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Sample records for relativistic mean-field models

  1. Nilsson parameters κ and μ in relativistic mean field models

    NASA Astrophysics Data System (ADS)

    Sulaksono, A.; Mart, T.; Bahri, C.

    2005-03-01

    Nilsson parameters κ and μ have been studied in the framework of relativistic mean field (RMF) models. They are used to investigate the reason why RMF models give a relatively good prediction of the spin-orbit splitting but fail to reproduce the placement of the states with different orbital angular momenta. Instead of the relatively small effective mass M*, the independence of M* from the angular momentum l is found to be the reason.

  2. Relativistic mean-field models and nuclear matter constraints

    NASA Astrophysics Data System (ADS)

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

    2013-05-01

    This work presents a preliminary study of 147 relativistic mean-field (RMF) hadronic models used in the literature, regarding their behavior in the nuclear matter regime. We analyze here different kinds of such models, namely: (i) linear models, (ii) nonlinear σ3 + σ4 models, (iii) σ3 + σ4 + ω4 models, (iv) models containing mixing terms in the fields σ and ω, (v) density dependent models, and (vi) point-coupling ones. In the finite range models, the attractive (repulsive) interaction is described in the Lagrangian density by the σ (ω) field. The isospin dependence of the interaction is modeled by the ρ meson field. We submit these sets of RMF models to eleven macroscopic (experimental and empirical) constraints, used in a recent study in which 240 Skyrme parametrizations were analyzed. Such constraints cover a wide range of properties related to symmetric nuclear matter (SNM), pure neutron matter (PNM), and both SNM and PNM.

  3. Relativistic mean field models for finite nuclei and neutron stars

    NASA Astrophysics Data System (ADS)

    Chen, Wei-Chia

    In this dissertation we have created theoretical models for finite nuclei, nuclear matter, and neutron stars within the framework of relativistic mean field (RMF) theory, and we have used these models to investigate the elusive isovector sector and related physics, in particular, the neutron-skin thickness of heavy nuclei, the nuclear symmetry energy, and the properties of neutron stars. To build RMF models that incorporate collective excitations in finite nuclei in addition to their ground-state properties, we have extended the non-relativistic sum rule approach to the relativistic domain. This allows an efficient estimate of giant monopole energies. Moreover, we have combined an exact shell-model-like approach with the mean-field calculation to describe pairing correlations in open-shell nuclei. All the ingredients were then put together to establish the calibration scheme. We have also extended the transformation between model parameters and pseudo data of nuclear matter within the RMF context. Performing calibration in this pseudo data space can not only facilitate the searching algorithm but also make the pseudo data genuine model predictions. This calibration scheme is also supplemented by a covariance analysis enabling us to extract the information content of a model, including theoretical uncertainties and correlation coefficients. A series of RMF models subject to the same isoscalar constraints but one differing isovector assumption were then created using this calibration scheme. By comparing their predictions of the nuclear matter equation of state to both experimental and theoretical constraints, we found that a small neutron skin of about 0.16 fm in Pb208 is favored, indicating that the symmetry energy should be soft. To obtain stronger evidence, we proceeded to examine the evolution of the isotopic chains in both oxygen and calcium. Again, it was found that the model with such small neutron skin and soft symmetry energy can best describe both isotopic

  4. 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.

  5. 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.

  6. Low density instability in relativistic mean field models

    NASA Astrophysics Data System (ADS)

    Sulaksono, A.; Mart, T.

    2006-10-01

    The effects of symmetry energy softening of relativistic mean field (RMF) models on the properties of matter with neutrino trapping are investigated. It is found that the effects are less significant than those in the case without neutrino trapping. The weak dependence of the equation of state on the symmetry energy is shown as the main reason for this finding. Using different RMF models the dynamical instabilities of uniform matters, with and without neutrino trapping, have been also studied. The interplay between the dominant contribution of the variation of matter composition and the role of effective masses of mesons and nucleons leads to higher critical densities for matter with neutrino trapping. Furthermore, the predicted critical density is insensitive to both the number of trapped neutrinos as well as the RMF model used in the investigation. It is also found that additional nonlinear terms in the Horowitz-Piekarewicz and Furnstahl-Serot-Tang models prevent another kind of instability, which occurs at relatively high densities, because the effective σ meson mass in their models increases as a function of matter density.

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

    NASA Astrophysics Data System (ADS)

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

    2014-11-01

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

  8. 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.

  9. Charge and parity projected relativistic mean field model with pion for finite nuclei

    SciTech Connect

    Ogawa, Yoko; Toki, Hiroshi; Tamenaga, Setsuo; Sugimoto, Satoru; Ikeda, Kiyomi

    2006-03-15

    We construct a new relativistic mean field model by explicitly introducing a {pi}-meson mean field with charge number and parity projection. We call this model the charge and parity projected relativistic mean field (CPPRMF) model. We take the chiral {sigma} model Lagrangian for the construction of finite nuclei. We apply this framework first for the {sup 4}He nucleus as a pilot case and study the role of the {pi}-meson field on the structure of nuclei. We demonstrate that it is essential to solve the mean field equation with the variation introduced after the projection in order to take the pionic correlations into account explicitly. We study the ground-state properties of {sup 4}He by varying several parameters, such as the {sigma}-meson mass and the {omega}-meson coupling constant. We are able to construct a good ground state for {sup 4}He. A depression appears in the central region of the density distribution, and the second maximum and the position of the dip in the form factor of {sup 4}He are naturally obtained in the CPPRMF model.

  10. Correlations between bulk parameters in relativistic and nonrelativistic hadronic mean-field models

    NASA Astrophysics Data System (ADS)

    Santos, B. M.; Dutra, M.; Lourenço, O.; Delfino, A.

    2015-07-01

    In this work, we study the arising of correlations among some isoscalar (Ko, Qo, and Io) and isovector (J , Lo, Ksymo, Qsymo, and Isymo) bulk parameters in nonrelativistic and relativistic hadronic mean-field models. For the former, we investigate correlations in Skyrme and Gogny parametrizations, as well as in the nonrelativistic (NR) limit of relativistic point-coupling models. We provide analytical correlations among bulk parameters for the NR limit, discussing the conditions in which they are linear ones. Based on a recent study [Santos et al., Phys. Rev. C 90, 035203 (2014), 10.1103/PhysRevC.90.035203], we also show that some correlations presented in the NR limit are reproduced for relativistic models presenting cubic and quartic self-interactions in the scalar field σ , mostly studied in this work in the context of the relativistic framework. We also discuss how the crossing points, observed in the density dependence of some bulk parameters, can be seen as a signature of linear correlations between the specific bulk quantity presenting the crossing and its immediately next order parameter.

  11. Relativistic mean field description of exotic nuclei

    NASA Astrophysics Data System (ADS)

    Meng, Jie; Ring, Peter; Zhao, Pengwei; Zhou, Shan-Gui

    In this chapter, we will present relativistic mean field (RMF) models with pairing treated by the Bardeen-Cooper-Schrieffer (BCS) and the relativistic Hartree-Bogoliubov (RHB) approaches and applications for exotic nuclear phenomena including nuclear halos, the position of the proton drip line and proton radioactivity, the surface diffuseness and its relation to nuclear exotic phenomena, and the effects of pairing correlations on the nuclear size.

  12. Antikaons in neutron star studied with recent versions of relativistic mean-field models

    NASA Astrophysics Data System (ADS)

    Gupta, Neha; Arumugam, P.

    2013-03-01

    We study the impact of additional couplings in the relativistic mean field (RMF) models, in conjunction with antikaon condensation, on various neutron star properties. We analyze different properties such as in-medium antikaon and nucleon effective masses, antikaon energies, chemical potentials and the mass-radius relations of neutron star (NS). We calculate the NS properties with the RMF (NL3), E-RMF (G1, G2) and FSU2.1 models, which are quite successful in explaining several finite nuclear properties. Our results show that the onset of kaon condensation in NS strongly depends on the parameters of the Lagrangian, especially the additional couplings which play a significant role at higher densities where antikaons dominate the behavior of equation of state.

  13. 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.

  14. Mass predictions of the relativistic mean-field model with the radial basis function approach

    NASA Astrophysics Data System (ADS)

    Zheng, J. S.; Wang, N. Y.; Wang, Z. Y.; Niu, Z. M.; Niu, Y. F.; Sun, B.

    2014-07-01

    The radial basis function (RBF) is a powerful tool to improve mass predictions of nuclear models. By combining the RBF approach with the relativistic mean-field (RMF) model, the systematic deviations between mass predictions of the RMF model and the experimental data are eliminated to a large extent and the resulting rms deviation is reduced from 2.217 to 0.488 MeV. Furthermore, it is found that the RBF approach has a relatively reliable extrapolative power along the distance from the β-stability line except for a large uncertainty around the region at magic number. From the deduced neutron separation energies, we found that the description of the nuclear shell structure and shape transition is also significantly improved by the RBF approach, thus improving agreement with the solar r-process abundances before A =130 and speeding up the r-matter flow. Therefore, a shorter irradiation time is enough to reproduce the solar r-process abundance distribution for the improved RMF mass model, which is closer to the irradiation time for those sophisticated mass models.

  15. Asymmetric nuclear matter and neutron skin in an extended relativistic mean-field model

    SciTech Connect

    Agrawal, B. K.

    2010-03-15

    The density dependence of the symmetry energy, instrumental in understanding the behavior of the asymmetric nuclear matter, is investigated within the extended relativistic mean-field (ERMF) model, which includes the contributions from the self- and mixed-interaction terms for the scalar-isoscalar ({sigma}), vector-isoscalar ({omega}), and vector-isovector ({rho}) mesons up to the quartic order. Each of the 26 different parametrizations of the ERMF model employed is compatible with the bulk properties of the finite nuclei. The behavior of the symmetry energy for several parameter sets is found to be consistent with the empirical constraints on them as extracted from the analyses of the isospin diffusion data. The neutron-skin thickness in the {sup 208}Pb nucleus for these parameter sets of the ERMF model lies in the range of {approx}0.20-0.24 fm, which is in harmony with the thickness predicted by the Skyrme Hartree-Fock model. We also investigate the role of various mixed-interaction terms that are crucial for the density dependence of the symmetry energy.

  16. Impacts of Parameters Adjustment of Relativistic Mean Field Model on Neutron Star Properties

    NASA Astrophysics Data System (ADS)

    Kasmudin; Sulaksono, A.

    Analysis of the parameters adjustment effects in isovector as well as in isoscalar sectors of effective field based relativistic mean field (E-RMF) model in the symmetric nuclear matter and neutron-rich matter properties has been performed. The impacts of the adjustment on slowly rotating neutron star are systematically investigated. It is found that the mass-radius relation obtained from adjusted parameter set G2** is compatible not only with neutron stars masses from 4U 0614+09 and 4U 1636-536, but also with the ones from thermal radiation measurement in RX J1856 and with the radius range of canonical neutron star of X7 in 47 Tuc, respectively. It is also found that the moment inertia of PSR J073-3039A and the strain amplitude of gravitational wave at the Earth's vicinity of PSR J0437-4715 as predicted by the E-RMF parameter sets used are in reasonable agreement with the extracted constraints of these observations from isospin diffusion data.

  17. 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.

  18. 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.

  19. Investigation of band termination in the lower fp shell within the cranked relativistic mean field model

    NASA Astrophysics Data System (ADS)

    Bhagwat, A.; Wyss, R.; Satuła, W.; Meng, J.; Gambhir, Y. K.

    2013-04-01

    The excitation energy difference (ΔE) between the terminating states built on the f7/2n and d3/2-1f7/2n+1 configurations (here, 'n' denotes the number of valence particles outside the 40Ca core and the particle hole excitation across the magic gap 20 is of proton type) in the lower fp shell are studied systematically within the framework of the cranked relativistic mean field model. The ΔE thus defined, depends predominantly on the f7/2 - d3/2 shell gap, and its evolution as a function of neutron - proton asymmetry. The latter, in turn, depends on the isoscalar - isovector balance in the spin - orbit potential. Therefore, a systematic investigation of the difference ΔE is expected to test quantitatively the predicted shell gaps as a function of isospin. We find that: 1) the conventional NL3 parameter set over estimates the ΔE values, implying that the said shell gap is over - estimated in this parametrization and 2) the largest deviation between the calculated and the experimental values of ΔE is obtained for the nucleus with the smallest asymmetry value in the set of nuclei considered, and that the deviation decreases with increasing asymmetry, indicating that the in RMF parametrization considered, the isoscalar - isovector balance in the spin - orbit potential requires improvement. We carry out a re - fit of the RMF parameters to attempt a remedy to these two problems. We find that in addition to the binding energies and charge radii, if a constraint is put on the f7/2 - d3/2 shell gap in the fit to the Lagrangian parameters, the overall agreement of ΔE with the experiment improves significantly, without disturbing the agreement already achieved for the bulk properties of the nuclei spanning the entire periodic table. At a finer level, however, it is found that the isoscalar - isovector balance in the spin orbit interaction is required to be improved further. A detailed work in this direction is in progress.

  20. Dynamical Instabilities in Relativistic Mean-Field Models and Inner Edge of the Compact Star Crust

    SciTech Connect

    Santos, Alexandre; Brito, Lucilia; Providencia, Constanca

    2010-04-26

    We take a dynamical spinodal approach to study the effects of different nuclear relativistic models on the instability zone of nuclear matter in beta equilibrium under the conditions expected to be found in the crust of neutron stars. In particular, we probe the predictive power of those models in the description of the inner edge of the crust. Pressure and the liquid-gas phase densities are evaluated and compared to the most recent 'pasta' phase results obtained with a Thomas-Fermi approach for the pasta phases. The collective response from n, p matter is also briefly commented.

  1. Building relativistic mean field models for finite nuclei and neutron stars

    NASA Astrophysics Data System (ADS)

    Chen, Wei-Chia; Piekarewicz, J.

    2014-10-01

    Background: Theoretical approaches based on density functional theory provide the only tractable method to incorporate the wide range of densities and isospin asymmetries required to describe finite nuclei, infinite nuclear matter, and neutron stars. Purpose: A relativistic energy density functional (EDF) is developed to address the complexity of such diverse nuclear systems. Moreover, a statistical perspective is adopted to describe the information content of various physical observables. Methods: We implement the model optimization by minimizing a suitably constructed χ2 objective function using various properties of finite nuclei and neutron stars. The minimization is then supplemented by a covariance analysis that includes both uncertainty estimates and correlation coefficients. Results: A new model, "FSUGold2," is created that can well reproduce the ground-state properties of finite nuclei, their monopole response, and that accounts for the maximum neutron-star mass observed up to date. In particular, the model predicts both a stiff symmetry energy and a soft equation of state for symmetric nuclear matter, suggesting a fairly large neutron-skin thickness in Pb208 and a moderate value of the nuclear incompressibility. Conclusions: We conclude that without any meaningful constraint on the isovector sector, relativistic EDFs will continue to predict significantly large neutron skins. However, the calibration scheme adopted here is flexible enough to create models with different assumptions on various observables. Such a scheme—properly supplemented by a covariance analysis—provides a powerful tool to identify the critical measurements required to place meaningful constraints on theoretical models.

  2. Isospin mixing within relativistic mean-field models including the delta meson

    NASA Astrophysics Data System (ADS)

    Graeff, C. A.; Marinelli, J. R.

    2011-09-01

    We investigate isospin mixing effects in the asymmetry as obtained in parity-violating electron scattering from 4He, 12C, 16O, 40Ca and 56Ni. The scattering analysis is developed within plane (PWBA) and distorted wave (DWBA) Born approximations accounting for nucleon form factors, which are given by the Galster parametrization. We use Walecka's Model (QHD), including the σ, ω, ρ and δ mesons as well as the electromagnetic interaction. The δ meson effects are specially interesting once it should add a contribution for isospin mixing together with the electromagnetic and ρ meson fields. Our model includes lagrangians with nonlinear terms as well as lagrangians including density dependent couplings. The model is solved in a Hartree approximation with spherical symmetry using a self-consistent calculation by means of an expansion of the nuclear wave functions and potentials in an harmonic oscillator basis. Results using four different parametrizations are obtained and compared with calculations using non-relativistic models.

  3. 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.

  4. Relativistic mean field for nuclear periphery

    NASA Astrophysics Data System (ADS)

    Gambhir, Y. K.; Bhagwat, A. A.

    2002-09-01

    The antiproton annihilation experiments help to extract so-called peripheral factors representing the ratio of neutron to proton densities at the annihilation site that is about 2.5 fm away from the half-density radius of the nucleus. The relativistic mean field (RMF) approach is used to calculate the peripheral factors. The RMF equations (with frozen gap) and relativistic Hartree-Bogoliubov (RHB) equations (with finite range Gogny interaction-D1S for pairing) are solved employing the basis expansion method. The RHB equations are also solved in the coordinate space using a large box (30 fm); with an effective zero range density dependent interaction (consistent with Gogny D1S interaction) for pairing. The results are analyzed to ascertain quantitatively the effect of using these different techniques for solving the RMF/RHB equations. The calculated peripheral factors obtained by solving RHB equations in the coordinate space are relatively closer to the corresponding experimental values.

  5. Temperature and density dependence of asymmetric nuclear matter and protoneutron star properties within an extended relativistic mean field model

    NASA Astrophysics Data System (ADS)

    Mahajan, Gulshan; Dhiman, Shashi K.

    2011-10-01

    The effect of temperature and density dependence of the asymmetric nuclear matter properties is studied within the extended relativistic mean field (ERMF) model, which includes the contribution from the self and mixed interaction terms by using different parametrizations obtained by varying the neutron skin thickness Δr and ω-meson self-coupling (ζ). We observed that the symmetry energy and its slope and incompressibility coefficients decrease with increasing temperatures up to saturation densities. The ERMF parametrizations were employed to obtain a new set of equations of state (EOS) of the protoneutron star (PNS) with and without inclusion of hyperons. In our calculations, in comparison with cold compact stars, we obtained that the gravitational mass of the protoneutron star with and without hyperons increased by ˜0.4M⊙ and its radius increased by ˜3 km. Whereas in case of the rotating PNS, the mass shedding limit decreased with increasing temperature, and this suggested that the keplerian frequency of the PNS at T=10 MeV should be smaller by 14%-20% for the EOS with hyperon, as compared to the keplerian frequency of a cold compact star.

  6. 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

  7. 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 http://skmf.eu website). We will show that the result of one SKMF run may correspond to the average of several KMC runs. The number of KMC runs is inversely proportional to the amplitude square of the noise in SKMF. This makes SKMF an ideal tool also for statistical purposes.

  8. Off-shell effects in the relativistic mean field model and their role in CC (anti)neutrino scattering at MiniBooNE kinematics

    NASA Astrophysics Data System (ADS)

    Ivanov, M. V.; González-Jiménez, R.; Caballero, J. A.; Barbaro, M. B.; Donnelly, T. W.; Udías, J. M.

    2013-11-01

    The relativistic mean field (RMF) model is used to describe nucleons in the nucleus and thereby to evaluate the effects of having dynamically off-shell spinors. Compared with free, on-shell nucleons as employed in some other models, within the RMF nucleons are described by relativistic spinors with strongly enhanced lower components. In this work it is seen that for MiniBooNE kinematics, neutrino charged-current quasielastic cross sections show some sensitivity to these off-shell effects, while for the antineutrino-nucleus case the total cross sections are seen to be essentially independent of the enhancement of the lower components. As was found to be the case when comparing the RMF results with the neutrino-nucleus data, the present impulse approximation predictions within the RMF also fall short of the MiniBooNE antineutrino-nucleus data.

  9. 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.

  10. Radius studies of 8Li and 8B using the optical-limit Glauber model in conjunction with relativistic mean-field theory

    NASA Astrophysics Data System (ADS)

    Fan, Guang-Wei; Xu, Wang; Fukuda, M.; Pan, Qiang-Yan; Cai, Xiao-Lu; Fan, Gong-Tao; Li, Yong-Jiang; Luo, Wen; Xu, Ben-Ji; Yan, Zhe; Yang, Li-Feng

    2010-10-01

    We study the reaction cross sections (σR) and root-mean-square (RMS) radii of 8Li and 8B, the halo-like nuclei, with stable target 12C, 27Al and 9Be within the standard optical-limit Glauber model, using densities obtained from relativistic mean-field (RMF) formalisms and other types of distributions. It is found that the experimental σR can be reproduced well at high energy. The RMS radius and Δr extracted by RMF-theory and harmonic oscillator distribution are compared. We find that the RMS radius and Δr of 8B are larger than those of 8Li. In addition, we analyze in detail the relationship between σR and density distribution.

  11. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2014-08-01

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

  13. Temperature dependent relativistic mean field for highly excited hot nuclei

    NASA Astrophysics Data System (ADS)

    Gambhir, Y. K.; Maharana, J. P.; Lalazissis, G. A.; Panos, C. P.; Ring, P.

    2000-11-01

    The temperature dependent relativistic mean field (RMF-T) results obtained by using nonlinear Lagrangian parameter set NL3 are presented for a few selected representative spherical and deformed nuclei. The calculated total binding energy (entropy) decrease (increase) as temperature (T) increases. The depths of the potentials and the single particle (sp) energies change very little with temperature. The density slightly spreads out; as a result the radius increases as temperature rises. For well deformed nuclei the shell effects disappear at around T~3 MeV. This value of T is relatively higher as compared to the corresponding value of T (~1.8 MeV) obtained in the Strutinsky-type calculations. This difference in the value of T is shown to be due to the use of the effective nucleon mass (< the bare mass) appearing in the Skyrme III interaction or emerging from the RMF Lagrangian.

  14. Symmetry energy of cold nucleonic matter within a relativistic mean field model encapsulating effects of high-momentum nucleons induced by short-range correlations

    NASA Astrophysics Data System (ADS)

    Cai, Bao-Jun; Li, Bao-An

    2016-01-01

    It is well known that short-range nucleon-nucleon correlations (SRC) from the tensor components and/or the repulsive core of nuclear forces lead to a high- (low-)momentum tail (depletion) in the single-nucleon momentum distribution above (below) the nucleon Fermi surface in cold nucleonic matter. Significant progress was made recently in constraining the isospin-dependent parameters characterizing the SRC-modified single-nucleon momentum distribution in neutron-rich nucleonic matter using both experimental data and microscopic model calculations. Using the constrained single-nucleon momentum distribution in a nonlinear relativistic mean field (RMF) model, we study the equation of state (EOS) of asymmetric nucleonic matter (ANM), especially the density dependence of nuclear symmetry energy Esym(ρ ) . First, as a test of the model, the average nucleon kinetic energy extracted recently from electron-nucleus scattering experiments using a neutron-proton dominance model is well reproduced by the RMF model incorporating effects of the SRC-induced high-momentum nucleons, while it is significantly under predicted by the RMF model using a step function for the single-nucleon momentum distribution as in free Fermi gas (FFG) models. Second, consistent with earlier findings within nonrelativistic models, the kinetic symmetry energy of quasinucleons is found to be Esymkin(ρ0) =-16.94 ±13.66 MeV which is dramatically different from the prediction of Esymkin(ρ0) ≈12.5 MeV by FFG models at nuclear matter saturation density ρ0=0.16 fm-3 . Third, comparing the RMF calculations with and without the high-momentum nucleons using two sets of model parameters both reproducing identically all empirical constraints on the EOS of symmetric nuclear matter (SNM) and the symmetry energy of ANM at ρ0, the SRC-modified single-nucleon momentum distribution is found to make the Esym(ρ ) more concave around ρ0 by softening it significantly at both subsaturation and suprasaturation

  15. Generic constraints on the relativistic mean-field and Skyrme-Hartree-Fock models from the pure neutron matter equation of state

    NASA Astrophysics Data System (ADS)

    Fattoyev, F. J.; Newton, W. G.; Xu, Jun; Li, Bao-An

    2012-08-01

    We study the nuclear symmetry energy S(ρ) and related quantities of nuclear physics and nuclear astrophysics predicted generically by relativistic mean-field (RMF) and Skyrme-Hartree-Fock (SHF) models. We establish a simple prescription for preparing equivalent RMF and SHF parametrizations starting from a minimal set of empirical constraints on symmetric nuclear matter, nuclear binding energy, and charge radii, enforcing equivalence of their Lorenz effective masses, and then using the pure neutron matter (PNM) equation of state obtained from ab initio calculations to optimize the pure isovector parameters in the RMF and SHF models. We find that the resulting RMF and SHF parametrizations give broadly consistent predictions of the symmetry energy J and its slope parameter L at saturation density within a tight range of ≲2 and ≲6 MeV, respectively, but that clear model dependence shows up in the predictions of higher-order symmetry energy parameters, leading to important differences in (a) the slope of the correlation between J and L from the confidence ellipse, (b) the isospin-dependent part of the incompressibility of nuclear matter Kτ, (c) the symmetry energy at suprasaturation densities, and (d) the predicted neutron star radii. The model dependence can lead to about 1-2 km difference in predictions of the neutron star radius given identical predicted values of J and L and symmetric nuclear matter (SNM) saturation properties. Allowing the full freedom in the effective masses in both models leads to constraints of 30≲J≲31.5 MeV, 35≲L≲60 MeV, and -330≲Kτ≲-216 MeV for the RMF model as a whole and 30≲J≲33 MeV, 28≲L≲65 MeV, and -420≲Kτ≲-325 MeV for the SHF model as a whole. Notably, given PNM constraints, these results place RMF and SHF models as a whole at odds with some constraints on Kτ inferred from giant monopole resonance and neutron skin experimental results.

  16. Beyond the relativistic mean-field approximation. III. Collective Hamiltonian in five dimensions

    SciTech Connect

    Niksic, T.; Li, Z. P.; Vretenar, D.; Prochniak, L.; Meng, J.; Ring, P.

    2009-03-15

    The framework of relativistic energy density functionals is extended to include correlations related to the restoration of broken symmetries and fluctuations of collective variables. A new implementation is developed for the solution of the eigenvalue problem of a five-dimensional collective Hamiltonian for quadrupole vibrational and rotational degrees of freedom, with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The model is tested in a series of illustrative calculations of potential energy surfaces and the resulting collective excitation spectra and transition probabilities of the chain of even-even gadolinium isotopes.

  17. 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

  18. 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.

  19. Relativistic mean-field study on proton skins and proton halos in exotic nuclei

    NASA Astrophysics Data System (ADS)

    Ren, Zhongzhou; Mittig, W.; Sarazin, F.

    1999-06-01

    We investigate the ground state properties of proton-rich nuclei in the framework of the relativistic mean-field model. Calculations show that the experimental proton halo in the nuclei 26,27,28P can be reproduced by the model. The proton halos can appear in proton-rich nuclei because the total nuclear potential is attractive up to the radial distance r ≈ 5.5 fm. But the size of proton halos is finite due to the limitation of the Coulomb potential barrier. The mean-square radius of a halo proton is not very sensitive to the separation energy of the last proton in some very proton-rich nuclei due to the effect of the Coulomb barrier. This behavior is different from the case of a neutron halo where the mean-square radius of a halo neutron is inversely proportional to the separation energy of the last halo neutron. We have also analysed the differences of the relativistic mean-field potentials of 25Al and 26P and found that the isovector potential from the p meson has an important effect on the differences.

  20. 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.

  1. 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.

  2. 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

  3. 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)

  4. 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.

  5. 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.

  6. Temperature Dependence of the Nuclear Energy in Relativistic Mean-Field Theory

    NASA Astrophysics Data System (ADS)

    Nerlo-Pomorska, B.; Pomorski, K.; Sykut, J.; Bartel, J.

    Self-consistent relativistic mean-field (RMF) calculations with the NL3 parameter set were performed for 171 spherical even-even nuclei with 16≤A≤224 at temperatures in the range 0≤T≤4 MeV. For this sample of nuclei single-particle level densities are determined by analyzing the data obtained for various temperatures. A new shell-correction method is used to evaluate shell effects at all temperatures. The single-particle level density is expressed as function of mass number A and relative isospin I and compared with previous estimates.

  7. 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.

  8. 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

  9. Hyperons in a relativistic mean-field approach to asymmetric nuclear matter

    SciTech Connect

    Bunta, J. Kotulic; Gmuca, Stefan

    2004-11-01

    Relativistic mean-field theory with {delta} mesons, nonlinear isoscalar self-interactions, and isoscalar-isovector cross interaction terms with parametrizations obtained to reproduce Dirac-Brueckner-Hartree-Fock calculations for nuclear matter is used to study asymmetric nuclear matter properties in {beta} equilibrium, including hyperon degrees of freedom and (hidden) strange mesons. The influence of cross interactions on the composition of hyperon matter and the electron chemical potential is examined. Softening of the nuclear equation of state by cross interactions results in a lowering of the hyperonization, although simultaneously enhancing a hyperon-induced decrease of the electron chemical potential, thus indicating a further shift of the kaon condensate occurrence to higher densities.

  10. Keplerian Frequency of Uniformly Rotating Neutron Stars in Relativistic Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Zhang, N. B.; Qi, B.; Wang, S. Y.; Ge, S. L.; Sun, B. Y.

    2013-11-01

    Adopting the equation of states (EOSs) from the relativistic mean field (RMF) theory, the relationships among the keplerian frequency fK, gravitational mass M and radius R for the rapidly rotating neutron stars with and without hyperons are presented and analyzed. For various RMF EOSs, the empirical formula fK(M) = 1.08 (M/M⊙)1/2(R_S/10 km)-3/2 kHz, proposed by P. Haensel et al. [Astron. Astrophys.502 (2009) 605], is found to be an approximation with the error at most 13% and such approximation is worse for the neutron stars with hyperons. It indicates that the errors should be considered when the empirical formula is used to discuss the properties of neutron stars.

  11. 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.

  12. Mean-field fluid behavior of the Gaussian core model

    NASA Astrophysics Data System (ADS)

    Louis, A. A.; Bolhuis, P. G.; Hansen, J. P.

    2000-12-01

    We show that the Gaussian core model of particles interacting via a penetrable repulsive Gaussian potential, first considered by Stillinger [J. Chem. Phys. 65, 3968 (1976)], behaves as a weakly correlated ``mean-field fluid'' over a surprisingly wide density and temperature range. In the bulk, the structure of the fluid phase is accurately described by the random phase approximation for the direct correlation function, and by the more sophisticated hypernetted chain integral equation. The resulting pressure deviates very little from a simple mean-field-like quadratic form in the density, while the low density virial expansion turns out to have an extremely small radius of convergence. Density profiles near a hard wall are also very accurately described by the corresponding mean-field free-energy functional. The binary version of the model exhibits a spinodal instability against demixing at high densities. Possible implications for semidilute polymer solutions are discussed.

  13. Nonequilibrium Dynamical Mean-Field Theory for Bosonic Lattice Models

    NASA Astrophysics Data System (ADS)

    Strand, Hugo U. R.; Eckstein, Martin; Werner, Philipp

    2015-01-01

    We develop the nonequilibrium extension of bosonic dynamical mean-field theory and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong-coupling perturbative approaches, nonequilibrium bosonic dynamical mean-field theory captures not only dynamical transitions but also damping and thermalization effects at finite temperature. We apply the formalism to quenches in the Bose-Hubbard model, starting from both the normal and the Bose-condensed phases. Depending on the parameter regime, one observes qualitatively different dynamical properties, such as rapid thermalization, trapping in metastable superfluid or normal states, as well as long-lived or strongly damped amplitude oscillations. We summarize our results in nonequilibrium "phase diagrams" that map out the different dynamical regimes.

  14. Sensitivity of neutron radii in a {sup 208}Pb nucleus and a neutron star to nucleon-{sigma}-{rho} coupling corrections in relativistic mean field theory

    SciTech Connect

    Shen, G.; Li, J.; Hillhouse, G.C.; Meng, J.

    2005-01-01

    We study the sensitivity of the neutron skin thickness S in a {sup 208}Pb nucleus to the addition of nucleon-{sigma}-{rho} coupling corrections to a selection (PK1, NL3, S271, and Z271) of interactions in a relativistic mean field model. The PK1 and NL3 effective interactions lead to a minimum value of S= 0.16 fm in comparison with the original value of S= 0.28 fm. The S271 and Z271 effective interactions yield even smaller values of S= 0.11 fm, which are similar to those for nonrelativistic mean field models. A precise measurement of the neutron radius, and therefore S, in {sup 208}Pb will place an important constraint on both relativistic and nonrelativistic mean field models. We also study the correlation between the radius of a 1.4-solar-mass neutron star and S.

  15. 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.

  16. Magnetic and antimagnetic rotation in 110Cd within tilted axis cranking relativistic mean-field theory

    NASA Astrophysics Data System (ADS)

    Peng, J.; Zhao, P. W.

    2015-04-01

    The self-consistent tilted axis cranking relativistic mean-field (TAC-RMF) theory based on a point-coupling interaction is applied to investigate the observed magnetic and antimagnetic rotations in the nucleus 110Cd . The energy spectra, the relation between the spin and the rotational frequency, the deformation parameters, and the reduced M 1 and E 2 transition probabilities are studied with the various configurations. It is found that the configuration has to be changed to reproduce the energy spectra and the relations between the spin and the rotational frequency for both the magnetic and antimagnetic rotational bands. The shears mechanism for the magnetic rotation and the two-shears-like mechanism for the antimagnetic rotation are examined by investigating the orientation of the neutron and proton angular momenta. The calculated electromagnetic transitions B (M 1 ) and B (E 2 ) are in reasonable agreement with the data, and their tendencies are coincident with the typical characteristics of the magnetic and antimagnetic rotations.

  17. α -decay chains of 288 173 115 and 287 172 1 15 in the relativistic mean field theory

    NASA Astrophysics Data System (ADS)

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

    2003-12-01

    In the recent experiments designed to synthesize the element 115 in the 243 Am+ 48 Ca reaction at Dubna in Russia, three similar decay chains consisting of five consecutive α decays and another different decay chain of four consecutive α decays are detected, and the decay properties of these synthesized nuclei are claimed to be consistent with consecutive α decays originating from the parent isotopes of the new element 115, 288 115 and 287 115 , respectively. Here in the present work, the recently developed deformed relativistic mean field + BCS method with a density-independent δ function interaction in the pairing channel is applied to the analysis of these newly synthesized superheavy nuclei. The calculated α -decay energies and half-lives agree well with the experimental values and with those of the macroscopic-microscopic finite-range droplet model with folded-Yukawa single-particle potentials and Yukawa-plus-exponential model with Woods-Saxon single-particle potentials. In the mean field Lagrangian, the TMA parameter set is used. Particular emphasis is laid on the influence to both the ground-state properties and energy surfaces introduced by different treatments of pairing. Two different effective interactions in the particle-particle channel, i.e., the constant pairing and the density-independent δ -function interaction, together with the blocking effect are discussed in detail.

  18. 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.

  19. Superheavy nuclei with the vector self-coupling of the ω-meson in relativistic mean-field theory

    NASA Astrophysics Data System (ADS)

    Saldanha, A. A.; Farhan, A. R.; Sharma, M. M.

    2009-11-01

    We have studied properties and the shell structure of the superheavy elements from Z = 102 to Z = 120 within the framework of relativistic mean field (RMF) theory. The region of study spans nuclides with neutron numbers N = 150-190. The Lagrangian model NL-SV1 with the inclusion of the vector self-coupling of the ω-meson has been employed in this work. We have performed RMF + BCS calculations for an axially deformed configuration of nuclei. The ground-state binding energies, single-particle properties and quadrupole deformation of nuclei have been obtained from the mean-field minimizations. Two-neutron separation energies, Qα values and α-decay half-life have been evaluated. It is shown that a large number of nuclides exhibit the phenomenon of shape coexistence over a significant region of the superheavy elements. Shape coexistence of a prolate and an oblate shape is prevalent in nuclides far below N = 184, whilst nuclei in the vicinity of N = 184 tend to show a shape coexistence between a spherical and an oblate shape. The shell structure and two-neutron separation energies obtained with RMF theory reinforce the neutron number N = 184 as a major magic number. It is shown that the neutron number N = 172 acts akin to a magic number in the deformed region. It is suggested that the combination of Z = 120 and N = 172 has the potential of being a doubly magic number in the superheavy region.

  20. Dimensional effects in a relativistic mean-field approach. II. Finite temperatures

    SciTech Connect

    Sa Martins, J. S.; Delfino, A.

    2000-04-01

    The Walecka model is studied at finite temperatures in one, two, and three spatial dimensions. The critical temperatures (T{sub c}) and densities ({rho}{sub c}) for the liquid-gas phase transition are calculated in these dimensions. As expected from a mean-field approach, the phase diagram in the T/T{sub c} versus {rho}/{rho}{sub c} plane is dimension independent in the vicinity of the critical point. An interesting finding is that, because the critical and ''flash'' temperatures are proportional, within numerical errors, dimension-independent curves can also be obtained for the incompressibility by scaling with the ''flash'' point coordinates (T{sub f},{rho}{sub f}). At the high-temperature regime, only the two- and three-dimensional systems present a phase transition. (c) 2000 The American Physical Society.

  1. 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.

  2. 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.

  3. 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

  4. 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.

  5. 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

  6. 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.

  7. Configuration mixing of angular-momentum-projected triaxial relativistic mean-field wave functions. II. Microscopic analysis of low-lying states in magnesium isotopes

    SciTech Connect

    Yao, J. M.; Mei, H.; Chen, H.; Meng, J.; Ring, P.; Vretenar, D.

    2011-01-15

    The recently developed structure model that uses the generator coordinate method to perform configuration mixing of angular-momentum projected wave functions, generated by constrained self-consistent relativistic mean-field calculations for triaxial shapes (3DAMP+GCM), is applied in a systematic study of ground states and low-energy collective states in the even-even magnesium isotopes {sup 20-40}Mg. Results obtained using a relativistic point-coupling nucleon-nucleon effective interaction in the particle-hole channel and a density-independent {delta} interaction in the pairing channel are compared to data and with previous axial 1DAMP+GCM calculations, both with a relativistic density functional and the nonrelativistic Gogny force. The effects of the inclusion of triaxial degrees of freedom on the low-energy spectra and E2 transitions of magnesium isotopes are examined.

  8. 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.

  9. Quark mean field model with pion and gluon corrections

    NASA Astrophysics Data System (ADS)

    Xing, Xueyong; Hu, Jinniu; Shen, Hong

    2016-10-01

    The properties of nuclear matter and finite nuclei are studied within the quark mean field (QMF) model by taking the effects of pions and gluons into account at the quark level. The nucleon is described as the combination of three constituent quarks confined by a harmonic oscillator potential. To satisfy the spirit of QCD theory, the contributions of pions and gluons on the nucleon structure are treated in second-order perturbation theory. In a nuclear many-body system, nucleons interact with each other by exchanging mesons between quarks. With different constituent quark mass, mq, we determine three parameter sets for the coupling constants between mesons and quarks, named QMF-NK1, QMF-NK2, and QMF-NK3, by fitting the ground-state properties of several closed-shell nuclei. It is found that all of the three parameter sets can give a satisfactory description of properties of nuclear matter and finite nuclei, moreover they also predict a larger neutron star mass around 2.3 M⊙ without hyperon degrees of freedom.

  10. 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.

  11. 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.

  12. Constraining mean-field models of the nuclear matter equation of state at low densities

    NASA Astrophysics Data System (ADS)

    Voskresenskaya, M. D.; Typel, S.

    2012-08-01

    An extension of the generalized relativistic mean-field (gRMF) model with density dependent couplings is introduced in order to describe thermodynamical properties and the composition of dense nuclear matter for astrophysical applications. Bound states of light nuclei and two-nucleon scattering correlations are considered as explicit degrees of freedom in the thermodynamical potential. They are represented by quasiparticles with medium-dependent properties. The model describes the correct low-density limit given by the virial equation of state (VEoS) and reproduces RMF results around nuclear saturation density where clusters are dissolved. A comparison between the fugacity expansions of the VEoS and the gRMF model provides consistency relations between the quasiparticles properties, the nucleon-nucleon scattering phase shifts and the meson-nucleon couplings of the gRMF model at zero density. Relativistic effects are found to be important at temperatures that are typical in astrophysical applications. Neutron matter and symmetric nuclear matter are studied in detail.

  13. 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.

  14. Sensitivity of de-excitation energies of superdeformed secondary minima to the density dependence of symmetry energy with the relativistic mean-field theory

    NASA Astrophysics Data System (ADS)

    Jiang, W. Z.; Ren, Z. Z.; Sheng, Z. Q.; Zhu, Z. Y.

    2010-06-01

    The relationship between de-excitation energies of superdeformed secondary minima relative to ground states and the density dependence of the symmetry energy is investigated for heavy nuclei using the relativistic mean-field (RMF) model. It is shown that the de-excitation energies of superdeformed secondary minima are sensitive to differences in the symmetry energy that are mimicked by the isoscalar-isovector coupling included in the model. With deliberate investigations on a few Hg isotopes that have data of de-excitation energies, we find that the description for the de-excitation energies can be improved due to the softening of the symmetry energy. Further, we have investigated de-excitation energies of odd-odd heavy nuclei that are nearly independent of pairing correlations, and have discussed the possible extraction of the constraint on the density dependence of the symmetry energy with the measurement of de-excitation energies of these nuclei.

  15. Effect of stochasticity in mean field dynamo models

    SciTech Connect

    Newton, Andrew P. L.; Kim, Eun-Jin

    2012-07-15

    We present a comprehensive investigation into the effect of choosing the stochastic control parameters in a simplified-Parker dynamo model. Through considering the manifold of marginal stability, i.e., the region of parameter space where the mean growth rate is zero, we show that stochastic fluctuations are not prohibitive to dynamo. Furthermore, by directly comparing results obtained by periodic and Gaussian coloured noise alpha with identical characteristic time-scales and fluctuating amplitudes, we find that the transition to dynamo is significantly eased for stochastically fluctuating alpha. The effect of stochasticity in magnetic diffusion is also investigated, highlighting the importance of resonance between poloidal and toroidal magnetic fields on the growth rate. Furthermore, we show that probability density functions of the growth-rate, magnetic field, and magnetic energy can provide a wealth of useful information regarding the dynamo behaviour/intermittency. Finally, the statistical properties of the dynamo such as temporal correlation and fluctuating amplitude are found to be dependent on the distribution of the fluctuations in stocastic parameters.

  16. {alpha}-decay and fusion phenomena in heavy ion collisions using nucleon-nucleon interactions derived from relativistic mean-field theory

    SciTech Connect

    Singh, BirBikram; Sahu, B. B.; Patra, S. K.

    2011-06-15

    Nucleus-nucleus potentials are determined in the framework of the double-folding model for a new microscopic nucleon-nucleon (NN) interaction relativistic mean field-3-Yukawa (R3Y) derived from the popular relativistic mean-field theory Lagrangian, and the results are compared for the use of Michigan-3-Yukawa (M3Y) effective NN interactions. The double-folding potentials so obtained are further taken up in the context of the preformed cluster model (PCM) of Gupta and collaborators and the barrier penetration model to study respectively the ground-state (g.s.) {alpha}-decay and low-energy fusion reactions. In this paper, using PCM, we deduce empirically the {alpha} preformation probability P{sub 0}{sup {alpha}(emp)} from experimental data on a few g.s. {alpha} decays in the trans-lead region. For fusion reactions, two projectile-target systems {sup 12}C+{sup 208}Pb and {sup 16}O+{sup 208}Pb are selected for calculating the barrier energies as well positions, fusion cross sections ({sigma}{sub fus}), and fusion barrier distribution [D(E{sub c.m.})]. The barrier energies and positions change for the R3Y NN interactions in comparison with those of the M3Y NN interactions. We find that in the {alpha}-decay studies the values of P{sub 0}{sup {alpha}(emp)}(R3Y) are similar to those of P{sub 0}{sup {alpha}(emp)}(M3Y). Further, both NN interactions give similar {sigma}{sub fus} values using the Wong formula specifically when the R3Y NN interaction calculated {sigma}{sub fus} values are reduced by 1.5 times, and the results are in agreement with the experimental data for both the systems, especially for the higher energies. Results for D(E{sub c.m.}) are also quite similar for both choices of NN interaction.

  17. Limit Theorems for Monomer-Dimer Mean-Field Models with Attractive Potential

    NASA Astrophysics Data System (ADS)

    Alberici, Diego; Contucci, Pierluigi; Fedele, Micaela; Mingione, Emanuele

    2016-09-01

    The number of monomers in a monomer-dimer mean-field model with an attractive potential fluctuates according to the central limit theorem when the parameters are outside the critical curve. At the critical point the model belongs to the same universality class of the mean-field ferromagnet. Along the critical curve the monomer and dimer phases coexist.

  18. Asymmetric Neutrino Emissions in Relativistic Mean-Field Approach and Observables: Pulsar Kick and Rapid Spin-Deceleration of Magnetized Proto-Neutron Stars

    NASA Astrophysics Data System (ADS)

    Maruyama, T.; Kajino, T.; Yasutake, N.; Hidaka, J.; Kuroda, T.; Cheoun, M. K.; Ryu, C. Y.; Mathews, G. J.

    2015-11-01

    We calculate absorption cross-sections of neutrino in proto-neutron stars with strong magnetic field in the relativistic mean-field theory. Then, we apply this result to the neutrino transfer in the matter, and study the pulsar kick and the rapid spin down of magnetars.

  19. 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.

  20. Dynamical Mean-Field Theory of Electronic Correlations in Models and Materials

    NASA Astrophysics Data System (ADS)

    Vollhardt, Dieter

    2010-11-01

    The concept of electronic correlations plays an important role in modern condensed matter physics. It refers to interaction effects which cannot be explained within a static mean-field picture as provided by Hartree-Fock theory. Electronic correlations can have a very strong influence on the properties of materials. For example, they may turn a metal into an insulator (Mott-Hubbard metal-insulator transition). In these lecture notes I (i) introduce basic notions of the physics of correlated electronic systems, (ii) discuss the construction of mean-field theories by taking the limit of high lattice dimensions, (iii) explain the simplifications of the many-body perturbation theory in this limit which provide the basis for the formulation of a comprehensive mean-field theory for correlated fermions, the dynamical mean-field theory (DMFT), (v) derive the DMFT self-consistency equations, and (vi) apply the DMFT to investigate electronic correlations in models and materials.

  1. Mean-field approach for a statistical mechanical model of proteins

    NASA Astrophysics Data System (ADS)

    Bruscolini, Pierpaolo; Cecconi, Fabio

    2003-07-01

    We study the thermodynamical properties of a topology-based model proposed by Galzitskaya and Finkelstein for the description of protein folding. We devise and test three different mean-field approaches for the model, that simplify the treatment without spoiling the description. The validity of the model and its mean-field approximations is checked by applying them to the β-hairpin fragment of the immunoglobulin-binding protein (GB1) and making a comparison with available experimental data and simulation results. Our results indicate that this model is a rather simple and reasonably good tool for interpreting folding experimental data, provided the parameters of the model are carefully chosen. The mean-field approaches substantially recover all the relevant exact results and represent reliable alternatives to the Monte Carlo simulations.

  2. 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.

  3. 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.

  4. A mean-field analysis of the simple model of evolving open systems

    NASA Astrophysics Data System (ADS)

    Shimada, Takashi; Ogushi, Fumiko

    2016-09-01

    A recently reported mechanism of letting evolving systems grow only if the interactions in it is moderately sparse is reviewed and examined. It is shown that the mean field analysis, which is known to give a good simple understanding for this transition from growing to non-growing phase but with about 30% difference in its position, is well improved by taking only mean field type information from the simulation of the original model. This supports the validity of the understanding for the mechanism of the transition, obtained from the mean field analysis. The transition stems from an essential balance of two effects: although having more interactions makes each node robust, it also increases the impact of the loss of a node.

  5. Activated processes and Inherent Structure dynamics of finite-size mean-field models for glasses

    NASA Astrophysics Data System (ADS)

    Crisanti, A.; Ritort, F.

    2000-12-01

    We investigate the Inherent Structure (IS) dynamics of mean-field finite-size spin-glass models whose high-temperature dynamics is described in the thermodynamic limit by the schematic Mode Coupling Theory for supercooled liquids. Near the threshold energy the dynamics is ruled by activated processes which induce a logarithmic slow relaxation. We show the presence of aging in both the IS correlation and integrated response functions and check the validity of the one-step replica symmetry breaking scenario in the presence of activated processes. Our work shows: 1) the violation of the fluctuation-dissipation theorem can be computed from the configurational entropy obtained in the Stillinger and Weber approach, 2) the intermediate time regime (log (t) ~ N) in mean-field theory automatically includes activated processes opening the way to analytically investigate activated processes by computing corrections beyond mean field.

  6. 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

  7. 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.

  8. Optical potential obtained from relativistic-mean-field theory-based microscopic nucleon-nucleon interaction: applied to cluster radioactive decays

    NASA Astrophysics Data System (ADS)

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

    2012-02-01

    A microscopic nucleon-nucleon (NN) interaction is derived from the popular relativistic-mean-field (RMF) theory Lagrangian and used to obtain the optical potential by folding it with the RMF densities of cluster and daughter nuclei. The NN-interaction is remarkably related to the inbuilt fundamental parameters of RMF theory, and the results of the application of the so obtained optical potential, made to exotic cluster radioactive decays and α+α scattering, are found comparable to that for the well-known, phenomenological M3Y effective NN-interaction. The RMF-based NN-interaction can also be used to calculate a number of other nuclear observables.

  9. 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.

  10. 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.

  11. Spectral properties of the one-dimensional Hubbard model: cluster dynamical mean-field approaches

    NASA Astrophysics Data System (ADS)

    Go, Ara; Jeon, Gun Sang

    2011-03-01

    We investigate static and dynamic properties of the one-dimensional Hubbard model using cluster extensions of the dynamical mean-field theory. It is shown that the two different extensions, the cellular dynamical mean-field theory and the dynamic cluster approximation, yield the ground-state properties which are qualitatively in good agreement with each other. We compare the results with the Bethe ansatz results to check the accuracy of the calculation with finite sizes of clusters. We also analyze the spectral properties of the model with the focus on the spin-charge separation and discuss the dependency on the cluster size in the two approaches. This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2010-0010937).

  12. 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

  13. 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.

  14. LETTER TO THE EDITOR: Car-oriented mean-field theory for traffic flow models

    NASA Astrophysics Data System (ADS)

    Schadschneider, Andreas; Schreckenberg, Michael

    1997-02-01

    We present a new analytical description of the cellular automaton model for single-lane traffic. In contrast to previous approaches we do not use the occupation number of sites as dynamical variable but rather the distance between consecutive cars. Therefore certain longer-ranged correlations are taken into account and even a mean-field approach yields non-trivial results. In fact for the model with 0305-4470/30/4/005/img5 the exact solution is reproduced. For 0305-4470/30/4/005/img6 the fundamental diagram shows a good agreement with results from simulations.

  15. Connecting mean field models of neural activity to EEG and fMRI data.

    PubMed

    Bojak, Ingo; Oostendorp, Thom F; Reid, Andrew T; Kötter, Rolf

    2010-06-01

    Progress in functional neuroimaging of the brain increasingly relies on the integration of data from complementary imaging modalities in order to improve spatiotemporal resolution and interpretability. However, the usefulness of merely statistical combinations is limited, since neural signal sources differ between modalities and are related non-trivially. We demonstrate here that a mean field model of brain activity can simultaneously predict EEG and fMRI BOLD with proper signal generation and expression. Simulations are shown using a realistic head model based on structural MRI, which includes both dense short-range background connectivity and long-range specific connectivity between brain regions. The distribution of modeled neural masses is comparable to the spatial resolution of fMRI BOLD, and the temporal resolution of the modeled dynamics, importantly including activity conduction, matches the fastest known EEG phenomena. The creation of a cortical mean field model with anatomically sound geometry, extensive connectivity, and proper signal expression is an important first step towards the model-based integration of multimodal neuroimages.

  16. 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

  17. 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.

  18. 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.

  19. 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

  20. 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

  1. 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.

  2. 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.

  3. Cluster dynamic mean-field study on the superconductivity in doped honeycomb lattice Hubbard model

    NASA Astrophysics Data System (ADS)

    Xu, Xiao Yan; Dang, Hung T.; Wessel, Stefen; Meng, Zi Yang

    The issue of superconductivities emerging from doped honeycomb lattice Mott insulator remains inconclusive. Existing proposals, such as p+ip triplet pairing driven by ferromagnetic fluctuations, d+id singlet pairing driven by antiferromagnetic fluctuations or van Hove singularities in the band structure, are not compatible. This is mainly due to the limitation of various approximated techniques employed in addressing such question with inherent strongly correlated nature. Trying to clarify the situation, we perform large-scale cluster dynamic mean-field simulations to explore the superconductivity instabilities in the doped honeycomb lattice Hubbard model, from medium to strong coupling. To benchmark, we make use of both interaction- and hybridization-expansion continuous time quantum Monte Carlo methods to exactly solve the quantum cluster embedded in self-consistently determined mean-field bath. Temperature dependence of various superconducting susceptibilities are calculated, hence, we provide the least biased results of the competition of the superconductivity in different channels in the phase diagram spanned by doping and electronic interaction.

  4. 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.

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

    PubMed

    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.

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

    PubMed

    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. PMID:27415217

  7. 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.

  8. Relativistic shell model calculations

    NASA Astrophysics Data System (ADS)

    Furnstahl, R. J.

    1986-06-01

    Shell model calculations are discussed in the context of a relativistic model of nuclear structure based on renormalizable quantum field theories of mesons and baryons (quantum hadrodynamics). The relativistic Hartree approximation to the full field theory, with parameters determined from bulk properties of nuclear matter, predicts a shell structure in finite nuclei. Particle-hole excitations in finite nuclei are described in an RPA calculation based on this QHD ground state. The particle-hole interaction is prescribed by the Hartree ground state, with no additional parameters. Meson retardation is neglected in deriving the RPA equations, but it is found to have negligible effects on low-lying states. The full Dirac matrix structure is maintained throughout the calculation; no nonrelativistic reductions are made. Despite sensitive cancellations in the ground state calculation, reasonable excitation spectra are obtained for light nuclei. The effects of including charged mesons, problems with heavy nuclei, and prospects for improved and extended calculations are discussed.

  9. 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.

  10. 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.

  11. Nondiagonalizable and nondivergent susceptibility tensor in the Hamiltonian mean-field model with asymmetric momentum distributions.

    PubMed

    Yamaguchi, Yoshiyuki Y

    2015-09-01

    We investigate the response to an external magnetic field in the Hamiltonian mean-field model, which is a paradigmatic toy model of a ferromagnetic body and consists of plane rotators like XY spins. Due to long-range interactions, the external field drives the system to a long-lasting quasistationary state before reaching thermal equilibrium, and the susceptibility tensor obtained in the quasistationary state is predicted by a linear response theory based on the Vlasov equation. For spatially homogeneous stable states, whose momentum distributions are asymmetric with 0 means, the theory reveals that the susceptibility tensor for an asymptotically constant external field is neither symmetric nor diagonalizable, and the predicted states are not stationary accordingly. Moreover, the tensor has no divergence even at the stability threshold. These theoretical findings are confirmed by direct numerical simulations of the Vlasov equation for skew-normal distribution functions. PMID:26465428

  12. Nondiagonalizable and nondivergent susceptibility tensor in the Hamiltonian mean-field model with asymmetric momentum distributions

    NASA Astrophysics Data System (ADS)

    Yamaguchi, Yoshiyuki Y.

    2015-09-01

    We investigate the response to an external magnetic field in the Hamiltonian mean-field model, which is a paradigmatic toy model of a ferromagnetic body and consists of plane rotators like XY spins. Due to long-range interactions, the external field drives the system to a long-lasting quasistationary state before reaching thermal equilibrium, and the susceptibility tensor obtained in the quasistationary state is predicted by a linear response theory based on the Vlasov equation. For spatially homogeneous stable states, whose momentum distributions are asymmetric with 0 means, the theory reveals that the susceptibility tensor for an asymptotically constant external field is neither symmetric nor diagonalizable, and the predicted states are not stationary accordingly. Moreover, the tensor has no divergence even at the stability threshold. These theoretical findings are confirmed by direct numerical simulations of the Vlasov equation for skew-normal distribution functions.

  13. 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.

  14. 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

  15. 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.

  16. Onset of synchronization in the disordered Hamiltonian mean-field model

    NASA Astrophysics Data System (ADS)

    Restrepo, Juan G.; Meiss, James D.

    2014-05-01

    We study the Hamiltonian mean field (HMF) model of coupled Hamiltonian rotors with a heterogeneous distribution of moments of inertia and coupling strengths. We show that when the parameters of the rotors are heterogeneous, finite-size fluctuations can greatly modify the coupling strength at which the incoherent state loses stability by inducing correlations between the momenta and parameters of the rotors. When the distribution of initial frequencies of the oscillators is sufficiently narrow, an analytical expression for the modification in critical coupling strength is obtained that confirms numerical simulations. We find that heterogeneity in the moments of inertia tends to stabilize the incoherent state, while heterogeneity in the coupling strengths tends to destabilize the incoherent state. Numerical simulations show that these effects disappear for a wide, bimodal frequency distribution.

  17. 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.

  18. 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.

  19. 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

  20. Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy*

    NASA Astrophysics Data System (ADS)

    Kechedzhi, Kostyantyn; Smelyanskiy, Vadim N.

    2016-04-01

    Real-life quantum computers are inevitably affected by intrinsic noise resulting in dissipative nonunitary dynamics realized by these devices. We consider an open-system quantum annealing algorithm optimized for such a realistic analog quantum device which takes advantage of noise-induced thermalization and relies on incoherent quantum tunneling at finite temperature. We theoretically analyze the performance of this algorithm considering a p -spin model that allows for a mean-field quasiclassical solution and, at the same time, demonstrates the first-order phase transition and exponential degeneracy of states, typical characteristics of spin glasses. We demonstrate that finite-temperature effects introduced by the noise are particularly important for the dynamics in the presence of the exponential degeneracy of metastable states. We determine the optimal regime of the open-system quantum annealing algorithm for this model and find that it can outperform simulated annealing in a range of parameters. Large-scale multiqubit quantum tunneling is instrumental for the quantum speedup in this model, which is possible because of the unusual nonmonotonous temperature dependence of the quantum-tunneling action in this model, where the most efficient transition rate corresponds to zero temperature. This model calculation is the first analytically tractable example where open-system quantum annealing algorithm outperforms simulated annealing, which can, in principle, be realized using an analog quantum computer.

  1. Algebraic Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Dankova, T. S.; Rosensteel, G.

    1998-10-01

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

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

    NASA Astrophysics Data System (ADS)

    Akerlund, Oscar; de Forcrand, Philippe

    2016-02-01

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

  3. Stable nonequilibrium probability densities and phase transitions for mean-field models in the thermodynamic limit

    SciTech Connect

    Bonilla, L.L.

    1987-02-01

    A nonlinear Fokker-Planck equation is derived to describe the cooperative behavior of general stochastic systems interacting via mean-field couplings, in the limit of a infinite number of such systems. Disordered systems are also considered. In the weak-noise limit; a general result yields the possibility of having bifurcations from stationary solutions of the nonlinear Fokker-Planck equation into stable time-dependent solutions. The latter are interpreted as nonequilibrium probability distributions (states), and the bifurcations to them as nonequilibrium phase transitions. In the thermodynamic limit, results for three models are given for illustrative purposes. A model of self-synchronization of nonlinear oscillators presents a Hopf bifurcation to a time-periodic probability density, which can be analyzed for any value of the noise. The effects of disorder are illustrated by a simplified version of the Sompolinsky-Zippelius model of spin-glasses. Finally, results for the Fukuyama-Lee-Fisher model of charge-density waves are given. A singular perturbation analysis shows that the depinning transition is a bifurcation problem modified by the disorder noise due to impurities. Far from the bifurcation point, the CDW is either pinned or free, obeying (to leading order) the Gruener-Zawadowki-Chaikin equation. Near the bifurcation, the disorder noise drastically modifies the pattern, giving a quenched average of the CDW current which is constant. Critical exponents are found to depend on the noise, and they are larger than Fisher's values for the two probability distributions considered.

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

    PubMed Central

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

    2012-01-01

    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. PMID:21517541

  5. 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.

  6. 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.

  7. Nuclear mean field and double-folding model of the nucleus-nucleus optical potential

    NASA Astrophysics Data System (ADS)

    Khoa, Dao T.; Phuc, Nguyen Hoang; Loan, Doan Thi; Loc, Bui Minh

    2016-09-01

    Realistic density dependent CDM3Yn versions of the M3Y interaction have been used in an extended Hartree-Fock (HF) calculation of nuclear matter (NM), with the nucleon single-particle potential determined from the total NM energy based on the Hugenholtz-van Hove theorem that gives rise naturally to a rearrangement term (RT). Using the RT of the single-nucleon potential obtained exactly at different NM densities, the density and energy dependence of the CDM3Yn interactions was modified to account properly for both the RT and observed energy dependence of the nucleon optical potential. Based on a local density approximation, the double-folding model of the nucleus-nucleus optical potential has been extended to take into account consistently the rearrangement effect and energy dependence of the nuclear mean-field potential, using the modified CDM3Yn interactions. The extended double-folding model was applied to study the elastic 12C+12C and 16O+12C scattering at the refractive energies, where the Airy structure of the nuclear rainbow has been well established. The RT was found to affect significantly the real nucleus-nucleus optical potential at small internuclear distances, giving a potential strength close to that implied by the realistic optical model description of the Airy oscillation.

  8. Critical behavior of a tumor growth model: Directed percolation with a mean-field flavor

    NASA Astrophysics Data System (ADS)

    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 , Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.85.010901 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⊥, 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.

  9. A mean-field study of the Hubbard model on the kagome lattice

    NASA Astrophysics Data System (ADS)

    Enjalran, Matthew

    The experimental work on the herbertsmithite compound, ZnCu3(OH)6Cl2, almost a decade ago ignited intense interest in the field of frustrated magnetism because it represented the best material realization of a spin- 1 / 2 Heisenberg antiferromagnet (AFM) on the kagome lattice and its ground state was a gapless spin liquid. Many theoretical and numerical studies of the quantum Heisenberg AFM on the kagome lattice have been performed since and have coalesced around the general consensus of a small gapped spin liquid ground state for the model. Although there is not currently a metallic kagome material system, the work on ZnCu3(OH)6Cl2 has motivated theoretical and numerical investigations of itinerant electrons on the kagome lattice. We contribute to this pursuit by studying the single band Hubbard model on the kagome lattice, where the frustration can be tuned by adjusting the hopping along different bonds, t1 and t2; however, we are mainly interested in the isotropic limit, t1 =t2 = t . We report preliminary results on the low temperature correlations in the half filled model as a function of frustration and interaction strength in the mean-field, Hartree-Fock, limit. CSU Research Grant.

  10. 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.

  11. Singular-potential random-matrix model arising in mean-field glassy systems

    NASA Astrophysics Data System (ADS)

    Akemann, Gernot; Villamaina, Dario; Vivo, Pierpaolo

    2014-06-01

    We consider an invariant random matrix ensemble where the standard Gaussian potential is distorted by an additional single pole of arbitrary fixed order. Potentials with first- and second-order poles have been considered previously and found applications in quantum chaos and number theory. Here we present an application to mean-field glassy systems. We derive and solve the loop equation in the planar limit for the corresponding class of potentials. We find that the resulting mean or macroscopic spectral density is generally supported on two disconnected intervals lying on the two sides of the repulsive pole, whose edge points can be completely determined imposing the additional constraint of traceless matrices on average. For an unbounded potential with an attractive pole, we also find a possible one-cut solution for certain values of the couplings, which is ruled out when the traceless condition is imposed. Motivated by the calculation of the distribution of the spin-glass susceptibility in the Sherrington-Kirkpatrick spin-glass model, we consider in detail a second-order pole for a zero-trace model and provide the most explicit solution in this case. In the limit of a vanishing pole, we recover the standard semicircle. Working in the planar limit, our results apply to matrices with orthogonal, unitary, and symplectic invariance. Numerical simulations and an independent analytical Coulomb fluid calculation for symmetric potentials provide an excellent confirmation of our results.

  12. Singular-potential random-matrix model arising in mean-field glassy systems.

    PubMed

    Akemann, Gernot; Villamaina, Dario; Vivo, Pierpaolo

    2014-06-01

    We consider an invariant random matrix ensemble where the standard Gaussian potential is distorted by an additional single pole of arbitrary fixed order. Potentials with first- and second-order poles have been considered previously and found applications in quantum chaos and number theory. Here we present an application to mean-field glassy systems. We derive and solve the loop equation in the planar limit for the corresponding class of potentials. We find that the resulting mean or macroscopic spectral density is generally supported on two disconnected intervals lying on the two sides of the repulsive pole, whose edge points can be completely determined imposing the additional constraint of traceless matrices on average. For an unbounded potential with an attractive pole, we also find a possible one-cut solution for certain values of the couplings, which is ruled out when the traceless condition is imposed. Motivated by the calculation of the distribution of the spin-glass susceptibility in the Sherrington-Kirkpatrick spin-glass model, we consider in detail a second-order pole for a zero-trace model and provide the most explicit solution in this case. In the limit of a vanishing pole, we recover the standard semicircle. Working in the planar limit, our results apply to matrices with orthogonal, unitary, and symplectic invariance. Numerical simulations and an independent analytical Coulomb fluid calculation for symmetric potentials provide an excellent confirmation of our results.

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

    PubMed

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

    2014-05-01

    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.

  14. Dynamic mean field theory for lattice gas models of fluid mixtures confined in mesoporous materials.

    PubMed

    Edison, J R; Monson, P A

    2013-11-12

    We present the extension of dynamic mean field theory (DMFT) for fluids in porous materials (Monson, P. A. J. Chem. Phys. 2008, 128, 084701) to the case of mixtures. The theory can be used to describe the relaxation processes in the approach to equilibrium or metastable equilibrium states for fluids in pores after a change in the bulk pressure or composition. It is especially useful for studying systems where there are capillary condensation or evaporation transitions. Nucleation processes associated with these transitions are emergent features of the theory and can be visualized via the time dependence of the density distribution and composition distribution in the system. For mixtures an important component of the dynamics is relaxation of the composition distribution in the system, especially in the neighborhood of vapor-liquid interfaces. We consider two different types of mixtures, modeling hydrocarbon adsorption in carbon-like slit pores. We first present results on bulk phase equilibria of the mixtures and then the equilibrium (stable/metastable) behavior of these mixtures in a finite slit pore and an inkbottle pore. We then use DMFT to describe the evolution of the density and composition in the pore in the approach to equilibrium after changing the state of the bulk fluid via composition or pressure changes. PMID:24102541

  15. 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.

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

    NASA Astrophysics Data System (ADS)

    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.

  17. Nonequilibrium Dynamical Mean-Field Theory for the Charge-Density-Wave Phase of the Falicov-Kimball Model

    SciTech Connect

    Matveev, O. P.; Shvaika, A. M.; Devereaux, T. P.; Freericks, J. K.

    2015-12-08

    Nonequilibrium dynamical mean-field theory (DMFT) is developed for the case of the charge-density-wave ordered phase. We consider the spinless Falicov-Kimball model which can be solved exactly. This strongly correlated system is then placed in an uniform external dc electric field. We present a complete derivation for nonequilibrium dynamical mean-field theory Green’s functions defined on the Keldysh-Schwinger time contour. We also discuss numerical issues involved in solving the coupled equations.

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

    PubMed

    Moosavi, S Amin; Montakhab, Afshin

    2015-01-01

    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.

  19. 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.

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

    PubMed

    Moosavi, S Amin; Montakhab, Afshin

    2015-01-01

    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

  1. Mean-field modeling of the basal ganglia-thalamocortical system. II Dynamics of parkinsonian oscillations.

    PubMed

    van Albada, S J; Gray, R T; Drysdale, P M; Robinson, P A

    2009-04-21

    Neuronal correlates of Parkinson's disease (PD) include a shift to lower frequencies in the electroencephalogram (EEG) and enhanced synchronized oscillations at 3-7 and 7-30 Hz in the basal ganglia, thalamus, and cortex. This study describes the dynamics of a recent physiologically based mean-field model of the basal ganglia-thalamocortical system, and shows how it accounts for many key electrophysiological correlates of PD. Its detailed functional connectivity comprises partially segregated direct and indirect pathways through two populations of striatal neurons, a hyperdirect pathway involving a corticosubthalamic projection, thalamostriatal feedback, and local inhibition in striatum and external pallidum (GPe). In a companion paper, realistic steady-state firing rates were obtained for the healthy state, and after dopamine loss modeled by weaker direct and stronger indirect pathways, reduced intrapallidal inhibition, lower firing thresholds of the GPe and subthalamic nucleus (STN), a stronger projection from striatum to GPe, and weaker cortical interactions. Here it is shown that oscillations around 5 and 20 Hz can arise with a strong indirect pathway, which also causes increased synchronization throughout the basal ganglia. Furthermore, increased theta power with progressive nigrostriatal degeneration is correlated with reduced alpha power and peak frequency, in agreement with empirical results. Unlike the hyperdirect pathway, the indirect pathway sustains oscillations with phase relationships that coincide with those found experimentally. Alterations in the responses of basal ganglia to transient stimuli accord with experimental observations. Reduced cortical gains due to both nigrostriatal and mesocortical dopamine loss lead to slower changes in cortical activity and may be related to bradykinesia. Finally, increased EEG power found in some studies may be partly explained by a lower effective GPe firing threshold, reduced GPe-GPe inhibition, and/or weaker

  2. Relativistic and nonrelativistic quarkonium models

    SciTech Connect

    Ono, S.

    1982-11-01

    We propose a quarkonium potential for the Klein-Gordon equation. The relativistic effects are small even for uu-bar and dd-bar systems because the introduction of a scalar constant potential in a Klein-Gordon equation allows a minimization of relativistic effects via cancellations in our model.

  3. Band mixing effects in mean field theories. I. E 2 transitions in the interacting boson model 1

    SciTech Connect

    Kuyucak, S.; Morrison, I. )

    1990-04-01

    The 1/{ital N} expansion method, which is an angular momentum projected mean field theory, is used to investigate the nature of electromagnetic transitions in the interacting boson model. Conversely, comparison with the exact interacting boson model results sheds light on the range of validity of the mean field theory. It is shown that the projected mean field results for the {ital E}2 transitions among the ground, {beta}, and {gamma} bands are incomplete for the spin-dependent terms, and it is essential to include band mixing effects for a correct (Mikhailov) analysis of {ital E}2 data. The algebraic expressions derived are general and will be useful in the analysis of experimental data in terms of both the {ital sd} and {ital sdg} boson models.

  4. Magnetic phase diagram of interacting nanoparticle systems under the mean-field model

    NASA Astrophysics Data System (ADS)

    Mao, Zhongquan; Chen, Xi

    2011-06-01

    The disordered random-anisotropy magnetic nanoparticle systems with competing dipolar interactions and ferromagnetic exchange couplings are investigated by Monte Carlo simulations. Superspin glass (SSG) and superferromagnetic (SFM) behaviors are found at low temperatures depending on the interactions. Based on the mean-field approximation, the Curie-Weiss temperature TCW = 0 is suggested as the phase boundary between the SSG systems and the SFM systems, which is evidenced by the spontaneous magnetizations and relaxations. The magnetic phase diagram is plotted.

  5. Ideal quarks and mesons in the relativistic quark model

    SciTech Connect

    Kaneko, K. )

    1994-05-01

    We propose a microscopic theory for interacting mesons and ideal quarks in the relativistic quark model using the time-dependent mean-field theory technique. For simplicity we examined the Nambu--Jona-Lasinio model. The dynamical chiral-symmetry breaking leads to a zero-frequency mode (pion) due to the restoration of chiral symmetry. The ideal quarks are represented as dressed particles independent of mean fields, and do not have the conventional properties of fermions. This is due to the constraints of eliminating the double counting of degrees of freedom between the mean fields and quarks. The small fluctuation around the static solution is then investigated. The pseudoscalar and scalar mesons are represented as the collective modes of the mean fields.

  6. Brain activity modeling in general anesthesia: Enhancing local mean-field models using a slow adaptive firing rate

    NASA Astrophysics Data System (ADS)

    Molaee-Ardekani, B.; Senhadji, L.; Shamsollahi, M. B.; Vosoughi-Vahdat, B.; Wodey, E.

    2007-10-01

    In this paper, an enhanced local mean-field model that is suitable for simulating the electroencephalogram (EEG) in different depths of anesthesia is presented. The main building elements of the model (e.g., excitatory and inhibitory populations) are taken from Steyn-Ross [M. L. Steyn-Ross , Phys. Rev. E 64, 011917 (2001), D. A. Steyn-Ross , Phys. Rev. E 64, 011918 (2001)] and Bojak and Liley [I. Bojak and D. T. Liley, Phys. Rev. E 71, 041902 (2005)] mean-field models and a new slow ionic mechanism is included in the main model. Generally, in mean-field models, some sigmoid-shape functions determine firing rates of neural populations according to their mean membrane potentials. In the enhanced model, the sigmoid function corresponding to excitatory population is redefined to be also a function of the slow ionic mechanism. This modification adapts the firing rate of neural populations to slow ionic activities of the brain. When an anesthetic drug is administered, the slow mechanism may induce neural cells to alternate between two levels of activity referred to as up and down states. Basically, the frequency of up-down switching is in the delta band (0-4Hz) and this is the main reason behind high amplitude, low frequency fluctuations of EEG signals in anesthesia. Our analyses show that the enhanced model may have different working states driven by anesthetic drug concentration. The model is settled in the up state in the waking period, it may switch to up and down states in moderate anesthesia while in deep anesthesia it remains in the down state.

  7. 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.

  8. Mean-field modeling of thalamocortical dynamics and a model-driven approach to EEG analysis.

    PubMed

    Victor, Jonathan D; Drover, Jonathan D; Conte, Mary M; Schiff, Nicholas D

    2011-09-13

    Higher brain function depends on task-dependent information flow between cortical regions. Converging lines of evidence suggest that interactions between cortical regions and the central thalamus play a key role in establishing the dynamic patterns of functional connectivity that normally support these processes. In patients with chronic disturbances of cognitive function due to severe brain injury, dysfunction of this circuitry likely plays a crucial role in pathogenesis. However, assaying thalamocortical interactions is challenging even in healthy subjects and more so in severely impaired patients. To approach this problem, we apply a dynamical-systems approach to motivate an analysis of the electroencephalogram (EEG). We begin with a model for a single thalamocortical module [Robinson PA, Rennie CJ, Rowe DL (2002) Phys Rev E Stat Nonlin Soft Matter Phys 65:041924; Robinson PA, Rennie CJ, Wright JJ, Bourke PD (1998) Phys Rev E Stat Nonlin Soft Matter Phys 58:3557-3571]. When two such modules interact via shared thalamic inhibition, multistable behavior emerges; each mode is characterized by a different pattern of coherence between cortical regions. This observation suggests that changing patterns of cortical coherence are a hallmark of normal thalamocortical dynamics. In a preliminary study, we test this idea by analyzing the EEG of a patient with chronic brain injury, who has a marked improvement in behavior and frontal brain metabolism in response to zolpidem. The analysis shows that following zolpidem administration, changing patterns of coherence are identified between the frontal lobes and between frontal and distant brain regions. These observations support the role of the central thalamus in the organization of patterns of cortical interactions and suggest how indexes of thalamocortical dynamics can be extracted from the EEG.

  9. 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.

  10. 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.

  11. 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.

  12. {sup 208}Pb neutron density: A mean field problem?

    SciTech Connect

    Gmuca, Stefan

    1998-12-21

    The ground-state nuclear densities and radii of {sup 208}Pb doubly-magic nucleus have been evaluated within the framework of the relativistic mean-field approach. It is pointed out that the neutron density and the neutron radius in the RMF approach are quite different from both, the empirical data and the predictions of the Skyrme-Hartree-Fock model.

  13. 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.

  14. 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.

  15. Mean-field methods in evolutionary duplication-innovation-loss models for the genome-level repertoire of protein domains

    NASA Astrophysics Data System (ADS)

    Angelini, A.; Amato, A.; Bianconi, G.; Bassetti, B.; Cosentino Lagomarsino, M.

    2010-02-01

    We present a combined mean-field and simulation approach to different models describing the dynamics of classes formed by elements that can appear, disappear, or copy themselves. These models, related to a paradigm duplication-innovation model known as Chinese restaurant process, are devised to reproduce the scaling behavior observed in the genome-wide repertoire of protein domains of all known species. In view of these data, we discuss the qualitative and quantitative differences of the alternative model formulations, focusing in particular on the roles of element loss and of the specificity of empirical domain classes.

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

    NASA Astrophysics Data System (ADS)

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

    2015-03-01

    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.

  17. 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.

  18. 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

  19. A statistical mechanical model of cell membrane ion channels in electric fields: The mean-field approximation

    NASA Astrophysics Data System (ADS)

    Yang, Y. S.; Thompson, C. J.; Anderson, V.; Wood, A. W.

    A statistical mechanical model of cell membrane ion channels is proposed which incorporates interactions between ion channels and external electric fields. The model provides a physical explanation of trans-membrane ion transport. Under a mean-field approximation, the maximum fractions of open potassium and sodium channels are obtained by solving a self-consistent nonlinear algebraic equation. Using known parameters for the squid giant axon, the model gives excellent agreement with experimental measurements for potassium and sodium trans-membrane conductance. The numerical results imply that the chemical potential of open channels and the interaction energy between channels are well above the thermal noise.

  20. 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.

  1. 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.

  2. 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

  3. 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.

  4. Beyond mean field study of excited states: Analysis within the Lipkin model

    SciTech Connect

    Severyukhin, A. P.; Bender, M.

    2006-08-15

    We compare the generator coordinate method (GCM) and the random-phase approximation (RPA) in the framework of the exactly solvable Lipkin-Meshkov-Glick model. We show that the discretized GCM works quite well and permits to obtain results close to the exact results with a small number of discretization points.

  5. 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.

  6. Fragility of the mean-field scenario of structural glasses for disordered spin models in finite dimensions

    NASA Astrophysics Data System (ADS)

    Cammarota, Chiara; Biroli, Giulio; Tarzia, Marco; Tarjus, Gilles

    2013-02-01

    At the mean-field level, on fully connected lattices, several disordered spin models have been shown to belong to the universality class of “structural glasses” with a “random first-order transition” (RFOT) characterized by a discontinuous jump of the order parameter and no latent heat. However, their behavior in finite dimensions is often drastically different, displaying either no glassiness at all or a conventional spin-glass transition. We clarify the physical reasons for this phenomenon and stress the unusual fragility of the RFOT to short-range fluctuations, associated, e.g., with the mere existence of a finite number of neighbors. Accordingly, the solution of fully connected models is only predictive in very high dimension, whereas despite being also mean-field in character, the Bethe approximation provides valuable information on the behavior of finite-dimensional systems. We suggest that before embarking on a full blown account of fluctuations on all scales through computer simulation or renormalization-group approach, models for structural glasses should first be tested for the effect of short-range fluctuations and we discuss ways to do it. Our results indicate that disordered spin models do not appear to pass the test and are therefore questionable models for investigating the glass transition in three dimensions. This also highlights how nontrivial is the first step of deriving an effective theory for the RFOT phenomenology from a rigorous integration over the short-range fluctuations.

  7. An analytical calculation of neighbourhood order probabilities for high dimensional Poissonian processes and mean field models

    NASA Astrophysics Data System (ADS)

    Sangaletti Terçariol, César Augusto; de Moura Kiipper, Felipe; Souto Martinez, Alexandre

    2007-03-01

    Consider that the coordinates of N points are randomly generated along the edges of a d-dimensional hypercube (random point problem). The probability P(d,N)m,n that an arbitrary point is the mth nearest neighbour to its own nth nearest neighbour (Cox probabilities) plays an important role in spatial statistics. Also, it has been useful in the description of physical processes in disordered media. Here we propose a simpler derivation of Cox probabilities, where we stress the role played by the system dimensionality d. In the limit d → ∞, the distances between pair of points become independent (random link model) and closed analytical forms for the neighbourhood probabilities are obtained both for the thermodynamic limit and finite-size system. Breaking the distance symmetry constraint drives us to the random map model, for which the Cox probabilities are obtained for two cases: whether a point is its own nearest neighbour or not.

  8. A mean field Ising model for cortical rotation in amphibian one-cell stage embryos.

    PubMed

    Tuszynski, Jack A; Gordon, Richard

    2012-09-01

    We propose a new physical mechanism of cortical rotation generation in one-cell embryos of amphibians based on a phase transition in the ensemble of microtubules localized to the cortical region of the cell interior. Microtubules, protein polymers formed from tubulin heterodimers, are highly negatively charged, which results in strong electrostatic interactions over tens of nanometers, even in the presence of counterions that partially screen electrostatic interactions. A simplified model that offers a plausible representation of these effects is based on the Ising Hamiltonian, which has been robustly applied to explain a wide range of order-disorder transitions in physics, chemistry and other sciences. An Ising model phase transition, especially with the supercooperative flow alignment effect of global rotation of the cortex, provides an alternative to models of cortical rotation based on microtubule polymerization or motor molecules. Insofar as there is any reality to the concept that microtubules are involved in consciousness, we propose that cortical rotation in the one-cell embryo is a better place to look for the purported microtubule entanglement or coherence properties than the adult brain. PMID:22626532

  9. 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.

  10. Mean field analysis of a spatial stochastic model of a gene regulatory network.

    PubMed

    Sturrock, M; Murray, P J; Matzavinos, A; Chaplain, M A J

    2015-10-01

    A gene regulatory network may be defined as a collection of DNA segments which interact with each other indirectly through their RNA and protein products. Such a network is said to contain a negative feedback loop if its products inhibit gene transcription, and a positive feedback loop if a gene product promotes its own production. Negative feedback loops can create oscillations in mRNA and protein levels while positive feedback loops are primarily responsible for signal amplification. It is often the case in real biological systems that both negative and positive feedback loops operate in parameter regimes that result in low copy numbers of gene products. In this paper we investigate the spatio-temporal dynamics of a single feedback loop in a eukaryotic cell. We first develop a simplified spatial stochastic model of a canonical feedback system (either positive or negative). Using a Gillespie's algorithm, we compute sample trajectories and analyse their corresponding statistics. We then derive a system of equations that describe the spatio-temporal evolution of the stochastic means. Subsequently, we examine the spatially homogeneous case and compare the results of numerical simulations with the spatially explicit case. Finally, using a combination of steady-state analysis and data clustering techniques, we explore model behaviour across a subregion of the parameter space that is difficult to access experimentally and compare the parameter landscape of our spatio-temporal and spatially-homogeneous models.

  11. 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.

  12. Mean field model of acetylcholine mediated dynamics in the thalamocortical system.

    PubMed

    Clearwater, J M; Rennie, C J; Robinson, P A

    2008-12-01

    A recent continuum model of the large scale electrical activity of the thalamocortical system is generalized to include cholinergic modulation. The model is examined analytically and numerically to determine the effect of acetylcholine (ACh) on its steady states, linear stability, spectrum, and temporal responses. Changing the ACh concentration moves the system between zones of one, three, and five steady states, showing that neuromodulation of synaptic strength is a possible mechanism by which multiple steady states emerge in the brain. The lowest firing rate steady state is always stable, and subsequent fixed points alternate between stable and unstable. Increasing ACh concentration changes the form of the spectrum. Increasing the tonic level of ACh concentration increases the magnitudes of the N100 and P200 in the evoked response potential (ERP), without changing the timing of these peaks. Driving the system with a pulse of cholinergic activity results in a transient increase in the firing rate of cortical neurons that lasts over 10s. Step-like increases in cortical ACh concentration cause increases in the firing rate of cortical neurons, with rapid responses due to fast acting nicotinic receptors and slower responses due to muscarinic receptor suppression of intracortical connections.

  13. Mean Field Theory of a Coupled Heisenberg Model and Its Application to an Organic Antiferromagnet with Magnetic Anions

    NASA Astrophysics Data System (ADS)

    Ito, Kazuhiro; Shimahara, Hiroshi

    2016-02-01

    We examine the mean field theory of a uniaxial coupled Heisenberg antiferromagnet with two subsystems, one of which consists of strongly interacting small spins and the other consists of weakly interacting large spins. We reanalyze the experimental data of specific heat and magnetic susceptibility obtained by previous authors for the organic compound λ-(BETS)2FeCl4 at low temperatures, where BETS stands for bis(ethylenedithio)tetraselenafulvalene. The model parameters for this compound are evaluated, where the applicability of the theory is checked. As a result, it is found that J1 ≫ J12 ≫ J2, where J1, J2, and J12 denote the exchange coupling constant between π spins, that between 3d spins, and that between π and 3d spins, respectively. At the low-temperature limit, both sublattice magnetizations of the 3d and π spins are saturated, and the present model is reduced to the Schottky model, which successfully explains experimental observations in previous studies. As temperature increases, fluctuations of 3d spins increase, while π spins remain almost saturated. Near the critical temperature, both spins fluctuate significantly, and thus the mean field approximation breaks down. It is revealed that the magnetic anisotropy, which may be crucial to the antiferromagnetic long-range order, originates from J12 rather than from J2 and that the angle between the magnetic easy-axis and the crystal c-axis is approximately 26-27° in the present effective model.

  14. Multiscale Modeling of Upper Mantle Plasticity: Integrating Experimental and Theoretical data into Mean-field Schemes

    NASA Astrophysics Data System (ADS)

    Raterron, P.; Castelnau, O.; Detrez, F.; Bollinger, C.; Cordier, P.; Fraysse, G.; Merkel, S.

    2013-12-01

    Quantifying peridotite plastic properties has been a major quest for experimental mineralogy, with direct implications for upper-mantle seismology and geodynamics. It raises, however, serious difficulties such as understanding the complex mechanisms involved within grains and at grain boundaries in multiphase aggregates deforming at high temperature (T), quantifying the effects of extreme pressures (P) on these mechanisms, and addressing stress and strain scaling issues between laboratory experiments and natural deformations. In order to address some of these issues, we developed a multiscale approach which integrates experimental deformation and diffusion data, together with first-principle calculations and theoretical considerations on mineral lattice friction (Peierls stress), within a viscoplastic self-consistent (VPSC) model for peridotite aggregates. We will present an application of a recently improved second-order (SO) VPSC scheme (e.g., Ponte Castañeda, 2002, J. Mech. Phys. Solids, 50, 737) to an olivine rich + pyroxenes aggregate deformed at geological strain rate along an oceanic geotherm. Beside mineral dislocation slip systems, the SO-model extension accounts for an isotropic relaxation mechanism representing ';diffusion-related' creep in olivine. Slip-system critical resolved shear stresses (CRSS) are evaluated - as functions of P, T, oxygen fugacity and strain rate - from previously reported (e.g., Raterron et al., 2012, PEPI, 200-201, 105) and new experimental data (see Fraysse et al., this session), or from theoretical Peierls stress computations (e.g., Metsue et al, 2010, PCM, 37, 711). The isotropic-mechanism dependence on T and P matches that of Si self-diffusion in olivine, while its relative activity with respect to that of dislocations is constrained by reported data. The model accounts for olivine and pyroxenes known lattice preferred orientations (LPO), as well as for observed sensitivities of aggregate strength to the volume fraction of

  15. 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.

  16. Complexity in mean-field spin-glass models: Ising p-spin

    SciTech Connect

    Crisanti, A.; Leuzzi, L.; Rizzo, T.

    2005-03-01

    The complexity of the Thouless-Anderson-Palmer (TAP) solutions of the Ising p-spin is investigated in the temperature regime where the equilibrium phase is one-step replica symmetry breaking. Two solutions of the resulting saddle point equations are found. One is supersymmetric (SUSY) and includes the equilibrium value of the free energy while the other is non-SUSY. The two solutions cross exactly at a value of the free energy where the replicon eigenvalue is zero; at low free energy the complexity is described by the SUSY solution while at high free energy it is described by the non-SUSY solution, the latter accounting for the total number of solutions. The relevant TAP solutions counted by the non-SUSY complexity share the same features of the corresponding solutions in the Sherrington-Kirkpatrick model; in particular their Hessian has a vanishing isolated eigenvalue. The TAP solutions corresponding to the SUSY complexity, instead, are well separated minima.

  17. 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.

  18. 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

  19. 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.

  20. 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.

  1. The nonrelativistic limit of the relativistic point coupling model

    NASA Astrophysics Data System (ADS)

    Sulaksono, A.; Bürvenich, T.; Maruhn, J. A.; Reinhard, P.-G.; Greiner, W.

    2003-11-01

    We relate the relativistic finite range mean-field model (RMF-FR) to the point-coupling variant and compare the nonlinear density dependence. From this, the effective Hamiltonian of the nonlinear point-coupling model in the nonrelativistic limit is derived. Different from the nonrelativistic models, the nonlinearity in the relativistic models automatically yields contributions in the form of a weak density dependence not only in the central potential but also in the spin-orbit potential. The central potential affects the bulk and surface properties while the spin-orbit potential is crucial for the shell structure of finite nuclei. A modification in the Skyrme-Hartree-Fock model with a density-dependent spin-orbit potential inspired by the point-coupling model is suggested.

  2. 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.

  3. Fractional Spin Fluctuations as a Precursor of Quantum Spin Liquids: Majorana Dynamical Mean-Field Study for the Kitaev Model

    NASA Astrophysics Data System (ADS)

    Yoshitake, Junki; Nasu, Joji; Motome, Yukitoshi

    2016-10-01

    Experimental identification of quantum spin liquids remains a challenge, as the pristine nature is to be seen in asymptotically low temperatures. We here theoretically show that the precursor of quantum spin liquids appears in the spin dynamics in the paramagnetic state over a wide temperature range. Using the cluster dynamical mean-field theory and the continuous-time quantum Monte Carlo method, which are newly developed in the Majorana fermion representation, we calculate the dynamical spin structure factor, relaxation rate in nuclear magnetic resonance, and magnetic susceptibility for the honeycomb Kitaev model whose ground state is a canonical example of the quantum spin liquid. We find that dynamical spin correlations show peculiar temperature and frequency dependence even below the temperature where static correlations saturate. The results provide the experimentally accessible symptoms of the fluctuating fractionalized spins evincing the quantum spin liquids.

  4. A nonlinear relativistic nuclear model for protoneutronstars

    NASA Astrophysics Data System (ADS)

    Razeira, M.; Vasconcellos, C. A. Z.; Dillig, M.

    2003-08-01

    In the last few decades, studies on the internal structure, composition, dynamics and evolution of protoneutron stars, neutron stars, pulsars, hybrid and strange stars became central topics for theoretical and experimental research. Since the observation of the first pulsar in 1967, whose characteristic observational features allowed its identification as a rotating neutron star, nuclear models have been widely employed in the description of the holly graal of modern physics, the equation of state of dense matter. As under the pull of gravity the energy density in the core of these compact stars is thought to approach or even exceed more than 6 times the density of ordinary nuclear matter, predictions on the structure of the stars depend sensitively on the equation of state provided by model calculations. Combined with the equations of the general relativity metric, predictions on the mass, radius, crust extent and moment of inertia of the stars are then susceptible to the comparison to observation. In this work, a theoretical modeling for protoneutron stars (nuclear matter at finite temperature) is studied in the framework of an effective many-body relativistic mean field theory and the Sommerfeld approximation which contains the fundamental baryon octet and leptonic degrees of freedom, sigma, omega, rho and delta mesons, chemical equilibrium and charge neutrality. Our predictions include the determination of the mass of protoneutron stars, the mass-radius relation, relative population, gravitational redshift among other properties.

  5. 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.

  6. 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.

  7. Mean-field modeling of the basal ganglia-thalamocortical system. I Firing rates in healthy and parkinsonian states.

    PubMed

    van Albada, S J; Robinson, P A

    2009-04-21

    Parkinsonism leads to various electrophysiological changes in the basal ganglia-thalamocortical system (BGTCS), often including elevated discharge rates of the subthalamic nucleus (STN) and the output nuclei, and reduced activity of the globus pallidus external (GPe) segment. These rate changes have been explained qualitatively in terms of the direct/indirect pathway model, involving projections of distinct striatal populations to the output nuclei and GPe. Although these populations partly overlap, evidence suggests dopamine depletion differentially affects cortico-striato-pallidal connection strengths to the two pallidal segments. Dopamine loss may also decrease the striatal signal-to-noise ratio, reducing both corticostriatal coupling and striatal firing thresholds. Additionally, nigrostriatal degeneration may cause secondary changes including weakened lateral inhibition in the GPe, and mesocortical dopamine loss may decrease intracortical excitation and especially inhibition. Here a mean-field model of the BGTCS is presented with structure and parameter estimates closely based on physiology and anatomy. Changes in model rates due to the possible effects of dopamine loss listed above are compared with experiment. Our results suggest that a stronger indirect pathway, possibly combined with a weakened direct pathway, is compatible with empirical evidence. However, altered corticostriatal connection strengths are probably not solely responsible for substantially increased STN activity often found. A lower STN firing threshold, weaker intracortical inhibition, and stronger striato-GPe inhibition help explain the relatively large increase in STN rate. Reduced GPe-GPe inhibition and a lower GPe firing threshold can account for the comparatively small decrease in GPe rate frequently observed. Changes in cortex, GPe, and STN help normalize the cortical rate, also in accord with experiments. The model integrates the basal ganglia into a unified framework along with an

  8. 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 .

  9. 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.

  10. 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

  11. A mean field model of the decrease of the specific surface area of dry snow during isothermal metamorphism

    NASA Astrophysics Data System (ADS)

    Legagneux, LoïC.; Domine, Florent

    2005-12-01

    The surface area of snow that is accessible to gases is an essential parameter for quantifying the exchange of trace gases between the snowpack and the atmosphere and is called the specific surface area (SSA). Snow SSA decreases during metamorphism, but this is not described in current snow models owing to the complexity of the physics and geometry of snow. In this paper, we test whether it is possible to model snow SSA changes during isothermal metamorphism without accounting for all the complexity of the three-dimensional (3-D) structure of real snow. We have developed a mean field model of snow metamorphism under isothermal conditions, grounded in the theoretical framework of transient Ostwald ripening and representing snow as a distribution of spherical particles. Analytical expressions of the growth rates of these spheres are obtained, and the evolution of two measurable parameters that characterize snow geometry, the SSA and the distribution of radii of curvature (DRC), are simulated and compared to experimental data obtained by X-ray tomography. The qualitative effects of temperature, snow density, and the condensation coefficient on the rate of SSA decrease are examined. The model predicts very well the rate of evolution of the particle size distribution, which validates our physical description of isothermal metamorphism. In particular, we find that vapor phase diffusion is rate limiting. However, the calculation of the SSA from the DRC appears delicate and evidences too crude approximations in our description of the 3-D geometry of snow. Finally, it is stressed that the initial DRC can greatly influence the rate of SSA decrease, while experimental measurements of the rate of SSA decrease suggest that all snow types evolve in a similar way. It is thus proposed that most natural fresh snows have similar DRCs.

  12. 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

  13. Analytical results for the statistical distribution related to a memoryless deterministic walk: dimensionality effect and mean-field models.

    PubMed

    Terçariol, César Augusto Sangaletti; Martinez, Alexandre Souto

    2005-08-01

    Consider a medium characterized by N points whose coordinates are randomly generated by a uniform distribution along the edges of a unitary d-dimensional hypercube. A walker leaves from each point of this disordered medium and moves according to the deterministic rule to go to the nearest point which has not been visited in the preceding mu steps (deterministic tourist walk). Each trajectory generated by this dynamics has an initial nonperiodic part of t steps (transient) and a final periodic part of p steps (attractor). The neighborhood rank probabilities are parametrized by the normalized incomplete beta function Id= I1/4 [1/2, (d+1) /2] . The joint distribution S(N) (mu,d) (t,p) is relevant, and the marginal distributions previously studied are particular cases. We show that, for the memory-less deterministic tourist walk in the euclidean space, this distribution is Sinfinity(1,d) (t,p) = [Gamma (1+ I(-1)(d)) (t+ I(-1)(d) ) /Gamma(t+p+ I(-1)(d)) ] delta(p,2), where t=0, 1,2, ... infinity, Gamma(z) is the gamma function and delta(i,j) is the Kronecker delta. The mean-field models are the random link models, which correspond to d-->infinity, and the random map model which, even for mu=0 , presents nontrivial cycle distribution [ S(N)(0,rm) (p) proportional to p(-1) ] : S(N)(0,rm) (t,p) =Gamma(N)/ {Gamma[N+1- (t+p) ] N( t+p)}. The fundamental quantities are the number of explored points n(e)=t+p and Id. Although the obtained distributions are simple, they do not follow straightforwardly and they have been validated by numerical experiments.

  14. Extended order parameter and conjugate field for the dynamic phase transition in a Ginzburg-Landau mean-field model in an oscillating field.

    PubMed

    Robb, Daniel T; Ostrander, Aaron

    2014-02-01

    We present numerical evidence for an extended order parameter and conjugate field for the dynamic phase transition in a Ginzburg-Landau mean-field model driven by an oscillating field. The order parameter, previously taken to be the time-averaged magnetization, comprises the deviations of the Fourier components of the magnetization from their values at the critical period. The conjugate field, previously taken to be the time-averaged magnetic field, comprises the even Fourier components of the field. The scaling exponents β and δ associated with the extended order parameter and conjugate field are shown numerically to be consistent with their values in the equilibrium mean-field model.

  15. Relativistic Corrections to the Bohr Model of the Atom

    ERIC Educational Resources Information Center

    Kraft, David W.

    1974-01-01

    Presents a simple means for extending the Bohr model to include relativistic corrections using a derivation similar to that for the non-relativistic case, except that the relativistic expressions for mass and kinetic energy are employed. (Author/GS)

  16. Relativistic nuclear matter with alternative derivative coupling models

    SciTech Connect

    Delfino, A.; Coelho, C.T.; Malheiro, M. )

    1995-04-01

    Effective Lagrangians involving nucleons coupled to scalar and vector fields are investigated within the framework of relativistic mean-field theory. The study presents the traditional Walecka model and different kinds of scalar derivative couplings suggested by Zimanyi and Moszkowski. The incompressibility (presented in an analytical form), scalar potential, and vector potential at the saturation point of nuclear matter are compared for these models. The real optical potential for the models are calculated and one of the models fits well the experimental curve from [minus]50 to 400 MeV while also giving a soft equation of state. By varying the coupling constants and keeping the saturation point of nuclear matter approximately fixed, only the Walecka model presents a first order phase transition for finite temperature at zero density.

  17. 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.

  18. Skyrme forces versus relativistic models: Reexamining instabilities

    SciTech Connect

    Dutra, M.; Lourenco, O.; Delfino, A.; Sa Martins, J. S.; Providencia, C.; Avancini, S. S.; Menezes, D. P.

    2008-03-15

    Experimental constraints are useful tools in helping to decide, among a number of candidates, which is the more suitable equation of state for nuclear matter. In this work we compare nonrelativistic Skyrme-type and relativistic Walecka-type models when they are used to describe processes related to binary system instabilities and phases coexistence. In general, nonrelativistic and relativistic models predict somewhat different behaviors, but we found that one of the parametrizations of the density-dependent hadronic model shows some similarities with nonrelativistic models in many of the features addressed in our investigation. We have checked that, once experimental data obtained in heavy-ion collisions are extrapolated to account for symmetric and neutron matter, some of the models discussed in the present work, both relativistic and nonrelativistic, should be ruled out.

  19. 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

  20. Exact quantisation of the relativistic Hopfield model

    NASA Astrophysics Data System (ADS)

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

    2016-11-01

    We investigate the quantisation in the Heisenberg representation of a relativistically covariant version of the Hopfield model for dielectric media, which entails the interaction of the quantum electromagnetic field with the matter dipole fields, represented by a mesoscopic polarisation field. A full quantisation of the model is provided in a covariant gauge, with the aim of maintaining explicit relativistic covariance. Breaking of the Lorentz invariance due to the intrinsic presence in the model of a preferred reference frame is also taken into account. Relativistic covariance forces us to deal with the unphysical (scalar and longitudinal) components of the fields, furthermore it introduces, in a more tricky form, the well-known dipole ghost of standard QED in a covariant gauge. In order to correctly dispose of this contribution, we implement a generalised Lautrup trick. Furthermore, causality and the relation of the model with the Wightman axioms are also discussed.

  1. Mean field phase diagram of an SU(2){sub {ital L}}{times}SU(2){sub {ital R}} lattice Higgs-Yukawa model at finite {lambda}

    SciTech Connect

    Pryor, C.

    1996-02-01

    The phase diagram of an SU(2){sub {ital L}}{times}SU(2){sub {ital R}} lattice Higgs-Yukawa model with finite {lambda} is constructed using mean field theory. The phase diagram bears a superficial resemblance to that for {lambda}={infinity}; however, as {lambda} is decreased the paramagnetic region shrinks in size. For small {lambda} the phase transitions remain second order, and no new first order transitions are seen. {copyright} {ital 1996 The American Physical Society.}

  2. 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.

  3. Relativistic model of disk-jet variability

    NASA Astrophysics Data System (ADS)

    Mohan, P.; Mangalam, A.

    2014-07-01

    We present a relativistic model of disk-jet variability in the optical/UV and X-ray wavelengths from AGN. The model treats the kinematics of a bulk inflow in orbital motion in a relativistic thin disk. A part of the advected plasma continues in a helical orbital motion onto a relativistic jet shaped by a magnetic surface with foot points near the innermost stable circular orbit. The model, cast in Kerr geometry includes Doppler and gravitational shifts, aberration, light bending and time delay effects on the outgoing radiation. Light curves are simulated for studying effects of the relativistic beaming and the quasi-periodic oscillation (QPO) phenomena with resulting typical timescales ranging between a few 1000 s and a few days. A power law power spectral density shape results with a typical slope of ˜ -2.5. Also, using a model for the quality factor of the QPO, we place constraints on black hole mass, spin and the size of the emission region.

  4. Energy landscape of the finite-size mean-field 2-spin spherical model and topology trivialization

    NASA Astrophysics Data System (ADS)

    Mehta, Dhagash; Hauenstein, Jonathan D.; Niemerg, Matthew; Simm, Nicholas J.; Stariolo, Daniel A.

    2015-02-01

    Motivated by the recently observed phenomenon of topology trivialization of potential energy landscapes (PELs) for several statistical mechanics models, we perform a numerical study of the finite-size 2-spin spherical model using both numerical polynomial homotopy continuation and a reformulation via non-Hermitian matrices. The continuation approach computes all of the complex stationary points of this model while the matrix approach computes the real stationary points. Using these methods, we compute the average number of stationary points while changing the topology of the PEL as well as the variance. Histograms of these stationary points are presented along with an analysis regarding the complex stationary points. This work connects topology trivialization to two different branches of mathematics: algebraic geometry and catastrophe theory, which is fertile ground for further interdisciplinary research.

  5. Relativistic diffusion processes and random walk models

    SciTech Connect

    Dunkel, Joern; Talkner, Peter; Haenggi, Peter

    2007-02-15

    The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As is well known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equation, whose solutions avoid superluminal propagation speeds but suffer from singular (noncontinuous) diffusion fronts on the light cone, which are unlikely to exist for massive particles. It is therefore advisable to explore other alternatives as well. In this paper, a generalized Wiener process is proposed that is continuous, avoids superluminal propagation, and reduces to the standard Wiener process in the nonrelativistic limit. The corresponding relativistic diffusion propagator is obtained directly from the nonrelativistic Wiener propagator, by rewriting the latter in terms of an integral over actions. The resulting relativistic process is non-Markovian, in accordance with the known fact that nontrivial continuous, relativistic Markov processes in position space cannot exist. Hence, the proposed process defines a consistent relativistic diffusion model for massive particles and provides a viable alternative to the solutions of the telegraph equation.

  6. 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%.

  7. 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

  8. 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.

  9. 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 .

  10. 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.

  11. 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.

  12. A Coupled Mean Field / Gurson-Tvergaard Micromechanical Model For Ductile Fracture In Multiphase Materials With Large Volume Fraction of Voids

    NASA Astrophysics Data System (ADS)

    Van Hoof, Thibaut; Piérard, Olivier; Lani, Frédéric

    2007-04-01

    In the framework of the European project PROHIPP (New design and manufacturing processes for high pressure fluid power product — NMP 2-CT-2004-50546), CENAERO develops a library of constitutive models used to predict the mechanical response of a family of cast iron. The present contribution focuses on one particular microstructure, corresponding to a ferrite matrix containing spheroidal graphite and isolated inclusions of pearlite. An incremental mean field homogenisation scheme such as the one developed by Doghri and Ouaar is used. In the present application, the ferrite matrix is described by a Gurson type constitutive law (porous plasticity) while the pearlite inclusions are assumed to obey the classical isotropic J2 plasticity. The predictions of the micromechanical model are compared to the results of Finite Element simulations performed on three-dimensional representative volume elements (RVEs).

  13. 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.

  14. 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.

  15. A mean field model of ligand-protein interactions: implications for the structural assessment of human immunodeficiency virus type 1 protease complexes and receptor-specific binding.

    PubMed Central

    Verkhivker, G M; Rejto, P A

    1996-01-01

    We propose a general mean field model of ligand-protein interactions to determine the thermodynamic equilibrium of a system at finite temperature. The method is employed in structural assessments of two human immuno-deficiency virus type 1 protease complexes where the gross effects of protein flexibility are incorporated by utilizing a data base of crystal structures. Analysis of the energy spectra for these complexes has revealed that structural and thermo-dynamic aspects of molecular recognition can be rationalized on the basis of the extent of frustration in the binding energy landscape. In particular, the relationship between receptor-specific binding of these ligands to human immunodeficiency virus type 1 protease and a minimal frustration principle is analyzed. Images Fig. 4 PMID:8552675

  16. 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.

  17. Relativistic Electrons at Geostationary Orbit: Modeling Results

    NASA Astrophysics Data System (ADS)

    Khazanov, G. V.; Lyatsky, W.

    2008-05-01

    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 stable and incredibly high (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.

  18. 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.

  19. Embedded mean-field theory.

    PubMed

    Fornace, Mark E; Lee, Joonho; Miyamoto, Kaito; Manby, Frederick R; Miller, Thomas F

    2015-02-10

    We introduce embedded mean-field theory (EMFT), an approach that flexibly allows for the embedding of one mean-field theory in another without the need to specify or fix the number of particles in each subsystem. EMFT is simple, is well-defined without recourse to parameters, and inherits the simple gradient theory of the parent mean-field theories. In this paper, we report extensive benchmarking of EMFT for the case where the subsystems are treated using different levels of Kohn-Sham theory, using PBE or B3LYP/6-31G* in the high-level subsystem and LDA/STO-3G in the low-level subsystem; we also investigate different levels of density fitting in the two subsystems. Over a wide range of chemical problems, we find EMFT to perform accurately and stably, smoothly converging to the high-level of theory as the active subsystem becomes larger. In most cases, the performance is at least as good as that of ONIOM, but the advantages of EMFT are highlighted by examples that involve partitions across multiple bonds or through aromatic systems and by examples that involve more complicated electronic structure. EMFT is simple and parameter free, and based on the tests provided here, it offers an appealing new approach to a multiscale electronic structure.

  20. Mean-field coarse-grained model for poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymer systems.

    PubMed

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

    2015-03-31

    The microscopic modeling of surfactant systems is of the utmost importance in understanding the mechanisms related to the micellization process because it allows for prediction and comparison with experimental data of diverse equilibrium system properties. In this work, we present a coarse-grained model for Pluronics, a trademarked type of triblock copolymer, from simulations based on a single-chain mean-field theory (SCMF). This microscopic model is used to quantify the micellization process of these nonionic surfactants at 37 °C and has been shown to be able to quantitatively reproduce experimental data of the critical micelle concentration (CMC) along with other equilibrium properties. In particular, these results correctly capture the experimental behavior with respect to the lengths of the hydrophobic and hydrophilic moieties of the surfactants for low and medium hydrophobicities. However, for the more highly hydrophobic systems with low CMCs, a deviation is found which has been previously attributed to nonequilibrium effects in the experimental data (Garcı́a Daza, F. A.; Mackie, A. D. Low Critical Micelle Concentration Discrepancy between Theory and Experiment. J. Phys. Chem. Lett. 2014, 5, 2027-2032).

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

    NASA Astrophysics Data System (ADS)

    Furnstahl, R. J.; Serot, Brian 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 (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 NN attraction, is discussed.

  2. 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.

  3. "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.

  4. Mean-field theory for the Mott-insulator-paired-superfluid phase transition in the two-species Bose-Hubbard model

    SciTech Connect

    Iskin, M.

    2010-11-15

    The standard mean-field theory for the Mott-insulator-superfluid phase transition is not sufficient to describe the Mott-insulator-paired-superfluid phase transition. Therefore, by restricting the two-species Bose-Hubbard Hamiltonian to the subspace of paired particles, and using perturbation theory, here we derive an analytic mean-field expression for the Mott-insulator-paired-superfluid transition boundary.

  5. 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.

  6. 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.

  7. 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.

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

    NASA Astrophysics Data System (ADS)

    Sato, Toshihiro; Tsunetsugu, Hirokazu

    2016-08-01

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

  9. 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

  10. 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.

  11. 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

  12. 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.

  13. 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

  14. Relativistic quark-diquark model of baryons

    SciTech Connect

    Ferretti, J.; Vassallo, A.; Santopinto, E.

    2011-06-15

    A relativistic quark-diquark mass operator with direct and exchange interaction has been constructed in the framework of point form dynamics. The nonstrange baryon spectrum has been calculated and compared with experimental data.

  15. 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

  16. A New Analytical Model for Trans-Relativistic Particle Acceleration

    NASA Astrophysics Data System (ADS)

    Becker, Peter A.

    2011-01-01

    Most existing analytical models describing the second-order Fermi acceleration of relativistic particles due to collisions with MHD waves assume that the injected seed particles are already highly relativistic, despite the fact that the most prevalent source of particles is usually the local thermal background, which is typically a non-relativistic gas. This presents a problem because the momentum dependence of the momentum diffusion coefficient describing the interaction between the particles and the MHD waves is qualitatively different in the non-relativistic and highly relativistic limits. Since the existing analytical models are not able to address this situation, workers have had to rely on numerical simulations to obtain particle spectra describing the trans-relativistic case. In this work we present the first analytical solution to the global, trans-relativistic problem, obtained by using a hybrid form for the momentum diffusion coefficient, given by the sum of the two asymptotic forms. The model also incorporates the appropriate momentum dependence for the particle escape timescale, and the effect of synchrotron and inverse-Compton losses, which are critical for establishing the location of the high-energy cutoff in the particle spectrum. The results can be used to model the acceleration of particles in AGN and solar environments, and can also be used to compute the spectra of the associated synchrotron and inverse-Compton emission. Applications of both types are discussed.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. Modeling the magnetic isotherms of (La0.56Ce0.14)Sr0.30MnO3 by a mean-field scaling method and estimation of magnetic entropy change

    NASA Astrophysics Data System (ADS)

    Yahyaoui, S.; Khalfaoui, M.; Kallel, S.; Kallel, N.; Amaral, J. S.; Ben Lamine, A.

    2015-11-01

    We report a study on the magnetic properties of the (La0.56Ce0.14)Sr0.30MnO3 perovskite, by a mean-field method. By scaling of the experimental magnetization data, the mean-field exchange parameter λ and the BS function of the equation of state BS [ (H +Hexch) / T ] are directly determined, as well as the order of the phase transition. The spin quantum number of the manganite has been also determined. The mean-field scaling has been used to estimate magnetic entropy change (- ΔSM) within the thermodynamics of the model and without using the usual numerical integration of a Maxwell relation. The maxima of the positive absolute value of (- ΔSM) upon variation of the applied magnetic field at 1 and 5 T are about 1.68 and 5.04 J kg-1 K-1, respectively. Satisfactory agreement between the mean-field model and experimental behavior has been found.

  2. 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.

  3. 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.

  4. Coulomb Glass: a Mean Field Study

    NASA Astrophysics Data System (ADS)

    Mandra, Salvatore; Palassini, Matteo

    2012-02-01

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

  5. 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.

  6. 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.

  7. Properties of Doubly Heavy Baryons in the Relativistic Quark Model

    SciTech Connect

    Ebert, D.; Faustov, R.N.; Galkin, V.O.; Martynenko, A.P.

    2005-05-01

    Mass spectra and semileptonic decay rates of baryons consisting of two heavy (b or c) and one light quark are calculated in the framework of the relativistic quark model. The doubly heavy baryons are treated in the quark-diquark approximation. The ground and excited states of both the diquark and quark-diquark bound systems are considered. The quark-diquark potential is constructed. The light quark is treated completely relativistically, while the expansion in the inverse heavy-quark mass is used. The weak transition amplitudes of heavy diquarks bb and bc going, respectively, to bc and cc are explicitly expressed through the overlap integrals of the diquark wave functions in the whole accessible kinematic range. The relativistic baryon wave functions of the quark-diquark bound system are used for the calculation of the decay matrix elements, the Isgur-Wise function, and decay rates in the heavy-quark limit.

  8. A relativistic toy model for Unruh black holes

    NASA Astrophysics Data System (ADS)

    Carbonaro, P.

    2014-08-01

    We consider the wave propagation in terms of acoustic geometry in a quantum relativistic system. This reduces, in the hydrodynamic limit, to the equations which govern the motion of a relativistic Fermi-degenerate gas in one space dimension. The derivation of an acoustic metric for one-dimensional (1D) systems is in general plagued with the impossibility of defining a conformal factor. Here we show that, although the system is intrinsically one-dimensional, the Unruh procedure continues to work because of the particular structure symmetry of the model. By analyzing the dispersion relation, attention is also paid to the quantum effects on the wave propagation.

  9. 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.

  10. Mean Field Analysis of Quantum Annealing Correction.

    PubMed

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

    2016-06-01

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

  11. Mean Field 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.

  12. 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

  13. 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

  14. Mean field approach to nuclear structure

    SciTech Connect

    Nazarewicz, W. |

    1993-12-01

    Several examples of mean-field calculations, relevant to the recent and planned low-spin experimental works, are presented. The perspectives for future studies (mainly related to spectroscopy of exotic nuclei) are reviewd.

  15. Deterministic Mean-Field Ensemble Kalman Filtering

    DOE PAGES

    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

  16. 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.

  17. Kinematic arguments against single relativistic shell models for GRBs

    SciTech Connect

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

    1997-09-01

    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{sup {minus}3}, implying that single relativistic shells require 10{sup 3} times more energy than previously thought. They conclude that either the central site of a GRB must produce {approx}10{sup 51} erg/s{sup {minus}1} for hundreds of seconds, or the relativistic shell must have structure on a scales the order of {radical}{epsilon}{Gamma}{sup {minus}1}, where {Gamma} is the bulk Lorentz factor ({approximately}10{sup 2} to 10{sup 3}) and {epsilon} is the efficiency.

  18. 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.

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

    NASA Astrophysics Data System (ADS)

    Hamlin, Nathaniel D.; Seyler, Charles E.

    2014-12-01

    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 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. Bosonic Dynamical Mean-Field Theory

    NASA Astrophysics Data System (ADS)

    Snoek, Michiel; Hofstetter, Walter

    2013-02-01

    We derive the bosonic dynamical mean-field equations for bosonic atoms in optical lattices with arbitrary lattice geometry. The equations are presented as a systematic expansion in 1/z, z being the number of lattice neighbours. Hence the theory is applicable in sufficiently high-dimensional lattices. We apply the method to a two-component mixture, for which a rich phase diagram with spin order is revealed.

  8. 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)

  9. Preequilibrium neutron emission in heavy ion reaction: Mean field effect and multiple emission

    NASA Astrophysics Data System (ADS)

    Paul, Sabyasachi; Nandy, Maitreyee; Mohanty, A. K.; Gambhir, Y. K.

    2016-09-01

    Effects of nuclear mean field and of multiple preequilibrium (PEQ) emission on double differential neutron multiplicity distribution from heavy ion reactions (12C+165Ho and 20Ne+165Ho ) at 10-30 MeV/u have been investigated in the framework of the semiclassical formalism for heavy ion reaction (henceforth termed "HION") developed earlier. HION follows the equilibration of a target+projectile composite system through the kinematics of two-body scattering. In the present work nuclear density distribution in the composite system is estimated in the relativistic mean field (RMF) approach. The nucleon-nucleon collision rates and subsequently the nucleon emission probability are calculated from this density distribution. A second approach based on a semiphenomenological formalism is also used for nuclear density distribution. Energy-angle distribution of neutron multiplicities calculated with this modified HION model coupled with multiple PEQ emission could reproduce the measured data of earlier workers in the projectile energy range of 10-30 MeV/u.

  10. Relativistic Pseudospin Symmetry

    SciTech Connect

    Ginocchio, Joseph N.

    2011-05-06

    We show that the pseudospin symmetry that Akito Arima discovered many years ago (with collaborators) is a symmetry of the the Dirac Hamiltonian for which the sum of the scalar and vector potentials are a constant. In this paper we discuss some of the implications of this relativistic symmetry and the experimental data that support these predictions. In his original paper Akito also discussed pseudo-U(3) symmetry. We show that pseudo-U(3) symmetry is a symmetry of the Dirac Hamiltonian for which the sum of harmonic oscillator vector and scalar potentials are equal to a constant, and we give the generators of pseudo-U(3) symmetry. Going beyond the mean field we summarize new results on non relativistic shell model Hamiltonians that have pseudospin symmetry and pseudo-orbital angular momentum symmetry as a dynamical symmetries.

  11. Generalized relativistic kinematics in Poincaré-invariant models

    NASA Astrophysics Data System (ADS)

    Ivetić, B.; Mignemi, S.; Samsarov, A.

    2016-09-01

    Assuming the validity of the relativity principle, we discuss the implications on relativistic kinematics of a deformation of the Poincaré invariance that preserves the Poincaré algebra, and only modifies its action on spacetime in a Lorentz-invariant way. We show that, in contrast to the case in which the Poincaré algebra is deformed, the action of boosts on two-particle states is not affected, while the addition law of momenta is to a large extent arbitrary. We discuss some nontrivial examples of deformed addition laws related to the Snyder model.

  12. 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.

  13. Relativistic fluid model of the resistive hose instability

    SciTech Connect

    Siambis, J.G. )

    1992-10-01

    A systematic analysis of the hose instability using the relativistic fluid formulation is reported. In its basic nature, the hose instability is a macroscopic, low-frequency instability, hence a fluid model should, in principle, give an accurate account of the hose instability. It has been found that for zeroth-order beam displacements, giving rise to rigid beam displacements, the fluid wave equation and resulting dispersion relation are identical to the spread-mass model and the energy-group model results. When first-order fluid displacements are included as well, giving rise to compressible, nonfrozen displacements in the axial direction and beam cross-section distortion in the radial direction, then there is obtained a wave equation similar, but not identical to the multicomponent model. The dispersion relation is solved for numerically. The hose instability growth rate is found to be similar to the multicomponent model result, over part of the beam frame, real hose frequency range.

  14. 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.

  15. 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.

  16. Dynamical mean-field theory from a quantum chemical perspective.

    PubMed

    Zgid, Dominika; Chan, Garnet Kin-Lic

    2011-03-01

    We investigate the dynamical mean-field theory (DMFT) from a quantum chemical perspective. Dynamical mean-field theory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local correlation approximation. In addition, quantum chemical techniques can be used to construct new ab initio Hamiltonians and impurity solvers for DMFT. Here, we explore some ways in which these things may be achieved. First, we present an informal overview of dynamical mean-field theory to connect to quantum chemical language. Next, we describe an implementation of dynamical mean-field theory where we start from an ab initio Hartree-Fock Hamiltonian that avoids double counting issues present in many applications of DMFT. We then explore the use of the configuration interaction hierarchy in DMFT as an approximate solver for the impurity problem. We also investigate some numerical issues of convergence within DMFT. Our studies are carried out in the context of the cubic hydrogen model, a simple but challenging test for correlation methods. Finally, we finish with some conclusions for future directions.

  17. 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.

  18. 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.

  19. Nonequilibrium dynamical mean-field theory

    NASA Astrophysics Data System (ADS)

    Freericks, James

    2007-03-01

    Dynamical mean-field theory (DMFT) is establishing itself as one of the most powerful approaches to the quantum many-body problem in strongly correlated electron materials. Recently, the formalism has been generalized to study nonequilibrium problems [1,2], such as the evolution of Bloch oscillations in a material that changes from a diffusive metal to a Mott insulator [2,3]. Using a real-time formalism on the Kadanoff-Baym-Keldysh contour, the DMFT algorithm can be generalized to the case of systems that are not time-translation invariant. The computational algorithm has a parallel implementation with essentially a linear scale up when running on thousands of processors. Results on the decay of Bloch oscillations, their change of character within the Mott insulator, and movies on how electrons redistribute themselves due to their response to an external electrical field will be presented. In addition to solid-state applications, this work also applies to the behavior of mixtures of light and heavy cold atoms in optical lattices. [1] V. M. Turkowski and J. K. Freericks, Spectral moment sum rules for strongly correlated electrons in time-dependent electric fields, Phys. Rev. B 075108 (2006); Erratum, Phys. Rev. B 73, 209902(E) (2006). [2] J. K. Freericks, V. M. Turkowski , and V. Zlati'c, Nonlinear response of strongly correlated materials to large electric fields, in Proceedings of the HPCMP Users Group Conference 2006, Denver, CO, June 26--29, 2006 edited by D. E. Post (IEEE Computer Society, Los Alamitos, CA, 2006), to appear. [3] J. K. Freericks, V. M. Turkowski, and V. Zlati'c, Nonequilibrium dynamical mean-field theory, submitted to Phys. Rev. Lett. cond-mat//0607053.

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

    NASA Astrophysics Data System (ADS)

    Lin, Jie; Wyart, Matthieu

    2016-01-01

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

  1. 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.

  2. Dynamical mean-field theory for flat-band ferromagnetism

    NASA Astrophysics Data System (ADS)

    Nguyen, Hong-Son; Tran, Minh-Tien

    2016-09-01

    The magnetically ordered phase in the Hubbard model on the infinite-dimensional hyper-perovskite lattice is investigated within dynamical mean-field theory. It turns out for the infinite-dimensional hyper-perovskite lattice the self-consistent equations of dynamical mean-field theory are exactly solved, and this makes the Hubbard model exactly solvable. We find electron spins are aligned in the ferromagnetic or ferrimagnetic configuration at zero temperature and half filling of the edge-centered sites of the hyper-perovskite lattice. A ferromagnetic-ferrimagnetic phase transition driven by the energy level splitting is found and it occurs through a phase separation. The origin of ferromagnetism and ferrimagnetism arises from the band flatness and the virtual hybridization between macroscopically degenerate flat bands and dispersive ones. Based on the exact solution in the infinite-dimensional limit, a modified exact diagonalization as the impurity solver for dynamical mean-field theory on finite-dimensional perovskite lattices is also proposed and examined.

  3. Nuclear fission with mean-field instantons

    SciTech Connect

    Skalski, Janusz

    2008-06-15

    We present a description of nuclear spontaneous fission, and generally of quantum tunneling, in terms of instantons, that is, periodic imaginary-time solutions to time-dependent mean-field equations. This description allows comparisons to be made with the more familiar generator coordinate (GCM) and adiabatic time-dependent Hartree-Fock (ATDHF) methods. It is shown that the action functional whose value for the instanton is the quasiclassical estimate of the decay exponent fulfills the minimum principle when additional constraints are imposed on trial fission paths. In analogy with mechanics, these are conditions of energy conservation and the velocity-momentum relations. In the adiabatic limit, the instanton method reduces to the time-odd ATDHF equation, with collective mass including the time-odd Thouless-Valatin term, while the GCM mass completely ignores velocity-momentum relations. This implies that GCM inertia generally overestimates the instanton-related decay rate. The very existence of the minimum principle offers hope for a variational search for instantons. After the inclusion of pairing, the instanton equations and the variational principle can be expressed in terms of the imaginary-time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The adiabatic limit of this theory reproduces ATDHFB inertia.

  4. 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.

  5. 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

  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. 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.

  8. Finite-temperature exact diagonalization cluster dynamical mean-field study of the two-dimensional Hubbard model: Pseudogap, non-Fermi-liquid behavior, and particle-hole asymmetry

    NASA Astrophysics Data System (ADS)

    Liebsch, Ansgar; Tong, Ning-Hua

    2009-10-01

    The effect of doping in the two-dimensional Hubbard model is studied within finite-temperature exact diagonalization combined with cluster dynamical mean-field theory. By employing a mixed basis involving cluster sites and bath molecular orbitals for the projection of the lattice Green’s function onto 2×2 clusters, a considerably more accurate description of the low-frequency properties of the self-energy is achieved than in a pure site picture. To evaluate the phase diagram, the transition from Fermi-liquid to non-Fermi-liquid behavior for decreasing hole doping is studied as a function of Coulomb energy, next-nearest-neighbor hopping, and temperature. The self-energy component ΣX associated with X=(π,0) is shown to develop a collective mode above EF , whose energy and strength exhibits a distinct dispersion with doping. This low-energy excitation gives rise to non-Fermi-liquid behavior as the hole doping decreases below a critical value δc , and to an increasing particle-hole asymmetry, in agreement with recent photoemission data. This behavior is consistent with the removal of spectral weight from electron states above EF and the opening of a pseudogap, which increases with decreasing doping. The phase diagram reveals that δc≈0.15…0.20 for various system parameters. For electron doping, the collective mode of ΣX(ω) and the concomitant pseudogap are located below the Fermi energy, which is consistent with the removal of spectral weight from the hole states just below EF . The critical doping, which marks the onset of non-Fermi-liquid behavior, is systematically smaller than for hole doping.

  9. 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.

  10. 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.

  11. 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

  12. MAP segmentation of magnetic resonance images using mean field annealing

    NASA Astrophysics Data System (ADS)

    Logenthiran, Ambalavaner; Snyder, Wesley E.; Santago, Peter, II; Link, Kerry M.

    1991-06-01

    An algorithm is described which segments magnetic resonance images while removing the noise from the images without blurring or other distortion of edges. The problem of segmentation and noise removal is posed as a restoration of an uncorrupted image, given additive white Gaussian noise and a segmentation cost. The problem is solved using a strategy called Mean Field Annealing. An a priori statistical model of the image, which includes the region classification, is chosen which drives the minimization toward solutions which are locally homogeneous and globally classified. Application of the algorithm to brain and knee images is presented.

  13. 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.

  14. 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.

  15. 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.

  16. Extension of the binary-encounter-dipole model to relativistic incident electrons

    NASA Astrophysics Data System (ADS)

    Kim, Yong-Ki; Santos, José Paulo; Parente, Fernando

    2000-11-01

    Formulas for the total ionization cross section by electron impact based on the binary-encounter-dipole (BED) model and its simpler version, the binary-encounter-Bethe (BEB) model are extended to relativistic incident electron energies. Total ionization cross sections for the hydrogen and helium atoms from the new relativistic formulas are compared to experimental data. Relativistic effects double the total ionization cross section of H and He at incident electron energy ~300 keV and dominate the cross section thereafter. A simple modification of the original BED-BEB formulas is proposed for applications to ion targets and inner-shell electrons of neutral atoms and molecules. The relativistic and nonrelativistic BEB cross sections are compared to the K-shell ionization cross sections by electron impact for the carbon, argon, nickel, niobium, and silver atoms. For carbon and argon, the relativistic effects are small, and both forms of the BEB cross sections agree well with available experimental data. For the nickel and heavier atoms, the relativistic increase of cross sections becomes noticeable from about 100 keV and higher in the incident electron energy. The empirical formula by Casnati et al. [J. Phys. B 15, 155 (1982)] after correcting for relativistic effects as shown by Quarles [Phys. Rev. A 13, 1278 (1976)] agrees well with the BEB cross sections for light atoms. However, the peak values of the Casnati cross sections become higher than the relativistic BEB peak cross sections as the atomic number increases. The BEB model is also applied to the total ionization cross section of the xenon atom, and the theory agrees well with experiments at low incident electron energies, but disagrees with experiment at relativistic incident energies.

  17. 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.

  18. 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.

  19. Kinetic and mean field description of Gibrat's law

    NASA Astrophysics Data System (ADS)

    Toscani, Giuseppe

    2016-11-01

    I introduce and analyze a linear kinetic model that describes the evolution of the probability density of the number of firms in a society, in which the microscopic rate of change obeys to the so-called law of proportional effect proposed by Gibrat (1930, 1931). Despite its apparent simplicity, the possible mean field limits of the kinetic model are varied. In some cases, the asymptotic limit can be described by a first-order partial differential equation. In other cases, the mean field equation is a linear diffusion with a non constant diffusion coefficient that can be studied analytically, by virtue of a transformation of variables recently utilized in Iagar and Sánchez (2013) to study the heat equation in a nonhomogeneous medium with critical density. In this case, it is shown that the large-time behavior of the solution is represented, for a large class of initial data, by a lognormal distribution with constant mean value and variance increasing exponentially in time at a precise rate.

  20. 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.

  1. 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.

  2. Relativistic three-boson bound-state model

    SciTech Connect

    Dulany, P.C.; Wallace, S.J.; Delfino, A.

    1995-04-01

    A three dimensional three-boson bound-state equation is derived from the four dimensional Bethe-Salpeter equation via an instant form of the quasipotential formalism. This provides a Schrodinger-like relativistic equation with a single, global Green`s function and relativistic dynamics. This equation is solved in momentum space for the lowest bound state without using partial wave decomposition. The lowest bound state is also calculated using the Schrodinger wavefunction. It is found that, using the Malfliet-Tjon V two particle interaction, perturbative calculations predict that the relativistic corrections decrease the binding energy by between 0.863 MeV to 1.461 MeV, while the actual corrections decrease the binding energy by between 0.014 MeV to 0.200 MeV.

  3. Derivation of the lattice Boltzmann model for relativistic hydrodynamics

    NASA Astrophysics Data System (ADS)

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

    2010-11-01

    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)PRLTAO0031-900710.1103/PhysRevLett.105.014502 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.

  4. 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.

  5. 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.

  6. 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.

  7. Variation after projection with a triaxially deformed nuclear mean field

    NASA Astrophysics Data System (ADS)

    Gao, Zao-Chun; Horoi, Mihai; Chen, Y. S.

    2015-12-01

    We implemented a variation after projection (VAP) algorithm based on a triaxially deformed Hartree-Fock-Bogoliubov vacuum state. This is the first projected mean field study that includes all the quantum numbers (except parity), i.e., spin (J ), isospin (T ), and mass number (A ). Systematic VAP calculations with JTA projection have been performed for the even-even s d -shell nuclei with the USDB Hamiltonian. All the VAP ground state energies are within 500 keV above the exact shell model values. Our VAP calculations show that the spin projection has two important effects: (1) the spin projection is crucial in achieving good approximation of the full shell model calculation; (2) the intrinsic shapes of the VAP wave functions with spin projection are always triaxial, while the Hartree-Fock-Bogoliubov methods likely provide axial intrinsic shapes. Finally, our analysis suggests that one may not be possible to associate an intrinsic shape to an exact shell model wave function.

  8. Mean-field theory of assortative networks of phase oscillators

    NASA Astrophysics Data System (ADS)

    Restrepo, Juan G.; Ott, Edward

    2014-09-01

    Employing the Kuramoto model as an illustrative example, we show how the use of the mean-field approximation can be applied to large networks of phase oscillators with assortativity. We then use the ansatz of Ott and Antonsen (Chaos, 19 (2008) 037113) to reduce the mean-field kinetic equations to a system of ordinary differential equations. The resulting formulation is illustrated by application to a network Kuramoto problem with degree assortativity and correlation between the node degrees and the natural oscillation frequencies. Good agreement is found between the solutions of the reduced set of ordinary differential equations obtained from our theory and full simulations of the system. These results highlight the ability of our method to capture all the phase transitions (bifurcations) and system attractors. One interesting result is that degree assortativity can induce transitions from a steady macroscopic state to a temporally oscillating macroscopic state through both (presumed) Hopf and SNIPER (saddle-node, infinite period) bifurcations. Possible use of these techniques to a broad class of phase oscillator network problems is discussed.

  9. 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.

  10. 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

  11. Large-Scale Dynamics of Mean-Field Games Driven by Local Nash Equilibria

    NASA Astrophysics Data System (ADS)

    Degond, Pierre; Liu, Jian-Guo; Ringhofer, Christian

    2014-02-01

    We introduce a new mean field kinetic model for systems of rational agents interacting in a game-theoretical framework. This model is inspired from non-cooperative anonymous games with a continuum of players and Mean-Field Games. The large time behavior of the system is given by a macroscopic closure with a Nash equilibrium serving as the local thermodynamic equilibrium. An application of the presented theory to a social model (herding behavior) is discussed.

  12. 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).

  13. 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

  14. 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.

  15. 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.

  16. Beyond the thermal model in relativistic heavy-ion collisions

    NASA Astrophysics Data System (ADS)

    Wolschin, Georg

    2016-08-01

    Deviations from thermal distribution functions of produced particles in relativistic heavy-ion collisions are discussed as indicators for nonequilibrium processes. The focus is on rapidity distributions of produced charged hadrons as functions of collision energy and centrality, which are used to infer the fraction of particles produced from a central fireball as compared with that from the fragmentation sources that are out of equilibrium with the rest of the system. Overall thermal equilibrium would only be reached for large times t →∞ .

  17. 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}.

  18. Relativistic compact anisotropic charged stellar models with Chaplygin equation of state

    NASA Astrophysics Data System (ADS)

    Bhar, Piyali; Murad, Mohammad Hassan

    2016-10-01

    This paper presents a new model of static spherically symmetric relativistic charged stellar objects with locally anisotropic matter distribution together with the Chaplygin equation of state. The interior spacetime has been matched continuously to the exterior Reissner-Nordström geometry. Different physical properties of the stellar model have been investigated, analyzed, and presented graphically.

  19. Modeling early time dynamics of relativistic heavy ion collisions

    NASA Astrophysics Data System (ADS)

    Oliva, Lucia; Ruggieri, Marco; Puglisi, Armando; Plumari, Salvatore; Scardina, Francesco; Coci, Gabriele; Greco, Vincenzo

    2016-08-01

    We studied isotropization and thermalization of the quark-gluon plasma produced by decaying color-electric flux tubes created at the very early stages of relativistic heavy ion collisions. We coupled the dynamical evolution of the initial field, which decays to a plasma by the Schwinger mechanism, to the dynamics of the many particles system produced by the decay. The evolution of such a system is described by relativistic transport theory at fixed values of the viscosity over entropy density ratio. Within a single self-consistent calculation scheme we computed quantities which serve as indicators of the equilibration of the plasma for a 1+1 dimensional expanding geometry. We find that the initial color-electric field decays within 1 fm/c and particles production occurs in less than 1 fm/c; however, in the case of large viscosity oscillations of the field appear along the entire time evolution of the system, affecting also the behaviour of the ratio between longitudinal and transverse pressure. In case of small viscosity we find that the isotropization time is about 0.8 fm/c and the thermalization time is about 1 fm/c, in agreement with the common lore of hydrodynamic approaches.

  20. Dynamics of polymers: A mean-field theory

    SciTech Connect

    Fredrickson, Glenn H.; Orland, Henri

    2014-02-28

    We derive a general mean-field theory of inhomogeneous polymer dynamics; a theory whose form has been speculated and widely applied, but not heretofore derived. Our approach involves a functional integral representation of a Martin-Siggia-Rose (MSR) type description of the exact many-chain dynamics. A saddle point approximation to the generating functional, involving conditions where the MSR action is stationary with respect to a collective density field ρ and a conjugate MSR response field ϕ, produces the desired dynamical mean-field theory. Besides clarifying the proper structure of mean-field theory out of equilibrium, our results have implications for numerical studies of polymer dynamics involving hybrid particle-field simulation techniques such as the single-chain in mean-field method.

  1. 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.

  2. 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.

  3. Elastic electron-deuteron scattering within a relativistic potential model

    SciTech Connect

    Khokhlov, N. A. Vakulyuk, A. A.

    2015-01-15

    Elastic electron-deuteron scattering was considered in the point form of relativistic quantum mechanics. Observables of this process and the dependence of the deuteron form factors on the 4-momentum transfer Q up to 8 fm{sup −1} were calculated. The nucleon-nucleon potentials used in the calculations included the Nijmegen potentials NijmI and NijmII, the Bonn potential CD-Bonn, and the Moscow potential involving forbidden states. A parametrization of the nucleon form factors that complies with present-day experimental results was used as input data. The results of the calculations that employ all of the above potential types describe experimental data at least up to Q ≈ 5 fm{sup −}1.

  4. 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.

  5. Covariant Newtonian and relativistic dynamics of (magneto)-elastic solid model for neutron star crust

    NASA Astrophysics Data System (ADS)

    Carter, B.; Chachoua, E.; Chamel, N.

    2006-01-01

    This work develops the dynamics of a perfectly elastic solid model for application to the outer crust of a magnetised neutron star. Particular attention is given to the Noether identities responsible for energy-momentum conservation, using a formulation that is fully covariant, not only (as is usual) in a fully relativistic treatment but also (sacrificing accuracy and elegance for economy of degrees of gravitational freedom) in the technically more complicated case of the Newtonian limit. The results are used to obtain explicit (relativistic and Newtonian) formulae for the propagation speeds of generalised (Alfven type) magneto-elastic perturbation modes.

  6. 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.

  7. 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.

  8. Relativistic hydrodynamical model in the presence of long-range correlations

    SciTech Connect

    Osada, T.

    2010-02-15

    The effects of dynamical long-range correlations over a fluid cell-size scale on a relativistic fluid are discussed. It is shown that such correlations among the fluid elements introduced into the hydrodynamical model induce some weak dissipation and viscosity into the fluid. The influence of the long-range correlations on the entropy current is also discussed.

  9. 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).

  10. 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.

  11. Mean-field theory for the inverse Ising problem at low temperatures.

    PubMed

    Nguyen, H Chau; Berg, Johannes

    2012-08-01

    The large amounts of data from molecular biology and neuroscience have lead to a renewed interest in the inverse Ising problem: how to reconstruct parameters of the Ising model (couplings between spins and external fields) from a number of spin configurations sampled from the Boltzmann measure. To invert the relationship between model parameters and observables (magnetizations and correlations), mean-field approximations are often used, allowing the determination of model parameters from data. However, all known mean-field methods fail at low temperatures with the emergence of multiple thermodynamic states. Here, we show how clustering spin configurations can approximate these thermodynamic states and how mean-field methods applied to thermodynamic states allow an efficient reconstruction of Ising models also at low temperatures.

  12. 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.

  13. 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.

  14. 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.

  15. A new method to optimize the satellite broadcasting schedules using the mean field annealing of a Hopfield neural network.

    PubMed

    Ansari, N; Hou, E H; Yu, Y

    1995-01-01

    Reports a new method for optimizing satellite broadcasting schedules based on the Hopfield neural model in combination with the mean field annealing theory. A clamping technique is used with an associative matrix, thus reducing the dimensions of the solution space. A formula for estimating the critical temperature for the mean field annealing procedure is derived, hence enabling the updating of the mean field theory equations to be more economical. Several factors on the numerical implementation of the mean field equations using a straightforward iteration method that may cause divergence are discussed; methods to avoid this kind of divergence are also proposed. Excellent results are consistently found for problems of various sizes.

  16. 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.

  17. 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.

  18. Mean Field Strategies Induce Unrealistic Non-Linearities in Calcium Puffs

    PubMed Central

    Solovey, Guillermo; Fraiman, Daniel; Dawson, Silvina Ponce

    2011-01-01

    Mean field models are often useful approximations to biological systems, but sometimes, they can yield misleading results. In this work, we compare mean field approaches with stochastic models of intracellular calcium release. In particular, we concentrate on calcium signals generated by the concerted opening of several clustered channels (calcium puffs). To this end we simulate calcium puffs numerically and then try to reproduce features of the resulting calcium distribution using mean field models were all the channels open and close simultaneously. We show that an unrealistic non-linear relationship between the current and the number of open channels is needed to reproduce the simulated puffs. Furthermore, a single channel current which is five times smaller than the one of the stochastic simulations is also needed. Our study sheds light on the importance of the stochastic kinetics of the calcium release channel activity to estimate the release fluxes. PMID:21869877

  19. Mean-field theory and ɛ expansion for Anderson localization

    NASA Astrophysics Data System (ADS)

    Harris, A. B.; Lubensky, T. C.

    1981-03-01

    A general field-theoretic formulation of the Anderson model for the localization of wave functions in a random potential is given in terms of n-component replicated fields in the limit n-->0, and is analyzed primarily for spatial dimension d>=4. Lengths ξ1 and ξ2 associated with the spatial decay of correlations in the single-particle and two-particle Green's functions, respectively, are introduced. Two different regimes, the weak coupling and strong coupling, are distinguished depending on whether ξ-11 or ξ-12, respectively, vanishes as the mobility energy, Ec, is approached. The weak-coupling regime vanishes as d-->4+. Mean-field theory is developed from the uniform minimum of the Lagrangian for both the strong- and weak-coupling cases. For the strong-coupling case it gives the exponents va=14, γa=βa=12, η=0, and μ=1, where βa is the exponent associated with the density of extended states and μ is that associated with the conductivity. Simple heuristic arguments are used to verify the correctness of these unusual mean-field values. Infrared divergences in perturbation theory for the strong-coupling case occur for d<8, and an ɛ expansion (ɛ=8-d) is developed which is found to be identical to that previously analyzed for the statistics of lattice animals and which gives βa=12-ɛ12, η=-ɛ9, va=14+ɛ36, and μ=1-5ɛ36. The results are consistent with the Ward identity, which in combination with scaling arguments requires that βa+γa=1. The treatment takes account of the fact that the average of the on-site Green's function [G(x-->,x-->E)]av is nonzero and is predicated on this quantity being real, i.e., on the density of states vanishing at the mobility edge. We also show that localized states emerge naturally from local minima of finite action in the Lagrangian. These instanton solutions are analyzed on a lattice where the cutoff produced by the lattice constant leads to lattice instantons which exist for all d, in contrast to the case for the

  20. Optical model description of momentum transfer in relativistic heavy ion collisions

    NASA Technical Reports Server (NTRS)

    Khan, F.; Khandelwal, G. S.; Townsend, L. W.; Wilson, J. W.; Norbury, J. W.

    1991-01-01

    An optical model description of momentum transfer in relativistic heavy ion collisions, based upon composite particle multiple scattering theory, is presented. The imaginary component of the complex momentum transfer, which comes from the absorptive part of the optical potential, is identified as the longitudinal momentum downshift of the projectile. Predictions of fragment momentum distribution observables are made and compared with experimental data. Use of the model as a tool for estimating collision impact parameters is discussed.

  1. 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

  2. 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.

  3. Mean Field Approach to the Giant Wormhole Problem

    NASA Astrophysics Data System (ADS)

    Gamba, A.; Kolokolov, I.; Martellini, M.

    We introduce a gaussian probability density for the space-time distribution of worm-holes, thus taking effectively into account wormhole interaction. Using a mean-field approximation for the free energy, we show that giant wormholes are probabilistically suppressed in a homogenous isotropic “large” universe.

  4. 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.

  5. 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.

  6. 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}.

  7. 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.

  8. 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.

  9. The application of the Gibbs-Bogoliubov-Feynman inequality in mean field calculations for Markov random fields.

    PubMed

    Zhang, J

    1996-01-01

    The Gibbs-Bogoliubov-Feynman (GBF) inequality of statistical mechanics is adopted, with an information-theoretic interpretation, as a general optimization framework for deriving and examining various mean field approximations for Markov random fields (MRF's). The efficacy of this approach is demonstrated through the compound Gauss-Markov (CGM) model, comparisons between different mean field approximations, and experimental results in image restoration.

  10. 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.

  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. Relativistic three-body quark model of light baryons based on hypercentral approach

    NASA Astrophysics Data System (ADS)

    Aslanzadeh, M.; Rajabi, A. A.

    2015-05-01

    In this paper, we have treated the light baryons as a relativistic three-body bound system. Inspired by lattice QCD calculations, we treated baryons as a spin-independent three-quark system within a relativistic three-quark model based on the three-particle Klein-Gordon equation. We presented the analytical solution of three-body Klein-Gordon equation with employing the constituent quark model based on a hypercentral approach through which two- and three-body forces are taken into account. Herewith the average energy values of the up, down and strange quarks containing multiplets are reproduced. To describe the hyperfine structure of the baryon, the splittings within the SU(6)-multiplets are produced by the generalized Gürsey Radicati mass formula. The considered SU(6)-invariant potential is popular "Coulomb-plus-linear" potential and the strange and non-strange baryons spectra are in general well reproduced.

  13. 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.

  14. 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.

  15. Analytic Beyond-Mean-Field BEC Wave Functions

    NASA Astrophysics Data System (ADS)

    Dunn, Martin; Laing, W. Blake; Watson, Deborah K.; Loeser, John G.

    2006-05-01

    We present analytic N-body beyond-mean-field wave functions for Bose-Einstein condensates. This extends our previous beyond-mean-field energy calculations to the substantially more difficult problem of determining correlated N-body wave functions for a confined system. The tools used to achieve this have been carefully chosen to maximize the use of symmetry and minimize the dependence on numerical computation. We handle the huge number of interactions when N is large (˜N^2/2 two-body interactions) by bringing together three theoretical methods. These are dimensional perturbation theory, the FG method of Wilson et al, and the group theory of the symmetric group. The wave function is then used to derive the density profile of a condensate in a cylindrical trap.This method makes no assumptions regarding the form or strength of the interactions and is applicable to both small-N and large-N systems.

  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. 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.

  18. Forecasting relativistic electron flux using dynamic multiple regression models

    NASA Astrophysics Data System (ADS)

    Wei, H.-L.; Billings, S. A.; Surjalal Sharma, A.; Wing, S.; Boynton, R. J.; Walker, S. N.

    2011-02-01

    The forecast of high energy electron fluxes in the radiation belts is important because the exposure of modern spacecraft to high energy particles can result in significant damage to onboard systems. A comprehensive physical model of processes related to electron energisation that can be used for such a forecast has not yet been developed. In the present paper a systems identification approach is exploited to deduce a dynamic multiple regression model that can be used to predict the daily maximum of high energy electron fluxes at geosynchronous orbit from data. It is shown that the model developed provides reliable predictions.

  19. 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.

  20. 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

  1. An analytic toy model for relativistic accretion in Kerr space-time

    NASA Astrophysics Data System (ADS)

    Tejeda, Emilio; Taylor, Paul A.; Miller, John C.

    2013-02-01

    We present a relativistic model for the stationary axisymmetric accretion flow of a rotating cloud of non-interacting particles falling on to a Kerr black hole. Based on a ballistic approximation, streamlines are described analytically in terms of time-like geodesics, while a simple numerical scheme is introduced for calculating the density field. A novel approach is presented for describing all of the possible types of orbit by means of a single analytic expression. This model is a useful tool for highlighting purely relativistic signatures in the accretion flow dynamics coming from a strong gravitational field with frame dragging. In particular, we explore the coupling due to this between the spin of the black hole and the angular momentum of the infalling matter. Moreover, we demonstrate how this analytic solution may be used for benchmarking general relativistic numerical hydrodynamics codes by comparing it against results of smoothed particle hydrodynamics simulations for a collapsar-like set-up. These simulations are performed first for a ballistic flow (with zero pressure) and then for a hydrodynamical one where we measure the effects of pressure gradients on the infall, thus exploring the extent of applicability of the ballistic approximation.

  2. Relativistic electromagnetic mass models in spherically symmetric spacetime

    NASA Astrophysics Data System (ADS)

    Maurya, S. K.; Gupta, Y. K.; Ray, Saibal; Chatterjee, Vikram

    2016-10-01

    Under the static spherically symmetric Einstein-Maxwell spacetime of embedding class one we explore possibility of constructing electromagnetic mass model where mass and other physical parameters have purely electromagnetic origin (Lorentz in Proc. Acad. Sci. Amst. 6, 1904). This work is in continuation of our earlier investigation of Maurya et al. (Eur. Phys. J. C 75:389, 2015a) where we developed an algorithm and found out three new solutions of electromagnetic mass model. In the present work we consider different metric potentials ν and λ and have analyzed them in a systematic way. It is observed that some of the previous solutions related to electromagnetic mass model are nothing but special cases of the presently obtained generalized solution set. We further verify the solution set and especially show that these are extremely applicable in the case of compact stars.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. Dynamical mean-field theory for quantum chemistry.

    PubMed

    Lin, Nan; Marianetti, C A; Millis, Andrew J; Reichman, David R

    2011-03-01

    The dynamical mean-field concept of approximating an unsolvable many-body problem in terms of the solution of an auxiliary quantum impurity problem, introduced to study bulk materials with a continuous energy spectrum, is here extended to molecules, i.e., finite systems with a discrete energy spectrum. The application to small clusters of hydrogen atoms yields ground state energies which are competitive with leading quantum chemical approaches at intermediate and large interatomic distances as well as good approximations to the excitation spectrum.

  10. 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.

  11. 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.

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

    PubMed

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

    2016-05-11

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

  13. Mean-field 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.

  14. 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.

  15. 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.

  16. 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).

  17. 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.

  18. Ground state heavy baryon production in a relativistic quark-diquark model

    NASA Astrophysics Data System (ADS)

    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', 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 Ωbbc, Ωbcc, and Ωccc 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.

  19. 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.

  20. 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.

  1. Fractional flux lattice and the anyon mean-field approximation

    SciTech Connect

    Pryor, C. )

    1991-12-01

    The anyon mean-field approximation (MFA) is tested by computing the band structure of a charged particle in an infinite two-dimensional square lattice of infinitesimal flux tubes. The band structure and density of states are compared with the MFA and found to be in agreement for {Phi}=1/{ital n}, with {ital n}{gt}3. For {Phi}=1/2 and 1/3, there is no gap, unlike the MFA which predicts a gap. For {Phi}={ital m}/{ital n} (with {ital m}{gt}1), there is a gap, opening up the possibility that a superfluid may form for any rational value of the statistical parameter. A physical realization of the {Phi}=1/2 flux lattice is proposed and a connection between the {Phi}={ital m}/{ital n} lattice and the fractional quantum Hall effect is discussed.

  2. 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.

  3. Density Functional Plus Dynamical Mean Field Theory of Correlated Oxides

    NASA Astrophysics Data System (ADS)

    Millis, Andrew

    2015-03-01

    The density functional plus dynamical mean field method is outlined and a few recent successes including applications to spin crossover molecules, oxide superlattices and metal-insulator transitions in bulk transition metals are outlined. Insights from the method into the essential role played by lattice distortions (both rotations and bond length changes) in determining the phase diagrams of correlated materials are presented. The key theoretical issue of the double counting correction is outlined, different approaches are compared, and a connection to the energy level differences between strongly and weakly correlated orbitals is presented. Charge transfer across oxide interfaces shown to depend crucially on the double counting correction, suggesting that experiments on oxide superlattices may provide insights into this important problem. Future directions are discussed. This work is performed in collaboration with Jia Chen, Hung Dang, Hyowon Park and Chris Marianetti. This research supported by the DOE Office of Science, Grant ER 046169.

  4. Helicity Inferences Stemming from a Mean-Field Solar Dynamo

    NASA Astrophysics Data System (ADS)

    Pipin, Valery

    The global magnetic field of the Sun is generated by dynamo instability that stems from interactions of magnetic field with the large and small-scale flows. Theoretically, it is expected that such interactions produce a helical magnetic field which evolves following to magnetic helicity conservation law. We discuss some consequences of magnetic helicity conservation for the mean-field solar dynamo. We also discuss the observational aspect of the problem including the recent results about observations of the current helicity of solar active regions, the magnetic helicity of the global magnetic field as revealed by SOHO/MDI observations, and the problem of magnetic helicity transport from the solar convection zone to the outer atmosphere.

  5. THREE-DIMENSIONAL MODELING OF RELATIVISTIC COLLISIONLESS ION-ELECTRON SHOCKS

    SciTech Connect

    Haugboelle, Troels

    2011-10-01

    Two-dimensional (2D) modeling of collisionless shocks has been of tremendous importance in understanding the physics of nonlinear evolution, momentum transfer, and particle acceleration, but current computer capacities have now reached a point where three-dimensional (3D) modeling is becoming feasible. We present the first 3D model of a fully developed and relaxed relativistic ion-electron shock, and analyze and compare it to similar 2D models. Quantitative and qualitative differences are found with respect to the 2D models. The shock jump conditions are naturally different, because of the extra degree of freedom, but in addition it is found that strong parallel electric fields develop at the shock interface, the level of magnetic field energy is lower, and the non-thermal particle distribution is shallower with a power-law index of {approx}2.2.

  6. 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.

  7. 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.

  8. Hadron Mass Spectra and Decay Rates in a Potential Model with Relativistic Wave Equations.

    NASA Astrophysics Data System (ADS)

    Namgung, Wuk

    Hadron properties of mass spectra and decay rates are calculated in a quark potential model. Wave equations based on the Klein-Gordon and Todorov equations both of which incorporate the feature of relativistic two-body kinematics are used. The wave equations are modified to contain potentials which transform either like a Lorentz scalar or like a time-component of a four-vector. Potentials based on the Fogleman-Lichtenberg-Wills potential which has the properties suggested by QCD of both confinement and asymptotic freedom are used. The potentials, motivated by QCD but otherwise phenomenological, are further generalized to forms which can apply to any color representation. To break the degeneracy between vector and pseudoscalar mesons or between spin-3/2 and spin-1/2 baryons, the essential feature of spin dependence is included in the potentials. The masses of vector and pseudoscalar mesons are calculated with only a small number of adjustable parameters, and good qualitative agreement with experiment is obtained for both heavy and light mesons. Baryons are treated in this framework by making use of a quark-diquark two-body model of baryons. First, diquark properties are calculated without any additional parameters. The g-factors of diquarks and spin-flavor configuration of baryons, which are necessary for the calculation of baryons, are given. Then baryon masses are calculated also without additional parameters. The results of the masses of ground-state baryons are in good qualitative agreement with experiment. Also effective constituent quark masses are obtained using current quark masses as input. The calculated effective constituent quark masses are in the right range of the values that most theoretical estimates have given. The general qualitative features of hadron spectra are similar with the two relativistic wave equations, although there are differences in detail. The Van Royen-Weisskopf formula for electromagnetic decay widths of vector mesons into lepton

  9. 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.

  10. Heterogeneous mean field for neural networks with short-term plasticity

    NASA Astrophysics Data System (ADS)

    di Volo, Matteo; Burioni, Raffaella; Casartelli, Mario; Livi, Roberto; Vezzani, Alessandro

    2014-08-01

    We report about the main dynamical features of a model of leaky integrate-and-fire excitatory neurons with short-term plasticity defined on random massive networks. We investigate the dynamics by use of a heterogeneous mean-field formulation of the model that is able to reproduce dynamical phases characterized by the presence of quasisynchronous events. This formulation allows one to solve also the inverse problem of reconstructing the in-degree distribution for different network topologies from the knowledge of the global activity field. We study the robustness of this inversion procedure by providing numerical evidence that the in-degree distribution can be recovered also in the presence of noise and disorder in the external currents. Finally, we discuss the validity of the heterogeneous mean-field approach for sparse networks with a sufficiently large average in-degree.

  11. H-mode transitions and limit cycle oscillations from mean field transport equations

    NASA Astrophysics Data System (ADS)

    Staebler, Gary M.; Groebner, R. J.

    2015-01-01

    The mean field toroidal and parallel momentum transport equations will be shown to admit both one-step transitions to suppressed transport (L/H) and limit cycle oscillations (LCO). Both types of transitions are driven by the suppression of turbulence by the mean field ExB velocity shear. Using experimental data to evaluate the coefficients of a reduced transport model, the observed frequency of the LCO can be matched. The increase in the H-mode power threshold above and below a minimum density agrees with the trends in the model. Both leading and lagging phase relations between the turbulent density fluctuation amplitude and the ExB velocity shear can occur depending on the evolution of the linear growth rate of the turbulence. The transport solutions match the initial phase of the L/H transition where the poloidal and ExB velocities are observed to change, and the density fluctuations drop, faster than the diamagnetic velocity.

  12. Many-Body Mobility Edge in a Mean-Field Quantum Spin Glass

    NASA Astrophysics Data System (ADS)

    Laumann, C. R.; Pal, A.; Scardicchio, A.

    2014-11-01

    The quantum random energy model provides a mean-field description of the equilibrium spin glass transition. We show that it further exhibits a many-body localization-delocalization (MBLD) transition when viewed as a closed quantum system. The mean-field structure of the model allows an analytically tractable description of the MBLD transition using the forward-scattering approximation and replica techniques. The predictions are in good agreement with the numerics. The MBLD transition lies at energy density significantly above the equilibrium spin glass transition, indicating that the closed system dynamics freezes well outside of the traditional glass phase. We also observe that the structure of the eigenstates at the MBLD critical point changes continuously with the energy density, raising the possibility of a family of critical theories for the MBLD transition.

  13. Correlated Dirac semimetal by periodized cluster dynamical mean-field theory

    NASA Astrophysics Data System (ADS)

    Li, Qing-Xiao; He, Rong-Qiang; Lu, Zhong-Yi

    2015-10-01

    The periodized cluster dynamical mean-field theory (PCDMFT) combined with exact diagonalization as the impurity solver has been applied to the half-filled standard Hubbard model on the honeycomb lattice. A correlated Dirac semimetal is found for weak interactions and it transforms into an antiferromagnetic insulating phase for strong interactions via a first-order quantum phase transition, not intervened by a spin liquid phase in between. In this application, the PCDMFT introduces the partial translation symmetry, but cures well the problem caused by the translation symmetry breaking in the cluster dynamical mean-field theory studies for the same model, which gives rise to a spurious insulating phase in the weakly interacting region.

  14. 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.

  15. 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.

  16. Relativistic BCS-BEC crossover in a boson-fermion model

    SciTech Connect

    Deng Jian; Wang Qun; Schmitt, Andreas

    2007-08-01

    We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) in a relativistic superfluid within a boson-fermion model. The model includes, besides the fermions, separate bosonic degrees of freedom, accounting for the bosonic nature of the Cooper pairs. The crossover is realized by tuning the difference between the boson mass and boson chemical potential as a free parameter. The model yields populations of condensed and uncondensed bosons as well as gapped and ungapped fermions throughout the crossover region for arbitrary temperatures. Moreover, we observe the appearance of antiparticles for sufficiently large values of the crossover parameter. As an application, we study pairing of fermions with imbalanced populations. The model can potentially be applied to color superconductivity in dense quark matter at strong couplings.

  17. 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.

  18. Relativistic Stark resonances in a simple exactly soluble model for a diatomic molecule

    NASA Astrophysics Data System (ADS)

    Fillion-Gourdeau, François; Lorin, Emmanuel; Bandrauk, André D.

    2012-06-01

    A simple 1D relativistic model for a diatomic molecule with a double-point interaction potential is solved exactly in a constant electric field. The Weyl-Titchmarsh-Kodaira method is used to evaluate the spectral density function, allowing the correct normalization of continuum states. The boundary conditions at the potential wells are evaluated using Colombeau’s generalized function theory along with charge conjugation invariance and general properties of self-adjoint extensions for point-like interactions. The resulting spectral density function exhibits resonances for quasi-bound states, which move in the complex energy plane as the model parameters are varied. It is observed that for a monotonically increasing interatomic distance, the ground-state resonance can either go deeper into the negative continuum or can give rise to a sequence of avoided crossings, depending on the strength of the potential wells. For the sufficiently low electric field strength or small interatomic distance, the behavior of resonances is qualitatively similar to non-relativistic results.

  19. 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

  20. Time-dependent mean field theory for quench dynamics in correlated electron systems.

    PubMed

    Schiró, Marco; Fabrizio, Michele

    2010-08-13

    A simple and very flexible variational approach to the out-of-equilibrium quantum dynamics in strongly correlated electron systems is introduced through a time-dependent Gutzwiller wave function. As an application, we study the simple case of a sudden change of the interaction in the fermionic Hubbard model and find at the mean-field level an extremely rich behavior. In particular, a dynamical transition between small and large quantum quench regimes is found to occur at half-filling, in accordance with the analysis of Eckstein, Phys. Rev. Lett. 103, 056403 (2009)10.1103/PhysRevLett.103.056403, obtained by dynamical mean-field theory, that turns into a crossover at any finite doping.

  1. Computer-Aided Design of Liquid Crystals: A Mean Field Approach

    NASA Astrophysics Data System (ADS)

    Weider, Titus; Glaser, Matthew A.; Clark, Noel A.

    1997-08-01

    The directed design of soft materials is challenging owing to their complex structure and interactions. A promising strategy for the modeling of organic materials involves the replacement of the explicit condensed phase environment of a molecule or group of molecules by an effective mean field potential. We have created mean field theory-based methods for the routine pre-synthesis prediction of materials properties of liquid crystals, including phase behavior, linear and nonlinear optical properties, and spontaneous polarization density. These methods are semi-empirical in the sense that they rely on experimental data (e.g. from NMR or FTIR measurements) for the development of transferable mean field potentials capable of yielding quantitative predictions for novel materials. Our calculations involve detailed quantum chemical studies of conformational energy surfaces and evaluation of statistical averages by exact enumeration (within an RIS approximation) or importance sampling (for fully flexible molecular models). This strategy appears to have great promise, and represents perhaps the only viable approach to computer-aided design of liquid crystalline materials.

  2. 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.

  3. Dynamical mean-field theory for molecules and nanostructures.

    PubMed

    Turkowski, Volodymyr; Kabir, Alamgir; Nayyar, Neha; Rahman, Talat S

    2012-03-21

    Dynamical mean-field theory (DMFT) has established itself as a reliable and well-controlled approximation to study correlation effects in bulk solids and also two-dimensional systems. In combination with standard density-functional theory (DFT), it has been successfully applied to study materials in which localized electronic states play an important role. It was recently shown that this approach can also be successfully applied to study correlation effects in nanostructures. Here, we provide some details on our recently proposed DFT+DMFT approach to study the magnetic properties of nanosystems [V. Turkowski, A. Kabir, N. Nayyar, and T. S. Rahman, J. Phys.: Condens. Matter 22, 462202 (2010)] and apply it to examine the magnetic properties of small FePt clusters. We demonstrate that DMFT produces meaningful results even for such small systems. For benchmarking and better comparison with results obtained using DFT+U, we also include the case of small Fe clusters. As in the case of bulk systems, the latter approach tends to overestimate correlation effects in nanostructures. Finally, we discuss possible ways to further improve the nano-DFT+DMFT approximation and to extend its application to molecules and nanoparticles on substrates and to nonequilibrium phenomena. PMID:22443749

  4. using multi-scale measurements of pitch angle distribution to test magnetospheric relativistic electron energization models

    NASA Astrophysics Data System (ADS)

    Kanekal, S. G.; Friedel, R. H. W.; Reeves, E. G. D.

    Detailed investigation of pitch angle distributions during the course of a relativistic electron energization event can aid in identifying the dominant physical process underlying the event. Current models of electron energization employ a variety physical processes ranging from radial diffusion to in-situ acceleration mechanisms. These processes result in different pitch angle distributions of energized electrons, for example radial diffusion dominated events have a pancake-type distribution. We present the results of a statistical survey of multi-scale electron pitch angle measurements during relativistic electron events. Measurements of in-situ pitch angle evolution at geosynchronous altitude are combined with measurements of global isotropization time scales. We use data from energetic particle sensors onboard SAMPEX and pitch angle data from the SOPA and ESP sensors onboard LANL spacecraft. The LANL measurements provide a microscopic view of the electron pitch angle distribution. Combining electron flux measurements at geosynchronous altitudes with those measured by SAMPEX which is in low earth orbit provides a macroscopic global view of the flux isotropization.

  5. Relativistic scalar-vector models of the N-N and N-nuclear interactions

    SciTech Connect

    Green, A.E.S.

    1985-01-01

    This paper for the Proceedings of Conference an Anti-Nucleon and Nucleon-Nucleus Interactions summarizes work by the principal investigator and his collaborators on the nucleon-nucleon (N-N) and nucleon-nuclear (N-eta) interactions. It draws heavily on a paper presented at the Many Body Conference in Rome in 1972 but also includes a brief review of our phenomenological N-eta interaction studies. We first summarize our 48-49 generalized scalar-vector meson field theory model of the N-N interactions. This is followed by a brief description of our phenomenological work in the 50's on the N-eta interaction sponsored by the Atomic Energy Commission (the present DOE). This work finally led to strong velocity dependent potentials with spin orbit and isospin terms for shell and optical model applications. This is followed by a section on the Emergence of One-Boson Exchange Models describing developments in the 60's of quantitative generalized one boson exchange potentials (GOBEP) including our purely relativistic N-N analyses. Then follows a section on the application of this meson field model to the N-eta interaction, in particular to spherical closed shell nuclei. This work was sponsored by AFOSR but funding was halted with the Mansfield amendment. We conclude with a discussion of subsequent collateral work by former colleagues and by others who have converged upon scalar-vector relativistic models of N-N, antiN-N, N-eta and antiN-eta interactions and some lessons learned from this extended endeavor. 61 refs.

  6. 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.

  7. The cumulative overlap distribution function in spin glasses: mean field vs. three dimensions

    NASA Astrophysics Data System (ADS)

    Yllanes, David; Billoire, Alain; Maiorano, Andrea; Marinari, Enzo; Martin-Mayor, Victor

    2015-03-01

    We use a sample-dependent analysis, based on medians and quantiles, to analyze the behavior of the overlap probability distribution in spin glasses. Using analytical and numerical mean-field results for the Sherrington-Kirkpatrick model, as well as data from toy models, we show that this approach is an effective tool to distinguish the low-temperature behavior of replica symmmetry breaking systems from that expected in the droplet picture. An application of the method to the three-dimensional Edwards-Anderson models shows agreement with the replica symmetry breaking predictions. Supported by ERC Grant No. 247328 and from MINECO (Spain), Contract No. FIS2012-35719-C02.

  8. Evolution of primordial magnetic fields in mean-field approximation

    NASA Astrophysics Data System (ADS)

    Campanelli, Leonardo

    2014-01-01

    We study the evolution of phase-transition-generated cosmic magnetic fields coupled to the primeval cosmic plasma in the turbulent and viscous free-streaming regimes. The evolution laws for the magnetic energy density and the correlation length, both in the helical and the non-helical cases, are found by solving the autoinduction and Navier-Stokes equations in the mean-field approximation. Analytical results are derived in Minkowski spacetime and then extended to the case of a Friedmann universe with zero spatial curvature, both in the radiation- and the matter-dominated era. The three possible viscous free-streaming phases are characterized by a drag term in the Navier-Stokes equation which depends on the free-streaming properties of neutrinos, photons, or hydrogen atoms, respectively. In the case of non-helical magnetic fields, the magnetic intensity and the magnetic correlation length evolve asymptotically with the temperature, , as and . Here, , , and are, respectively, the temperature, the number of magnetic domains per horizon length, and the bulk velocity at the onset of the particular regime. The coefficients , , , , , and , depend on the index of the assumed initial power-law magnetic spectrum, , and on the particular regime, with the order-one constants and depending also on the cutoff adopted for the initial magnetic spectrum. In the helical case, the quasi-conservation of the magnetic helicity implies, apart from logarithmic corrections and a factor proportional to the initial fractional helicity, power-like evolution laws equal to those in the non-helical case, but with equal to zero.

  9. Frozen core potential scheme with a relativistic electronic Hamiltonian: Theoretical connection between the model potential and all-electron treatments

    NASA Astrophysics Data System (ADS)

    Seino, Junji; Tarumi, Moto; Nakai, Hiromi

    2014-01-01

    This Letter proposes an accurate scheme using frozen core orbitals, called the frozen core potential (FCP) method, to theoretically connect model potential calculations to all-electron (AE) ones. The present scheme is based on the Huzinaga-Cantu equation combined with spin-free relativistic Douglas-Kroll-Hess Hamiltonians. The local unitary transformation scheme for efficiently constructing the Hamiltonian produces a seamless extension to the FCP method in a relativistic framework. Numerical applications to coinage diatomic molecules illustrate the high accuracy of this FCP method, as compared to AE calculations. Furthermore, the efficiency of the FCP method is also confirmed by these calculations.

  10. Weak decays of the B c meson to B s and B mesonsin the relativistic quark model

    NASA Astrophysics Data System (ADS)

    Ebert, D.; Faustov, R. N.; Galkin, V. O.

    2003-12-01

    Semileptonic and non-leptonic decays of the B c meson to B s and B mesons, caused by the cto s,d quark transitions, are studied in the framework of the relativistic quark model. The heavy quark expansion in inverse powers of the active c and spectator bar b quark is used to simplify calculations while the final s and d quarks in the B s and B mesons are treated relativistically. The decay form factors are explicitly expressed through the overlap integrals of the meson wave functions in the whole accessible kinematical range. The obtained results are compared with the predictions of other approaches.

  11. Relativistic description of inclusive quasielastic proton-nucleus scattering with relativistic distorted-wave impulse approximation and random-phase approximation

    NASA Astrophysics Data System (ADS)

    van Niekerk, D. D.; van der Ventel, B. I. S.; Titus, N. P.; Hillhouse, G. C.

    2011-04-01

    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 Ca40(p⃗,p⃗') at an energy of 500 MeV and an angle θc.m.=40°. 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.

  12. 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.

  13. 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.

  14. Relativistic, model-independent, multichannel 2→2 transition amplitudes in a finite volume

    DOE PAGES

    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

  15. Modeling the QCD Equation of State in Relativistic Heavy Ion Collisions on BlueGene/L

    SciTech Connect

    Soltz, R; Grady, J; Hartouni, E P; Gupta, R; Vitev, I; Mottola, E; Petreczky, P; Karsch, F; Christ, N; Mawhinney, R; Bass, S; Mueller, B; Vranas, P; Levkova, L; Molnar, D; Teaney, D; De Tar, C; Toussaint, D; Sugar, R

    2006-04-10

    On 9,10 Feb 2006 a workshop was held at LLNL to discuss how a 10% allocation of the ASC BG/L supercomputer performing a finite temperature Lattice QCD (LQCD) calculation of the equation of state and non-equilibrium properties of the quark-gluon state of matter could lead to a breakthrough in our understanding of recent data from the Relativistic Heavy Ion Collider at Brookhaven National Lab. From this meeting and subsequent discussions we present a detailed plan for this calculation, including mechanisms for working in a secure computing environment and inserting the resulting equation of state into hydrodynamic transport models that will be compared directly to the RHIC data. We discuss expected benefits for DOE Office of Science research programs within the context of the NNSA mission.

  16. 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.

  17. 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

  18. Computation of masses and binding energies of some hadrons and bosons according to the rotating lepton model and the relativistic Newton equation

    NASA Astrophysics Data System (ADS)

    Vayenas, C. G.; Fokas, A. S.; Grigoriou, D.

    2016-08-01

    We compute analytically the masses, binding energies and hamiltonians of gravitationally bound Bohr-type states via the rotating relativistic lepton model which utilizes the de Broglie wavelength equation in conjunction with special relativity and Newton's relativistic gravitational law. The latter uses the inertial-gravitational masses, rather than the rest masses, of the rotating particles. The model also accounts for the electrostatic charge- induced dipole interactions between a central charged lepton, which is usually a positron, with the rotating relativistic lepton ring. We use three rotating relativistic neutrinos to model baryons, two rotating relativistic neutrinos to model mesons, and a rotating relativistic electron neutrino - positron (or electron) pair to model the W± bosons. It is found that gravitationally bound ground states comprising three relativistic neutrinos have masses in the baryon mass range (∼⃒ 0.9 to 1 GeV/c2), while ground states comprising two neutrinos have masses in the meson mass range (∼⃒ 0.4 to 0.8 GeV/c2). It is also found that the rest mass values of quarks are in good agreement with the heaviest neutrino mass value of 0.05 eV/c2 and that the mass of W± bosons (∼⃒ 81 GeV/c2) corresponds to the mass of a rotating gravitationally confined e± — ve pair. A generalized expression is also derived for the gravitational potential energy of such relativistic Bohr-type structures.

  19. 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.

  20. 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.

  1. 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.

  2. 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

  3. 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.

  4. 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.

  5. 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

  6. 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).

  7. Continuum theory of critical phenomena in polymer solutions: Formalism and mean field approximation

    NASA Astrophysics Data System (ADS)

    Goldstein, Raymond E.; Cherayil, Binny J.

    1989-06-01

    A theoretical description of the critical point of a polymer solution is formulated directly from the Edwards continuum model of polymers with two- and three-body excluded-volume interactions. A Hubbard-Stratonovich transformation analogous to that used in recent work on the liquid-vapor critical point of simple fluids is used to recast the grand partition function of the polymer solution as a functional integral over continuous fields. The resulting Landau-Ginzburg-Wilson (LGW) Hamiltonian is of the form of a generalized nonsymmetric n=1 component vector model, with operators directly related to certain connected correlation functions of a reference system. The latter is taken to be an ensemble of Gaussian chains with three-body excluded-volume repulsions, and the operators are computed in three dimensions by means of a perturbation theory that is rapidly convergent for long chains. A mean field theory of the functional integral yields a description of the critical point in which the power-law variations of the critical polymer volume fraction φc, critical temperature Tc, and critical amplitudes on polymerization index N are essentially identical to those found in the Flory-Huggins theory. In particular, we find φc ˜N-1/2, Tθ-Tc˜N-1/2 with (Tθ the theta temperature), and that the composition difference between coexisting phases varies with reduced temperature t as N-1/4t1/2. The mean field theory of the interfacial tension σ between coexisting phases near the critical point, developed by considering the LGW Hamiltonian for a weakly inhomogeneous solution, yields σ˜N-1/4t3/2, with the correlation length diverging as ξ˜N1/4t-1/2 within the same approximation, consistent with the mean field limit of de Gennes' scaling form. Generalizations to polydisperse systems are discussed.

  8. 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.

  9. 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.

  10. A mean-field approach to the propagation of field patterns in stratified magnetorotational turbulence

    NASA Astrophysics Data System (ADS)

    Gressel, Oliver

    2010-06-01

    Local shearing box simulations of stratified magnetorotational turbulence invariably exhibit cyclic field patterns which propagate away from the disc mid-plane. A common explanation for this is magnetic buoyancy. The recent analysis by Shi et al. however shows that the flow is buoyantly stable below one disc scaleheight H, necessitating an alternative explanation in this region. We here conduct and analyse direct numerical simulations to explain the observed behaviour by means of a mean-field description. Apart from the mean radial and azimuthal field, we monitor the small-scale current helicity, which we propose as a key indicator for saturation. Reconstructing the horizontally averaged field, we demonstrate that the problem can be reduced to a 1D induction equation. By means of the so-called test field method, we then determine the underlying closure parameters. Our analysis shows that, apart from a possible direct magnetorotational instability (MRI) dynamo, two distinct indirect dynamo mechanisms operate in the disc. This resolves the issue of the `wrong' sign of the MRI dynamo effect. Finally, we use the obtained closure parameters to run a dynamically quenched dynamo model. This model approximately recovers the observed field patterns in the mean fields. Moreover, the model reproduces the prevailing parity and the distinct phase pattern in the small-scale current helicity. The latter property might open a potential route to understand the saturation of MRI induced turbulence.

  11. Finite-size critical scaling in Ising spin glasses in the mean-field regime

    NASA Astrophysics Data System (ADS)

    Aspelmeier, T.; Katzgraber, Helmut G.; Larson, Derek; Moore, M. A.; Wittmann, Matthew; Yeo, Joonhyun

    2016-03-01

    We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida-Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size scaling function associated with the spin-glass susceptibility of the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as that of one-dimensional spin-glass models with power-law long-range interactions in the regime where they can be a proxy for the Edwards-Anderson short-range spin-glass model above the upper critical dimension. We also calculate a simple analytical approximation for the spin-glass susceptibility crossover function. The behavior of the spin-glass susceptibility near the de Almeida-Thouless transition line has also been studied, but here we have only been able to obtain analytically its behavior in the asymptotic limit above and below the transition. We have also simulated the one-dimensional system in a field in the non-mean-field regime to illustrate that when the Imry-Ma droplet length scale exceeds the system size one can then be erroneously lead to conclude that there is a de Almeida-Thouless transition even though it is absent.

  12. Finite-size critical scaling in Ising spin glasses in the mean-field regime.

    PubMed

    Aspelmeier, T; Katzgraber, Helmut G; Larson, Derek; Moore, M A; Wittmann, Matthew; Yeo, Joonhyun

    2016-03-01

    We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida-Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size scaling function associated with the spin-glass susceptibility of the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as that of one-dimensional spin-glass models with power-law long-range interactions in the regime where they can be a proxy for the Edwards-Anderson short-range spin-glass model above the upper critical dimension. We also calculate a simple analytical approximation for the spin-glass susceptibility crossover function. The behavior of the spin-glass susceptibility near the de Almeida-Thouless transition line has also been studied, but here we have only been able to obtain analytically its behavior in the asymptotic limit above and below the transition. We have also simulated the one-dimensional system in a field in the non-mean-field regime to illustrate that when the Imry-Ma droplet length scale exceeds the system size one can then be erroneously lead to conclude that there is a de Almeida-Thouless transition even though it is absent. PMID:27078308

  13. Correcting mean-field approximations for birth-death-movement processes

    NASA Astrophysics Data System (ADS)

    Baker, Ruth E.; Simpson, Matthew J.

    2010-10-01

    On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description.

  14. 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

  15. Comparing models of rapidly rotating relativistic stars constructed by two numerical methods

    NASA Astrophysics Data System (ADS)

    Stergioulas, Nikolaos; Friedman, John L.

    1995-05-01

    We present the first direct comparison of codes based on two different numerical methods for constructing rapidly rotating relativistic stars. A code based on the Komatsu-Eriguchi-Hachisu (KEH) method (Komatsu et al. 1989), written by Stergioulas, is compared to the Butterworth-Ipser code (BI), as modified by Friedman, Ipser, & Parker. We compare models obtained by each method and evaluate the accuracy and efficiency of the two codes. The agreement is surprisingly good, and error bars in the published numbers for maximum frequencies based on BI are dominated not by the code inaccuracy but by the number of models used to approximate a continuous sequence of stars. The BI code is faster per iteration, and it converges more rapidly at low density, while KEH converges more rapidly at high density; KEH also converges in regions where BI does not, allowing one to compute some models unstable against collapse that are inaccessible to the BI code. A relatively large discrepancy recently reported (Eriguchi et al. 1994) for models based on Friedman-Pandharipande equation of state is found to arise from the use of two different versions of the equation of state. For two representative equations of state, the two-dimensional space of equilibrium configurations is displayed as a surface in a three-dimensional space of angular momentum, mass, and central density. We find, for a given equation of state, that equilibrium models with maximum values of mass, baryon mass, and angular momentum are (generically) either all unstable to collapse or are all stable. In the first case, the stable model with maximum angular velocity is also the model with maximum mass, baryon mass, and angular momentum. In the second case, the stable models with maximum values of these quantities are all distinct. Our implementation of the KEH method will be available as a public domain program for interested users.

  16. 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.

  17. Non-mean-field theory of anomalously large double layer capacitance

    NASA Astrophysics Data System (ADS)

    Loth, M. S.; Skinner, Brian; Shklovskii, B. I.

    2010-07-01

    Mean-field theories claim that the capacitance of the double layer formed at a metal/ionic conductor interface cannot be larger than that of the Helmholtz capacitor, whose width is equal to the radius of an ion. However, in some experiments the apparent width of the double layer capacitor is substantially smaller. We propose an alternate non-mean-field theory of the ionic double layer to explain such large capacitance values. Our theory allows for the binding of discrete ions to their image charges in the metal, which results in the formation of interface dipoles. We focus primarily on the case where only small cations are mobile and other ions form an oppositely charged background. In this case, at small temperature and zero applied voltage dipoles form a correlated liquid on both contacts. We show that at small voltages the capacitance of the double layer is determined by the transfer of dipoles from one electrode to the other and is therefore limited only by the weak dipole-dipole repulsion between bound ions so that the capacitance is very large. At large voltages the depletion of bound ions from one of the capacitor electrodes triggers a collapse of the capacitance to the much smaller mean-field value, as seen in experimental data. We test our analytical predictions with a Monte Carlo simulation and find good agreement. We further argue that our “one-component plasma” model should work well for strongly asymmetric ion liquids. We believe that this work also suggests an improved theory of pseudocapacitance.

  18. Mean-field description of ionic size effects with nonuniform ionic sizes: a numerical approach.

    PubMed

    Zhou, Shenggao; Wang, Zhongming; Li, Bo

    2011-08-01

    Ionic size effects are significant in many biological systems. Mean-field descriptions of such effects can be efficient but also challenging. When ionic sizes are different, explicit formulas in such descriptions are not available for the dependence of the ionic concentrations on the electrostatic potential, that is, there is no explicit Boltzmann-type distributions. This work begins with a variational formulation of the continuum electrostatics of an ionic solution with such nonuniform ionic sizes as well as multiple ionic valences. An augmented Lagrange multiplier method is then developed and implemented to numerically solve the underlying constrained optimization problem. The method is shown to be accurate and efficient, and is applied to ionic systems with nonuniform ionic sizes such as the sodium chloride solution. Extensive numerical tests demonstrate that the mean-field model and numerical method capture qualitatively some significant ionic size effects, particularly those for multivalent ionic solutions, such as the stratification of multivalent counterions near a charged surface. The ionic valence-to-volume ratio is found to be the key physical parameter in the stratification of concentrations. All these are not well described by the classical Poisson-Boltzmann theory, or the generalized Poisson-Boltzmann theory that treats uniform ionic sizes. Finally, various issues such as the close packing, limitation of the continuum model, and generalization of this work to molecular solvation are discussed. PMID:21929014

  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. 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.

  1. 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.

  2. 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.

  3. A statistical model for relativistic quantum fluids interacting with an intense electromagnetic wave

    NASA Astrophysics Data System (ADS)

    Mahajan, Swadesh M.; Asenjo, Felipe A.

    2016-05-01

    A statistical model for relativistic quantum fluids interacting with an arbitrary amplitude circularly polarized electromagnetic wave is developed in two steps. First, the energy spectrum and the wave function for a quantum particle (Klein Gordon and Dirac) embedded in the electromagnetic wave are calculated by solving the appropriate eigenvalue problem. The energy spectrum is anisotropic in the momentum K and reflects the electromagnetic field through the renormalization of the rest mass m to M =√{m2+q2A2 } . Based on this energy spectrum of this quantum particle plus field combination (QPF), a statistical mechanics model of the quantum fluid made up of these weakly interacting QPF is developed. Preliminary investigations of the formalism yield highly interesting results—a new scale for temperature, and fundamental modification of the dispersion relation of the electromagnetic wave. It is expected that this formulation could, inter alia, uniquely advance our understanding of laboratory as well as astrophysical systems where one encounters arbitrarily large electromagnetic fields.

  4. 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.

  5. Global study of beyond-mean-field correlation energies in covariant energy density functional theory using a collective Hamiltonian method

    NASA Astrophysics Data System (ADS)

    Lu, K. Q.; Li, Z. X.; Li, Z. P.; Yao, J. M.; Meng, J.

    2015-02-01

    We report the first global study of dynamic correlation energies (DCEs) associated with rotational motion and quadrupole shape vibrational motion in a covariant energy density functional (CEDF) for 575 even-even nuclei with proton numbers ranging from Z =8 to Z =108 by solving a five-dimensional collective Hamiltonian, the collective parameters of which are determined from triaxial relativistic mean field plus BCS calculation using the PC-PK1 force. After taking into account these beyond mean-field DCEs, the root-mean-square (rms) deviation with respect to nuclear masses is reduced significantly down to 1.14 MeV, which is smaller than those of other successful CEDFs: NL3* (2.96 MeV), DD-ME2 (2.39 MeV), DD -ME δ (2.29 MeV), and DD-PC1 (2.01 MeV). Moreover, the rms deviation for two-nucleon separation energies is reduced by ˜34 % in comparison with the cranking prescription.

  6. Weakly relativistic plasma expansion

    SciTech Connect

    Fermous, Rachid Djebli, Mourad

    2015-04-15

    Plasma expansion is an important physical process that takes place in laser interactions with solid targets. Within a self-similar model for the hydrodynamical multi-fluid equations, we investigated the expansion of both dense and under-dense plasmas. The weakly relativistic electrons are produced by ultra-intense laser pulses, while ions are supposed to be in a non-relativistic regime. Numerical investigations have shown that relativistic effects are important for under-dense plasma and are characterized by a finite ion front velocity. Dense plasma expansion is found to be governed mainly by quantum contributions in the fluid equations that originate from the degenerate pressure in addition to the nonlinear contributions from exchange and correlation potentials. The quantum degeneracy parameter profile provides clues to set the limit between under-dense and dense relativistic plasma expansions at a given density and temperature.

  7. 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.

  8. 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.

  9. 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.

  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. 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.

  13. Numerical modeling and experiments by forming electron beam for relativistic klystron on linear induction accelerator

    NASA Astrophysics Data System (ADS)

    Furman, Edvin G.; Isakov, Petr Y.; Sulakshin, Alexander S.; Vasil'ev, Vasilii V.

    1995-09-01

    The results of numercial modeling and experimental investigations of the linear induction accelerator operation where relativistic clystron is applied as a load are presented. The electron gun with the dielectric emitter (DE) is employed as the injector for this system. As a result of this investigation, the electro-optical system has been successfully realized allowing us to form electron beams sufficiently homogeneous in cross-section with current level of no less than 150 A. Compression of the beam from DE at the first stage of moving is supported, essentially, due to a system of focusing electrodes, similar to Pierce optics. Then, compression of the beam to the size required for its free motion in the anode tract and clystron's drift tube occurs in increasing external magnetic field. In this purpose, the configuration of tracking magnetic field was calculated and suitable magnetic system has been made. The results obtained experimentally are in good agreement with calculated data. With emitting dielectric surface of 50mm in diameter the laminar electron beam of 8mm in diameter was obtained. At accelerating voltage of 400kV and pulse duration of 120ns, required for the excitation of the X-band clystron amplifier the value of current was of the order of 200 A. Prints of the beam on targets allow us to make the same findings.

  14. Mass prediction of proton-rich nuclides with the Coulomb displacement energies in the relativistic point-coupling model

    NASA Astrophysics Data System (ADS)

    Sun, BaoHua; Zhao, PengWei; Meng, Jie

    2011-02-01

    The masses, one- and two-proton separation energies of proton-rich nuclei with Z = 20-55, are computed using the measured masses of mirror neutron-rich nuclei and the Coulomb displacement energies calculated from the relativistic point-coupling model. The implications for the proton drip lines, candidates for two-proton emitters, as well as the impact on the astrophysical rp-process are discussed.

  15. Electroexcitation of the Δ(1232)32+ and Δ(1600)32+ in a light-front relativistic quark model

    DOE PAGES

    Aznauryan, Inna G.; Burkert, Volker D.

    2015-09-30

    Here, the magnetic-dipole form factor and the ratios REM and RSM for the γ* N → Δ(1232)3/2+ transition are predicted within light-front relativistic quark model up to photon virtuality Q2=12 GeV2. Furthermore, we predict the helicity amplitudes of the γ* N → Δ(1600)3/2+ transition assuming the Δ(1600)3/2+ is the first radial excitation of the ground state Delta(1232)3/2+.

  16. Relativistic viscoelastic fluid mechanics

    SciTech Connect

    Fukuma, Masafumi; Sakatani, Yuho

    2011-08-15

    A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.

  17. Relativistic viscoelastic fluid mechanics.

    PubMed

    Fukuma, Masafumi; Sakatani, Yuho

    2011-08-01

    A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.

  18. How self-organized criticality works: A unified mean-field picture

    NASA Astrophysics Data System (ADS)

    Vespignani, Alessandro; Zapperi, Stefano

    1998-06-01

    We present a unified dynamical mean-field theory, based on the single site approximation to the master-equation, for stochastic self-organized critical models. In particular, we analyze in detail the properties of sandpile and forest-fire (FF) models. In analogy with other nonequilibrium critical phenomena, we identify an order parameter with the density of ``active'' sites, and control parameters with the driving rates. Depending on the values of the control parameters, the system is shown to reach a subcritical (absorbing) or supercritical (active) stationary state. Criticality is analyzed in terms of the singularities of the zero-field susceptibility. In the limit of vanishing control parameters, the stationary state displays scaling characteristics of self-organized criticality (SOC). We show that this limit corresponds to the breakdown of space-time locality in the dynamical rules of the models. We define a complete set of critical exponents, describing the scaling of order parameter, response functions, susceptibility and correlation length in the subcritical and supercritical states. In the subcritical state, the response of the system to small perturbations takes place in avalanches. We analyze their scaling behavior in relation with branching processes. In sandpile models, because of conservation laws, a critical exponents subset displays mean-field values (ν=12 and γ=1) in any dimensions. We treat bulk and boundary dissipation and introduce a critical exponent relating dissipation and finite size effects. We present numerical simulations that confirm our results. In the case of the forest-fire model, our approach can distinguish between different regimes (SOC-FF and deterministic FF) studied in the literature, and determine the full spectrum of critical exponents.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. Phase-space moment-equation model of highly relativistic electron-beams in plasma-wakefield accelerators

    SciTech Connect

    Robson, R.E.; Mehrling, T.; Osterhoff, J.

    2015-05-15

    We formulate a new procedure for modelling the transverse dynamics of relativistic electron beams with significant energy spread when injected into plasma-based accelerators operated in the blow-out regime. Quantities of physical interest, such as the emittance, are furnished directly from solution of phase space moment equations formed from the relativistic Vlasov equation. The moment equations are closed by an Ansatz, and solved analytically for prescribed wakefields. The accuracy of the analytic formulas is established by benchmarking against the results of a semi-analytic/numerical procedure which is described within the scope of this work, and results from a simulation with the 3D quasi-static PIC code HiPACE.

  4. Relativistic ab initio model potential calculations including spin-orbit effects through the Wood-Boring Hamiltonian

    NASA Astrophysics Data System (ADS)

    Seijo, Luis

    1995-05-01

    Presented in this paper, is a practical implementation of the use of the Wood-Boring Hamiltonian [Phys. Rev. B 18, 2701 (1978)] in atomic and molecular ab initio core model potential calculations (AIMP), as a means to include spin-orbit relativistic effects, in addition to the mass-velocity and Darwin operators, which were already included in the spin-free version of the relativistic AIMP method. Calculations on the neutral and singly ionized atoms of the halogen elements and sixth-row p-elements Tl-Rn are presented, as well as on the one or two lowest lying states of the diatomic molecules HX, HX+, (X=F, Cl, Br, I, At) TlH, PbH, BiH, and PoH. The calculated spin-orbit splittings and bonding properties show a stable, good quality, of the size of what can be expected from an effective potential method.

  5. relline: Relativistic line profiles calculation

    NASA Astrophysics Data System (ADS)

    Dauser, Thomas

    2015-05-01

    relline calculates relativistic line profiles; it is compatible with the common X-ray data analysis software XSPEC (ascl:9910.005) and ISIS (ascl:1302.002). The two basic forms are an additive line model (RELLINE) and a convolution model to calculate relativistic smearing (RELCONV).

  6. Point form relativistic quantum mechanics and relativistic SU(6)

    NASA Technical Reports Server (NTRS)

    Klink, W. H.

    1993-01-01

    The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.

  7. 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

  8. Weiss mean-field approximation for multicomponent stochastic spatially extended systems.

    PubMed

    Kurushina, Svetlana E; Maximov, Valerii V; Romanovskii, Yurii M

    2014-08-01

    We develop a mean-field approach for multicomponent stochastic spatially extended systems and use it to obtain a multivariate nonlinear self-consistent Fokker-Planck equation defining the probability density of the state of the system, which describes a well-known model of autocatalytic chemical reaction (brusselator) with spatially correlated multiplicative noise, and to study the evolution of probability density and statistical characteristics of the system in the process of spatial pattern formation. We propose the finite-difference method for the numerical solving of a general class of multivariate nonlinear self-consistent time-dependent Fokker-Planck equations. We illustrate the accuracy and reliability of the method by applying it to an exactly solvable nonlinear Fokker-Planck equation (NFPE) for the Shimizu-Yamada model [Prog. Theor. Phys. 47, 350 (1972)] and nonlinear Fokker-Planck equation [Desai and Zwanzig, J. Stat. Phys. 19, 1 (1978)] obtained for a nonlinear stochastic mean-field model introduced by Kometani and Shimizu [J. Stat. Phys. 13, 473 (1975)]. Taking the problems indicated above as an example, the accuracy of the method is compared with the accuracy of Hermite distributed approximating functional method [Zhang et al., Phys. Rev. E 56, 1197 (1997)]. Numerical study of the NFPE solutions for a stochastic brusselator shows that in the region of Turing bifurcation several types of solutions exist if noise intensity increases: unimodal solution, transient bimodality, and an interesting solution which involves multiple "repumping" of probability density through bimodality. Additionally, we study the behavior of the order parameter of the system under consideration and show that the second type of solution arises in the supercritical region if noise intensity values are close to the values appropriate for the transition from bimodal stationary probability density for the order parameter to the unimodal one. PMID:25215716

  9. Weiss mean-field approximation for multicomponent stochastic spatially extended systems

    NASA Astrophysics Data System (ADS)

    Kurushina, Svetlana E.; Maximov, Valerii V.; Romanovskii, Yurii M.

    2014-08-01

    We develop a mean-field approach for multicomponent stochastic spatially extended systems and use it to obtain a multivariate nonlinear self-consistent Fokker-Planck equation defining the probability density of the state of the system, which describes a well-known model of autocatalytic chemical reaction (brusselator) with spatially correlated multiplicative noise, and to study the evolution of probability density and statistical characteristics of the system in the process of spatial pattern formation. We propose the finite-difference method for the numerical solving of a general class of multivariate nonlinear self-consistent time-dependent Fokker-Planck equations. We illustrate the accuracy and reliability of the method by applying it to an exactly solvable nonlinear Fokker-Planck equation (NFPE) for the Shimizu-Yamada model [Prog. Theor. Phys. 47, 350 (1972), 10.1143/PTP.47.350] and nonlinear Fokker-Planck equation [Desai and Zwanzig, J. Stat. Phys. 19, 1 (1978), 10.1007/BF01020331] obtained for a nonlinear stochastic mean-field model introduced by Kometani and Shimizu [J. Stat. Phys. 13, 473 (1975), 10.1007/BF01013146]. Taking the problems indicated above as an example, the accuracy of the method is compared with the accuracy of Hermite distributed approximating functional method [Zhang et al., Phys. Rev. E 56, 1197 (1997), 10.1103/PhysRevE.56.1197]. Numerical study of the NFPE solutions for a stochastic brusselator shows that in the region of Turing bifurcation several types of solutions exist if noise intensity increases: unimodal solution, transient bimodality, and an interesting solution which involves multiple "repumping" of probability density through bimodality. Additionally, we study the behavior of the order parameter of the system under consideration and show that the second type of solution arises in the supercritical region if noise intensity values are close to the values appropriate for the transition from bimodal stationary probability density

  10. Aspects of the decoherence in high-spin environments: Breakdown of the mean-field approximation

    NASA Astrophysics Data System (ADS)

    Hamdouni, Yamen

    2016-08-01

    The study of the decoherence of qubits in spin systems is almost restricted to environments whose constituents are spin-1/2 particles. In this paper we consider environments that are composed of particles of higher spin, and we investigate the consequences on the dynamics of a qubit coupled to such baths via Heisenberg X Y and Ising interactions. It is shown that, while the short time decay in both cases gets faster as the magnitude of the spin increases, the asymptotic behavior exhibits an improvement of the suppression of the decoherence when the coupling is through Heisenberg X Y interactions. In the case of a transverse Ising model, we find that the mean-field approximation breaks down for high values of the spin.

  11. Occupation numbers of spherical orbits in self-consistent beyond-mean-field methods

    NASA Astrophysics Data System (ADS)

    Rodríguez, Tomás R.; Poves, Alfredo; Nowacki, Frédéric

    2016-05-01

    We present a method to compute the number of particles occupying spherical single-particle (SSP) levels within the energy density functional (EDF) framework. These SSP levels are defined for each nucleus by performing self-consistent mean-field calculations. The nuclear many-body states, in which the occupation numbers are evaluated, are obtained with a symmetry conserving configuration mixing (SCCM) method based on the Gogny EDF. The method allows a closer comparison between EDF and shell model with configuration mixing in large valence spaces (SM-CI) results, and can serve as a guidance to define physically sound valence spaces for SM-CI calculations. As a first application of the method, we analyze the onset of deformation in neutron-rich N =40 isotones and the role of the SSP levels around this harmonic oscillator magic number, with particular emphasis in the structure of 64Cr.

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

    SciTech Connect

    Napitu, B. D.; Berakdar, J.

    2010-05-15

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

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

    NASA Astrophysics Data System (ADS)

    Cichy, Agnieszka; Sotnikov, Andrii

    2016-05-01

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

  14. Mean-field density functional theory of a three-phase contact line.

    PubMed

    Lin, Chang-You; Widom, Michael; Sekerka, Robert F

    2012-01-01

    A three-phase contact line in a three-phase fluid system is modeled by a mean-field density functional theory. We use a variational approach to find the Euler-Lagrange equations. Analytic solutions are obtained in the two-phase regions at large distances from the contact line. We employ a triangular grid and use a successive overrelaxation method to find numerical solutions in the entire domain for the special case of equal interfacial tensions for the two-phase interfaces. We use the Kerins-Boiteux formula to obtain a line tension associated with the contact line. This line tension turns out to be negative. We associate line adsorption with the change of line tension as the governing potentials change.

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

    SciTech Connect

    Tang, Jiuzhou; Zhang, Xinghua; Yan, Dadong

    2015-11-28

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

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

    NASA Astrophysics Data System (ADS)

    Chou, Yen-Liang; Ihle, Thomas

    2015-02-01

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

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

    NASA Astrophysics Data System (ADS)

    Tang, Jiuzhou; Zhang, Xinghua; Yan, Dadong

    2015-11-01

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

  18. Active matter beyond mean-field: ring-kinetic theory for self-propelled particles.

    PubMed

    Chou, Yen-Liang; Ihle, Thomas

    2015-02-01

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

  19. Zero-Temperature, Mean-Field Theory of Atomic Bose-Einstein Condensates

    PubMed Central

    Edwards, Mark; Dodd, R. J.; Clark, Charles W.; Burnett, K.

    1996-01-01

    We review the application of zero-temperature, mean-field theory to current experimental atomic Bose-Einstein condensates. We assess the validity of the approximations made by comparing the mean-field results with a variety of experimental data.

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

    NASA Astrophysics Data System (ADS)

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

    1992-06-01

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

  1. Mean-field interactions between nucleic-acid-base dipoles can drive the formation of the double helix

    PubMed Central

    He, Yi; Maciejczyk, Maciej; Ołdziej, Stanisław; Scheraga, Harold A.; Liwo, Adam

    2013-01-01

    A proposed coarse-grained model of nucleic acids demonstrates that average interactions between base dipoles, together with chain connectivity and excluded-volume interactions, are sufficient to form double-helical structures of DNA and RNA molecules. Additionally, local interactions determine helix handedness and direction of strand packing. This result, and earlier research on reduced protein models, suggest that mean-field multipole-multipole interactions are the principal factors responsible for the formation of regular structure of biomolecules. PMID:23496746

  2. Nucleon electromagnetic form factors and electroexcitation of low lying nucleon resonances in a light-front relativistic quark model

    SciTech Connect

    Aznauryan Inna, Burkert Volker

    2012-05-01

    We utilize a light-front relativistic quark model (LF RQM) to predict the 3q core contribution to the electroexcitation amplitudes for the {Delta}(1232)P{sub 33}, N(1440)P{sub 11}, N(1520)D{sub 13}, and N(1535)S{sub 11} up to Q{sup 2} = 12 GeV{sup 2}. The parameters of the model have been specified via description of the nucleon electromagnetic form factors in the approach that combines 3q and pion-cloud contributions in the LF dynamics.

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

    SciTech Connect

    Burnett, James; Ford, Ian J.

    2015-05-21

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

  4. A Simple Relativistic Bohr Atom

    ERIC Educational Resources Information Center

    Terzis, Andreas F.

    2008-01-01

    A simple concise relativistic modification of the standard Bohr model for hydrogen-like atoms with circular orbits is presented. As the derivation requires basic knowledge of classical and relativistic mechanics, it can be taught in standard courses in modern physics and introductory quantum mechanics. In addition, it can be shown in a class that…

  5. Poisson-Boltzmann equation and electro-convective instability in ferroelectric liquid crystals: a mean-field approach

    NASA Astrophysics Data System (ADS)

    Lahiri, T.; Pal Majumder, T.; Ghosh, N. K.

    2014-07-01

    Commercialization of ferroelectric liquid crystal displays (FLCDs) suffers from mechanical and electro-convective instabilities. Impurity ions play a pivotal role in the latter case, and therefore we developed a mean-field type model to understand the complex role of space charges, particularly ions in a ferroelectric liquid crystal. Considering an effective ion-chirality relation, we obtained a modified Poisson-Boltzmann equation for ions dissolved into a chiral solvent like the ferroelectric smectic phase. A nonuniform director profile induced by the mean electrostatic potential of the ions is then calculated by solving an Euler-Lagrange equation for a helically twisted smectic state. A combination of effects resulting from molecular chirality and an electrostatically driven twist created by the ions seems to produce this nonuniform fluctuation in the director orientation. Finally, both theoretical and experimental points of view are presented on the prediction of this mean-field model.

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

    PubMed Central

    LI, BO; WEN, JIAYI; ZHOU, SHENGGAO

    2015-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  8. Two-body nucleon-nucleon correlations in Glauber models of relativistic heavy-ion collisions

    SciTech Connect

    Broniowski, Wojciech; Rybczynski, Maciej

    2010-06-15

    We investigate the influence of the central two-body nucleon-nucleon correlations on several quantities observed in relativistic heavy-ion collisions. It is demonstrated with explicit Monte Carlo simulations that the basic correlation measures observed in relativistic heavy-ion collisions, such as the fluctuations of participant eccentricity, initial size fluctuations, or the fluctuations of the number of sources producing particles, are all sensitive to the inclusion of the two-body correlations. The effect is at the level of about 10-20%. Moreover, the realistic (Gaussian) correlation function gives indistinguishable results from the hard-core repulsion, with the expulsion distance set to 0.9 fm. Thus, we verify that for investigations of the considered correlation measures, it is sufficient to use the Monte Carlo generators accounting for the hard-core repulsion.

  9. Universal Quantum Computing:. Third Gen Prototyping Utilizing Relativistic `Trivector' R-Qubit Modeling Surmounting Uncertainty

    NASA Astrophysics Data System (ADS)

    Amoroso, Richard L.; Kauffman, Louis H.; Giandinoto, Salvatore

    2013-09-01

    We postulate bulk universal quantum computing (QC) cannot be achieved without surmounting the quantum uncertainty principle, an inherent barrier by empirical definition in the regime described by the Copenhagen interpretation of quantum theory - the last remaining hurdle to bulk QC. To surmount uncertainty with probability 1, we redefine the basis for the qubit utilizing a unique form of M-Theoretic Calabi-Yau mirror symmetry cast in an LSXD Dirac covariant polarized vacuum with an inherent `Feynman synchronization backbone'. This also incorporates a relativistic qubit (r-qubit) providing additional degrees of freedom beyond the traditional Block 2-sphere qubit bringing the r-qubit into correspondence with our version of Relativistic Topological Quantum Field Theory (RTQFT). We present a 3rd generation prototype design for simplifying bulk QC implementation.

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

    NASA Astrophysics Data System (ADS)

    Wang, Ying-Long; Wang, Xing-Yuan; Liu, Yang; Liu, Bao-Ting; Fu, Guang-Sheng

    2010-11-01

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

  11. College students' role models, learning style preferences, and academic achievement in collaborative teaching: absolute versus relativistic thinking.

    PubMed

    Chiou, Wen-Bin

    2008-01-01

    Based on the perspective of postformal operations, this study investigated whether college students' role models (technical teachers vs. lecturing teachers) and preferred learning styles (experience-driven mode vs. theory-driven mode) in collaborative teaching courses would be moderated by their cognitive development (absolute thinking vs. relativistic thinking) and examine whether academic achievement of students would be contingent upon their preferred learning styles. Two hundred forty-four college students who have taken the technical courses with collaborative teaching participated in this study. The results showed that those participants with absolute thinking perceived the modeling advantage of technical teachers was greater than that of lecturing teachers, preferred the experience-driven mode over the theory-driven mode, and displayed differential academic achievement between technical courses and general courses. On the other hand, the students with relativistic thinking revealed no difference in perceived modeling advantage of role models, learning styles preferences, and academic achievement between two categories of courses. In addition, this research indicates that college students' preferred learning styles would interact with course category (technical courses vs. general courses) to display differential academic achievement. Implications and future directions are discussed.

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

    NASA Astrophysics Data System (ADS)

    Gangbo, Wilfrid; Święch, Andrzej

    2015-12-01

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

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

    NASA Astrophysics Data System (ADS)

    Osterloh, Andreas; Schützhold, Ralf

    2015-03-01

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

  14. Calculation of the ionization state for LTE plasmas using a new relativistic-screened hydrogenic model based on analytical potentials

    NASA Astrophysics Data System (ADS)

    Rubiano, J. G.; Rodríguez, R.; Gil, J. M.; Martel, P.; Mínguez, E.

    2002-01-01

    In this work, the Saha equation is solved using atomic data provided by means of a new relativistic-screened hydrogenic model based on analytical potentials to calculate the ionization state and ion abundance for LTE iron plasmas. The plasma effects on the atomic structure are taken into account by including the classical continuum lowering correction of Stewart and Pyatt. For high density, the Saha equation is modified to consider the degeneration of free electrons using the Fermi Dirac statistics instead of the Maxwellian distribution commonly used. The results are compared with more sophisticated self-consistent codes.

  15. On the Mass Difference Between pi and rho Using a Relativistic Two-Body Model

    SciTech Connect

    Wong, Cheuk-Yin; Kim, Byeong-Noh; Crater, H. W.; Yoon, Jin-Hee

    2012-01-01

    The big mass difference between the pion(pi) and rho meson(rho) possibly originated from the spin-dependent nature of the interactions in the two states since these two states are similar except for spin. Both pi and rho are quark-antiquark systems which can be treated using the two-body Dirac equations (TBDE) of constraint dynamics. This relativistic approach for the two-body system has the advantage over the non-relativistic treatment in the sense that the spin-dependent nature is automatically coming out from the formalism. We employed Dirac's relativistic constraint dynamics to describe quark-antiquark systems. Within this formalism, the 16-component Dirac equation is reduced to the 4-component 2nd-order differential equation and the radial part of this equation is simply a Schroedinger-type equation with various terms calculated from the basic radial potential. We used a modified Richardson potential for quark-antiquark systems which satisfies the conditions of confinement and asymptotic freedom. We obtained the wave functions for these two mesons which are not singular at short distances. We also found that the cancellation between the Darwin and spin-spin interaction terms occurs in the pi mass but not in the rho mass, and this is the main source of the big difference in the two meson masses.

  16. Relativistically-Compressed Exploding White-Dwarf Model for Sgr A East

    SciTech Connect

    Dearborn, D P; Wilson, J R; Mathews, G J

    2004-11-10

    Recently, a new mechanism for Type I supernovae has been proposed whereby relativistic terms enhance the self gravity of a carbon-oxygen white dwarf as it passes near a black hole. It was suggested but not confirmed that this relativistic compression can cause the central density to exceed the threshold for pycnonuclear reactions so that a thermonuclear runaway ensues. Here, we present numerical studies of such relativistically induced explosions of white dwarfs and red giant cores of various mass (particularly a typical 0.6 M{sub {circle_dot}} white dwarf) as they pass near a 3.7 x 10{sup 6} black hole like Sgr A* in the Galactic center. We confirm by hydrodynamic thermonuclear burn simulations in three spatial dimensions that white dwarfs and red giant cores do indeed ignite and explode. In fact they seem to explode even farther from the black hole than earlier estimates due to increased internal temperatures from adiabatic heating as the stars are compressed. We find that the compression is sufficiently fast that red giant cores, or young (< 10{sup 8} yr) white dwarfs can even be heated to thermonuclear rather than pychnonuclear ignition. We propose that such an event might explain the observed ''mixed-morphology'' Sgr A East supernova remnant in the Galactic center.

  17. Relativistic diffusion

    NASA Astrophysics Data System (ADS)

    Haba, Z.

    2009-02-01

    We discuss relativistic diffusion in proper time in the approach of Schay (Ph.D. thesis, Princeton University, Princeton, NJ, 1961) and Dudley [Ark. Mat. 6, 241 (1965)]. We derive (Langevin) stochastic differential equations in various coordinates. We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form. We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution. We discuss drag terms leading to an equilibrium distribution. The relativistic analog of the Ornstein-Uhlenbeck process is not unique. We show that if the drag comes from a diffusion approximation to the master equation then its form is strongly restricted. The drag leading to the Tsallis equilibrium distribution satisfies this restriction whereas the one of the Jüttner distribution does not. We show that any function of the relativistic energy can be the equilibrium distribution for a particle in a static electric field. A preliminary study of the time evolution with friction is presented. It is shown that the problem is equivalent to quantum mechanics of a particle moving on a hyperboloid with a potential determined by the drag. A relation to diffusions appearing in heavy ion collisions is briefly discussed.

  18. Relativistic diffusion.

    PubMed

    Haba, Z

    2009-02-01

    We discuss relativistic diffusion in proper time in the approach of Schay (Ph.D. thesis, Princeton University, Princeton, NJ, 1961) and Dudley [Ark. Mat. 6, 241 (1965)]. We derive (Langevin) stochastic differential equations in various coordinates. We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form. We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution. We discuss drag terms leading to an equilibrium distribution. The relativistic analog of the Ornstein-Uhlenbeck process is not unique. We show that if the drag comes from a diffusion approximation to the master equation then its form is strongly restricted. The drag leading to the Tsallis equilibrium distribution satisfies this restriction whereas the one of the Jüttner distribution does not. We show that any function of the relativistic energy can be the equilibrium distribution for a particle in a static electric field. A preliminary study of the time evolution with friction is presented. It is shown that the problem is equivalent to quantum mechanics of a particle moving on a hyperboloid with a potential determined by the drag. A relation to diffusions appearing in heavy ion collisions is briefly discussed.

  19. Relativistic nuclear dynamics

    SciTech Connect

    Coester, F.

    1985-01-01

    A review is presented of three distinct approaches to the construction of relativistic dynamical models: (1) Relativistic canonical quantum mechanics. (The Hilbert space of states is independent of the interactions, which are introduced by modifying the energy operator.) (2) Hilbert spaces of manifestly covariant wave functions. (The interactions modify the metric of the Hilbert space.) (3) Covariant Green functions. In each of the three approaches the focus is on the formulation of the two-body dynamics, and problems in the construction of the corresponding many-body dynamics are discussed briefly. 21 refs.

  20. Towards the island of stability with relativistic energy density functionals

    SciTech Connect

    Prassa, V.; Niksic, T.; Lalazissis, G. A.; Vretenar, D.

    2012-10-20

    Relativistic energy density functionals (REDF) provide a complete and accurate, global description of nuclear structure phenomena. Modern semi-empirical functionals, adjusted to the nuclear matter equation of state and to empirical masses of deformed nuclei, are applied to studies of shapes of superheavy nuclei. The theoretical framework is tested in a comparison to empirical masses, quadrupole deformations, and energy barriers of actinide nuclei. The model is used in a self-consistent mean-field calculation of spherical, axial and triaxial shapes of superheavy nuclei, alpha-decay energies and lifetimes. The effect of explicit treatment of collective correlations is analyzed in calculations that consistently use a collective Hamiltonian model based on REDFs.