of odd parity, but no toroidal modes of even parity are found. The frequencies of the toroidal modes form distinct mode sequences and the frequency in a given mode sequence gradually decreases as the number of radial nodes of the eigenfunction increases. From the frequency spectra computed for neutron stars of different masses, we find that the frequency is almost exactly proportional to B{sub S} and is well represented by a linear function of R/M for a given B{sub S}, where M and R are the mass and radius of the star. The toroidal mode frequencies for B{sub S} ∼ 10{sup 15} G are in the frequency range of the quasi-periodic oscillations (QPOs) detected in the soft-gamma-ray repeaters, but we find that the toroidal normal modes cannot explain all the detected QPO frequencies.

  8. Mean-Field Theory of the Solar Dynamo

    NASA Astrophysics Data System (ADS)

    Schmitt, D.

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

  9. Mean-field theory of the solar dynamo

    NASA Astrophysics Data System (ADS)

    Schmitt, Dieter

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

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

    NASA Astrophysics Data System (ADS)

    Graefe, Eva-Maria; Liverani, Chiara

    2013-11-01

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

  11. Particle spectra and efficiency in nonlinear relativistic shock acceleration - survey of scattering models

    NASA Astrophysics Data System (ADS)

    Ellison, Donald C.; Warren, Donald C.; Bykov, Andrei M.

    2016-03-01

    We include a general form for the scattering mean free path, λmfp(p), in a nonlinear Monte Carlo model of relativistic shock formation and Fermi acceleration. Particle-in-cell simulations, as well as analytic work, suggest that relativistic shocks tend to produce short-scale, self-generated magnetic turbulence that leads to a scattering mean free path with a stronger momentum dependence than the λmfp ∝ p dependence for Bohm diffusion. In unmagnetized shocks, this turbulence is strong enough to dominate the background magnetic field so the shock can be treated as parallel regardless of the initial magnetic field orientation, making application to γ-ray bursts, pulsar winds, type Ibc supernovae, and extragalactic radio sources more straightforward and realistic. In addition to changing the scale of the shock precursor, we show that, when nonlinear effects from efficient Fermi acceleration are taken into account, the momentum dependence of λmfp(p) has an important influence on the efficiency of cosmic ray production as well as the accelerated particle spectral shape. These effects are absent in non-relativistic shocks and do not appear in relativistic shock models unless nonlinear effects are self-consistently described. We show, for limited examples, how the changes in Fermi acceleration translate to changes in the intensity and spectral shape of γ-ray emission from proton-proton interactions and pion-decay radiation.

  12. The Mean-Field Limit for a Regularized Vlasov-Maxwell Dynamics

    NASA Astrophysics Data System (ADS)

    Golse, François

    2012-03-01

    The present work establishes the mean-field limit of a N-particle system towards a regularized variant of the relativistic Vlasov-Maxwell system, following the work of Braun-Hepp [Commun Math Phys 56:101-113, 1977] and Dobrushin [Func Anal Appl 13:115-123, 1979] for the Vlasov-Poisson system. The main ingredients in the analysis of this system are (a) a kinetic formulation of the Maxwell equations in terms of a distribution of electromagnetic potential in the momentum variable, (b) a regularization procedure for which an analogue of the total energy—i.e. the kinetic energy of the particles plus the energy of the electromagnetic field—is conserved and (c) an analogue of Dobrushin's stability estimate for the Monge-Kantorovich-Rubinstein distance between two solutions of the regularized Vlasov-Poisson dynamics adapted to retarded potentials.

  13. Unstable infinite nuclear matter in stochastic mean field approach

    SciTech Connect

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

    1994-04-01

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

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

    NASA Astrophysics Data System (ADS)

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

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

  15. Mean field dynamo saturation: toward understanding conflicting results

    NASA Astrophysics Data System (ADS)

    Blackman, Eric G.; Field, George B.

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

  16. Stochastic Mean-Field Dynamics For Nuclear Collisions

    SciTech Connect

    Ayik, Sakir

    2008-11-11

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

  17. Absorbing boundaries in the mean-field approximation

    SciTech Connect

    Jhala, Chirag; Dreissigacker, Ingo; Lein, Manfred

    2010-12-15

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

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

    SciTech Connect

    Jiang Yin; Zhuang Pengfei

    2011-03-15

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

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

    SciTech Connect

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

    1999-06-28

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

  20. Project: Modeling Relativistic Electrons from Nuclear Explosions in the Magnetosphere

    SciTech Connect

    Cowee, Misa; Gary, S. Peter; Winske, Dan; Liu, Kaijun

    2012-07-17

    We present a summary of the FY12 activities for DTRA-funded project 'Modeling Relativistic Electrons from Nuclear Explosions in the Magnetosphere'. We briefly review the outstanding scientific questions and discuss the work done in the last year to try to answer these questions. We then discuss the agenda for this Technical Meeting with the DTRA sponsors. In the last year, we have continued our efforts to understand artificial radiation belts from several different perspectives: (1) Continued development of Electron Source Model (ESM) and comparison to HANE test data; (2) Continued studies of relativistic electron scattering by waves in the natural radiation belts; (3) Began study of self-generated waves from the HANE electrons; and (4) Began modeling for the UCLA laser experiment.

  1. Relativistic model of secondary-electron energy spectra in electron-impact ionization

    SciTech Connect

    Miller, J.H. ); Manson, S.T. )

    1991-10-01

    A relativistic model for differential electron-impact-ionization cross sections that allows the energy spectrum of secondary electrons to be calculated over a wide range of primary-electron energies is presented. The semiempirical method requires only experimental total ionization cross sections and optical oscillator strengths for the target species of interest, but other information, if available, can be incorporated to make the formulation still more accurate. Results for ionization of helium indicate that the lower limit on primary-electron energy for application of the model is about 100 eV. The simple analytic form of the model facilitates investigation of the regions of the secondary-electron energy spectrum where relativistic effects are important.

  2. Thermal entanglement of spins in mean-field clusters

    SciTech Connect

    Asoudeh, M.; Karimipour, V.

    2006-06-15

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

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

    NASA Astrophysics Data System (ADS)

    Nguyen, Toan; Bruinsma, Robijn; Gelbart, William

    2006-03-01

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

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

    NASA Astrophysics Data System (ADS)

    Huang, Haiping; Toyoizumi, Taro

    2015-05-01

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

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

    PubMed

    Suárez, G; Hoyuelos, M; Mártin, H

    2015-12-01

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

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

    SciTech Connect

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

    1993-11-01

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

  7. Applicability of self-consistent mean-field theory

    SciTech Connect

    Guo Lu; Sakata, Fumihiko; Zhao Enguang

    2005-02-01

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

  8. The model with many moments for relativistic electron beams: A simplified solution

    SciTech Connect

    Carrisi, Maria Cristina; Pennisi, Sebastiano

    2011-02-15

    In the 1980s, Amendt and Weitzner proposed an interesting model capable to describe relativistic electron beams. It concerned 14 independent variables and the closure was obtained by using the entropy and the Einstein relativity principles. As we know from literature, an extension to many moments allows to achieve an improvement in the results. Three years ago, we exhibited a macroscopic model with an arbitrary but fixed number of moments for relativistic extended thermodynamics. Such model was more general than those previously appeared in literature, so it was applicable even to materials different from an electron beam. Subsequently, we found the closure of such model consistent with the entropy and the Einstein relativity principles, up to whatever order with respect to equilibrium. The solution was determined in terms of a family of arbitrary single variable functions arising from integration. Those results have a very complex shape and are very difficult to handle so a simplification is necessary. In this paper we will reach this goal. Furthermore, we will prove that by fixing a certain order n{sub p} with respect to equilibrium and a scalar valued single variable function, appearing at that order, then all the terms appearing at orders n{<=}n{sub p} are determined without introducing any other function. This result has already been found for the nonrelativistic case but its extension to the relativistic framework is not straightforward and it requires a supplementary mathematical tool: the above mentioned simplification in the shape of the solutions.

  9. Improved modeling of relativistic collisions and collisional ionization in particle-in-cell codes

    SciTech Connect

    Perez, F.; Gremillet, L.; Decoster, A.; Drouin, M.; Lefebvre, E.

    2012-08-15

    An improved Monte Carlo collisional scheme modeling both elastic and inelastic interactions has been implemented into the particle-in-cell code CALDER[E. Lefebvre et al., Nucl. Fusion 43, 629 (2003)]. Based on the technique proposed by Nanbu and Yonemura [J. Comput. Phys. 145, 639 (1998)] allowing to handle arbitrarily weighted macro-particles, this binary collision scheme uses a more compact and accurate relativistic formulation than the algorithm recently worked out by Sentoku and Kemp [J. Comput. Phys. 227, 6846 (2008)]. Our scheme is validated through several test cases, demonstrating, in particular, its capability of modeling the electrical resistivity and stopping power of a solid-density plasma over a broad parameter range. A relativistic collisional ionization scheme is developed within the same framework, and tested in several physical scenarios. Finally, our scheme is applied in a set of integrated particle-in-cell simulations of laser-driven fast electron transport.

  10. Relativistic model for the nonmesonic weak decay of single-lambda hypernuclei

    NASA Astrophysics Data System (ADS)

    Fontoura, C. E.; Krmpotić, F.; Galeão, A. P.; De Conti, C.; Krein, G.

    2016-06-01

    Having in mind its future extension for theoretical investigations related to charmed nuclei, we develop a relativistic formalism for the nonmesonic weak decay (NMWD) of single-Λ hypernuclei in the framework of the independent-particle shell model and with the dynamics represented by the (π ,K) one-meson-exchange model. Numerical results for the one-nucleon-induced transition rates of {}{{Λ }}12{{C}} are presented and compared with those obtained in the analogous nonrelativistic calculation. There is satisfactory agreement between the two approaches, and the only noteworthy difference is that the ratio {{{Γ }}}n/{{{Γ }}}p is appreciably higher and closer to the experimental value in the relativistic calculation. The ability of describing existing data, including the most recent ones, on NMWD of Λ-hypernuclei, warrants application of the formalism to evaluate similar decay processes in charmed nuclei.

  11. Structure of relativistic shocks in pulsar winds: A model of the wisps in the Crab Nebula

    NASA Technical Reports Server (NTRS)

    Gallant, Yves A.; Arons, Jonathan

    1994-01-01

    We propose a model of a optical 'wisps' of the Crab Nebula, features observed in the nebular synchrotron surface brightness near the central pulsar, as manifestations of the internal structure of the shock terminating the pulsar wind. We assume that this wind is composed of ions and a much denser plasma of electrons and positrons, frozen together to a toroidal magnetic field and flowing relativistically. We construct a form of solitary wave model of the shock structure in which we self-consistently solve for the ion orbits and the dynamics of the relativistically hot, magnetized e(+/-) background flow. We ignore dispersion in the ion energies, and we treat the pairs as an adiabatic fluid. The synchrotron emission enhancements, observed as the wisps, are then explained as the regions where reflection of the ions in the self-consistent magnetic field causes compressions of the e(+/-).

  12. Breit and Quantum Electrodynamics Energy Contributions in Multielectron Atoms from the Relativistic Screened Hydrogenic Model

    NASA Astrophysics Data System (ADS)

    Di Rocco, Héctor O.; Lanzini, Fernando

    2016-04-01

    The correction to the Coulomb repulsion between two electrons due to the exchange of a transverse photon, referred to as the Breit interaction, as well as the main quantum electrodynamics contributions to the atomic energies (self-energy and vacuum polarization), are calculated using the recently formulated relativistic screened hydrogenic model. Comparison with the results of multiconfiguration Dirac-Hartree-Fock calculations and experimental X- ray energies is made.

  13. Dynamical gap generation in graphene nanoribbons: An effective relativistic field theoretical model

    SciTech Connect

    Chaves, A. J.; Paula, W. de; Frederico, T.; Lima, G. D.; Cordeiro, C. E.; Delfino, A.

    2011-04-15

    We show that the assumption of a nontrivial zero band gap for a graphene sheet within an effective relativistic field theoretical model description of interacting Dirac electrons on the surface of graphene describes the experimental band gap of graphene nanoribbons for a wide range of widths. The graphene band gap is dynamically generated, corresponding to a nontrivial gapless solution, found in the limit of an infinitely wide graphene ribbon. The nanoribbon band gap is determined by the experimental graphene work function.

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

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

  15. Applicability of fluid-dynamical modeling of nucleus-nucleus collisions at relativistic energies

    NASA Astrophysics Data System (ADS)

    Hazineh, Dean; Auvinen, Jussi; Nahrgang, Marlene; Bass, Steffen

    2015-10-01

    At sufficiently high temperatures and densities, similar to the conditions found in the early universe, QCD matter forms a deconfined state called the quark gluon plasma (QGP). This state of matter can be created in collisions of ultra-relativistic heavy-ions, and RHIC data suggests that this QGP behaves similar to an ideal fluid. Viscous relativistic fluid dynamics therefore is one of the preferred theoretical tools to model the time-evolution and properties of the QGP. As the collision energy or the system size is decreased, the range of applicability of viscous fluid dynamics becomes smaller as the length scale of the interaction among the basic constituents is similar to the overall scale of the collision system itself. In order to investigate the validity of fluid-dynamical modeling of proton-nucleus and nucleus-nucleus collisions at LHC and RHIC, we conduct an analysis of the spatial and temporal evolution of the Knudsen number, i.e. the ratio of the microscopic mean free path to the macroscopic length scale of the system. We show results for large and small collision systems, as a function of the specific shear viscosity, and discuss the range of applicability of fluid-dynamical modeling in relativistic proton-nucleus and nucleus-nucleus collisions at different energies.

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

    PubMed

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

    2005-11-01

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

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

    PubMed

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

    2014-10-17

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-10-01

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

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

    PubMed

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

    2016-05-11

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

  20. Multi Module Modeling of Ultra-Relativistic Heavy Ion Collisions.

    SciTech Connect

    Magas, V. K.; Csernai, L. P.; Keranen, A.; Manninen, J.; Strottman, D. D.

    2002-01-01

    Multi Module Model is required for the realistic and detailed description of an ultrarelativistic heavy ion reaction. We are working in the framework of such a model: initial stages are described by Effective String Rope Model with expanding final streaks; hydrodynamical approach is used for the intermediate stages. This paper is mainly devoted to Third Module - the one dealing with Freeze Out (FO). Two possibilities are discussed in details: (A) freeze out at the constant time hypersurface, where the statistical production model is used to describe post FO particle species; and (B) simultaneous hadronization and freeze out from supercooled QGP. For the last case the ALCOR-like algorithm for calculation of the post FO particle species is presented, due to the fact that these do not have time to reach chemical equilibrium.

  1. Breaking of relativistically intense longitudinal space charge waves: A description using Dawson sheet model

    NASA Astrophysics Data System (ADS)

    Sengupta, Sudip

    2014-02-01

    Spatio-temporal evolution of relativistically intense longitudinal space charge waves in a cold homogeneous plasma is studied analytically as well as numerically, as an initial value problem, using Dawson sheet model. It is found that, except for very special initial conditions which generates the well known longitudinal Akhiezer-Polovin mode, for all other initial conditions, the waves break through a novel mechanism called phase mixing at an amplitude well below the Akhiezer-Polovin limit. An immediate consequence of this is, that Akhiezer-Polovin waves break when subjected to arbitrarily small longitudinal perturbations. We demonstrate this by performing extensive numerical simulations. This result may be of direct relevance to ultrashort, ultraintense laser/beam pulse-plasma interaction experiments where relativistically intense waves are routinely excited.

  2. Breaking of relativistically intense longitudinal space charge waves: A description using Dawson sheet model

    SciTech Connect

    Sengupta, Sudip

    2014-02-11

    Spatio-temporal evolution of relativistically intense longitudinal space charge waves in a cold homogeneous plasma is studied analytically as well as numerically, as an initial value problem, using Dawson sheet model. It is found that, except for very special initial conditions which generates the well known longitudinal Akhiezer-Polovin mode, for all other initial conditions, the waves break through a novel mechanism called phase mixing at an amplitude well below the Akhiezer-Polovin limit. An immediate consequence of this is, that Akhiezer-Polovin waves break when subjected to arbitrarily small longitudinal perturbations. We demonstrate this by performing extensive numerical simulations. This result may be of direct relevance to ultrashort, ultraintense laser/beam pulse-plasma interaction experiments where relativistically intense waves are routinely excited.

  3. Initial fields and instabilities in the classical model of relativistic heavy-ion collisions

    SciTech Connect

    Fukushima, Kenji

    2007-08-15

    Color Glass Condensate (CGC) provides a classical description of dense gluon matter at high energies. Using the McLerran-Venugopalan (MV) model we calculate the initial energy density {epsilon}({tau}) in the early stage of the relativistic nucleus-nucleus collision. Our analytical formula reproduces the quantitative results from lattice discretized simulations and leads to an estimate {epsilon}({tau}=0.1 fm)=40{approx}50 GeV{center_dot}fm{sup -3} in the (central) Au-Au collision at BNL Relativistic Heavy Ion Collider. We then formulate instabilities with respect to soft fluctuations that violate boost invariance inherent in hard CGC backgrounds. We find unstable modes arising, which are attributed to ensemble average over the initial CGC fields.

  4. Initial fields and instabilities in the classical model of relativistic heavy-ion collisions

    NASA Astrophysics Data System (ADS)

    Fukushima, Kenji

    2007-08-01

    Color Glass Condensate (CGC) provides a classical description of dense gluon matter at high energies. Using the McLerran-Venugopalan (MV) model we calculate the initial energy density ɛ(τ) in the early stage of the relativistic nucleus-nucleus collision. Our analytical formula reproduces the quantitative results from lattice discretized simulations and leads to an estimate ɛ(τ=0.1fm)=40~50GeV·fm-3 in the (central) Au-Au collision at BNL Relativistic Heavy Ion Collider. We then formulate instabilities with respect to soft fluctuations that violate boost invariance inherent in hard CGC backgrounds. We find unstable modes arising, which are attributed to ensemble average over the initial CGC fields.

  5. Weakly nonlinear ion-acoustic excitations in a relativistic model for dense quantum plasma.

    PubMed

    Behery, E E; Haas, F; Kourakis, I

    2016-02-01

    The dynamics of linear and nonlinear ionic-scale electrostatic excitations propagating in a magnetized relativistic quantum plasma is studied. A quantum-hydrodynamic model is adopted and degenerate statistics for the electrons is taken into account. The dispersion properties of linear ion acoustic waves are examined in detail. A modified characteristic charge screening length and "sound speed" are introduced, for relativistic quantum plasmas. By employing the reductive perturbation technique, a Zakharov-Kuznetzov-type equation is derived. Using the small-k expansion method, the stability profile of weakly nonlinear slightly supersonic electrostatic pulses is also discussed. The effect of electron degeneracy on the basic characteristics of electrostatic excitations is investigated. The entire analysis is valid in a three-dimensional as well as in two-dimensional geometry. A brief discussion of possible applications in laboratory and space plasmas is included. PMID:26986431

  6. Thermoinertial bouncing of a relativistic collapsing sphere: A numerical model

    SciTech Connect

    Herrera, L.; Di Prisco, A.; Barreto, W.

    2006-01-15

    We present a numerical model of a collapsing radiating sphere, whose boundary surface undergoes bouncing due to a decreasing of its inertial mass density (and, as expected from the equivalence principle, also of the 'gravitational' force term) produced by the 'inertial' term of the transport equation. This model exhibits for the first time the consequences of such an effect, and shows that under physically reasonable conditions this decreasing of the gravitational term in the dynamic equation may be large enough as to revert the collapse and produce a bouncing of the boundary surface of the sphere.

  7. Relativistic quark model for the Omega- electromagnetic form factors

    SciTech Connect

    G. Ramalho, K. Tsushima, Franz Gross

    2009-08-01

    We compute the Omega- electromagnetic form factors and the decuplet baryon magnetic moments using a quark model application of the Covariant Spectator Theory. Our predictions for the Omega- electromagnetic form factors can be tested in the future by lattice QCD simulations at the physical strange quark mass.

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

    SciTech Connect

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

    2013-05-20

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

  9. Particle Identification in the Dynamical String-Parton Model of Relativistic Heavy-Ion Collisions

    NASA Astrophysics Data System (ADS)

    Malov, D. E.; Umar, A. S.; Ernst, D. J.; Dean, D. J.

    The dynamical string-parton model for relativistic heavy-ion collisions is generalized to include particle identification of the final-state hadrons by phenomenologically quantizing the masses of the classical strings which result from string breaking. General features of the Nambu-Gotō strings are used to motivate a model that identifies a mass window near the physical mass of a meson, and does not allow the string to decay further if its mass falls within the window. Data from e+e- collisions in the region √ {s} =10 to 30 GeV are well reproduced by this model.

  10. Relativistic model of anisotropic charged fluid sphere in general relativity

    NASA Astrophysics Data System (ADS)

    Pant, Neeraj; Pradhan, N.; Bansal, Rajeev K.

    2016-01-01

    In this present paper, we present a class of static, spherically symmetric charged anisotropic fluid models of super dense stars in isotropic coordinates by considering a particular type of metric potential, a specific choice of electric field intensity E and pressure anisotropy factor Δ which involve parameters K (charge) and α (anisotropy) respectively. The solutions so obtained are utilized to construct the models for super-dense stars like neutron stars and strange quark stars. Our solutions are well behaved within the following ranges of different constant parameters. In the absence of pressure anisotropy and charge present model reduces to the isotropic model Pant et al. (Astrophys. Space Sci. 330:353-359, 2010). Our solution is well behaved in all respects for all values of X lying in the range 0< X ≤ 0.18, α lying in the range 0 ≤ α ≤6.6, K lying in the range 0< K ≤ 6.6 and Schwarzschild compactness parameter "u" lying in the range 0< u ≤ 0.38. Since our solution is well behaved for a wide ranges of the parameters, we can model many different types of ultra-cold compact stars like quark stars and neutron stars. We have shown that corresponding to X=0.088, α=0.6 and K=4.3 for which u=0.2054 and by assuming surface density ρb = 4.6888 × 10^{14} g/cm3 the mass and radius are found to be 1.51 M_{\\varTheta} and 10.90 km respectively. Assuming surface density ρb = 2 × 10^{14} g/cm3 the mass and radius for a neutron star candidate are found to be 2.313 M_{\\varTheta} and 16.690 km respectively. Hence we obtain masses and radii that fall in the range of what is generally expected for quark stars and neutron stars.

  11. Octet Baryon Electromagnetic Form Factors in a Relativistic Quark Model

    SciTech Connect

    Gilberto Ramalho, Kazuo Tsushima

    2011-09-01

    We study the octet baryon electromagnetic properties by applying the covariant spectator quark model, and provide covariant parametrization that can be used to study baryon electromagnetic reactions. While we use the lattice QCD data in the large pion mass regime (small pion cloud effects) to determine the parameters of the model in the valence quark sector, we use the nucleon physical and octet baryon magnetic moment data to parameterize the pion cloud contributions. The valence quark contributions for the octet baryon electromagnetic form factors are estimated by extrapolating the lattice parametrization in the large pion mass regime to the physical regime. As for the pion cloud contributions, we parameterize them in a covariant, phenomenological manner, combined with SU(3) symmetry. We also discuss the impact of the pion cloud effects on the octet baryon electromagnetic form factors and their radii.

  12. On redshift and parallaxes in general relativistic kinematical world models

    SciTech Connect

    Perlick, V. )

    1990-08-01

    A Lorentzian space-time ({ital M},{ital g}), along with an observer field (=timelike vector field) {ital V}, are considered. Several theorems are presented that are concerned with the redshift and parallaxes in such a model. Here the term parallaxes'' stands for the relative motion of two observers at the celestial sphere of a third observer. As an important mathematical tool, the index form along a lightlike geodesic is used.

  13. Relativistic Modelling of Stable Anisotropic Super-Dense Star

    NASA Astrophysics Data System (ADS)

    Maurya, S. K.; Gupta, Y. K.; Jasim, M. K.

    2015-08-01

    In the present article we have obtained new set of exact solutions of Einstein field equations for anisotropic fluid spheres by using the Herrera et al. [1] algorithm. The anisotropic fluid solutions so obtained join continuously to the Schwarzschild exterior solution across the pressure-free boundary. It is observed that most of the new anisotropic solutions are well-behaved and are used to construct the super-dense star models such as neutron stars and pulsars.

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

    NASA Astrophysics Data System (ADS)

    Qi, Chong

    2012-10-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2012-09-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2012-01-01

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

  17. Photoelectron energy spectra from elastic rescattering in ultrastrong laser fields: A relativistic extension of the three-step model

    NASA Astrophysics Data System (ADS)

    Luo, S. S.; Grugan, P. D.; Walker, B. C.

    2015-03-01

    Using a relativistic adaptation of a three-step recollision model we calculate photoelectron energy spectra for ionization with elastic scattering in ultrastrong laser fields up to 24 a.u. (2 ×1019 W/cm 2) . Hydrogenlike and noble gas species with Hartree-Fock scattering potentials show a reduction in elastic rescattering beyond 6 ×1016 W/cm 2 when the laser Lorentz deflection of the photoelectron exceeds its wave-function spread. A relativistic rescattering enhancement occurs at 2 ×1018 W/cm 2, commensurate with the relativistic motion of a classical electron in a single field cycle. The noble gas results are compared with available experiments. The theory approach is well suited to modeling scattering in the ultrastrong intensity regime that lies between traditional strong fields and extreme relativistic interactions.

  18. Critical rotation of general-relativistic polytropic models revisited

    NASA Astrophysics Data System (ADS)

    Geroyannis, V.; Karageorgopoulos, V.

    2013-09-01

    We develop a perturbation method for computing the critical rotational parameter as a function of the equatorial radius of a rigidly rotating polytropic model in the "post-Newtonia approximation" (PNA). We treat our models as "initial value problems" (IVP) of ordinary differential equations in the complex plane. The computations are carried out by the code dcrkf54.f95 (Geroyannis and Valvi 2012 [P1]; modified Runge-Kutta-Fehlberg code of fourth and fifth order for solving initial value problems in the complex plane). Such a complex-plane treatment removes the syndromes appearing in this particular family of IVPs (see e.g. P1, Sec. 3) and allows continuation of the numerical integrations beyond the surface of the star. Thus all the required values of the Lane-Emden function(s) in the post-Newtonian approximation are calculated by interpolation (so avoiding any extrapolation). An interesting point is that, in our computations, we take into account the complete correction due to the gravitational term, and this issue is a remarkable difference compared to the classical PNA. We solve the generalized density as a function of the equatorial radius and find the critical rotational parameter. Our computations are extended to certain other physical characteristics (like mass, angular momentum, rotational kinetic energy, etc). We find that our method yields results comparable with those of other reliable methods. REFERENCE: V.S. Geroyannis and F.N. Valvi 2012, International Journal of Modern Physics C, 23, No 5, 1250038:1-15.

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

    SciTech Connect

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

    2007-10-15

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

  20. Rigid rotor equilibria with non-neutral plasma: analytical relativistic two fluid model

    NASA Astrophysics Data System (ADS)

    Braga, Filipe L.; Soares, Diego N.; Lourenço, Weslley A.

    2016-07-01

    The analysis of non-neutral plasmas using fluid models in general implies on the resolutions of coupled differential equations, in particular the so-called rigid-rotor plasma equilibrium involves the solution of the Poisson-Ampère and moment equations. The present work shows an analytical solution for this model at a relativistic cold adiabatic plasma approximation considering a two species plasma where electric field gives an important contribution for the plasma confinement. According to the present study the most important plasma parameters responsible for confinement are the particles angular velocities, as expected, and mass ratio between the species.

  1. One-pion exchange current effects on magnetic form factor in the relativistic formalism

    NASA Astrophysics Data System (ADS)

    Zhang, Cun; Liu, Jian; Ren, Zhongzhou

    2016-08-01

    One-pion exchange current effects on the magnetic form factors of some odd nuclei are studied in the relativistic formalism. The Dirac wave functions of nucleons are calculated from the relativistic mean-field theory. After fitting to experimental data by quenching factors, it is found that taking the one-pion exchange currents into account gives a better description of the magnetic form factor. The root-mean-square radii of the valance nucleon orbits are also calculated in RMF model, which coincide with experimental radii extracted with meson exchange current corrections.

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

    NASA Astrophysics Data System (ADS)

    Kadanoff, Leo P.

    2009-12-01

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

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

    NASA Astrophysics Data System (ADS)

    Han, Xizhi; Wu, Biao

    2016-02-01

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

  4. Non-relativistic matter and dark energy in a quantum conformal model

    NASA Astrophysics Data System (ADS)

    Kashyap, Gopal; Jain, Pankaj; Mitra, Subhadip

    2016-02-01

    We consider a generalization of the Standard Model whose action displays conformal invariance in d dimensions. The model contains a strongly coupled dark matter sector which breaks conformal symmetry dynamically. The model evades conformal anomaly and leads to identically zero vacuum energy in flat space-time. Hence it does not suffer from the problem of fine tuning of the cosmological constant. We determine the contribution of non-relativistic matter to the energy-momentum tensor and determine a parameter regime in which it approximately reduces to the standard result. We show how dark energy and dark matter arises in this model. We discuss the parameter range for which the model reduces to the ΛCDM model and hence is consistent with observations.

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

    NASA Astrophysics Data System (ADS)

    Banerjee, Tanmoy

    2015-06-01

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

  6. Mean-field inference of Hawkes point processes

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-03-01

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

  8. A Semi-Empirical Model for Forecasting Relativistic Electrons at Geostationary Orbit

    NASA Technical Reports Server (NTRS)

    Lyatsky, Wladislaw; Khazanov, George V.

    2008-01-01

    We developed a new prediction model for forecasting relativistic (>2MeV) electrons, which provides a VERY HIGH correlation between predicted and actually measured electron fluxes at geostationary orbit. This model implies the multi-step particle acceleration and is based on numerical integrating two linked continuity equations for primarily accelerated particles and relativistic electrons. The model includes a source and losses, and used solar wind data as only input parameters. We used the coupling function which is a best-fit combination of solar wind/Interplanetary Magnetic Field parameters, responsible for the generation of geomagnetic activity, as a source. The loss function was derived from experimental data. We tested the model for four year period 2004-2007. The correlation coefficient between predicted and actual values of the electron fluxes for whole four year period as well as for each of these years is about 0.9. The high and stable correlation between the computed and actual electron fluxes shows that the reliable forecasting these electrons at geostationary orbit is possible. The correlation coefficient between predicted and actual electron fluxes is stable and incredibly high.

  9. Relativistic blast-wave model for the rapid flux variations of AO 0235+164 and other compact radio sources

    NASA Technical Reports Server (NTRS)

    Marscher, A. P.

    1978-01-01

    A relativistic blast-wave version of a signal-screen model is developed which can adequately explain the details of the flux-density and structural variations of compact extragalactic radio sources. The relativistic motion implied by flux variations is analyzed with respect to the synchrotron spectrum of the BL Lac object AO 0235+164 observed during outbursts, and a signal-screen model for rapidly expanding shells produced by ultrarelativistic blast waves is examined. The approximate observed structure of the blast wave at three stages in its evolution is illustrated, each stage is described, and the model is applied to the flux density outburst in AO 0235+164 observed in late 1975. The results show that a relativistic blast-wave model can in general reproduce the main features of the observed flux variations in compact sources. Some problems with the proposed model are briefly discussed.

  10. Normalizing a relativistic model of X-ray reflection. Definition of the reflection fraction and its implementation in relxill

    NASA Astrophysics Data System (ADS)

    Dauser, T.; García, J.; Walton, , D. J.; Eikmann, W.; Kallman, T.; McClintock, J.; Wilms, J.

    2016-05-01

    Aims: The only relativistic reflection model that implements a parameter relating the intensity incident on an accretion disk to the observed intensity is relxill. The parameter used in earlier versions of this model, referred to as the reflection strength, is unsatisfactory; it has been superseded by a parameter that provides insight into the accretion geometry, namely the reflection fraction. The reflection fraction is defined as the ratio of the coronal intensity illuminating the disk to the coronal intensity that reaches the observer. Methods: The relxill model combines a general relativistic ray-tracing code and a photoionization code to compute the component of radiation reflected from an accretion that is illuminated by an external source. The reflection fraction is a particularly important parameter for relativistic models with well-defined geometry, such as the lamp post model, which is a focus of this paper. Results: Relativistic spectra are compared for three inclinations and for four values of the key parameter of the lamp post model, namely the height above the black hole of the illuminating, on-axis point source. In all cases, the strongest reflection is produced for low source heights and high spin. A low-spin black hole is shown to be incapable of producing enhanced relativistic reflection. Results for the relxill model are compared to those obtained with other models and a Monte Carlo simulation. Conclusions: Fitting data by using the relxill model and the recently implemented reflection fraction, the geometry of a system can be constrained. The reflection fraction is independent of system parameters such as inclination and black hole spin. The reflection-fraction parameter was implemented with the name refl_frac in all flavours of the relxill model, and the non-relativistic reflection model xillver, in v0.4a (18 January 2016).

  11. Ground state heavy baryon production in a relativistic quark-diquark model

    SciTech Connect

    Gomshi Nobary, M. A.; Sepahvand, R.

    2007-12-01

    We use current-current interaction to calculate the fragmentation functions to describe the production of spin-1/2, spin-1/2{sup '}, and spin-3/2 baryons with massive constituents in a relativistic quark-diquark model. Our results are in their analytic forms and are applicable for singly, doubly, and triply heavy baryons. We discuss the production of {omega}{sub bbc}, {omega}{sub bcc}, and {omega}{sub ccc} baryons in some detail. The results are satisfactorily compared with those obtained for triply heavy baryons calculated in a perturbative regime within reasonable values of the parameters involved.

  12. A relativistic quark model with infrared confinement and the tetraquark state

    SciTech Connect

    Dubnicka, S.; Dubnickova, A. Z.; Ivanov, M. A.; Koerner, J. G.; Saidullaeva, G. G.

    2011-05-23

    We explore the consequences of treating the X(3872) meson as a tetraquark bound state. As dynamical framework we employ a relativistic constituent quark model which includes infrared confinement in an effective way. We calculate the decay widths of the observed channels X{yields}J/{psi}+2{pi}(3{pi}) and X{yields}D-bar{sup 0}+D{sup 0}+{pi}{sup 0} via the intermediate off-shell states X{yields}J/{psi}+{rho}({omega}) and X{yields}D-bar+D*. For reasonable values of the size parameter {Lambda}{sub X} of the X(3872) we find consistency with the available experimental data.

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

    NASA Astrophysics Data System (ADS)

    Blackman, E. G.

    2010-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2011-09-01

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

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

    PubMed

    Abe, Kiharu; Sumi, Tomonari; Koga, Kenichiro

    2016-03-01

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

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

    PubMed

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

    2011-09-01

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

  17. A New Multi-dimensional General Relativistic Neutrino Hydrodynamics Code for Core-collapse Supernovae. II. Relativistic Explosion Models of Core-collapse Supernovae

    NASA Astrophysics Data System (ADS)

    Müller, Bernhard; Janka, Hans-Thomas; Marek, Andreas

    2012-09-01

    We present the first two-dimensional general relativistic (GR) simulations of stellar core collapse and explosion with the COCONUT hydrodynamics code in combination with the VERTEX solver for energy-dependent, three-flavor neutrino transport, using the extended conformal flatness condition for approximating the space-time metric and a ray-by-ray-plus ansatz to tackle the multi-dimensionality of the transport. For both of the investigated 11.2 and 15 M ⊙ progenitors we obtain successful, though seemingly marginal, neutrino-driven supernova explosions. This outcome and the time evolution of the models basically agree with results previously obtained with the PROMETHEUS hydro solver including an approximative treatment of relativistic effects by a modified Newtonian potential. However, GR models exhibit subtle differences in the neutrinospheric conditions compared with Newtonian and pseudo-Newtonian simulations. These differences lead to significantly higher luminosities and mean energies of the radiated electron neutrinos and antineutrinos and therefore to larger energy-deposition rates and heating efficiencies in the gain layer with favorable consequences for strong nonradial mass motions and ultimately for an explosion. Moreover, energy transfer to the stellar medium around the neutrinospheres through nucleon recoil in scattering reactions of heavy-lepton neutrinos also enhances the mentioned effects. Together with previous pseudo-Newtonian models, the presented relativistic calculations suggest that the treatment of gravity and energy-exchanging neutrino interactions can make differences of even 50%-100% in some quantities and is likely to contribute to a finally successful explosion mechanism on no minor level than hydrodynamical differences between different dimensions.

  18. A NEW MULTI-DIMENSIONAL GENERAL RELATIVISTIC NEUTRINO HYDRODYNAMICS CODE FOR CORE-COLLAPSE SUPERNOVAE. II. RELATIVISTIC EXPLOSION MODELS OF CORE-COLLAPSE SUPERNOVAE

    SciTech Connect

    Mueller, Bernhard; Janka, Hans-Thomas; Marek, Andreas E-mail: thj@mpa-garching.mpg.de

    2012-09-01

    We present the first two-dimensional general relativistic (GR) simulations of stellar core collapse and explosion with the COCONUT hydrodynamics code in combination with the VERTEX solver for energy-dependent, three-flavor neutrino transport, using the extended conformal flatness condition for approximating the space-time metric and a ray-by-ray-plus ansatz to tackle the multi-dimensionality of the transport. For both of the investigated 11.2 and 15 M{sub Sun} progenitors we obtain successful, though seemingly marginal, neutrino-driven supernova explosions. This outcome and the time evolution of the models basically agree with results previously obtained with the PROMETHEUS hydro solver including an approximative treatment of relativistic effects by a modified Newtonian potential. However, GR models exhibit subtle differences in the neutrinospheric conditions compared with Newtonian and pseudo-Newtonian simulations. These differences lead to significantly higher luminosities and mean energies of the radiated electron neutrinos and antineutrinos and therefore to larger energy-deposition rates and heating efficiencies in the gain layer with favorable consequences for strong nonradial mass motions and ultimately for an explosion. Moreover, energy transfer to the stellar medium around the neutrinospheres through nucleon recoil in scattering reactions of heavy-lepton neutrinos also enhances the mentioned effects. Together with previous pseudo-Newtonian models, the presented relativistic calculations suggest that the treatment of gravity and energy-exchanging neutrino interactions can make differences of even 50%-100% in some quantities and is likely to contribute to a finally successful explosion mechanism on no minor level than hydrodynamical differences between different dimensions.

  19. THE EVOLUTION OF PSR J0737-3039B AND A MODEL FOR RELATIVISTIC SPIN PRECESSION

    SciTech Connect

    Perera, B. B. P.; McLaughlin, M. A.; Kramer, M.; Lyne, A. G.; Stairs, I. H.; Ferdman, R. D.; Freire, P. C. C.; Possenti, A.; Burgay, M.; Breton, R. P.; Manchester, R. N.; Camilo, F.

    2010-10-01

    We present the evolution of the radio emission from the 2.8 s pulsar of the double pulsar system PSR J0737- 3039A/B. We provide an update on the Burgay et al. analysis by describing the changes in the pulse profile and flux density over five years of observations, culminating in the B pulsar's radio disappearance in 2008 March. Over this time, the flux density decreases by 0.177 mJy yr{sup -1} at the brightest orbital phases and the pulse profile evolves from a single to a double peak, with a separation rate of 2.{sup 0}6 yr{sup -1}. The pulse profile changes are most likely caused by relativistic spin precession but cannot be easily explained with a circular hollow-cone beam as in the model of Clifton and Weisberg. Relativistic spin precession, coupled with an elliptical beam, can model the pulse profile evolution well and the reappearance is expected to happen in {approx}2035 with the same part of the beam or in {approx}2014 if we assume a symmetric beam shape. This particular beam shape predicts geometrical parameters for the two bright orbital phases which are consistent with and similar to those derived by Breton et al. However, the observed decrease in flux over time and B's eventual disappearance cannot be easily explained by the model and may be due to the changing influence of A on B.

  20. A magnetohydrodynamic model of the M87 jet. II. Self-consistent quad-shock jet model for optical relativistic motions and particle acceleration

    SciTech Connect

    Nakamura, Masanori

    2014-04-20

    We describe a new paradigm for understanding both relativistic motions and particle acceleration in the M87 jet: a magnetically dominated relativistic flow that naturally produces four relativistic magnetohydrodynamic (MHD) shocks (forward/reverse fast and slow modes). We apply this model to a set of optical super- and subluminal motions discovered by Biretta and coworkers with the Hubble Space Telescope during 1994-1998. The model concept consists of ejection of a single relativistic Poynting jet, which possesses a coherent helical (poloidal + toroidal) magnetic component, at the remarkably flaring point HST-1. We are able to reproduce quantitatively proper motions of components seen in the optical observations of HST-1 with the same model we used previously to describe similar features in radio very long baseline interferometry observations in 2005-2006. This indicates that the quad relativistic MHD shock model can be applied generally to recurring pairs of super/subluminal knots ejected from the upstream edge of the HST-1 complex as observed from radio to optical wavelengths, with forward/reverse fast-mode MHD shocks then responsible for observed moving features. Moreover, we identify such intrinsic properties as the shock compression ratio, degree of magnetization, and magnetic obliquity and show that they are suitable to mediate diffusive shock acceleration of relativistic particles via the first-order Fermi process. We suggest that relativistic MHD shocks in Poynting-flux-dominated helical jets may play a role in explaining observed emission and proper motions in many active galactic nuclei.

  1. Ground-based VLBI relativistic time delay model of solar system objects

    NASA Astrophysics Data System (ADS)

    Zhang, Han-wei; Zheng, Yong; Du, Lane

    A relativistic time delay model for ground-based VLBI observations of solar system objects is derived first in the barycentric reference system of the solar system, and then transformed to the non-spinning geocentric reference system. A universal analytic expression is presented, from which the model given by Pin Jin-song can be obtained. It is also pointed out that the several models for extragalactic source observations, such as those proposed by Zhu & Groten, Shapiro and those recommended by IERS(92, 96), can be derived from this formula if the geocentric distance of the source is taken to be infinite. This formula is recommended for practical applications because it is rigorously analytic and errorless. The range of application of the derived formula and the estimation of the size of various neglected terms, as well as the calculation procedures of the model are discussed in detail.

  2. Ground-based VLBI relativistic time delay model for Spacecrafts in Solar System

    NASA Astrophysics Data System (ADS)

    Zhang, H. W.; Zheng, Y.; Du, L.

    2003-02-01

    The ground VLBI relativistic time delay model for spacecraft in the solar system is derived, first in the barycentric reference system and then transferred to the non-spinning geocentric reference system. A universal analyzed expression is presented, from which another model given by Ping Jinsong can be obtained. It is also pointed that several models for extra-galactic sources are available from the formula such as Zhu-Groten?Shapiro and IERS(92,96) recommended models if the geocentric distances of the sources become infinite large. Adopting the formula given here is recommended in processing VLBI observable due to its rigorousness and errors-free. The using limitation of the formula and estimation in magnitude for various neglecting items as well as the computation steps in details are also discussed.

  3. Lagrangian theory of structure formation in relativistic cosmology. II. Average properties of a generic evolution model

    NASA Astrophysics Data System (ADS)

    Buchert, Thomas; Nayet, Charly; Wiegand, Alexander

    2013-06-01

    Kinematical and dynamical properties of a generic inhomogeneous cosmological model, spatially averaged with respect to free-falling (generalized fundamental) observers, are investigated for the matter model “irrotational dust.” Paraphrasing a previous Newtonian investigation, we present a relativistic generalization of a backreaction model based on volume-averaging the “relativistic Zel’dovich approximation.” In this model we investigate the effect of “kinematical backreaction” on the evolution of cosmological parameters as they are defined in an averaged inhomogeneous cosmology, and we show that the backreaction model interpolates between orthogonal symmetry properties by covering subcases of the plane-symmetric solution, the Lemaître-Tolman-Bondi solution and the Szekeres solution. We so obtain a powerful model that lays the foundations for quantitatively addressing curvature inhomogeneities as they would be interpreted as “dark energy” or “dark matter” in a quasi-Newtonian cosmology. The present model, having a limited architecture due to an assumed Friedmann-Lemaître-Robertson-Walker background, is nevertheless capable of replacing 1/4 of the needed amount for dark energy on domains of 200 Mpc in diameter for typical (one-sigma) fluctuations in a cold dark matter initial power spectrum. However, the model is far from explaining dark energy on larger scales (spatially), where a 6% effect on 400 Mpc domains is identified that can be traced back to an on average negative intrinsic curvature today. One drawback of the quantitative results presented is the fact that the epoch when backreaction is effective on large scales and leads to volume acceleration lies in the future. We discuss this issue in relation to the initial spectrum, the dark matter problem, the coincidence problem, and the fact that large-scale dark energy is an effect on the past light cone (not spatial), and we pinpoint key elements of future research.

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

    NASA Astrophysics Data System (ADS)

    Contucci, Pierluigi; Gallo, Ignacio; Menconi, Giulia

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

  6. Modeling the relativistic runaway electron avalanche and the feedback mechanism with GEANT4

    NASA Astrophysics Data System (ADS)

    Skeltved, Alexander Broberg; Østgaard, Nikolai; Carlson, Brant; Gjesteland, Thomas; Celestin, Sebastien

    2014-11-01

    This paper presents the first study that uses the GEometry ANd Tracking 4 (GEANT4) toolkit to do quantitative comparisons with other modeling results related to the production of terrestrial gamma ray flashes and high-energy particle emission from thunderstorms. We will study the relativistic runaway electron avalanche (RREA) and the relativistic feedback process, as well as the production of bremsstrahlung photons from runaway electrons. The Monte Carlo simulations take into account the effects of electron ionization, electron by electron (Møller), and electron by positron (Bhabha) scattering as well as the bremsstrahlung process and pair production, in the 250 eV to 100 GeV energy range. Our results indicate that the multiplication of electrons during the development of RREAs and under the influence of feedback are consistent with previous estimates. This is important to validate GEANT4 as a tool to model RREAs and feedback in homogeneous electric fields. We also determine the ratio of bremsstrahlung photons to energetic electrons Nγ/Ne. We then show that the ratio has a dependence on the electric field, which can be expressed by the avalanche time τ(E) and the bremsstrahlung coefficient α(ɛ). In addition, we present comparisons of GEANT4 simulations performed with a "standard" and a "low-energy" physics list both validated in the 1 keV to 100 GeV energy range. This comparison shows that the choice of physics list used in GEANT4 simulations has a significant effect on the results.

  7. Stellar electron-capture rates calculated with the finite-temperature relativistic random-phase approximation

    SciTech Connect

    Niu, Y. F.; Paar, N.; Vretenar, D.; Meng, J.

    2011-04-15

    We introduce a self-consistent microscopic theoretical framework for modeling the process of electron capture on nuclei in stellar environment, based on relativistic energy density functionals. The finite-temperature relativistic mean-field model is used to calculate the single-nucleon basis and the occupation factors in a target nucleus, and J{sup {pi}}=0{sup {+-}}, 1{sup {+-}}, and 2{sup {+-}} charge-exchange transitions are described by the self-consistent finite-temperature relativistic random-phase approximation. Cross sections and rates are calculated for electron capture on {sup 54,56}Fe and {sup 76,78}Ge in stellar environment, and results compared with predictions of similar and complementary model calculations.

  8. Structure of hypernuclei in relativistic approaches

    NASA Astrophysics Data System (ADS)

    Hagino, Kouichi; Yao, Jiangming

    We review the relativistic mean-field approaches to hypernuclear physics. This includes Lambda hypernuclei, anti-Lambda hypernuclei, and multistrangeness hypernuclei. We particularly focus on the properties of both ground state and collective excitations, hyperon binding energies, spinorbit splittings, magnetic moments, a stabilization of drip-line nuclei, and the hyperon impurity effect on nuclear collectivity. We also discuss briefly the influence of hyperons on neutron stars. We conclude that the relativistic mean-field approaches have achieved a great success in the studies of hypernuclear physics.

  9. Mean-field study of the role of lateral cracks in microtubule dynamics

    NASA Astrophysics Data System (ADS)

    Margolin, Gennady; Goodson, Holly V.; Alber, Mark S.

    2011-04-01

    A link between dimer-scale processes and microtubule (MT) dynamics at macroscale is studied by comparing simulations obtained using computational dimer-scale model with its mean-field approximation. The novelty of the mean-field model (MFM) is in its explicit representation of inter-protofilament cracks, as well as in the direct incorporation of the dimer-level kinetics. Due to inclusion of both longitudinal and lateral dimer interactions, the MFM is two dimensional, in contrast to previous theoretical models of MTs. It is the first analytical model that predicts and quantifies crucial features of MT dynamics such as (i) existence of a minimal soluble tubulin concentration needed for the polymerization (with concentration represented as a function of model parameters), (ii) existence of steady-state growth and shortening phases (given with their respective velocities), and (iii) existence of an unstable pause state near zero velocity. In addition, the size of the GTP cap of a growing MT is estimated. Theoretical predictions are shown to be in good agreement with the numerical simulations.

  10. Model of spatial distribution of relativistic electron fluxes in vicinity of Jupiter's moon Europa

    NASA Astrophysics Data System (ADS)

    Podzolko, Mikhail; Veselovsky, Igor; Getselev, Igor; Gubar, Yury

    This research was made as a part of a project of future space mission to the system of Jupiter, being developed by Russian Federal Space Agency. Currently several mission strategies are being considered, including placing the spacecraft into the low-altitude orbit around Jupiter’s moon Europa and possibly landing on its surface. In the region of Europa’s orbit the spacecraft will be affected by very strong radiation from the Jupiter’s radiation belts. The absorbed dose during 2 months under shielding compared to that for “Galileo” spacecraft will amount to almost 1 megarad. The major contribution to the dose will originate from relativistic electrons. However, near Europa part of the charged particle flux will be shaded by the moon. This reduction of the fluxes is nonuniform, depends on the particle energy and pitch-angle and differs for the surface and the low-altitude orbit. It is caused by a number of factors: complexity of particle trajectories relative to Europa, the flux anisotropy, variations of Europa’s position relative to Jupiter’s magnetic equator plane, magnetic and electric field disturbance in vicinity of Europa, the tenuous atmosphere of the moon. In the current study modeling of relativistic electron flux spatial distribution near Europa and on its surface and computation of the radiation doses have been made, taking into account several of mentioned above factors.

  11. Radiative Models of Sagittarius A* and M87 from Relativistic MHD Simulations

    NASA Astrophysics Data System (ADS)

    Dexter, J.; Agol, E.; Fragile, P. C.; McKinney, J. C.

    2012-07-01

    Ongoing millimeter VLBI observations with the Event Horizon Telescope allow unprecedented study of the innermost portion of black hole accretion flows. Interpreting the observations requires relativistic, time-dependent physical modeling. We discuss the comparison of radiative transfer calculations from general relativistic MHD simulations of Sagittarius A* and M87 with current and future mm-VLBI observations. This comparison allows estimates of the viewing geometry and physical conditions of the Sgr A* accretion flow. The viewing geometry for M87 is already constrained from observations of its large-scale jet, but, unlike Sgr A*, there is no consensus for its millimeter emission geometry or electron population. Despite this uncertainty, as long as the emission region is compact, robust predictions for the size of its jet launching region can be made. For both sources, the black hole shadow may be detected with future observations including ALMA and/or the LMT, which would constitute the first direct evidence for a black hole event horizon.

  12. The Analysis of Lagrangian and Hamiltonian Properties of the Classical Relativistic Electrodynamics Models and Their Quantization

    NASA Astrophysics Data System (ADS)

    Bogolubov, Nikolai N.; Prykarpatsky, Anatoliy K.

    2010-05-01

    The Lagrangian and Hamiltonian properties of classical electrodynamics models and their associated Dirac quantizations are studied. Using the vacuum field theory approach developed in (Prykarpatsky et al. Theor. Math. Phys. 160(2): 1079-1095, 2009 and The field structure of a vacuum, Maxwell equations and relativity theory aspects. Preprint ICTP) consistent canonical Hamiltonian reformulations of some alternative classical electrodynamics models are devised, and these formulations include the Lorentz condition in a natural way. The Dirac quantization procedure corresponding to the Hamiltonian formulations is developed. The crucial importance of the rest reference systems, with respect to which the dynamics of charged point particles is framed, is explained and emphasized. A concise expression for the Lorentz force is derived by suitably taking into account the duality of electromagnetic field and charged particle interactions. Finally, a physical explanation of the vacuum field medium and its relativistic properties fitting the mathematical framework developed is formulated and discussed.

  13. Spin Hall effect in two-dimensional systems within the relativistic phase shift model

    NASA Astrophysics Data System (ADS)

    Johansson, Annika; Herschbach, Christian; Fedorov, Dmitry V.; Henk, Jürgen; Mertig, Ingrid

    2015-11-01

    Recently, a relativistic phase shift model (RPSM) was introduced [D. V. Fedorov et al., Phys. Rev. B 88, 085116 (2013), 10.1103/PhysRevB.88.085116] to describe the skew-scattering mechanism of the spin Hall effect caused by impurities in bulk crystals. Here, we present its analog derived for two-dimensional (2D) systems. The proposed 2D-RPSM is applied to one-monolayer noble-metal films with various substitutional impurities and the obtained results are compared with those of corresponding first-principles calculations. We demonstrate that, in contrast to the three-dimensional RPSM, the considered model does not provide a sufficient qualitative description of the transport properties. Therefore, an ab initio treatment is necessary for the description of the spin Hall effect in two-dimensional crystals.

  14. Isospin dependence of entrainment in superfluid neutron stars in a relativistic model

    NASA Astrophysics Data System (ADS)

    Kheto, Apurba; Bandyopadhyay, Debades

    2014-01-01

    We study the entrainment effect between superfluid neutrons and charge neutral fluid (called the proton fluid) which is made of protons and electrons in a neutron star interior within the two-fluid formalism and using a relativistic model where baryon-baryon interaction is mediated by the exchange of σ, ω, and ρ mesons. This model of strong interaction also includes scalar self-interactions. The entrainment matrix and entrainment parameter are calculated using the parameter sets of Glendenning (GL) and another non-linear (NL3) interaction. The inclusion of ρ mesons strongly influences the entrainment parameter (ɛmom) in a superfluid neutron star. The entrainment parameter is constant at the core and drops rapidly at the surface. It takes values within the physical range.

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

    SciTech Connect

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

    2009-01-28

    We study the spherical to prolate-deformed shape transition in {sup 144-158}Sm and {sup 146-160}Gd isotopes with modern calculations beyond the mean field with the Gogny D1S force. We compare the results with the shape-phase transition predicted by the collective Hamiltonian model and with the experimental data. Our calculations do not support the existence of a first order phase transition in these isotopic chains in the viewpoint of the Bohr Hamiltonian neither the interpretation of the nuclei N = 90 as critical points.

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

    NASA Astrophysics Data System (ADS)

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

    2014-07-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2010-11-01

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

  18. Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral

    NASA Astrophysics Data System (ADS)

    Tanizaki, Yuya; Nishimura, Hiromichi; Kashiwa, Kouji

    2015-05-01

    The fermion sign problem appearing in the mean-field approximation is considered, and the systematic computational scheme of the free energy is devised by using the Lefschetz-thimble method. We show that the Lefschetz-thimble method respects the reflection symmetry, which makes physical quantities manifestly real at any order of approximations using complex saddle points. The formula is demonstrated through the Airy integral as an example, and its application to the Polyakov-loop effective model of dense QCD is discussed in detail.

  19. Mean-field analysis of quantum annealing with XX-type terms

    NASA Astrophysics Data System (ADS)

    Nishimori, Hidetoshi

    I analyze the role of XX-type terms in quantum annealing for a few mean-field systems including the Ising ferromagnet and the Hopfield model, both with many-body interactions. The XX-type terms are shown to be effective to remove first-order quantum phase transitions, which exist in the conventional implementation of quantum annealing using only transverse fields. This means an exponential increase in efficiency, and is suggestive for the design of quantum annealers. I will discuss how and why this phenomenon emerges and what may happen on realistic finite-dimensional lattices.

  20. Solving the inverse Ising problem by mean-field methods in a clustered phase space with many states

    NASA Astrophysics Data System (ADS)

    Decelle, Aurélien; Ricci-Tersenghi, Federico

    2016-07-01

    In this work we explain how to properly use mean-field methods to solve the inverse Ising problem when the phase space is clustered, that is, many states are present. The clustering of the phase space can occur for many reasons, e.g., when a system undergoes a phase transition, but also when data are collected in different regimes (e.g., quiescent and spiking regimes in neural networks). Mean-field methods for the inverse Ising problem are typically used without taking into account the eventual clustered structure of the input configurations and may lead to very poor inference (e.g., in the low-temperature phase of the Curie-Weiss model). In this work we explain how to modify mean-field approaches when the phase space is clustered and we illustrate the effectiveness of our method on different clustered structures (low-temperature phases of Curie-Weiss and Hopfield models).

  1. Solving the inverse Ising problem by mean-field methods in a clustered phase space with many states.

    PubMed

    Decelle, Aurélien; Ricci-Tersenghi, Federico

    2016-07-01

    In this work we explain how to properly use mean-field methods to solve the inverse Ising problem when the phase space is clustered, that is, many states are present. The clustering of the phase space can occur for many reasons, e.g., when a system undergoes a phase transition, but also when data are collected in different regimes (e.g., quiescent and spiking regimes in neural networks). Mean-field methods for the inverse Ising problem are typically used without taking into account the eventual clustered structure of the input configurations and may lead to very poor inference (e.g., in the low-temperature phase of the Curie-Weiss model). In this work we explain how to modify mean-field approaches when the phase space is clustered and we illustrate the effectiveness of our method on different clustered structures (low-temperature phases of Curie-Weiss and Hopfield models). PMID:27575082

  2. Modelling the high-energy emission from gamma-ray binaries using numerical relativistic hydrodynamics

    NASA Astrophysics Data System (ADS)

    Dubus, G.; Lamberts, A.; Fromang, S.

    2015-09-01

    Context. Detailed modelling of the high-energy emission from gamma-ray binaries has been propounded as a path to pulsar wind physics. Aims: Fulfilling this ambition requires a coherent model of the flow and its emission in the region where the pulsar wind interacts with the stellar wind of its companion. Methods: We have developed a code that follows the evolution and emission of electrons in the shocked pulsar wind based on inputs from a relativistic hydrodynamical simulation. The code is used to model the well-documented spectral energy distribution and orbital modulations from LS 5039. Results: The pulsar wind is fully confined by a bow shock and a back shock. The particles are distributed into a narrow Maxwellian, emitting mostly GeV photons, and a power law radiating very efficiently over a broad energy range from X-rays to TeV gamma rays. Most of the emission arises from the apex of the bow shock. Doppler boosting shapes the X-ray and very high energy (VHE) lightcurves, constraining the system inclination to i ≈ 35°. There is tension between the hard VHE spectrum and the level of X-ray to MeV emission, which requires differing magnetic field intensities that are hard to achieve with constant magnetisation σ and Lorentz factor Γp of the pulsar wind. Our best compromise implies σ ≈ 1 and Γp ≈ 5 × 103, so respectively higher and lower than the typical values in pulsar wind nebulae. Conclusions: The high value of σ derived here, where the wind is confined close to the pulsar, supports the classical picture that has pulsar winds highly magnetised at launch. However, such magnetisations will require that further investigations are based on relativistic MHD simulations. Movies associated to Figs. A.1-A.4 are available in electronic form at http://www.aanda.org

  3. Mean Field Approximation for Biased Diffusion on Japanese Inter-Firm Trading Network

    PubMed Central

    Watanabe, Hayafumi

    2014-01-01

    By analysing the financial data of firms across Japan, a nonlinear power law with an exponent of 1.3 was observed between the number of business partners (i.e. the degree of the inter-firm trading network) and sales. In a previous study using numerical simulations, we found that this scaling can be explained by both the money-transport model, where a firm (i.e. customer) distributes money to its out-edges (suppliers) in proportion to the in-degree of destinations, and by the correlations among the Japanese inter-firm trading network. However, in this previous study, we could not specifically identify what types of structure properties (or correlations) of the network determine the 1.3 exponent. In the present study, we more clearly elucidate the relationship between this nonlinear scaling and the network structure by applying mean-field approximation of the diffusion in a complex network to this money-transport model. Using theoretical analysis, we obtained the mean-field solution of the model and found that, in the case of the Japanese firms, the scaling exponent of 1.3 can be determined from the power law of the average degree of the nearest neighbours of the network with an exponent of −0.7. PMID:24626149

  4. Mean field approximation for biased diffusion on Japanese inter-firm trading network.

    PubMed

    Watanabe, Hayafumi

    2014-01-01

    By analysing the financial data of firms across Japan, a nonlinear power law with an exponent of 1.3 was observed between the number of business partners (i.e. the degree of the inter-firm trading network) and sales. In a previous study using numerical simulations, we found that this scaling can be explained by both the money-transport model, where a firm (i.e. customer) distributes money to its out-edges (suppliers) in proportion to the in-degree of destinations, and by the correlations among the Japanese inter-firm trading network. However, in this previous study, we could not specifically identify what types of structure properties (or correlations) of the network determine the 1.3 exponent. In the present study, we more clearly elucidate the relationship between this nonlinear scaling and the network structure by applying mean-field approximation of the diffusion in a complex network to this money-transport model. Using theoretical analysis, we obtained the mean-field solution of the model and found that, in the case of the Japanese firms, the scaling exponent of 1.3 can be determined from the power law of the average degree of the nearest neighbours of the network with an exponent of -0.7. PMID:24626149

  5. Quasi-Radial Modes of Pulsating Neutron Stars: Numerical Results for General-Relativistic Rigidly Rotating Polytropic Models

    NASA Astrophysics Data System (ADS)

    Geroyannis, Vassilis; Tzelati, Eleftheria

    In this paper we compute general-relativistic polytropic models simulating rigidly rotating, pulsating neutron stars. These relativistic compact objects, with a radius of $\\sim 10 \\, \\mathrm{km}$ and mass between $\\sim 1.4$ and $3.2$ solar masses, are closely related to pulsars. We emphasize on computing the change in the pulsation eigenfrequencies owing to a rigid rotation, which, in turn, is a decisive issue for studying stability of such objects. In our computations, we keep rotational perturbation terms of up to second order in the angular velocity.

  6. Relativistic description of inclusive quasielastic proton-nucleus scattering with relativistic distorted-wave impulse approximation and random-phase approximation

    SciTech Connect

    Niekerk, D. D. van; Ventel, B. I. S. van der; Titus, N. P.; Hillhouse, G. C.

    2011-04-15

    We present a fully relativistic model for polarized inclusive quasielastic proton-nucleus scattering that includes relativistic distorted waves for the projectile and ejectile (RDWIA), as well as the relativistic random-phase approximation (RPA) applied to the target nucleus. Using a standard relativistic impulse approximation treatment of quasielastic scattering and a two-body Scalar, Pseudoscalar, Vector, Axial vector, Tensor (SPVAT) form of the current operator, it is shown how the behavior of the projectile/ejectile and target can be decoupled. Distortion effects are included via a full partial-wave expansion of the relativistic wave functions. Target correlations are included via the relativistic RPA applied to mean-field theory in quantum hadrodynamics. A number of novel analytical and numerical techniques are employed to aid in this highly nontrivial calculation. A baseline plane-wave calculation is performed for the reaction {sup 40}Ca(p-vector,p-vector{sup '}) at an energy of 500 MeV and an angle {theta}{sub c.m.}=40 deg. Here it is found that the effect of isoscalar correlations is a quenching of the cross section that is expected to become more pronounced at lower energies or for higher-density targets. A RDWIA calculation shows additional reduction and if isoscalar target correlations are included this effect is enhanced.

  7. Relativistic, model-independent, multichannel 2 →2 transition amplitudes in a finite volume

    NASA Astrophysics Data System (ADS)

    Briceño, Raúl A.; Hansen, Maxwell T.

    2016-07-01

    We derive formalism for determining 2 +J →2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or nonidentical and, in the latter case, can be either degenerate or nondegenerate. We further accommodate any number of strongly coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of the ρ -meson form factor, in which the unstable nature of the ρ is rigorously accommodated.

  8. Higher-dimensional charged shear-free relativistic models with heat flux

    NASA Astrophysics Data System (ADS)

    Nyonyi, Y.; Maharaj, S. D.; Govinder, K. S.

    2014-07-01

    We analyze shear-free spherically symmetric relativistic models of gravitating fluids with heat flow and electric charge defined on higher-dimensional manifolds. The solution to the Einstein-Maxwell system is governed by the pressure isotropy condition, which depends on the space-time dimension. We study this highly nonlinear partial differential equation using Lie's group theoretic approach. The Lie symmetry generators that leave the equation invariant are determined. We provide exact solutions to the gravitational potentials using the first symmetry admitted by the equation. Our new exact solutions contain the earlier results for the four-dimensional case. Using the other Lie generators, we are able to provide solutions to the gravitational potentials or reduce the order of the master equation to a first order nonlinear differential equation. We also find expressions for the causal and Eckart temperatures and show their dependence on the dimension.

  9. Relativistic density functional theory modeling of plutonium and americium higher oxide molecules.

    PubMed

    Zaitsevskii, Andréi; Mosyagin, Nikolai S; Titov, Anatoly V; Kiselev, Yuri M

    2013-07-21

    The results of electronic structure modeling of plutonium and americium higher oxide molecules (actinide oxidation states VI through VIII) by two-component relativistic density functional theory are presented. Ground-state equilibrium molecular structures, main features of charge distributions, and energetics of AnO3, AnO4, An2On (An=Pu, Am), and PuAmOn, n = 6-8, are determined. In all cases, molecular geometries of americium and mixed plutonium-americium oxides are similar to those of the corresponding plutonium compounds, though chemical bonding in americium oxides is markedly weaker. Relatively high stability of the mixed heptoxide PuAmO7 is noticed; the Pu(VIII) and especially Am(VIII) oxides are expected to be unstable. PMID:23883027

  10. Spectroscopy and Regge trajectories of heavy quarkonia in the relativistic quark model

    SciTech Connect

    Ebert, D.; Faustov, R. N.; Galkin, V. O.

    2013-12-15

    The mass spectra of charmonia and bottomonia are calculated in the framework of the relativistic quark model up to high orbital and radial excitations. The Regge trajectories of heavy quarkonia are constructed both in the (J,M{sup 2}) and (n{sub r},M{sup 2}) planes, where J is the total angular momentum and nr is the radial quantum number. All daughter trajectories turn out to be almost linear and parallel, while parent trajectories exhibit some nonlinearity. Such nonlinearity occurs only in the vicinity of ground states and few lowest excitations and is more pronounced for bottomonia, while it is only marginal for charmonia. The obtained results are compared with available experimental data, and a possible interpretation of the new charmonium-like states above open charm production threshold is discussed.

  11. AN ANGLE-DEPENDENT SYNCHROTRON SELF-COMPTON MODEL FOR RELATIVISTIC JET SOURCES

    SciTech Connect

    Jamil, O.; Boettcher, M.

    2012-11-01

    We report on the development of a numerical code to calculate the angle-dependent synchrotron + synchrotron self-Compton radiation from relativistic jet sources with partially ordered magnetic fields and anisotropic particle distributions. Using a multi-zone radiation transfer approach, we can simulate magnetic-field configurations ranging from perfectly ordered (unidirectional) to randomly oriented (tangled). We demonstrate that synchrotron self-Compton model fits to the spectral energy distributions (SEDs) of extragalactic jet sources may be possible with a wide range of magnetic-field values, depending on their orientation with respect to the jet axis and the observer. This is illustrated with the example of a spectral fit to the SED of Mrk 421 from multiwavelength observations in 2006, where acceptable fits are possible with magnetic-field values varying within a range of an order of magnitude for different degrees of B-field alignment and orientation.

  12. Relativistic Quark-Model Results for Baryon Ground and Resonant States

    SciTech Connect

    Plessas, W.; Melde, T.

    2008-10-13

    Latest results from a study of baryon ground and resonant states within relativistic constituent quark models are reported. After recalling some typical spectral properties, the description of ground states, especially with regard to the nucleon and hyperon electromagnetic structures, is addressed. In the following, recent covariant predictions for pion, eta, and kaon partial decay widths of light and strange baryon resonances below 2 GeV are summarized. These results exhibit a characteristic pattern that is distinct from nonrelativistic or relativized decay studies performed so far. Together with a detailed analysis of the spin, flavor, and spatial structures of the wave functions, it supports a new and extended classification scheme of baryon ground and resonant states into SU(3) flavor multiplets.

  13. Relativistic, model-independent, multichannel 2→2 transition amplitudes in a finite volume

    DOE PAGESBeta

    Briceno, Raul A.; Hansen, Maxwell T.

    2016-07-13

    We derive formalism for determining 2 + J → 2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or non-identical and, in the latter case, can be either degenerate or non-degenerate. We further accommodate any number of strongly-coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of themore » $$\\rho$$-meson form factor, in which the unstable nature of the $$\\rho$$ is rigorously accommodated. In conclusion, we also discuss how this work will impact future extractions of nuclear parity and hadronic long-range matrix elements from lattice QCD.« less

  14. Relativistic density functional theory modeling of plutonium and americium higher oxide molecules

    NASA Astrophysics Data System (ADS)

    Zaitsevskii, Andréi; Mosyagin, Nikolai S.; Titov, Anatoly V.; Kiselev, Yuri M.

    2013-07-01

    The results of electronic structure modeling of plutonium and americium higher oxide molecules (actinide oxidation states VI through VIII) by two-component relativistic density functional theory are presented. Ground-state equilibrium molecular structures, main features of charge distributions, and energetics of AnO3, AnO4, An2On (An=Pu, Am), and PuAmOn, n = 6-8, are determined. In all cases, molecular geometries of americium and mixed plutonium-americium oxides are similar to those of the corresponding plutonium compounds, though chemical bonding in americium oxides is markedly weaker. Relatively high stability of the mixed heptoxide PuAmO7 is noticed; the Pu(VIII) and especially Am(VIII) oxides are expected to be unstable.

  15. Modeling the relativistic runaway electron avalanche and the feedback mechanism with GEANT4

    PubMed Central

    Skeltved, Alexander Broberg; Østgaard, Nikolai; Carlson, Brant; Gjesteland, Thomas; Celestin, Sebastien

    2014-01-01

    This paper presents the first study that uses the GEometry ANd Tracking 4 (GEANT4) toolkit to do quantitative comparisons with other modeling results related to the production of terrestrial gamma ray flashes and high-energy particle emission from thunderstorms. We will study the relativistic runaway electron avalanche (RREA) and the relativistic feedback process, as well as the production of bremsstrahlung photons from runaway electrons. The Monte Carlo simulations take into account the effects of electron ionization, electron by electron (Møller), and electron by positron (Bhabha) scattering as well as the bremsstrahlung process and pair production, in the 250 eV to 100 GeV energy range. Our results indicate that the multiplication of electrons during the development of RREAs and under the influence of feedback are consistent with previous estimates. This is important to validate GEANT4 as a tool to model RREAs and feedback in homogeneous electric fields. We also determine the ratio of bremsstrahlung photons to energetic electrons Nγ/Ne. We then show that the ratio has a dependence on the electric field, which can be expressed by the avalanche time τ(E) and the bremsstrahlung coefficient α(ε). In addition, we present comparisons of GEANT4 simulations performed with a “standard” and a “low-energy” physics list both validated in the 1 keV to 100 GeV energy range. This comparison shows that the choice of physics list used in GEANT4 simulations has a significant effect on the results. Key Points Testing the feedback mechanism with GEANT4 Validating the GEANT4 programming toolkit Study the ratio of bremsstrahlung photons to electrons at TGF source altitude PMID:26167437

  16. Looking into the inner black hole accretion disc with relativistic models of iron line

    NASA Astrophysics Data System (ADS)

    Svoboda, Jiri

    2010-07-01

    We discuss black hole spin measurements employing the relativistic iron line profiles in the X-ray domain. We investigate the iron line band for two representative sources -- MCG -6-30-15 (active galaxy) and GX 339-4 (X-ray binary). We compare two models of the broad iron line, LAOR and KYRLINE. We realise that the spin is currently determined entirely from the position of the marginally stable orbit while the effect of the spin on the overall line shape would be resolvable with higher resolution X-ray missions. We show that the precision of the spin measurements depends on an unknown angular distribution of the disc emission. We study how sensitive the spin determination is to the assumptions about the intrinsic angular distribution of the emitted photons. We find that the uncertainty of the directional emission distribution translates to 20% uncertainty in the determination of the radius of marginally stable orbit. We perform radiation transfer computations of an X-ray irradiated disc atmosphere (NOAR code) to determine the directionality of outgoing X-rays in the 2-10 keV energy band. Based on these computations, we find that from the simple formulae for the directionality, the isotropic case reproduces the simulated data with the best accuracy. The most frequently used limb-darkening law favours higher values of spin and, in addition, a steeper radial emissivity profile. Furthermore, we present a spectral analysis of an XMM-Newton observation of a Seyfert 1.5 galaxy IRAS 05078+1626 being the first X-ray spectroscopic study of this source. The lack of the significant relativistic blurring of the reflection model component suggests the accretion disc to be truncated at a farther radius.

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

    NASA Astrophysics Data System (ADS)

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

    2009-03-01

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

  18. A mean-field thermodynamic description of the kinetics of overdriven interfaces

    NASA Astrophysics Data System (ADS)

    Haxhimali, Tomorr; Belof, Jonathan; Sadigh, Babak

    A key aspect of an accurate description of shock-induced structural phase transitions is the rigorous computation of the dynamics of the interfaces between coexisting phases. In the wake of the shock, the system will be exposed to strong gradient fields that give rise to overdriven interfaces during the induced phase transformation. In this work we take a mean-field approach using a time-dependent Ginzburg-Landau formalism to describe the dynamics of such overdriven interfaces. We make a connection of the mean-field result to a quasi-Langevin description, the Kardar-Parisi-Zhang (KPZ) equation, of the kinetics of the interface. Further, larger coarse-grained descriptions of the phase transition such as the Kolmogorov-Johnson-Mehl-Avrami (KJMA) model, which are commonly coupled to hydrodynamic equations that describe the evolution of the temperature and pressure during the shock propagation, ignore the details of the dynamics and structure of the interfacial regions. Overlaying the KPZ description of the interface evolution to these coarse-grained methods will result in physically more accurate multiscale models for shock propagation. We will present results from our efforts in this regard. This work is performed under the auspices of the U. S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

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

    NASA Astrophysics Data System (ADS)

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

    2013-05-01

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

  20. Non-relativistic leptogenesis

    NASA Astrophysics Data System (ADS)

    Bödeker, Dietrich; Wörmann, Mirco

    2014-02-01

    In many phenomenologically interesting models of thermal leptogenesis the heavy neutrinos are non-relativistic when they decay and produce the baryon asymmetry of the Universe. We propose a non-relativistic approximation for the corresponding rate equations in the non-resonant case, and a systematic way for computing relativistic corrections. We determine the leading order coefficients in these equations, and the first relativistic corrections. The non-relativistic approximation works remarkably well. It appears to be consistent with results obtained using a Boltzmann equation taking into account the momentum distribution of the heavy neutrinos, while being much simpler. We also compute radiative corrections to some of the coefficients in the rate equations. Their effect is of order 1% in the regime favored by neutrino oscillation data. We obtain the correct leading order lepton number washout rate in this regime, which leads to large ( ~ 20%) effects compared to previous computations.

  1. Relativistic Effects and Polarization in Three High-Energy Pulsar Models

    NASA Technical Reports Server (NTRS)

    Dyks, J.; Harding, Alice K.; Rudak, B.

    2004-01-01

    We present the influence of the special relativistic effects of aberration and light travel time delay on pulsar high-energy lightcurves and polarization characteristics predicted by three models: the two-pole caustic model, the outer gap model, and the polar cap model. Position angle curves and degree of polarization are calculated for the models and compared with the optical data on the Crab pulsar. The relative positions of peaks in gamma-ray and radio lightcurves are discussed in detail for the models. We find that the two-pole caustic model can reproduce qualitatively the optical polarization characteristics of the Crab pulsar - fast swings of the position angle and minima in polarization degree associated with both peaks. The anticorrelation between the observed flux and the polarization degree (observed in the optical band also for B0656+14) naturally results from the caustic nature of the peaks which are produced in the model due to the superposition of radiation from many different altitudes, ie. polarized at different angles. The two-pole caustic model also provides an acceptable interpretation of the main features in the Crab's radio profile. Neither the outer gap model nor the polar cap model are able to reproduce the optical polarization data on the Crab. Although the outer gap model is very successful in reproducing the relative positions of gamma-ray and radio peaks in pulse profiles, it can reproduce the high-energy lightcurves only when photon emission from regions very close to the light cylinder is included.

  2. Phase transitions of nuclear matter beyond mean field theory

    SciTech Connect

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

    2007-10-15

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

  3. Modeling solar near-relativistic electron events. Insights into solar injection and interplanetary transport conditions

    NASA Astrophysics Data System (ADS)

    Agueda, N.; Lario, D.; Vainio, R.; Sanahuja, B.; Kilpua, E.; Pohjolainen, S.

    2009-11-01

    Context: Solar near-relativistic electrons (>30 keV) are observed as discrete events in the inner heliosphere following different types of solar transient activity. Several mechanisms have been proposed for the production of these electrons. One candidate is related to solar flare activity. Other candidates include shocks driven by fast coronal mass ejections (CMEs) or processes of magnetic reconnection in the aftermath of CMEs. Aims: We study eleven near-relativistic (NR) electron events observed by the Advanced Composition Explorer (ACE) between 1998 and 2005 with the aim of estimating the roles played by solar flares, CME-driven shocks, and processes of magnetic restructuring in the aftermath of the CMEs in the injection of NR electrons. The main goal is to infer the underlying injection profile from particle observations at 1 AU, as well as the interplanetary transport conditions. Methods: We used Monte Carlo simulations to model the transport of particles along the interplanetary magnetic field. By taking the angular response of the LEFS60 telescope of the EPAM instrument onboard ACE into account, we were able to deconvolve the transport effects from the observed intensities, and thus infer the solar injection profile. Results: In this set of events, we have identified two types of injection episodes: short (<15 min) and time-extended (>1 h). Short injection episodes seem to be associated with the flare processes and/or the reconnection phenomena in the aftermath of the CME, while time-extended episodes seem to be consistent with injection from CME-driven shocks. Conclusions: We find that there is no single scenario that operates in all the events. The interplanetary propagation of NR electrons can occur both under strong scattering and under almost scatter-free propagation conditions and several injection phases (related to flares and/or CMEs) are possible.

  4. A GENERAL RELATIVISTIC MODEL OF ACCRETION DISKS WITH CORONAE SURROUNDING KERR BLACK HOLES

    SciTech Connect

    You Bei; Cao Xinwu; Yuan Yefei E-mail: cxw@shao.ac.cn

    2012-12-20

    We calculate the structure of a standard accretion disk with a corona surrounding a massive Kerr black hole in the general relativistic frame, in which the corona is assumed to be heated by the reconnection of the strongly buoyant magnetic fields generated in the cold accretion disk. The emergent spectra of accretion disk-corona systems are calculated by using the relativistic ray-tracing method. We propose a new method to calculate the emergent Comptonized spectra from the coronae. The spectra of disk-corona systems with a modified {alpha}-magnetic stress show that both the hard X-ray spectral index and the hard X-ray bolometric correction factor L{sub bol}/L{sub X,2-10keV} increase with the dimensionless mass accretion rate, which is qualitatively consistent with the observations of active galactic nuclei. The fraction of the power dissipated in the corona decreases with increasing black hole spin parameter a, which leads to lower electron temperatures of the coronae for rapidly spinning black holes. The X-ray emission from the coronae surrounding rapidly spinning black holes becomes weak and soft. The ratio of the X-ray luminosity to the optical/UV luminosity increases with the viewing angle, while the spectral shape in the X-ray band is insensitive to the viewing angle. We find that the spectral index in the infrared waveband depends on the mass accretion rate and the black hole spin a, which deviates from the f{sub {nu}}{proportional_to}{nu}{sup 1/3} relation expected by the standard thin disk model.

  5. Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations

    NASA Astrophysics Data System (ADS)

    Vrettas, Michail D.; Opper, Manfred; Cornford, Dan

    2015-01-01

    This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.

  6. Relativistic spin effects in the baryon spectrum

    SciTech Connect

    Garcilazo, Humberto

    2005-04-01

    We study the nonstrange baryon spectrum within a three-body theory that treats relativistically both the space and the spin variables. The relativistic effects of the spin are about one order of magnitude smaller than those due to the use of relativistic momentum variables. The relativistic treatment of the spin breaks the degenerancy that is present in the nonrelativistic model and in the model with only relativistic momentum variables.

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

    NASA Astrophysics Data System (ADS)

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

    2012-07-01

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

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

    NASA Astrophysics Data System (ADS)

    Qin, Jingbo; Jie, Quanlin; Fan, Zhuo

    2016-07-01

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

  9. Cluster Mean-Field Approach to the Steady-State Phase Diagram of Dissipative Spin Systems

    NASA Astrophysics Data System (ADS)

    Jin, Jiasen; Biella, Alberto; Viyuela, Oscar; Mazza, Leonardo; Keeling, Jonathan; Fazio, Rosario; Rossini, Davide

    2016-07-01

    We show that short-range correlations have a dramatic impact on the steady-state phase diagram of quantum driven-dissipative systems. This effect, never observed in equilibrium, follows from the fact that ordering in the steady state is of dynamical origin, and is established only at very long times, whereas in thermodynamic equilibrium it arises from the properties of the (free) energy. To this end, by combining the cluster methods extensively used in equilibrium phase transitions to quantum trajectories and tensor-network techniques, we extend them to nonequilibrium phase transitions in dissipative many-body systems. We analyze in detail a model of spin-1 /2 on a lattice interacting through an X Y Z Hamiltonian, each of them coupled to an independent environment that induces incoherent spin flips. In the steady-state phase diagram derived from our cluster approach, the location of the phase boundaries and even its topology radically change, introducing reentrance of the paramagnetic phase as compared to the single-site mean field where correlations are neglected. Furthermore, a stability analysis of the cluster mean field indicates a susceptibility towards a possible incommensurate ordering, not present if short-range correlations are ignored.

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

    NASA Astrophysics Data System (ADS)

    Burnett, James; Ford, Ian J.

    2015-05-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-05-01

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

  14. Mean field spin glasses treated with PDE techniques

    NASA Astrophysics Data System (ADS)

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

    2013-07-01

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

  15. Collisional radiative average atom code based on a relativistic Screened Hydrogenic Model

    NASA Astrophysics Data System (ADS)

    Benita, A. J.; Mínguez, E.; Mendoza, M. A.; Rubiano, J. G.; Gil, J. M.; Rodríguez, R.; Martel, P.

    2015-03-01

    A steady-state and time-dependent collisional-radiative ''average-atom'' (AA) model (ATMED CR) is presented for the calculation of atomic and radiative properties of plasmas for a wide range of laboratory and theoretical conditions: coronal, local thermodynamic equilibrium or nonlocal thermodynamic equilibrium, optically thin or thick plasmas and photoionized plasmas. The radiative and collisional rates are a set of analytical approximations that compare well with more sophisticated quantum treatment of atomic rates that yield fast calculations. The atomic model is based on a new Relativistic Screened Hydrogenic Model (NRSHM) with a set of universal screening constants including nlj-splitting that has been obtained by fitting to a large database of ionization potentials and excitation energies compiled from the National Institute of Standards and Technology (NIST) database and the Flexible Atomic Code (FAC). The model NRSHM has been validated by comparing the results with ionization energies, transition energies and wave functions computed using sophisticated self-consistent codes and experimental data. All the calculations presented in this work were performed using ATMED CR code.

  16. General relativistic, nonstandard model for the dark sector of the Universe

    NASA Astrophysics Data System (ADS)

    Stichel, P. C.; Zakrzewski, W. J.

    2015-01-01

    We present a general relativistic version of the self-gravitating fluid model for the dark sector of the Universe (darkon fluid) introduced in Stichel and Zakrzewski (Phys Rev D 80:083513, 2009) and extended and reviewed in Stichel and Zakrzewski (Entropy 15:559, 2013). This model contains no free parameters in its Lagrangian. The resulting energy-momentum tensor is dustlike with a nontrivial energy flow. In an approximation valid at sub-Hubble scales we find that the present-day cosmic acceleration is not attributed to any kind of negative pressure but it is due to a dynamically determined negative energy density. This property turns out to be equivalent to a time-dependent spatial curvature. The obtained cosmological equations, at sub-Hubble scales, agree with those of the nonrelativistic model but they are given a new physical interpretation. Furthermore, we have derived the self-consistent equation to be satisfied by the nonrelativistic gravitational potential produced by a galactic halo in our model from a weak-field limit of a generalized Tolman-Oppenheimer-Volkoff equation.

  17. General relativistic considerations of the field shedding model of fast radio bursts

    NASA Astrophysics Data System (ADS)

    Punsly, Brian; Bini, Donato

    2016-06-01

    Popular models of fast radio bursts (FRBs) involve the gravitational collapse of neutron star progenitors to black holes. It has been proposed that the shedding of the strong neutron star magnetic field (B) during the collapse is the power source for the radio emission. Previously, these models have utilized the simplicity of the Schwarzschild metric which has the restriction that the magnetic flux is magnetic `hair' that must be shed before final collapse. But neutron stars have angular momentum and charge and a fully relativistic Kerr-Newman solution exists in which B has its source inside of the event horizon. In this Letter, we consider the magnetic flux to be shed as a consequence of the electric discharge of a metastable collapsed state of a Kerr-Newman black hole. It has also been argued that the shedding model will not operate due to pair creation. By considering the pulsar death line, we find that for a neutron star with B = 1011-1013 G and a long rotation period, >1s this is not a concern. We also discuss the observational evidence supporting the plausibility of magnetic flux shedding models of FRBs that are spawned from rapidly rotating progenitors.

  18. Relativistic effects on plasma expansion

    SciTech Connect

    Benkhelifa, El-Amine; Djebli, Mourad

    2014-07-15

    The expansion of electron-ion plasma is studied through a fully relativistic multi-fluids plasma model which includes thermal pressure, ambipolar electrostatic potential, and internal energy conversion. Numerical investigation, based on quasi-neutral assumption, is performed for three different regimes: nonrelativistic, weakly relativistic, and relativistic. Ions' front in weakly relativistic regime exhibits spiky structure associated with a break-down of quasi-neutrality at the expanding front. In the relativistic regime, ion velocity is found to reach a saturation limit which occurs at earlier stages of the expansion. This limit is enhanced by higher electron velocity.

  19. Nonrelativistic nucleon effective masses in nuclear matter: Brueckner-Hartree-Fock model versus relativistic Hartree-Fock model

    NASA Astrophysics Data System (ADS)

    Li, A.; Hu, J. N.; Shang, X. L.; Zuo, W.

    2016-01-01

    The density and isospin dependencies of nonrelativistic nucleon effective mass (mN*) are studied, which is a measure of the nonlocality of the single particle (s.p.) potential. It can be decoupled as the so-called k mass (mk*, i.e., the nonlocality in space) and E mass (mE*, i.e., the nonlocality in time). Both k mass and E mass are determined and compared by using the latest versions of the nonrelativistic Brueckner-Hartree-Fock (BHF) model and the relativistic Hartree-Fock (RHF) model. The latter is achieved based on the corresponding Schrödinger equivalent s.p. potential in a relativistic framework. We demonstrate the origins of different effective masses and discuss also their neutron-proton splitting in the asymmetric matter in different models. We find that the neutron-proton splittings of both the k mass and the E mass have the same asymmetry dependencies at the densities considered; namely, mk,n *>mk,p * and mE,p *>mE,n * . However, the resulting splittings of nucleon effective masses could have different asymmetry dependencies in these two models because they could be dominated either by the k mass (then we have mn*>mp* in the BHF model), or by the E mass (then we have mp*>mn* in the RHF model). The isospin splitting in the BHF model is more consistent with the recent analysis from the nucleon-nucleus-scattering data, while the small E mass mE* in the RHF case as a result of the missing ladder summation finally leads to an opposite splitting behavior.

  20. Gup-Based and Snyder Noncommutative Algebras, Relativistic Particle Models, Deformed Symmetries and Interaction: a Unified Approach

    NASA Astrophysics Data System (ADS)

    Pramanik, Souvik; Ghosh, Subir

    2013-10-01

    We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.

  1. Gup-Based and Snyder Noncommutative Algebras, Relativistic Particle Models, Deformed Symmetries and Interaction: a Unified Approach

    NASA Astrophysics Data System (ADS)

    Pramanik, Souvik; Ghosh, Subir

    2013-08-01

    We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.

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

    NASA Astrophysics Data System (ADS)

    Omori, Yukiko; Tsuchiizu, Masahisa; Suzumura, Yoshikazu

    2011-02-01

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

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

    NASA Astrophysics Data System (ADS)

    Rizzo, Tommaso

    2016-03-01

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

  4. β-decay of magic nuclei: Beyond mean-field description

    SciTech Connect

    Niu, Yifei; Niu, Zhongming; Colò, Gianluca; Vigezzi, Enrico

    2015-10-15

    Nuclear β-decay plays an important role not only in nuclear physics but also in astrophysics. The widely used self-consistent Random Phase Approximation (RPA) models tend to overestimate the half-lives of magic nuclei. To overcome this problem, we go beyond the mean-field description and include the effects of particle-vibration coupling (PVC) on top of the RPA model. The β-decay half-lives of {sup 34}Si, {sup 68}Ni, {sup 78}Ni, and {sup 132}Sn are studied within this approach in the case of the Skyrme interaction SkM*. It is found that the low-lying Gamow-Teller (GT) strength is shifted downwards with the inclusion of the PVC effect, and as a consequence, the half-lives are reduced due to the increase of the phase space available for β-decay, which leads to a good agreement between theoretical and experimental lifetimes.

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

    PubMed

    Zhang, J

    1993-01-01

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

  6. β-decay of magic nuclei: Beyond mean-field description

    NASA Astrophysics Data System (ADS)

    Niu, Yifei; Niu, Zhongming; Colò, Gianluca; Vigezzi, Enrico

    2015-10-01

    Nuclear β-decay plays an important role not only in nuclear physics but also in astrophysics. The widely used self-consistent Random Phase Approximation (RPA) models tend to overestimate the half-lives of magic nuclei. To overcome this problem, we go beyond the mean-field description and include the effects of particle-vibration coupling (PVC) on top of the RPA model. The β-decay half-lives of 34Si, 68Ni, 78Ni, and 132Sn are studied within this approach in the case of the Skyrme interaction SkM*. It is found that the low-lying Gamow-Teller (GT) strength is shifted downwards with the inclusion of the PVC effect, and as a consequence, the half-lives are reduced due to the increase of the phase space available for β-decay, which leads to a good agreement between theoretical and experimental lifetimes.

  7. Isospin-symmetry-breaking effects in A∼70 nuclei within beyond-mean-field approach

    SciTech Connect

    Petrovici, A.; Andrei, O.

    2015-02-24

    Particular isospin-symmetry-breaking probes including Coulomb energy differences (CED), mirror energy differences (MED), and triplet energy differences (TED) manifest anomalies in the A∼70 isovector triplets of nuclei. The structure of proton-rich nuclei in the A∼70 mass region suggests shape coexistence and competition between pairing correlations in different channels. Recent results concerning the interplay between isospin-mixing and shape-coexistence effects on exotic phenomena in A∼70 nuclei obtained within the beyond-mean-field complex Excited Vampir variational model with symmetry projection before variation using a realistic effective interaction in a relatively large model space are presented. Excited Vampir predictions concerning the Gamow-Teller β decay to the odd-odd N=Z {sup 66}As and {sup 70}Br nuclei correlated with the pair structure analysis in the T=1 and T=0 channel of the involved wave functions are discussed.

  8. Black hole thermodynamics as seen through a microscopic model of a relativistic Bose gas

    NASA Astrophysics Data System (ADS)

    Skákala, Jozef; Shankaranarayanan, S.

    2016-02-01

    Equations of gravity when projected on spacetime horizons resemble Navier-Stokes equation of a fluid with a specific equation of state [T. Damour, Surface effects of black hole physics, in Proc. M. Grossman Meeting (North Holland, 1982), p. 587, T. Padmanabhan, Phys. Rev. D 83 (2011) 044048, arXiv:gr-qc/1012.0119, S. Kolekar and T. Padmanabhan, Phys. Rev. D 85 (2011) 024004, arXiv:gr-qc/1012.5421]. We show that this equation of state describes massless ideal relativistic gas. We use these results, and build an explicit and simple molecular model of the fluid living on the Schwarzschild and Reissner-Nordström black hole horizons. For the spin zero Bose gas, our model makes two predictions: (i) The horizon area/entropy is quantized as given by Bekenstein’s quantization rule, (ii) The model explains the correct type of proportionality between horizon area and entropy. However, for the physically relevant range of parameters, the proportionality constant is never equal to 1/4.

  9. How deep cells feel: Mean-field Computations and Experiments

    NASA Astrophysics Data System (ADS)

    Buxboim, Amnon; Sen, Shamik; Discher, Dennis E.

    2009-03-01

    Most cells in solid tissues exert contractile forces that mechanically couple them to elastic surroundings and that significantly influence cell adhesion, cytoskeletal organization and differentiation. However, strains within the depths of matrices are often unclear and are likely relevant to thin matrices, such as basement membranes, relative to cell size as well as to defining how far cells can ``feel.'' We present experimental results for cell spreading on thin, ligand- coated gels and for prestress in stem cells in relation to gel stiffness. Matrix thickness affects cell spread area, focal adhesions and cytoskeleton organization in stem cells, which we will compare to differentiated cells. We introduce a finite element computation to estimate the elastostatic deformations within the matrix on which a cell is placed. Interfacial strains between cell and matrix show large deviations only when soft matrices are a fraction of cell dimensions, proving consistent with experiments. 3-D cell morphologies that model stem cell-derived neurons, myoblasts, and osteoblasts show that a cylinder-shaped myoblast induces the highest strains, consistent with the prominent contractility of muscle. Groups of such cells show a weak crosstalk via matrix strains only when cells are much closer than a cell-width. Cells thus feel on length scales closer to that of adhesions than on cellular scales.

  10. Mean-field analysis of an inductive reasoning game: Application to influenza vaccination

    NASA Astrophysics Data System (ADS)

    Breban, Romulus; Vardavas, Raffaele; Blower, Sally

    2007-09-01

    Recently we have introduced an inductive reasoning game of voluntary yearly vaccination to establish whether or not a population of individuals acting in their own self-interest would be able to prevent influenza epidemics. Here, we analyze our model to describe the dynamics of the collective yearly vaccination uptake. We discuss the mean-field equations of our model and first order effects of fluctuations. We explain why our model predicts that severe epidemics are periodically expected even without the introduction of pandemic strains. We find that fluctuations in the collective yearly vaccination uptake induce severe epidemics with an expected periodicity that depends on the number of independent decision makers in the population. The mean-field dynamics also reveal that there are conditions for which the dynamics become robust to the fluctuations. However, the transition between fluctuation-sensitive and fluctuation-robust dynamics occurs for biologically implausible parameters. We also analyze our model when incentive-based vaccination programs are offered. When a family-based incentive is offered, the expected periodicity of severe epidemics is increased. This results from the fact that the number of independent decision makers is reduced, increasing the effect of the fluctuations. However, incentives based on the number of years of prepayment of vaccination may yield fluctuation-robust dynamics where severe epidemics are prevented. In this case, depending on prepayment, the transition between fluctuation-sensitive and fluctuation-robust dynamics may occur for biologically plausible parameters. Our analysis provides a practical method for identifying how many years of free vaccination should be provided in order to successfully ameliorate influenza epidemics.

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

    NASA Astrophysics Data System (ADS)

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

    2015-08-01

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

  12. A SCILAB Program for Computing General-Relativistic Models of Rotating Neutron Stars by Implementing Hartle's Perturbation Method

    NASA Astrophysics Data System (ADS)

    Papasotiriou, P. J.; Geroyannis, V. S.

    We implement Hartle's perturbation method to the computation of relativistic rigidly rotating neutron star models. The program has been written in SCILAB (© INRIA ENPC), a matrix-oriented high-level programming language. The numerical method is described in very detail and is applied to many models in slow or fast rotation. We show that, although the method is perturbative, it gives accurate results for all practical purposes and it should prove an efficient tool for computing rapidly rotating pulsars.

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

    SciTech Connect

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

    2000-08-07

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

  14. A relativistically interacting exactly solvable multi-time model for two massless Dirac particles in 1 + 1 dimensions

    NASA Astrophysics Data System (ADS)

    Lienert, Matthias

    2015-04-01

    The question how to Lorentz transform an N-particle wave function naturally leads to the concept of a so-called multi-time wave function, i.e., a map from (space-time)N to a spin space. This concept was originally proposed by Dirac as the basis of relativistic quantum mechanics. In such a view, interaction potentials are mathematically inconsistent. This fact motivates the search for new mechanisms for relativistic interactions. In this paper, we explore the idea that relativistic interaction can be described by boundary conditions on the set of coincidence points of two particles in space-time. This extends ideas from zero-range physics to a relativistic setting. We illustrate the idea at the simplest model which still possesses essential physical properties like Lorentz invariance and a positive definite density: two-time equations for massless Dirac particles in 1 + 1 dimensions. In order to deal with a spatio-temporally non-trivial domain, a necessity in the multi-time picture, we develop a new method to prove existence and uniqueness of classical solutions: a generalized version of the method of characteristics. Both mathematical and physical considerations are combined to precisely formulate and answer the questions of probability conservation, Lorentz invariance, interaction, and antisymmetry.

  15. A relativistically interacting exactly solvable multi-time model for two massless Dirac particles in 1 + 1 dimensions

    SciTech Connect

    Lienert, Matthias

    2015-04-15

    The question how to Lorentz transform an N-particle wave function naturally leads to the concept of a so-called multi-time wave function, i.e., a map from (space-time){sup N} to a spin space. This concept was originally proposed by Dirac as the basis of relativistic quantum mechanics. In such a view, interaction potentials are mathematically inconsistent. This fact motivates the search for new mechanisms for relativistic interactions. In this paper, we explore the idea that relativistic interaction can be described by boundary conditions on the set of coincidence points of two particles in space-time. This extends ideas from zero-range physics to a relativistic setting. We illustrate the idea at the simplest model which still possesses essential physical properties like Lorentz invariance and a positive definite density: two-time equations for massless Dirac particles in 1 + 1 dimensions. In order to deal with a spatio-temporally non-trivial domain, a necessity in the multi-time picture, we develop a new method to prove existence and uniqueness of classical solutions: a generalized version of the method of characteristics. Both mathematical and physical considerations are combined to precisely formulate and answer the questions of probability conservation, Lorentz invariance, interaction, and antisymmetry.

  16. Biopolymers under large external forces and mean-field RNA virus evolutionary dynamics

    NASA Astrophysics Data System (ADS)

    Ahsan, Syed Amir

    The modeling of the mechanical response of single-molecules of DNA and RNA under large external forces through statistical mechanical methods is central to this thesis with a small portion devoted to modeling the evolutionary dynamics of positive-sense single-stranded RNA viruses. In order to develop and test models of biopolymer mechanics and illuminate the mechanisms underlying biological processes where biopolymers undergo changes in energy on the order of the thermal energy, , entails measuring forces and lengths on the scale of piconewtons (pN) and nanometers (nm), respectively. A capacity achieved in the past two decades at the single-molecule level through the development of micromanipulation techniques such as magnetic and optical tweezers, atomic force microscopy, coupled with advances in micro- and nanofabrication. The statistical mechanical models of biopolymers developed in this dissertation are dependent upon and the outcome of these advancements and resulting experiments. The dissertation begins in chapter 1 with an introduction to the structure and thermodynamics of DNA and RNA, highlighting the importance and effectiveness of simple, two-state models in their description as a prelude to the emergence of two-state models in the research manuscripts. In chapter 2 the standard models of the elasticity of polymers and of a polymer gel are reviewed, characterizing the continuum and mean-field models, including the scaling behavior of DNA in confined spaces. The research manuscript presented in the last section of chapter 2 (section 2.5), subsequent to a review of a Flory gel and in contrast to it, is a model of the elasticity of RNA as a gel, with viral RNA illustrating an instance of such a network, and shown to exhibit anomalous elastic behavior, a negative Poisson ratio, and capable of facilitating viral RNA encapsidation with further context provided in section 5.1. In chapter 3 the experimental methods and behavior of DNA and RNA under mechanical

  17. Simulation of a rapid dropout event for highly relativistic electrons with the RBE model

    NASA Astrophysics Data System (ADS)

    Kang, S.-B.; Fok, M.-C.; Glocer, A.; Min, K.-W.; Choi, C.-R.; Choi, E.; Hwang, J.

    2016-05-01

    A flux dropout is a sudden and sizable decrease in the energetic electron population of the outer radiation belt on the time scale of a few hours. We simulated a flux dropout of highly relativistic >2.5 MeV electrons using the Radiation Belt Environment model, incorporating the pitch angle diffusion coefficients caused by electromagnetic ion cyclotron (EMIC) waves for the geomagnetic storm event of 23-26 October 2002. This simulation showed a remarkable decrease in the >2.5 MeV electron flux during main phase of the storm, compared to those without EMIC waves. This decrease was independent of magnetopause shadowing or drift loss to the magnetopause. We suggest that the flux decrease was likely to be primarily due to pitch angle scattering to the loss cone by EMIC waves. Furthermore, the >2.5 MeV electron flux calculated with EMIC waves correspond very well with that observed from Solar Anomalous and Magnetospheric Particle EXplorer spacecraft. EMIC wave scattering is therefore likely one of the key mechanisms to understand flux dropouts. We modeled EMIC wave intensities by the Kp index. However, the calculated dropout is a several hours earlier than the observed one. We propose that Kp is not the best parameter to predict EMIC waves.

  18. Superheavy Element Chemistry by Relativistic Density Functional Theory Electronic Structure Modeling

    NASA Astrophysics Data System (ADS)

    Zaitsevskii, A. V.; Polyaev, A. V.; Demidov, Yu. A.; Mosyagin, N. S.; Lomachuk, Yu. V.; Titov, A. V.

    2015-06-01

    Two-component density functional theory in its non-collinear formulation combined with the accurate relativistic electronic structure model defined by shape-consistent small-core pseudopotentials (PP/RDFT) provides a robust basis of efficient computational schemes for predicting energetic and structural properties of complex polyatomic systems including superheavy elements (SHEs). Because of the exceptional role of thermochromatography in the experiments on the "chemical" identification of SHEs with atomic numbers Z ≥ 112, we focus on the description of the adsorption of single SHE atoms on the surfaces of solids through cluster modeling of adsorption complexes. In some cases our results differ significantly from those of previous theoretical studies. The results of systematic comparative studies on chemical bonding in simple molecules of binary compounds of SHEs and their nearest homologs with most common light elements, obtained at the PP/RDFT level and visualized through the "chemical graphs", provide the understanding of the general chemistry of SHEs which at present cannot be derived from the experimental data. These results are used to discuss the main trends in changing chemical properties of the elements in the given group of the periodic table and demonstrate the specificity of SHEs.

  19. Relativistic precessing jets in quasars and radio galaxies - Models to fit high resolution data

    NASA Technical Reports Server (NTRS)

    Gower, A. C.; Gregory, P. C.; Unruh, W. G.; Hutchings, J. B.

    1982-01-01

    The formulation of generalized models tracing the geometry and intensity of the synchrotron emission from precessing, twin, relativistic jets as projected on the plane of the sky is presented. It is shown that neither the shape of the image nor its relative intensities are altered by including the effects of a cosmological redshift and a relative velocity between the source and observer. The models are fitted to the available data for several quasars and radio galaxies and demonstrate the plausibility of the phenomenon. Probable selection effects are considered and diagnostics given for recognizing objects showing this behavior. In the radio galaxies considered, velocities up to about 0.2c and precession periods of 1,000,000 yr are deduced. In the QSOs investigated, velocities of 0.7c and greater are found and periods of order 10,000 yr. In some cases precession cone angles increase with time. Consequences in terms of lifetimes of QSO behavior and binary supermassive objects are discussed.

  20. Empirical predictive models of daily relativistic electron flux at geostationary orbit: Multiple regression analysis

    NASA Astrophysics Data System (ADS)

    Simms, Laura E.; Engebretson, Mark J.; Pilipenko, Viacheslav; Reeves, Geoffrey D.; Clilverd, Mark

    2016-04-01

    The daily maximum relativistic electron flux at geostationary orbit can be predicted well with a set of daily averaged predictor variables including previous day's flux, seed electron flux, solar wind velocity and number density, AE index, IMF Bz, Dst, and ULF and VLF wave power. As predictor variables are intercorrelated, we used multiple regression analyses to determine which are the most predictive of flux when other variables are controlled. Empirical models produced from regressions of flux on measured predictors from 1 day previous were reasonably effective at predicting novel observations. Adding previous flux to the parameter set improves the prediction of the peak of the increases but delays its anticipation of an event. Previous day's solar wind number density and velocity, AE index, and ULF wave activity are the most significant explanatory variables; however, the AE index, measuring substorm processes, shows a negative correlation with flux when other parameters are controlled. This may be due to the triggering of electromagnetic ion cyclotron waves by substorms that cause electron precipitation. VLF waves show lower, but significant, influence. The combined effect of ULF and VLF waves shows a synergistic interaction, where each increases the influence of the other on flux enhancement. Correlations between observations and predictions for this 1 day lag model ranged from 0.71 to 0.89 (average: 0.78). A path analysis of correlations between predictors suggests that solar wind and IMF parameters affect flux through intermediate processes such as ring current (Dst), AE, and wave activity.