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Sample records for relativistic mean-field models

  1. Relativistic mean-field mass models

    NASA Astrophysics Data System (ADS)

    Peña-Arteaga, D.; Goriely, S.; Chamel, N.

    2016-10-01

    We present a new effort to develop viable mass models within the relativistic mean-field approach with density-dependent meson couplings, separable pairing and microscopic estimations for the translational and rotational correction energies. Two interactions, DD-MEB1 and DD-MEB2, are fitted to essentially all experimental masses, and also to charge radii and infinite nuclear matter properties as determined by microscopic models using realistic interactions. While DD-MEB1 includes the σ, ω and ρ meson fields, DD-MEB2 also considers the δ meson. Both mass models describe the 2353 experimental masses with a root mean square deviation of about 1.1 MeV and the 882 measured charge radii with a root mean square deviation of 0.029 fm. In addition, we show that the Pb isotopic shifts and moments of inertia are rather well reproduced, and the equation of state in pure neutron matter as well as symmetric nuclear matter are in relatively good agreement with existing realistic calculations. Both models predict a maximum neutron-star mass of more than 2.6 solar masses, and thus are able to accommodate the heaviest neutron stars observed so far. However, the new Lagrangians, like all previously determined RMF models, present the drawback of being characterized by a low effective mass, which leads to strong shell effects due to the strong coupling between the spin-orbit splitting and the effective mass. Complete mass tables have been generated and a comparison with other mass models is presented.

  2. Critical parameters of consistent relativistic mean-field models

    NASA Astrophysics Data System (ADS)

    Lourenço, O.; Dutra, M.; Menezes, D. P.

    2017-06-01

    In the present work, the critical temperature, critical pressure, and critical density, known as the critical parameters related to the liquid-gas phase transition are calculated for 34 relativistic mean-field models, which were shown to satisfy nuclear matter constraints in a comprehensive study involving 263 models. The compressibility factor was calculated and all 34 models present values lower than the one obtained with the van der Waals equation of state. The critical temperatures were compared with experimental data and just two classes of models can reach values close to them. A correlation between the critical parameters and the incompressibility was obtained.

  3. An approach to adjustment of relativistic mean field model parameters

    NASA Astrophysics Data System (ADS)

    Bayram, Tuncay; Akkoyun, Serkan

    2017-09-01

    The Relativistic Mean Field (RMF) model with a small number of adjusted parameters is powerful tool for correct predictions of various ground-state nuclear properties of nuclei. Its success for describing nuclear properties of nuclei is directly related with adjustment of its parameters by using experimental data. In the present study, the Artificial Neural Network (ANN) method which mimics brain functionality has been employed for improvement of the RMF model parameters. In particular, the understanding capability of the ANN method for relations between the RMF model parameters and their predictions for binding energies (BEs) of 58Ni and 208Pb have been found in agreement with the literature values.

  4. 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

  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. Systematic study of bubble nuclei in relativistic mean field model

    SciTech Connect

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

    2016-01-15

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

  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. Giant halos in medium nuclei within modified relativistic mean field (MRMF) model

    SciTech Connect

    Nugraha, A. M. Sulaksono, A.; Sumaryada, T.

    2016-04-19

    The large number of neutrons in a region beyond a closed shell core indicates the presence of giant halos in nuclei. In this work, by using the Rotival method within a modified relativistic mean field (MRMF) model, we predict theoretically the formation of giant halos in Cr and Zr isotopes. The MRMF model is a modification of standard RMF model augmented with isoscalar and isovector tensor terms, isovector-isoscalar vector cross coupling term and electromagnetic exchange term for Coulomb interaction in local density approximation (LDA).

  9. Antikaons in the extended relativistic mean-field models for neutron star

    SciTech Connect

    Gupta, Neha; Arumugam, P.

    2012-10-20

    We review the role of antikaons in recent versions of relativistic mean field models and focus on the interactions in which all parameters are obtained by fitting finite nuclear data and successfully applied to reproduce a variety of nuclear and neutron star (NS) properties. We show that the recently observed 1.97 solar mass NS can be explained in three ways: (i) A stiffer EoS with both antikaons (K{sup -}, K-bar {sup 0}), (ii) a relatively softer EoS with K{sup -} and (iii) a softer EoS with nucleon phase only.

  10. Hadronic matter at finite temperature and density within an effective relativistic mean-field model

    NASA Astrophysics Data System (ADS)

    Lavagno, A.

    2012-10-01

    We study hot and dense hadronic matter by means of an effective relativistic mean-field model with the inclusion of the full octet of baryons, the Δ-isobar degrees of freedom and the lightest pseudoscalar and vector mesons. These last particles are considered by taking into account an effective chemical potential and an effective mass depending on the self-consistent interaction between baryons. The analysis is performed by requiring the Gibbs conditions on the global conservation of baryon number, electric charge fraction and zero net strangeness.

  11. Cluster decay in very heavy nuclei in a relativistic mean field model

    NASA Astrophysics Data System (ADS)

    Bhattacharya, Madhubrata; Gangopadhyay, G.

    2008-02-01

    Exotic cluster decay of very heavy nuclei was studied in the microscopic Super-Asymmetric Fission Model. The Relativistic Mean Field model with the force FSU Gold was employed to obtain the densities of the cluster and the daughter nuclei. The microscopic nuclear interaction DDM3Y1, which has an exponential density dependence, and the Coulomb interaction were used in the double folding model to obtain the potential between the cluster and the daughter. Half-life values were calculated in the WKB approximation and the spectroscopic factors were extracted. The latter values are seen to have a simple dependence of the mass of the cluster as has been observed earlier. Predictions were made for some possible decays.

  12. Building Relativistic Mean-Field Models for Atomic Nuclei and Neutron Stars

    NASA Astrophysics Data System (ADS)

    Chen, Wei-Chia; Piekarewicz, Jorge

    2014-03-01

    Nuclear energy density functional (EDF) theory has been quite successful in describing nuclear systems such as atomic nuclei and nuclear matter. However, when building new models, attention is usually paid to the best-fit parameters only. In recent years, focus has been shifted to the neighborhood around the minimum of the chi-square function as well. This powerful covariance analysis is able to provide important information bridging experiments, observations, and theories. In this work, we attempt to build a specific type of nuclear EDFs, the relativistic mean-field models, which treat atomic nuclei, nuclear matter, and neutron stars on the same footing. The application of covariance analysis can reveal correlations between observables of interest. The purpose is to elucidate the alleged relations between the neutron skin of heavy nuclei and the size of neutron stars, and to develop insight into future investigations.

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

    SciTech Connect

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

    2009-12-15

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

  15. New parameterization of the effective field theory motivated relativistic mean field model

    NASA Astrophysics Data System (ADS)

    Kumar, Bharat; Singh, S. K.; Agrawal, B. K.; Patra, S. K.

    2017-10-01

    A new parameter set is generated for finite and infinite nuclear system within the effective field theory motivated relativistic mean field (ERMF) formalism. The isovector part of the ERMF model employed in the present study includes the coupling of nucleons to the δ and ρ mesons and the cross-coupling of ρ mesons to the σ and ω mesons. The results for the finite and infinite nuclear systems obtained using our parameter set are in harmony with the available experimental data. We find the maximum mass of the neutron star to be 2.03M⊙ and yet a relatively smaller radius at the canonical mass, 12.69 km, as required by the available data.

  16. Neutron driplines for Ca and Pb using modified relativistic mean field (MRMF) model

    SciTech Connect

    Diningrum, J. P. Sulaksono, A.

    2016-04-19

    The position of two neutron driplines for Ca and Pb nuclei are studied using four different parameter sets obtained from Modified Relativistic Mean Field (MRMF) model. The roles of isovector-isoscalar and electromagnetic exchange couplings to predict the position of two neutron driplines for Ca and Pb nuclei are also investigated. The prediction of the position of nuclei dripline is calculated using two different methods, i.e., by observing the separation energy of two neutrons in the corresponding isotopes chains and analyzing the corresponding single particle energies. Our results showed that the appearance of driplines for Ca and Pb nuclei are influenced by all these couplings that characterized by different position prediction on each parameter set.

  17. 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.

  18. Caloric curve for nuclear liquid-gas phase transition in relativistic mean-field hadronic model

    NASA Astrophysics Data System (ADS)

    Parvan, A. S.

    2012-08-01

    The main thermodynamical properties of the first order phase transition of the relativistic mean-field (RMF) hadronic model were explored in the isobaric, the canonical and the grand canonical ensembles on the basis of the method of the thermodynamical potentials and their first derivatives. It was proved that the first order phase transition of the RMF model is the liquid-gas type one associated with the Gibbs free energy G. The thermodynamical potential G is the piecewise smooth function and its first order partial derivatives with respect to variables of state are the piecewise continuous functions. We have found that the energy in the caloric curve is discontinuous in the isobaric and the grand canonical ensembles at fixed values of the pressure and the chemical potential, respectively, and it is continuous, i.e. it has no plateau, in the canonical and microcanonical ensembles at fixed values of baryon density, while the baryon density in the isotherms is discontinuous in the isobaric and the canonical ensembles at fixed values of the temperature. The general criterion for the nuclear liquid-gas phase transition in the canonical ensemble was identified.

  19. 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.

  20. The effect of inclusion of Δ resonances in relativistic mean-field model with scaled hadron masses and coupling constants

    NASA Astrophysics Data System (ADS)

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

    2017-01-01

    Knowledge of the equation of state of the baryon matter plays a decisive role in the description of neutron stars. With an increase of the baryon density the filling of Fermi seas of hyperons and Δ isobars becomes possible. Their inclusion into standard relativistic mean-field models results in a strong softening of the equation of state and a lowering of the maximum neutron star mass below the measured values. We extend a relativistic mean-field model with scaled hadron masses and coupling constants developed in our previous works and take into account now not only hyperons but also the Δ isobars. We analyze available empirical information to put constraints on coupling constants of Δs to mesonic mean fields. We show that the resulting equation of state satisfies majority of presently known experimental constraints.

  1. Ground State Properties of Z=126 Isotopes within the Relativistic Mean Field Model

    NASA Astrophysics Data System (ADS)

    Yu, Qi-Xin; Li, Jun-Qing; Zhang, Hong-Fei

    2017-01-01

    The ground state properties of Z = 126 isotopes with neutron numbers N = 174-244 are calculated by the relativistic mean field (RMF) theory with effective interactions NL-Z2. In order to make a comprehensive understanding of the possible proton magic number Z = 126, we also perform the calculations in the vicinity of Z = 126, such as Z = 114,116,118,120,122,124,128 and 130 isotopic chains. The calculated results show there exist evident magicity for proton number Z = 120 and relatively weak magicity for proton number Z = 126. Supported by the National Natural Science Foundation of China under Grant Nos. 11675066, 11475050, 11265013, and the CAS Knowledge Innovation under Grant No. KJCX2-EW-N02

  2. 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.

  3. 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.

  4. Viscosity of hadron matter within relativistic mean-field-based model with scaled hadron masses and couplings

    SciTech Connect

    Khvorostukhin, A. S. Toneev, V. D.; Voskresensky, D. N.

    2011-04-15

    The shear ({eta}) and bulk ({zeta}) viscosities are calculated in a quasiparticle relaxation-time approximation for a hadron matter described within the relativistic mean-field-based model with scaled hadron masses and couplings. Comparison with results of other models is presented. We demonstrate that a small value of the shear viscosity to entropy density ratio required for explaining a large elliptic flow observed at RHIC may be reached in the hadron phase. Relatively large values of the bulk viscosity are noted in the case of a baryon-enriched matter.

  5. 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.

  6. Relativistic mean field description of cluster radioactivity

    NASA Astrophysics Data System (ADS)

    Bhagwat, A.; Gambhir, Y. K.

    2005-01-01

    Comprehensive investigations of the observed cluster radioactivity are carried out. First, the relativistic mean field (RMF) theory is employed for the calculations of the ground-state properties of relevant nuclei. The calculations reproduce the experiment well. The calculated RMF point densities are folded with the density-dependent M3Y nucleon-nucleon interaction to obtain the cluster-daughter interaction potential. This, along with the calculated and experimental Q values, is used in the WKB approximation for estimating the half-lives of the parent nuclei against cluster decay. The calculations qualitatively agree with the experiment. Sensitive dependence of the half-lives on Q values is explicitly demonstrated.

  7. Investigation of the Mg isotopes using the shell-model-like approach in relativistic mean field theory

    NASA Astrophysics Data System (ADS)

    Bai, Hong-Bo; Zhang, Zhen-Hua; Li, Xiao-Wei

    2016-11-01

    Ground state properties for Mg isotopes, including binding energies, one- and two-neutron separation energies, pairing energies, nuclear matter radii and quadrupole deformation parameters, are obtained from the self-consistent relativistic mean field (RMF) model with the pairing correlations treated by a shell-mode-like approach (SLAP), in which the particle-number is conserved and the blocking effects are treated exactly. The experimental data, including the binding energies and the one- and two-neutron separation energies, which are sensitive to the treatment of pairing correlations and block effects, are well reproduced by the RMF+SLAP calculations. Supported by NSFC (11465001,11275098, 11275248, 11505058,11165001) and Natural Science Foundation of Inner Mongolia of China (2016BS0102)

  8. Coulomb form factors of odd-A nuclei within an axially deformed relativistic mean-field model

    NASA Astrophysics Data System (ADS)

    Liu, Jian; Xu, Chang; Wang, Shuo; Ren, Zhongzhou

    2017-09-01

    Background: The nuclear Coulomb form factor | FC(q) | 2 is a useful tool to study nuclear structure. For spherical nuclei, | FC(q) | 2 can be calculated by combining the spherical relativistic mean-field (RMF) model and the distorted wave Born approximation (DWBA) method. Purpose: In a previous paper, the axially deformed RMF model + DWBA method was successfully applied to study the Coulomb form factors of deformed even-even nuclei. In this paper, we further extend this method to study the Coulomb form factors of deformed odd-A nuclei. Method: First, the charge distributions of odd-A nuclei are calculated with the deformed RMF model and expanded into multipole components. Next, with the multipole moment charge distributions, the Coulomb multipoles C 0 , C 2 , and C 4 are calculated. Finally, by summing over Coulomb multipoles required, the Coulomb form factors of odd-A nuclei can be obtained. Results: For deformed odd-A nuclei, the theoretical Coulomb form factors calculated from the deformed RMF charge densities are in better agreement with the experimental data. For nuclei with J ≥1 , the diffraction minima of Coulomb form factors are much flatter, which is due to the contributions of quadrupole charge distributions. Conclusions: Results indicate that the axially deformed RMF model can give reasonable descriptions for multipole moment charge distributions of odd-A nuclei. The method in this paper can provide a useful guide for future experiments of electron scattering off exotic odd-A nuclei.

  9. Relativistic mean field approximation to baryons

    SciTech Connect

    Dmitri Diakonov

    2005-02-01

    We stress the importance of the spontaneous chiral symmetry breaking for understanding the low-energy structure of baryons. The Mean Field Approximation to baryons is formulated, which solves several outstanding paradoxes of the naive quark models, and which allows to compute parton distributions at low virtuality in a consistent way. We explain why this approach to baryons leads to the prediction of relatively light exotic pentaquark baryons, in contrast to the constituent models which do not take seriously the importance of chiral symmetry breaking. We briefly discuss why, to our mind, it is easier to produce exotic pentaquarks at low than at high energies.

  10. Application of the relativistic mean-field mass model to the r-process and the influence of mass uncertainties

    SciTech Connect

    Sun, B.; Montes, F.; Geng, L. S.; Geissel, H.; Litvinov, Yu. A.; Meng, J.

    2008-08-15

    A new mass table calculated by the relativistic mean-field approach with the state-dependent BCS method for the pairing correlation is applied for the first time to study r-process nucleosynthesis. The solar r-process abundance is well reproduced within a waiting-point approximation approach. Using an exponential fitting procedure to find the required astrophysical conditions, the influence of mass uncertainty is investigated. The r-process calculations using the FRDM, ETFSI-Q, and HFB-13 mass tables have been used for that purpose. It is found that the nuclear physical uncertainty can significantly influence the deduced astrophysical conditions for the r-process site. In addition, the influence of the shell closure and shape transition have been examined in detail in the r-process simulations.

  11. Beyond the relativistic mean-field approximation -- collective correlations

    NASA Astrophysics Data System (ADS)

    Li, Zhipan; Nikšić, Tamara; Vretenar, Dario; Yao, Jiangming

    Semi-empirical relativistic energy density functionals (EDFs) or effective interactions implicitly comprise short-range correlations related to the repulsive core of the inter-nucleon interaction, and long-range correlations mediated by nuclear resonance modes. To model spectroscopic properties of finite nuclei, the self-consistent mean-field method must be extended to include collective correlations that arise from restoration of broken symmetries and fluctuations in collective coordinates. These correlations are sensitive to shell effects, vary with particle number, and cannot be included in a universal EDF. We review and compare recent advances in "beyond mean-field" methods based on relativistic EDFs: the angular-momentum and particle-number projected triaxial generator coordinate method, the five-dimensional quadrupole collective Hamiltonian and the axial quadrupole-octupole collective Hamiltonian models. Illustrative applications include low-energy collective excitation spectra and electromagnetic transition rates of nuclei characterised by quadrupole and/or octupole deformations: 24Mg, 76Kr, 240Pu and 224Ra, in comparison with available data.

  12. 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

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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

  18. Green's function relativistic mean field theory for Λ hypernuclei

    NASA Astrophysics Data System (ADS)

    Ren, S.-H.; Sun, T.-T.; Zhang, W.

    2017-05-01

    The relativistic mean field theory with the Green's function method is extended to study Λ hypernuclei. Taking the hypernucleus Ca61Λ as an example, the single-particle resonant states for Λ hyperons are investigated by analyzing the density of states, and the corresponding energies and widths are given. Different behaviors are observed for the resonant states, i.e., the distributions of the very narrow 1 f5 /2 and 1 f7 /2 states are very similar to bound states while those of the wide 1 g7 /2 and 1 g9 /2 states are like scattering states. Besides, the impurity effect of Λ hyperons on the single-neutron resonant states is investigated. For most of the resonant states, both the energies and widths decrease with adding more Λ hyperons due to the attractive Λ N interaction. Finally, the energy level structure of Λ hyperons in the Ca hypernucleus isotopes with mass number A =53 -73 are studied; obvious shell structure and small spin-orbit splitting are found for the single-Λ spectrum.

  19. Minimization method for relativistic electrons in a mean-field approximation of quantum electrodynamics

    SciTech Connect

    Hainzl, Christian; Lewin, Mathieu; Sere, Eric; Solovej, Jan Philip

    2007-11-15

    We study a mean-field relativistic model which is able to describe both the behavior of finitely many spin-1/2 particles such as electrons and of the Dirac sea which is self-consistently polarized in the presence of the real particles. The model is derived from the QED Hamiltonian in Coulomb gauge neglecting the photon field. All our results are nonperturbative and mathematically rigorous.

  20. 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

  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. K--nucleus relativistic mean field potentials consistent with kaonic atoms

    NASA Astrophysics Data System (ADS)

    Friedman, E.; Gal, A.; Mareš, J.; Cieplý, A.

    1999-08-01

    K- atomic data are used to test several models of the K- nucleus interaction. The t(ρ)ρ optical potential, due to coupled channel models incorporating the Λ(1405) dynamics, fails to reproduce these data. A standard relativistic mean field (RMF) potential, disregarding the Λ(1405) dynamics at low densities, also fails. The only successful model is a hybrid of a theoretically motivated RMF approach in the nuclear interior and a completely phenomenological density dependent potential, which respects the low density theorem in the nuclear surface region. This best-fit K- optical potential is found to be strongly attractive, with a depth of 180+/-20 MeV at the nuclear interior, in agreement with previous phenomenological analyses.

  3. Systematic nuclear structure studies using relativistic mean field theory in mass region A ˜ 130

    NASA Astrophysics Data System (ADS)

    Shukla, A.; Åberg, Sven; Bajpeyi, Awanish

    2017-02-01

    Nuclear structure studies for even-even nuclei in the mass region \\backsim 130, have been performed, with a special focus around N or Z = 64. On the onset of deformation and lying between two closed shell, these nuclei have attracted attention in a number of studies. A revisit to these experimentally accessible nuclei has been made via the relativistic mean field. The role of pairing and density depletion in the interior has been specially investigated. Qualitative analysis between two versions of relativistic mean field suggests that there is no significant difference between the two approaches. Moreover, the role of the filling {{{s}}}1/2 orbital in density depletion towards the centre has been found to be consistent with our earlier work on the subject Shukla and Åberg (2014 Phys. Rev. C 89 014329).

  4. 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.

  5. A Study of Multi-Λ Hypernuclei Within Spherical Relativistic Mean-Field Approach

    NASA Astrophysics Data System (ADS)

    Rather, Asloob A.; Ikram, M.; Usmani, A. A.; Kumar, B.; Patra, S. K.

    2017-09-01

    This research article is a follow up of an earlier work by M. Ikram et al., reported in Int. J. Mod. Phys. E 25, 1650103 (2016) where we searched for Λ magic numbers in experimentally confirmed doubly magic nucleonic cores in light to heavy mass region (i.e., 16 O-208 P b) by injecting Λ's into them. In the present manuscript, working within the state of the art relativistic mean field theory with the inclusion of ΛN and ΛΛ interaction in addition to nucleon-meson NL 3∗ effective force, we extend the search of lambda magic numbers in multi- Λ hypernuclei using the predicted doubly magic nucleonic cores 292120, 304120, 360132, 370132, 336138, 396138 of the elusive superheavy mass regime. In analogy to well established signatures of magicity in conventional nuclear theory, the prediction of hypernuclear magicities is made on the basis of one-, two- Λ separation energy (S Λ,S 2Λ) and two lambda shell gaps (δ 2Λ) in multi- Λ hypernuclei. The calculations suggest that the Λ numbers 92, 106, 126, 138, 184, 198, 240, and 258 might be the Λ shell closures after introducing the Λ's in the elusive superheavy nucleonic cores. The appearance of new lambda shell closures apart from the nucleonic ones predicted by various relativistic and non-relativistic theoretical investigations can be attributed to the relatively weak strength of the spin-orbit coupling in hypernuclei compared to normal nuclei. Further, the predictions made in multi- Λ hypernuclei under study resembles closely the magic numbers in conventional nuclear theory suggested by various relativistic and non-relativistic theoretical models. Moreover, in support of the Λ shell closure, the investigation of Λ pairing energy and effective Λ pairing gap has been made. We noticed a very close agreement of the predicted Λ shell closures with the survey made on the pretext of S Λ, S 2Λ, and δ 2Λ except for the appearance of magic numbers corresponding to Λ = 156 which manifest in Λ effective

  6. Tidal deformability of neutron and hyperon stars within relativistic mean field equations of state

    NASA Astrophysics Data System (ADS)

    Kumar, Bharat; Biswal, S. K.; Patra, S. K.

    2017-01-01

    We systematically study the tidal deformability for neutron and hyperon stars using relativistic mean field equations of state (EOSs). The tidal effect plays an important role during the early part of the evolution of compact binaries. Although, the deformability associated with the EOSs has a small correction, it gives a clean gravitational wave signature in binary inspiral. These are characterized by various Love numbers kl(l =2 ,3 ,4 ), that depend on the EOS of a star for a given mass and radius. The tidal effect of star could be efficiently measured through an advanced LIGO detector from the final stages of an inspiraling binary neutron star merger.

  7. Relative fragmentation in ternary systems within the temperature-dependent relativistic mean-field approach

    NASA Astrophysics Data System (ADS)

    Kannan, M. T. Senthil; Kumar, Bharat; Balasubramaniam, M.; Agrawal, B. K.; Patra, S. K.

    2017-06-01

    For the first time, we apply the temperature-dependent relativistic mean-field (TRMF) model to study the ternary fragmentation of heavy nuclei using the level density approach. The relative fragmentation probability of a particular fragment is obtained by evaluating the convolution integrals that employ the excitation energy and the level density parameter for a given temperature calculated within the TRMF formalism. To illustrate, we have considered the ternary fragmentations in 252Cf, 242Pu, and 236U with a fixed third fragment A3=48Ca , 20O, and 16O, respectively. The relative fragmentation probabilities are studied for the temperatures T =1 , 2, and 3 MeV. For the comparison, the relative fragmentation probabilities are also calculated from the single-particle energies of the finite range droplet model (FRDM). In general, the larger phase space for the ternary fragmentation is observed indicating that such fragmentations are most probable ones. For T =2 and 3 MeV, Sn +Ni +Ca is the most probable combination for the nucleus 252Cf. However, for the nuclei 242Pu and 236U, the maximum fragmentation probabilities at T =2 MeV differ from those at T =3 MeV. For T =3 MeV, the closed shell (Z =8 ) light-mass fragment with its corresponding partners has larger scission point probabilities. But, at T =2 MeV, Si, P, and S are favorable fragments with the corresponding partners. It is noticed that the symmetric binary fragmentation along with the fixed third fragment for 242Pu and 236U is also favored at T =1 MeV.

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

    SciTech Connect

    Uechi, Schun T.; Uechi, Hiroshi

    2011-10-21

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

  9. 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

  10. Dynamical mean field solution of the Bose-Hubbard model.

    PubMed

    Anders, Peter; Gull, Emanuel; Pollet, Lode; Troyer, Matthias; Werner, Philipp

    2010-08-27

    We present the effective action and self-consistency equations for the bosonic dynamical mean field approximation to the bosonic Hubbard model and show that it provides remarkably accurate phase diagrams and correlation functions. To solve the bosonic dynamical mean field equations, we use a continuous-time Monte Carlo method for bosonic impurity models based on a diagrammatic expansion in the hybridization and condensate coupling. This method is readily generalized to bosonic mixtures, spinful bosons, and Bose-Fermi mixtures.

  11. 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.

  12. 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.

  13. Mean-field fluid behavior of the gaussian core model

    PubMed

    Louis; Bolhuis; Hansen

    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.

  14. 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.

  15. 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.

  16. Incorporating spatial correlations into multispecies mean-field models

    NASA Astrophysics Data System (ADS)

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

    2013-11-01

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

  17. 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.

  18. Asymptotics of Mean-Field O( N) Models

    NASA Astrophysics Data System (ADS)

    Kirkpatrick, Kay; Nawaz, Tayyab

    2016-12-01

    We study mean-field classical N-vector models, for integers N≥2. We use the theory of large deviations and Stein's method to study the total spin and its typical behavior, specifically obtaining non-normal limit theorems at the critical temperatures and central limit theorems away from criticality. Important special cases of these models are the XY (N=2) model of superconductors, the Heisenberg (N=3) model [previously studied in Kirkpatrick and Meckes (J Stat Phys 152:54-92, 2013) but with a correction to the critical distribution here], and the Toy (N=4) model of the Higgs sector in particle physics.

  19. 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.

  20. A Monte Carlo investigation of the Hamiltonian mean field model

    NASA Astrophysics Data System (ADS)

    Pluchino, Alessandro; Andronico, Giuseppe; Rapisarda, Andrea

    2005-04-01

    We present a Monte Carlo numerical investigation of the Hamiltonian mean field (HMF) model. We begin by discussing canonical Metropolis Monte Carlo calculations, in order to check the caloric curve of the HMF model and study finite size effects. In the second part of the paper, we present numerical simulations obtained by means of a modified Monte Carlo procedure with the aim to test the stability of those states at minimum temperature and zero magnetization (homogeneous Quasi stationary states), which exist in the condensed phase of the model just below the critical point. For energy densities smaller than the limiting value U∼0.68, we find that these states are unstable confirming a recent result on the Vlasov stability analysis applied to the HMF model.

  1. Some Observations for Mean-Field Spin Glass Models

    NASA Astrophysics Data System (ADS)

    Starr, Shannon; Vermesi, Brigitta

    2008-03-01

    We obtain bounds to show that the pressure of a two-body, mean-field spin glass is a Lipschitz function of the underlying distribution of the random coupling constants, with respect to a particular semi-norm. This allows us to re-derive a result of Carmona and Hu, on the universality of the SK model, by a different proof, and to generalize this result to the Viana Bray model. We also prove another bound, suitable when the coupling constants are not independent, which is what is necessary if one wants to consider “canonical” instead of “grand canonical” versions of the SK and Viana Bray models. Finally, we review Viana Bray type models, using the language of Lévy processes, which is natural in this context.

  2. Topological properties of the mean-field ϕ4 model

    NASA Astrophysics Data System (ADS)

    Andronico, A.; Angelani, L.; Ruocco, G.; Zamponi, F.

    2004-10-01

    We study the thermodynamics and the properties of the stationary points (saddles and minima) of the potential energy for a ϕ4 mean-field model. We compare the critical energy vc [i.e., the potential energy v(T) evaluated at the phase transition temperature Tc ] with the energy vθ at which the saddle energy distribution show a discontinuity in its derivative. We find that, in this model, vc≫vθ , at variance to what has been found in different mean-field and short ranged systems, where the thermodynamic phase transitions take place at vc=vθ [Casetti, Pettini and Cohen, Phys. Rep. 337, 237 (2000)]. By direct calculation of the energy vs(T) of the “inherent saddles,” i.e., the saddles visited by the equilibrated system at temperature T , we find that vs(Tc)˜vθ . Thus, we argue that the thermodynamic phase transition is related to a change in the properties of the inherent saddles rather than to a change of the topology of the potential energy surface at T=Tc . Finally, we discuss the approximation involved in our analysis and the generality of our method.

  3. Chaos in the Hamiltonian mean-field model

    NASA Astrophysics Data System (ADS)

    Ginelli, Francesco; Takeuchi, Kazumasa A.; Chaté, Hugues; Politi, Antonio; Torcini, Alessandro

    2011-12-01

    We study the dynamical properties of the canonical ordered phase of the Hamiltonian mean-field (HMF) model, in which N particles, globally coupled via pairwise attractive interactions, form a rotating cluster. Using a combination of numerical and analytical arguments, we first show that the largest Lyapunov exponent remains strictly positive in the infinite-size limit, converging to its asymptotic value with 1/lnN corrections. We then elucidate the scaling laws ruling the behavior of this asymptotic value in the critical region separating the ordered, clustered phase and the disordered phase present at high-energy densities. We also show that the full spectrum of Lyapunov exponents consists of a bulk component converging to the (zero) value taken by a test oscillator forced by the mean field, plus subextensive bands of O(lnN) exponents taking finite values. We finally investigate the robustness of these results by studying a “2D” extension of the HMF model where each particle is endowed with 4 degrees of freedom, thus allowing the emergence of chaos at the level of a single particle. Altogether, these results illustrate the subtle effects of global (or long-range) coupling and the importance of the order in which the infinite-time and infinite-size limits are taken: For an infinite-size HMF system represented by the Vlasov equation, no chaos is present, while chaos exists and subsists for any finite system size.

  4. 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.

  5. The Thermodynamic Limit in Mean Field Spin Glass Models

    NASA Astrophysics Data System (ADS)

    Guerra, Francesco; Toninelli, Fabio Lucio

    We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and the Derrida p-spin model. The main argument is based on a smooth interpolation between a large system, made of N spin sites, and two similar but independent subsystems, made of N1 and N2 sites, respectively, with N1+N2=N. The quenched average of the free energy turns out to be subadditive with respect to the size of the system. This gives immediately convergence of the free energy per site, in the infinite volume limit. Moreover, a simple argument, based on concentration of measure, gives the almost sure convergence, with respect to the external noise. Similar results hold also for the ground state energy per site.

  6. Mean-field vs. Stochastic Models for Transcriptional Regulation

    NASA Astrophysics Data System (ADS)

    Blossey, Ralf; Giuraniuc, Claudiu

    2009-03-01

    We introduce a minimal model description for the dynamics of transcriptional regulatory networks. It is studied within a mean-field approximation, i.e., by deterministic ode's representing the reaction kinetics, and by stochastic simulations employing the Gillespie algorithm. We elucidate the different results both approaches can deliver, depending on the network under study, and in particular depending on the level of detail retained in the respective description. Two examples are addressed in detail: the repressilator, a transcriptional clock based on a three-gene network realized experimentally in E. coli, and a bistable two-gene circuit under external driving, a transcriptional network motif recently proposed to play a role in cellular development.

  7. Mean-field versus stochastic models for transcriptional regulation

    NASA Astrophysics Data System (ADS)

    Blossey, R.; Giuraniuc, C. V.

    2008-09-01

    We introduce a minimal model description for the dynamics of transcriptional regulatory networks. It is studied within a mean-field approximation, i.e., by deterministic ODE’s representing the reaction kinetics, and by stochastic simulations employing the Gillespie algorithm. We elucidate the different results that both approaches can deliver, depending on the network under study, and in particular depending on the level of detail retained in the respective description. Two examples are addressed in detail: The repressilator, a transcriptional clock based on a three-gene network realized experimentally in E. coli, and a bistable two-gene circuit under external driving, a transcriptional network motif recently proposed to play a role in cellular development.

  8. 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.

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

    PubMed

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

    2011-12-21

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

  10. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2015-09-01

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

  12. 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.

  13. 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.

  14. Study of high-energy heavy-ion collisions in a relativistic BUU approach with momentum-dependent mean fields

    NASA Astrophysics Data System (ADS)

    Tomoyuki, Maruyama; Wolfgang, Cassing; Ulrich, Mosel; Stefan, Teis; Klaus, Weber

    1994-06-01

    We introduce momentum-dependent scalar and vector fields into the Lorentz covariant relativistic BUU (RBUU) approach employing a polynomial ansatz for the relativistic nucleon-nucleon interaction. The momentum-dependent parametrizations are shown to be valid up to about 1 GeV/u for the empirical proton-nucleus optical potential. We perform numerical simulations for heavy-ion collisions within the RBUU approach adopting momentum-dependent and momentum-independent mean fields and calculate the transverse flow in and perpendicular to the reaction plane, the directivity distribution as well as subthreshold K +-production. By means of these observables we discuss the particular role of the momentum-dependent forces and their implications on the nuclear equation of state. We find that only a momentum-dependent parameter set can explain the experimental data on the transverse flow in the reaction plane from 150-1000 MeV/u and the differential K +-production cross sections at 1 GeV/u at the same time.

  15. Deformed neutron stars due to strong magnetic field in terms of relativistic mean field theories

    NASA Astrophysics Data System (ADS)

    Yanase, Kota; Yoshinaga, Naotaka

    2014-09-01

    Some observations suggest that magnetic field intensity of neutron stars that have particularly strong magnetic field, magnetars, reaches values up to 1014-15G. It is expected that there exists more strong magnetic field of several orders of magnitude in the interior of such stars. Neutron star matter is so affected by magnetic fields caused by intrinsic magnetic moments and electric charges of baryons that masses of neutron stars calculated by using Tolman-Oppenheimer-Volkoff equation is therefore modified. We calculate equation of state (EOS) in density-dependent magnetic field by using sigma-omega-rho model that can reproduce properties of stable nuclear matter in laboratory Furthermore we calculate modified masses of deformed neutron stars.

  16. Neural Population Dynamics Modeled by Mean-Field Graphs

    NASA Astrophysics Data System (ADS)

    Kozma, Robert; Puljic, Marko

    2011-09-01

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

  17. {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.

  18. 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.

  19. Tuning of the mean-field geodynamo model

    NASA Astrophysics Data System (ADS)

    Reshetnyak, M. Yu.

    2017-07-01

    Parker's two-dimensional (2D) dynamo model with an algebraic form of nonlinearity for the α-effect is considered. The model uses geostrophic distributions for the α-effect and differential rotation, which are derived from the three-dimensional (3D) convection models. The resulting configurations of the magnetic field in the liquid core are close to the solutions in Braginsky's Z-model. The implications of the degree of geostrophy observed in the 3D dynamo models for the behavior of the mean magnetic field are explored. It is shown that the reduction in geostrophy leads to magnetic field reversals accompanied by the relative growth of the nondipole component of the field on the surface of the liquid core. The simulations with a random α-effect which causes turbulent pulsations are carried out. The approach is capable of producing realistic sequences of magnetic reversals.

  20. 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.

  1. Bound-state energy of double magic number plus one nucleon nuclei with relativistic mean-field approach

    NASA Astrophysics Data System (ADS)

    Mousavi, M.; Shojaei, M. R.

    2017-02-01

    In this work, we have obtained energy levels and charge radius for the β-stability line nucleus, in relativistic shell model. In this model, we considered a close shell for each nucleus containing double magic number and a single nucleon energy level. Here we have taken 41Ca with a single neutron in the 40Ca core as an illustrative example. Then we have selected the Eckart plus Hulthen potentials for interaction between the core and the single nucleon. By using parametric Nikiforov-Uvarov (PNU) method, we have calculated the energy values and wave function. Finally, we have calculated the charge radius for 17O, 41Ca, 49Ca and 57Ni. Our results are in agreement with experimental values and hence this model can be applied for similar nuclei.

  2. Mean-Field Models of Structure and Dispersion of Polymer-nanoparticle Mixtures

    DTIC Science & Technology

    2010-07-29

    bare polymer matrix by as much as an order of magnitude.2,3,12–14 Gas barrier properties of butyl rubber latexes was shown to be reduced by almost 2...research developments in coarse-grained modeling based on mean-field approaches of the equilibrium dispersion and structure of polymer nanoparticle...polymernanoparticle mixtures Report Title ABSTRACT We review some recent research developments in coarse-grained modeling based on mean-field approaches of the

  3. MODEL STUDY OF THE SIGN PROBLEM IN A MEAN-FIELD APPROXIMATION.

    SciTech Connect

    HIDAKA,Y.

    2007-07-30

    We study the sign problem of the fermion determinant at nonzero baryon chemical potential. For this purpose we apply a simple model derived from Quantum Chromodynamics, in the limit of large chemical potential and mass. For SU(2) color, there is no sign problem and the mean-field approximation is similar to data from the lattice. For SU(3) color the sign problem is unavoidable, even in a mean-field approximation. We apply a phase-reweighting method, combined with the mean-field approximation, to estimate thermodynamic quantities. We also investigate the meanfield free energy using a saddle-point approximation [1].

  4. A Tractable Complex Network Model Based onthe Stochastic Mean-Field Model of Distance

    NASA Astrophysics Data System (ADS)

    Aldous, David J.

    Much recent research activity has been devoted to empirical study and theoretical models of complex networks (random graphs) possessing three qualitative features: power-law degree distributions, local clustering, and slowly-growing diameter. We point out a new (in this context) platform for such models - the stochastic mean-field model of distances - and within this platform study a simple two-parameter proportional attachment (or copying) model. The model is mathematically natural, permits a wide variety of explicit calculations, has the desired three qualitative features, and fits the complete range of degree scaling exponents and clustering parameters; in these respects it compares favorably with existing models.

  5. Mean-field approximation for the potts model of a diluted magnet in the external field

    NASA Astrophysics Data System (ADS)

    Semkin, S. V.; Smagin, V. P.

    2016-07-01

    The Potts model of a diluted magnet with an arbitrary number of states placed in the external field has been considered. Phase transitions of this model have been studied in the mean-field approximation, the dependence of the critical temperature on the external field and the density of magnetic atoms has been found, and the magnetic susceptibility has been calculated. An improved mean-field technique has been proposed, which provides more accurate account of the effects associated with nonmagnetic dilution. The influence of dilution on the first-order phase transition curve and the magnetization jump at the phase transition has been studied by this technique.

  6. 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.

  7. 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

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

    PubMed

    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.

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

    NASA Astrophysics Data System (ADS)

    Simard, Corinne; Charbonneau, Paul; Bouchat, Amélie

    2013-05-01

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

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

    SciTech Connect

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

    2013-05-01

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

  11. Model-independent mean-field theory as a local method for approximate propagation of information.

    PubMed

    Haft, M; Hofmann, R; Tresp, V

    1999-02-01

    We present a systematic approach to mean-field theory (MFT) in a general probabilistic setting without assuming a particular model. The mean-field equations derived here may serve as a local, and thus very simple, method for approximate inference in probabilistic models such as Boltzmann machines or Bayesian networks. Our approach is 'model-independent' in the sense that we do not assume a particular type of dependences; in a Bayesian network, for example, we allow arbitrary tables to specify conditional dependences. In general, there are multiple solutions to the mean-field equations. We show that improved estimates can be obtained by forming a weighted mixture of the multiple mean-field solutions. Simple approximate expressions for the mixture weights are given. The general formalism derived so far is evaluated for the special case of Bayesian networks. The benefits of taking into account multiple solutions are demonstrated by using MFT for inference in a small and in a very large Bayesian network. The results are compared with the exact results.

  12. Quark mean field model with pion and gluon corrections for Λ and Ξ0 hypernuclei and neutron stars

    NASA Astrophysics Data System (ADS)

    Xing, Xueyong; Hu, Jinniu; Shen, Hong

    2017-05-01

    Properties of Λ and Ξ0 hypernuclei and neutron stars are investigated in a quark mean field model with pion and gluon corrections. First, u , d , and s quarks are confined by relativistic harmonic oscillator potentials to generate baryons, such as nucleons and Λ , Σ , and Ξ hyperons. The effects of pion-quark coupling and one-gluon exchange are considered perturbatively. Then, the baryons interact with each other through exchanging σ , ω , and ρ mesons between quarks in hypernuclei and nuclear matter. The strengths of confinement potentials for u , d , and s quarks are determined by the masses and radii of free baryons. The coupling constants between the quarks and mesons are fixed by the ground-state properties of several nuclei and single-hyperon potentials at nuclear saturation density, which yields three parameter sets for the coupling constants between mesons and quarks, named QMF-NK1S, QMF-NK2S, and QMF-NK3S. Compared to the results of the previous quark mean field model without pion and gluon corrections, it is found that properties of Λ hypernuclei, i.e., the single-Λ energies, are more consistent with the experimental observables. Properties of Ξ0 hypernuclei are also calculated and compared with the results in the previous quark mean field model. With these three parameter sets, the neutron stars containing hyperons are investigated through solving the Tolman-Oppenheimer-Volkoff equation. Maximum masses of neutron stars approach 2.1 M⊙ with hyperons, and corresponding radii are around 13 km.

  13. Going Beyond a Mean-field Model for the Learning Cortex: Second-Order Statistics

    PubMed Central

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

    2008-01-01

    Mean-field models of the cortex have been used successfully to interpret the origin of features on the electroencephalogram under situations such as sleep, anesthesia, and seizures. In a mean-field scheme, dynamic changes in synaptic weights can be considered through fluctuation-based Hebbian learning rules. However, because such implementations deal with population-averaged properties, they are not well suited to memory and learning applications where individual synaptic weights can be important. We demonstrate that, through an extended system of equations, the mean-field models can be developed further to look at higher-order statistics, in particular, the distribution of synaptic weights within a cortical column. This allows us to make some general conclusions on memory through a mean-field scheme. Specifically, we expect large changes in the standard deviation of the distribution of synaptic weights when fluctuation in the mean soma potentials are large, such as during the transitions between the “up” and “down” states of slow-wave sleep. Moreover, a cortex that has low structure in its neuronal connections is most likely to decrease its standard deviation in the weights of excitatory to excitatory synapses, relative to the square of the mean, whereas a cortex with strongly patterned connections is most likely to increase this measure. This suggests that fluctuations are used to condense the coding of strong (presumably useful) memories into fewer, but dynamic, neuron connections, while at the same time removing weaker (less useful) memories. PMID:19669541

  14. Mean-field-like behavior of the generalized voter-model-class kinetic Ising model

    NASA Astrophysics Data System (ADS)

    Krause, Sebastian M.; Böttcher, Philipp; Bornholdt, Stefan

    2012-03-01

    We analyze a kinetic Ising model with suppressed bulk noise, which is a prominent representative of the generalized voter model phase transition. On the one hand, we discuss the model in the context of social systems and opinion formation in the presence of a tunable social temperature. On the other hand, we characterize the abrupt phase transition. The system shows nonequilibrium dynamics in the presence of absorbing states. We slightly change the system to get a stationary-state model variant exhibiting the same kind of phase transition. Using a Fokker-Planck description and comparing to mean-field calculations, we investigate the phase transition, finite-size effects, and the effect of the absorbing states resulting in a dynamic slowing down.

  15. A self-consistent mean-field model for polyelectrolyte gels.

    PubMed

    Rud, Oleg; Richter, Tobias; Borisov, Oleg; Holm, Christian; Košovan, Peter

    2017-03-01

    We present a novel approach to modeling polyelectrolyte gels, exploiting the analogy between star-branched polymers and polymer networks as a computationally inexpensive yet reliable alternative to full-scale simulations. In the numerical mean-field model of a star-like polymer we modify the boundary conditions to represent an infinite network. We validate the predictions of our new model against a coarse-grained simulation model. We also validate it against a phenomenological analytical model which has been previously shown to agree with simulations in a limited range of parameters. The mean-field model explicitly considers local density gradients and agrees with the simulation results in a broad range of parameters, beyond that of the analytical model. Finally, we use the mean-field model for predictions of the swelling behaviour of weak polyelectrolyte gels under different pH conditions. We demonstrate that the local density gradients are important and that the ionization of the weak polyelectrolyte gel is significantly suppressed. Under the studied conditions the effective pKA is about one unit higher than that of the free monomer. This shift in the effective pKA stems from the different pH values inside and outside the gel.

  16. Exact solution of the mean-field plus separable pairing model reexamined

    NASA Astrophysics Data System (ADS)

    Pan, Feng; Zhou, Dan; Dai, Lianrong; Draayer, J. P.

    2017-03-01

    Exact solution of the nuclear mean-field plus separable pairing model is reexamined. New auxiliary constraints for solving the Bethe ansatz equations of the model are proposed. By using these auxiliary constraints, the Bethe ansatz form of eigenvectors of the mean-field plus separable pairing Hamiltonian with nondegenerate single-particle energies and nondegenerate separable pairing strengths purposed previously is verified. Since the solutions of the model with one- and two-orbit cases are known, verification of the solutions for these two special cases is made. To demonstrate structure and features of the solution, the model with three orbits in the d s shell is taken as a nontrivial example, of which two-pair results and the ground state of the three-pair case are provided explicitly. Since the number of equations involved increases with the number of orbits and pairs, to solve these equations for a large number of orbits and pairs seems still difficult.

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

    PubMed

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

    2016-04-01

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

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

    SciTech Connect

    Kahana, S.; Ripka, G.

    1983-01-01

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

  19. Mean field theory of the linear sigma-model: Chiral solitons

    NASA Astrophysics Data System (ADS)

    Kahana, S.; Ripka, G.

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

  20. Phase transition in a mean-field model for sympatric speciation

    NASA Astrophysics Data System (ADS)

    Schwämmle, V.; Luz-Burgoa, K.; Sá Martins, J. S.; de Oliveira, S. Moss

    2006-09-01

    We introduce an analytical model for population dynamics with intra-specific competition, mutation and assortative mating as basic ingredients. The set of equations that describes the time evolution of population size in a mean-field approximation may be decoupled. We find a phase transition leading to sympatric speciation as a parameter that quantifies competition strength is varied. This transition, previously found in a computational model, occurs to be of first order.

  1. Mean field theory of the linear sigma-model: Chiral solitons

    SciTech Connect

    Kahana, S.; Ripka, G.

    1984-02-20

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

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

    SciTech Connect

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

    2015-12-28

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

  3. Octupole degree of freedom for the critical-point candidate nucleus Sm152 in a reflection-asymmetric relativistic mean-field approach

    NASA Astrophysics Data System (ADS)

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

    2010-03-01

    The potential energy surfaces of even-even Sm146-156 are investigated in the constrained reflection-asymmetric relativistic mean-field approach with parameter set PK1. It is shown that the critical-point candidate nucleus Sm152 marks the shape/phase transition not only from U(5) to SU(3) symmetry, but also from the octupole-deformed ground state in Sm150 to the quadrupole-deformed ground state in Sm154. By including the octupole degree of freedom, an energy gap near the Fermi surface for single-particle levels in Sm152 with β2=0.14~0.26 is found and the important role of the octupole deformation driving pair ν2f7/2 and ν1i13/2 is demonstrated.

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

    SciTech Connect

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

    2010-03-15

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

  5. A mean-field monomer-dimer model with attractive interaction: Exact solution and rigorous results

    SciTech Connect

    Alberici, D. Contucci, P. Mingione, E.

    2014-06-15

    A mean-field monomer-dimer model which includes an attractive interaction among both monomers and dimers is introduced and its exact solution rigorously derived. The Heilmann-Lieb method for the pure hard-core interacting case is used to compute upper and lower bounds for the pressure. The bounds are shown to coincide in the thermodynamic limit for a suitable choice of the monomer density m. The computation of the monomer density is achieved by solving a consistency equation in the phase space (h, J), where h tunes the monomer potential and J the attractive potential. The critical point and exponents are computed and show that the model is in the mean-field ferromagnetic universality class.

  6. Mott transition in the dynamic Hubbard model within slave boson mean-field approach

    NASA Astrophysics Data System (ADS)

    Le, Duc-Anh

    2014-04-01

    At zero temperature, the Kotliar-Ruckenstein slave boson mean-field approach is applied to the dynamic Hubbard model. In this paper, the influences of the dynamics of the auxiliary boson field on the Mott transition are investigated. At finite boson frequency, the Mott-type features of the Hubbard model is found to be enhanced by increasing the pseudospin coupling parameter g. For sufficiently large pseudospin coupling g, the Mott transition occurs even for modest values of the bare Hubbard interaction U. The lack of electron-hole symmetry is highlighted through the quasiparticle weight. Our results are in good agreement with the ones obtained by two-site dynamical mean-field theory and determinant quantum Monte Carlo simulation.

  7. Truncated Lévy flights and weak ergodicity breaking in the Hamiltonian mean-field model

    NASA Astrophysics Data System (ADS)

    Figueiredo, A.; Filho, T. M. Rocha; Amato, M. A.; Oliveira, Z. T.; Matsushita, R.

    2014-02-01

    The dynamics of the Hamiltonian mean-field model is studied in the context of continuous-time random walks. We show that the sojourn times in cells in the momentum space are well described by a one-sided truncated Lévy distribution. Consequently, the system is nonergodic for long observation times that diverge with the number of particles. Ergodicity is attained only after very long times both at thermodynamic equilibrium and at quasistationary out-of-equilibrium states.

  8. Truncated Lévy flights and weak ergodicity breaking in the Hamiltonian mean-field model.

    PubMed

    Figueiredo, A; Filho, T M Rocha; Amato, M A; Oliveira, Z T; Matsushita, R

    2014-02-01

    The dynamics of the Hamiltonian mean-field model is studied in the context of continuous-time random walks. We show that the sojourn times in cells in the momentum space are well described by a one-sided truncated Lévy distribution. Consequently, the system is nonergodic for long observation times that diverge with the number of particles. Ergodicity is attained only after very long times both at thermodynamic equilibrium and at quasistationary out-of-equilibrium states.

  9. Application of mean-field model of polymer melt intercalation in organo-silicates for nanocomposites.

    PubMed

    Meneghetti, Paulo; Qutubuddin, Syed

    2005-08-15

    The mean-field, lattice-based model of polymer melt intercalation in organically-modified layered silicates (OLS) originally developed by Vaia and Giannelis was applied for different polymers such as poly(methyl methacrylate) (PMMA), polypropylene (PP), and poly(ethylene oxide) (PEO). The nature of each polymer controls significantly the intercalation of the system. The internal energy change caused by the interaction of polymer, surfactant and clay is the strongest factor in determining the equilibrium structure of the nanocomposite system.

  10. Modeling relativistic nuclear collisions.

    SciTech Connect

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

    2001-01-01

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

  11. Mean field study of a propagation-turnover lattice model for the dynamics of histone marking

    NASA Astrophysics Data System (ADS)

    Yao, Fan; Li, FangTing; Li, TieJun

    2017-02-01

    We present a mean field study of a propagation-turnover lattice model, which was proposed by Hodges and Crabtree [Proc. Nat. Acad. Sci. 109, 13296 (2012)] for understanding how posttranslational histone marks modulate gene expression in mammalian cells. The kinetics of the lattice model consists of nucleation, propagation and turnover mechanisms, and exhibits second-order phase transition for the histone marking domain. We showed rigorously that the dynamics essentially depends on a non-dimensional parameter κ = k +/ k -, the ratio between the propagation and turnover rates, which has been observed in the simulations. We then studied the lowest order mean field approximation, and observed the phase transition with an analytically obtained critical parameter. The boundary layer analysis was utilized to investigate the structure of the decay profile of the mark density. We also studied the higher order mean field approximation to achieve sharper estimate of the critical transition parameter and more detailed features. The comparison between the simulation and theoretical results shows the validity of our theory.

  12. Generalized Keller-Segel Models of Chemotaxis: Analogy with Nonlinear Mean Field Fokker-Planck Equations

    NASA Astrophysics Data System (ADS)

    Chavanis, Pierre-Henri

    We consider a generalized class of Keller-Segel models describing the chemo-taxis of biological populations (bacteria, amoebae, endothelial cells, social insects,…). We show the analogy with nonlinear mean field Fokker-Planck equations and generalized thermodynamics. As an illustration, we introduce a new model of chemotaxis incorporating both effects of anomalous diffusion and exclusion principle (volume filling). We also discuss the analogy between biological populations described by the Keller-Segel model and self-gravitating Brownian particles described by the Smoluchowski-Poisson system.

  13. 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.

  14. Mean Field Limit and Propagation of Chaos for a Pedestrian Flow Model

    NASA Astrophysics Data System (ADS)

    Chen, Li; Göttlich, Simone; Yin, Qitao

    2017-01-01

    In this paper a rigorous proof of the mean field limit for a pedestrian flow model in two dimensions is given by using a probabilistic method. The model under investigation is an interacting particle system coupled to the eikonal equation on the microscopic scale. For stochastic initial data, it is proved that the solution of the N-particle pedestrian flow system with properly chosen cut-off converges in the probability sense to the solution of the characteristics of the non-cut-off Vlasov equation. Furthermore, the result on propagation of chaos is also deduced in terms of bounded Lipschitz distance.

  15. Mean field lattice model for adsorption isotherms in zeolite NaA

    NASA Astrophysics Data System (ADS)

    Ayappa, K. G.; Kamala, C. R.; Abinandanan, T. A.

    1999-05-01

    Using a lattice model for adsorption in microporous materials, pure component adsorption isotherms are obtained within a mean field approximation for methane at 300 K and xenon at 300 and 360 K in zeolite NaA. It is argued that the increased repulsive adsorbate-adsorbate interactions at high coverages must play an important role in determining the adsorption behavior. Therefore, this feature is incorporated through a "coverage-dependent interaction" model, which introduces a free, adjustable parameter. Another important feature, the site volume reduction, has been treated in two ways: a van der Waal model and a 1D hard-rod theory [van Tassel et al., AIChE J. 40, 925 (1994)]; we have also generalized the latter to include all possible adsorbate overlap scenarios. In particular, the 1D hard-rod model, with our coverage-dependent interaction model, is shown to be in best quantitative agreement with the previous grand canonical Monte Carlo isotherms. The expressions for the isosteric heats of adsorption indicate that attractive and repulsive adsorbate-adsorbate interactions increase and decrease the heats of adsorption, respectively. It is concluded that within the mean field approximation, our simple model for repulsive interactions and the 1D hard-rod model for site volume reduction are able to capture most of the important features of adsorption in confined regions.

  16. Elementary proof of convergence to the mean-field model for the SIR process.

    PubMed

    Armbruster, Benjamin; Beck, Ekkehard

    2016-12-21

    The susceptible-infected-recovered (SIR) model has been used extensively to model disease spread and other processes. Despite the widespread usage of this ordinary differential equation (ODE) based model which represents the mean-field approximation of the underlying stochastic SIR process on contact networks, only few rigorous approaches exist and these use complex semigroup and martingale techniques to prove that the expected fraction of the susceptible and infected nodes of the stochastic SIR process on a complete graph converges as the number of nodes increases to the solution of the mean-field ODE model. Extending the elementary proof of convergence for the SIS process introduced by Armbruster and Beck (IMA J Appl Math, doi: 10.1093/imamat/hxw010 , 2016) to the SIR process, we show convergence using only a system of three ODEs, simple probabilistic inequalities, and basic ODE theory. Our approach can also be generalized to many other types of compartmental models (e.g., susceptible-infected-recovered-susceptible (SIRS)) which are linear ODEs with the addition of quadratic terms for the number of new infections similar to the SI term in the SIR model.

  17. Self-Consistent Chaotic Transport in a High-Dimensional Mean-Field Hamiltonian Map Model

    DOE PAGES

    Martínez-del-Río, D.; del-Castillo-Negrete, D.; Olvera, A.; ...

    2015-10-30

    We studied the self-consistent chaotic transport in a Hamiltonian mean-field model. This model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Self-consistency is incorporated through a mean-field that couples all the degrees-of-freedom. The model is formulated as a large set of N coupled standard-like area-preserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherentmore » structures. Furthermore, numerical simulations show that self-consistency leads to the formation of a coherent macro-particle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a non-autonomous map that allows a detailed study of the onset of global transport. A turnstile-type transport mechanism that allows transport across instantaneous KAM invariant circles in non-autonomous systems is discussed. As a first step to understand transport, we study a special type of orbits referred to as sequential periodic orbits. Using symmetry properties we show that, through replication, high-dimensional sequential periodic orbits can be generated starting from low-dimensional periodic orbits. We show that sequential periodic orbits in the self-consistent map can be continued from trivial (uncoupled) periodic orbits of standard-like maps using numerical and asymptotic methods. Normal forms are used to describe these orbits and to find the values of the map parameters that guarantee their existence. Numerical simulations are used to verify the prediction from the asymptotic methods.« less

  18. Self-Consistent Chaotic Transport in a High-Dimensional Mean-Field Hamiltonian Map Model

    SciTech Connect

    Martínez-del-Río, D.; del-Castillo-Negrete, D.; Olvera, A.; Calleja, R.

    2015-10-30

    We studied the self-consistent chaotic transport in a Hamiltonian mean-field model. This model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Self-consistency is incorporated through a mean-field that couples all the degrees-of-freedom. The model is formulated as a large set of N coupled standard-like area-preserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherent structures. Furthermore, numerical simulations show that self-consistency leads to the formation of a coherent macro-particle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a non-autonomous map that allows a detailed study of the onset of global transport. A turnstile-type transport mechanism that allows transport across instantaneous KAM invariant circles in non-autonomous systems is discussed. As a first step to understand transport, we study a special type of orbits referred to as sequential periodic orbits. Using symmetry properties we show that, through replication, high-dimensional sequential periodic orbits can be generated starting from low-dimensional periodic orbits. We show that sequential periodic orbits in the self-consistent map can be continued from trivial (uncoupled) periodic orbits of standard-like maps using numerical and asymptotic methods. Normal forms are used to describe these orbits and to find the values of the map parameters that guarantee their existence. Numerical simulations are used to verify the prediction from the asymptotic methods.

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

    NASA Astrophysics Data System (ADS)

    Slanina, František

    2001-11-01

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

  20. Slave-boson mean field versus quantum Monte Carlo results for the Hubbard model

    NASA Astrophysics Data System (ADS)

    Lilly, L.; Muramatsu, A.; Hanke, W.

    1990-09-01

    The one-band Hubbard model is considered in the slave-boson formulation first introduced by Kotliar and Ruckenstein. It is shown that a mean-field approximation, where broken-symmetry states appropriate for a bipartite lattice are allowed, leads to a quantitative agreement with quantum Monte Carlo results for local observables over a wide range of interactions (0<=1). Thus, our saddle-point solutions constitute an excellent starting point for a systematic treatment of fluctuations.

  1. Metastability of Non-reversible, Mean-Field Potts Model with Three Spins

    NASA Astrophysics Data System (ADS)

    Landim, C.; Seo, I.

    2016-11-01

    We examine a non-reversible, mean-field Potts model with three spins on a set with N\\uparrow ∞ points. Without an external field, there are three critical temperatures and five different metastable regimes. The analysis can be extended by a perturbative argument to the case of small external fields, and it can be carried out in the case where the external field is in the direction or in the opposite direction to one of the values of the spins. Numerical computations permit to identify other phenomena which are not present in the previous situations.

  2. An exact solution of spherical mean-field plus a special separable pairing model

    NASA Astrophysics Data System (ADS)

    Dai, Lianrong; Pan, Feng; Draayer, J. P.

    2017-01-01

    An exact solution of nuclear spherical mean-field plus a special orbit-dependent separable pairing model is studied, of which the separable pairing interaction parameters are obtained by a linear fitting in terms of the single-particle energies considered. The advantage of the model is that, similar to the standard pairing case, it can be solved easily by using the extended Heine-Stieltjes polynomial approach. With the analysis of the model in the ds- and pf-shell subspace, it is shown that this special separable pairing model indeed provides similar pair structures of the model with the original separable pairing interaction, and is obviously better than the standard pairing model in many aspects.

  3. 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

  4. Free energy of mean-field spin-glass models: Evolution operator and perturbation expansion

    NASA Astrophysics Data System (ADS)

    Janiš, V.; Kauch, A.; Klíč, A.

    2013-02-01

    The full mean-field solution of spin glass models with a continuous order-parameter function is not directly available and approximate schemes must be used to assess its properties. One of the authors recently proposed a representation of the free energy generating this solution via an evolution operator parametrized by attainable values of overlap of magnetizations between different states. Here, we introduce a perturbation expansion for the evolution operator that we use to derive all thermodynamic characteristics via the standard methods of statistical mechanics. We obtain a generic scheme for an approximate calculation of physical quantities of different mean-field spin-glass models at all temperatures. The small expansion parameter is a difference between the continuous order-parameter function and the corresponding order parameter from the solution with one level of replica-symmetry breaking. The first correction beyond the approximation with one level of replica-symmetry breaking is explicitly evaluated in the glassy phase of the Sherrington-Kirkpatrick model.

  5. 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.

  6. 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.

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

    PubMed

    Yoshida, Ryo; West, Mike

    2010-05-01

    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.

  8. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2015-02-01

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

  10. Mean field model for synchronization of coupled two-state units and the effect of memory

    NASA Astrophysics Data System (ADS)

    Escaff, D.; Lindenberg, K.

    2014-01-01

    A prototypical model for a mean field second order transition is presented, which is based on an ensemble of coupled two-states units. This system is used as a basic model to study the effect of memory. To wit, we distinguish two types of memories: weak and strong, depending on the feasibility of linearizing the generalized mean field master equation. For weak memory we find static solutions that behave much like those of the memoryless (Markovian) system. The latter exhibits a pitchfork bifurcation as the control parameter is increased, with two stable and one unstable solution. The former exhibits an imperfect pitchfork bifurcation to states with the same behaviors. In both cases, the stability of the static solutions is analyzed via the usual linearization around the equilibrium solution. For strong memories we again find an imperfect pitchfork bifurcation, with two stable and one unstable branch. However, it is no longer possible to analyze these behaviors via the usual linearization, which is local in time, because a strong memory requires knowledge of the system for its entire past. Finally, we are pleased to dedicate this publication to Helmut Brand on the occasion of his 60th birthday.

  11. Anomalous mean-field behavior of the fully connected Ising model.

    PubMed

    Colonna-Romano, Louis; Gould, Harvey; Klein, W

    2014-10-01

    Although the fully connected Ising model does not have a length scale, we show that the critical exponents for thermodynamic quantities such as the mean magnetization and the susceptibility can be obtained using finite size scaling with the scaling variable equal to N, the number of spins. Surprisingly, the mean value and the most probable value of the magnetization are found to scale differently with N at the critical temperature of the infinite system, and the magnetization probability distribution is not a Gaussian, even for large N. Similar results inconsistent with the usual understanding of mean-field theory are found at the spinodal. We relate these results to the breakdown of hyperscaling and show that hyperscaling can be restored by increasing N while holding the Ginzburg parameter rather than the temperature fixed, or by doing finite size scaling at the pseudocritical temperature where the susceptibility is a maximum for a given value of N. We conclude that finite size scaling for the fully connected Ising model yields different results depending on how the mean-field limit is approached.

  12. Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model

    NASA Astrophysics Data System (ADS)

    Guerra, Francesco

    By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend this argument in order to compare the limiting free energy with the expression given by the Parisi Ansatz, and including full spontaneous replica symmetry breaking. Our main result is that the quenched average of the free energy is bounded from below by the value given in the Parisi Ansatz, uniformly in the size of the system. Moreover, the difference between the two expressions is given in the form of a sum rule, extending our previous work on the comparison between the true free energy and its replica symmetric Sherrington-Kirkpatrick approximation. We give also a variational bound for the infinite volume limit of the ground state energy per site.

  13. 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.

  14. 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.

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

    SciTech Connect

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

    2014-04-10

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

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

    NASA Astrophysics Data System (ADS)

    Coslovich, Daniele; Ikeda, Atsushi; Miyazaki, Kunimasa

    2016-04-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-08-01

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

  18. Quantum mean-field approximation for lattice quantum models: Truncating quantum correlations and retaining classical ones

    NASA Astrophysics Data System (ADS)

    Malpetti, Daniele; Roscilde, Tommaso

    2017-02-01

    The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical

  19. Mean-Field-Game Model for Botnet Defense in Cyber-Security

    SciTech Connect

    Kolokoltsov, V. N.; Bensoussan, A.

    2016-12-15

    We initiate the analysis of the response of computer owners to various offers of defence systems against a cyber-hacker (for instance, a botnet attack), as a stochastic game of a large number of interacting agents. We introduce a simple mean-field game that models their behavior. It takes into account both the random process of the propagation of the infection (controlled by the botner herder) and the decision making process of customers. Its stationary version turns out to be exactly solvable (but not at all trivial) under an additional natural assumption that the execution time of the decisions of the customers (say, switch on or out the defence system) is much faster that the infection rates.

  20. Collisional relaxation in the inhomogeneous Hamiltonian mean-field model: Diffusion coefficients

    NASA Astrophysics Data System (ADS)

    Benetti, F. P. C.; Marcos, B.

    2017-02-01

    Systems of particles with long-range interactions present two important processes: first, the formation of out-of-equilibrium quasistationary states (QSS) and, second, the collisional relaxation towards Maxwell-Boltzmann equilibrium in a much longer time scale. In this paper, we study the collisional relaxation in the Hamiltonian mean-field model using the appropriate kinetic equations for a system of N particles at order 1 /N : the Landau equation when collective effects are neglected and the Lenard-Balescu equation when they are taken into account. We derive explicit expressions for the diffusion coefficients using both equations for any magnetization, and we obtain analytic expressions for highly clustered configurations. An important conclusion is that in this system collective effects are crucial in order to describe the relaxation dynamics. We compare the diffusion calculated with the kinetic equations with simulations set up to simulate the system with or without collective effects, obtaining a very good agreement between theory and simulations.

  1. Extended dynamical mean-field study of the Hubbard model with long-range interactions

    NASA Astrophysics Data System (ADS)

    Huang, Li; Ayral, Thomas; Biermann, Silke; Werner, Philipp

    2014-11-01

    Using extended dynamical mean-field theory and its combination with the G W approximation, we compute the phase diagrams and local spectral functions of the single-band extended Hubbard model on the square and simple cubic lattices, considering long-range interactions up to the third nearest neighbors. The longer-range interactions shift the boundaries between the metallic, charge-ordered insulating, and Mott insulating phases, and lead to characteristic changes in the screening modes and local spectral functions. Momentum-dependent self-energy contributions enhance the correlation effects and thus compete with the additional screening effect from longer-range Coulomb interactions. Our results suggest that the influence of longer-range intersite interactions is significant, and that these effects deserve attention in realistic studies of correlated materials.

  2. Rhythmic behavior in a two-population mean-field Ising model.

    PubMed

    Collet, Francesca; Formentin, Marco; Tovazzi, Daniele

    2016-10-01

    Many real systems composed of a large number of interacting components, as, for instance, neural networks, may exhibit collective periodic behavior even though single components have no natural tendency to behave periodically. Macroscopic oscillations are indeed one of the most common self-organized behavior observed in living systems. In the present paper we study some dynamical features of a two-population generalization of the mean-field Ising model with the scope of investigating simple mechanisms capable to generate rhythms in large groups of interacting individuals. We show that the system may undergo a transition from a disordered phase, where the magnetization of each population fluctuates closely around zero, to a phase in which they both display a macroscopic regular rhythm. In particular, there exists a region in the parameter space where having two groups of spins with inter- and intrapopulation interactions of different strengths suffices for the emergence of a robust periodic behavior.

  3. Rhythmic behavior in a two-population mean-field Ising model

    NASA Astrophysics Data System (ADS)

    Collet, Francesca; Formentin, Marco; Tovazzi, Daniele

    2016-10-01

    Many real systems composed of a large number of interacting components, as, for instance, neural networks, may exhibit collective periodic behavior even though single components have no natural tendency to behave periodically. Macroscopic oscillations are indeed one of the most common self-organized behavior observed in living systems. In the present paper we study some dynamical features of a two-population generalization of the mean-field Ising model with the scope of investigating simple mechanisms capable to generate rhythms in large groups of interacting individuals. We show that the system may undergo a transition from a disordered phase, where the magnetization of each population fluctuates closely around zero, to a phase in which they both display a macroscopic regular rhythm. In particular, there exists a region in the parameter space where having two groups of spins with inter- and intrapopulation interactions of different strengths suffices for the emergence of a robust periodic behavior.

  4. 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.

  5. 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.

  6. Numerical evidence against both mean field and droplet scenarios of the Edwards-Anderson model

    NASA Astrophysics Data System (ADS)

    Fernandez, Julio F.; Alonso, Juan J.

    2013-03-01

    From tempered Monte Carlo simulations, we have obtained accurate probability distributions p (q) of the spin-overlap parameter q for finite Edwards-Anderson (EA) and Sherrington-Kirkpatrick (SK) spin-glass systems at low temperatures. Our results for p (q) follow from averages over 105 disordered samples of linear sizes L = 4 - 8 and over 15 000 samples for L = 10 . In both the SK and EA models, at temperatures as low as 0 . 2Tsg , where Tsg is the transition temperature, p (q) varies insignificantly with L. This does not fit the trend that the droplet model predicts for large L. We have also calculated correlation functions, F (q1 ,q2) , from which rms deviations, δp , over different realizations of quenched disorder, as well as thermal fluctuations, w, of q values, follow. Our numerical results for δp and w scale as √{ L} and 1 / L , respectively, in the SK model. This fits in well with mean field predictions. On the other hand, our data for w and δp vary little, if at all, for the EA model.

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

    PubMed

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

    2014-04-01

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

  8. Treatment of Fluctuation Effects in Mean-field Models of Chain Stretching

    NASA Astrophysics Data System (ADS)

    Douglas, Jack; Mansfield, Marc

    1997-03-01

    Many recent studies of chain stretching in block copolymer materials, polymer brushes, and many-arm stars have been formulated in terms of mean- field models, leading generally to power-law potentials describing the chain stretching arising from interchain and intrachain excluded volume interactions. This type of model has been highly successful, but fluctuation effects associated with finite chain length are often neglected in model calculations. We investigate whether fluctuation effects can be accounted for by reintroducing these effective pseudo-potentials into a path-integral description to calculate the chain streching. Numerical treatment of chain swelling with repulsive power-law potentials leads to universal scaling curves which are similar to those found for chain swelling due to excluded volume in polymer solutions. Density profiles are also calculated and the parabolic potential led to a density profile having a "foot" for finite chain lengths, as in measurements on polymer "brushes". Analytic calculations indicate a general relation between the polymer size exponent nu and the power of the potential which also holds for Hamiltonian dynamical systems and thus the 2/3 power law describing the strong segregation scaling of block copolymer lamellae with chain mass corresponds to Kepler's third law of planetary motion relating the orbital scale to its period.

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

    NASA Astrophysics Data System (ADS)

    Curilef, Sergio; Atenas, Boris

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

  10. Mean-field message-passing equations in the Hopfield model and its generalizations

    NASA Astrophysics Data System (ADS)

    Mézard, Marc

    2017-02-01

    Motivated by recent progress in using restricted Boltzmann machines as preprocessing algorithms for deep neural network, we revisit the mean-field equations [belief-propagation and Thouless-Anderson Palmer (TAP) equations] in the best understood of such machines, namely the Hopfield model of neural networks, and we explicit how they can be used as iterative message-passing algorithms, providing a fast method to compute the local polarizations of neurons. In the "retrieval phase", where neurons polarize in the direction of one memorized pattern, we point out a major difference between the belief propagation and TAP equations: The set of belief propagation equations depends on the pattern which is retrieved, while one can use a unique set of TAP equations. This makes the latter method much better suited for applications in the learning process of restricted Boltzmann machines. In the case where the patterns memorized in the Hopfield model are not independent, but are correlated through a combinatorial structure, we show that the TAP equations have to be modified. This modification can be seen either as an alteration of the reaction term in TAP equations or, more interestingly, as the consequence of message passing on a graphical model with several hidden layers, where the number of hidden layers depends on the depth of the correlations in the memorized patterns. This layered structure is actually necessary when one deals with more general restricted Boltzmann machines.

  11. 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.

  12. 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.

  13. Relativistic dynamical collapse model

    NASA Astrophysics Data System (ADS)

    Pearle, Philip

    2015-05-01

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

  14. 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.

  15. 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.

  16. Testing the Monte Carlo-mean field approximation in the one-band Hubbard model

    NASA Astrophysics Data System (ADS)

    Mukherjee, Anamitra; Patel, Niravkumar D.; Dong, Shuai; Johnston, Steve; Moreo, Adriana; Dagotto, Elbio

    2014-11-01

    The canonical one-band Hubbard model is studied using a computational method that mixes the Monte Carlo procedure with the mean field approximation. This technique allows us to incorporate thermal fluctuations and the development of short-range magnetic order above ordering temperatures, contrary to the crude finite-temperature Hartree-Fock approximation, which incorrectly predicts a Néel temperature TN that grows linearly with the Hubbard U /t . The effective model studied here contains quantum and classical degrees of freedom. It thus belongs to the "spin fermion" model family widely employed in other contexts. Using exact diagonalization, supplemented by the traveling cluster approximation, for the fermionic sector, and classical Monte Carlo for the classical fields, the Hubbard U /t vs temperature T /t phase diagram is studied employing large three- and two-dimensional clusters. We demonstrate that the method is capable of capturing the formation of local moments in the normal state without long-range order, the nonmonotonicity of TN with increasing U /t , the development of gaps and pseudogaps in the density of states, and the two-peak structure in the specific heat. Extensive comparisons with determinant quantum Monte Carlo results suggest that the present approach is qualitatively, and often quantitatively, accurate, particularly at intermediate and high temperatures. Finally, we study the Hubbard model including plaquette diagonal hopping (i.e., the t -t' Hubbard model) in two dimensions and show that our approach allows us to study low-temperature properties where determinant quantum Monte Carlo fails due to the fermion sign problem. Future applications of this method include multiorbital Hubbard models such as those needed for iron-based superconductors.

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

    NASA Astrophysics Data System (ADS)

    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.

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

    SciTech Connect

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

    2014-05-07

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

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

    PubMed

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

    2014-05-07

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

  20. 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.

  1. 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.

  2. 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.

  3. Renormalized parameters and perturbation theory in dynamical mean-field theory for the Hubbard model

    NASA Astrophysics Data System (ADS)

    Hewson, A. C.

    2016-11-01

    We calculate the renormalized parameters for the quasiparticles and their interactions for the Hubbard model in the paramagnetic phase as deduced from the low-energy Fermi-liquid fixed point using the results of a numerical renormalization-group calculation (NRG) and dynamical mean-field theory (DMFT). Even in the low-density limit there is significant renormalization of the local quasiparticle interaction U ˜, in agreement with estimates based on the two-particle scattering theory of J. Kanamori [Prog. Theor. Phys. 30, 275 (1963), 10.1143/PTP.30.275]. On the approach to the Mott transition we find a finite ratio for U ˜/D ˜ , where 2 D ˜ is the renormalized bandwidth, which is independent of whether the transition is approached by increasing the on-site interaction U or on increasing the density to half filling. The leading ω2 term in the self-energy and the local dynamical spin and charge susceptibilities are calculated within the renormalized perturbation theory (RPT) and compared with the results calculated directly from the NRG-DMFT. We also suggest, more generally from the DMFT, how an approximate expression for the q ,ω spin susceptibility χ (q ,ω ) can be derived from repeated quasiparticle scattering with a local renormalized scattering vertex.

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

    PubMed

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

    2015-11-01

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

  5. Clusters die hard: Time-correlated excitation in the Hamiltonian mean field model

    NASA Astrophysics Data System (ADS)

    Koyama, Hiroko; Konishi, Tetsuro; Ruffo, Stefano

    2008-07-01

    The Hamiltonian mean field (HMF) model has a low-energy phase where N particles are trapped inside a cluster. Here, we investigate some properties of the trapping/untrapping mechanism of a single particle into/outside the cluster. Since the single particle dynamics of the HMF model resembles the one of a simple pendulum, each particle can be identified as a high-energy particle (HEP) or a low-energy particle (LEP), depending on whether its energy is above or below the separatrix energy. We then define the trapping ratio as the ratio of the number of LEP to the total number of particles and the "fully-clustered" and "excited" dynamical states as having either no HEP or at least one HEP. We analytically compute the phase-space average of the trapping ratio by using the Boltzmann-Gibbs stable stationary solution of the Vlasov equation associated with the N → ∞ limit of the HMF model. The same quantity, obtained numerically as a time average, is shown to be in very good agreement with the analytical calculation. Another important feature of the dynamical behavior of the system is that the dynamical state changes transitionally: the "fully-clustered" and "excited" states appear in turn. We find that the distribution of the lifetime of the "fully-clustered" state obeys a power law. This means that clusters die hard, and that the excitation of a particle from the cluster is not a Poisson process and might be controlled by some type of collective motion with long memory. Such behavior should not be specific of the HMF model and appear also in systems where itinerancy among different "quasi-stationary" states has been observed. It is also possible that it could mimick the behavior of transient motion in molecular clusters or some observed deterministic features of chemical reactions.

  6. 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.

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

    PubMed

    Moosavi, S Amin; Montakhab, Afshin

    2015-01-01

    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.

  8. Out-of-equilibrium phase transitions in the Hamiltonian mean-field model: A closer look

    NASA Astrophysics Data System (ADS)

    Staniscia, F.; Chavanis, P. H.; de Ninno, G.

    2011-05-01

    We provide a detailed discussion of out-of-equilibrium phase transitions in the Hamiltonian mean-field (HMF) model in the framework of Lynden-Bell’s statistical theory of the Vlasov equation. For two-level initial conditions, the caloric curve β(E) only depends on the initial value f0 of the distribution function. We evidence different regions in the parameter space where the nature of the phase transitions between magnetized and nonmagnetized states changes: (i) For f0>0.10965, the system displays a second-order phase transition; (ii) for 0.109497

  9. On the genesis of spike-wave oscillations in a mean-field model of human thalamic and corticothalamic dynamics

    NASA Astrophysics Data System (ADS)

    Rodrigues, Serafim; Terry, John R.; Breakspear, Michael

    2006-07-01

    In this Letter, the genesis of spike-wave activity—a hallmark of many generalized epileptic seizures—is investigated in a reduced mean-field model of human neural activity. Drawing upon brain modelling and dynamical systems theory, we demonstrate that the thalamic circuitry of the system is crucial for the generation of these abnormal rhythms, observing that the combination of inhibition from reticular nuclei and excitation from the cortical signal, interplay to generate the spike-wave oscillation. The mechanism revealed provides an explanation of why approaches based on linear stability and Heaviside approximations to the activation function have failed to explain the phenomena of spike-wave behaviour in mean-field models. A mathematical understanding of this transition is a crucial step towards relating spiking network models and mean-field approaches to human brain modelling.

  10. 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

  11. Lambda matter in the effective density dependent mean-field model

    NASA Astrophysics Data System (ADS)

    Petrík, K.; Gmuca, S.

    2013-11-01

    The density dependent relativistic hadron field (DDRHF) theory is introduced with various forms of the density dependence of the nuclear interaction to study the Λ matter in the β-equilibrium. Several new parametrizations are extracted from the Dirac-Brueckner-Hartree-Fock (DBHF) calculations. We have compared and analysed high density extrapolations of Λ matter properties and shown that the choice of the density dependence has important effects on the structure of compact stars.

  12. 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.

  13. Beyond mean-field approximations for accurate and computationally efficient models of on-lattice chemical kinetics.

    PubMed

    Pineda, M; Stamatakis, M

    2017-07-14

    Modeling the kinetics of surface catalyzed reactions is essential for the design of reactors and chemical processes. The majority of microkinetic models employ mean-field approximations, which lead to an approximate description of catalytic kinetics by assuming spatially uncorrelated adsorbates. On the other hand, kinetic Monte Carlo (KMC) methods provide a discrete-space continuous-time stochastic formulation that enables an accurate treatment of spatial correlations in the adlayer, but at a significant computation cost. In this work, we use the so-called cluster mean-field approach to develop higher order approximations that systematically increase the accuracy of kinetic models by treating spatial correlations at a progressively higher level of detail. We further demonstrate our approach on a reduced model for NO oxidation incorporating first nearest-neighbor lateral interactions and construct a sequence of approximations of increasingly higher accuracy, which we compare with KMC and mean-field. The latter is found to perform rather poorly, overestimating the turnover frequency by several orders of magnitude for this system. On the other hand, our approximations, while more computationally intense than the traditional mean-field treatment, still achieve tremendous computational savings compared to KMC simulations, thereby opening the way for employing them in multiscale modeling frameworks.

  14. Beyond mean-field approximations for accurate and computationally efficient models of on-lattice chemical kinetics

    NASA Astrophysics Data System (ADS)

    Pineda, M.; Stamatakis, M.

    2017-07-01

    Modeling the kinetics of surface catalyzed reactions is essential for the design of reactors and chemical processes. The majority of microkinetic models employ mean-field approximations, which lead to an approximate description of catalytic kinetics by assuming spatially uncorrelated adsorbates. On the other hand, kinetic Monte Carlo (KMC) methods provide a discrete-space continuous-time stochastic formulation that enables an accurate treatment of spatial correlations in the adlayer, but at a significant computation cost. In this work, we use the so-called cluster mean-field approach to develop higher order approximations that systematically increase the accuracy of kinetic models by treating spatial correlations at a progressively higher level of detail. We further demonstrate our approach on a reduced model for NO oxidation incorporating first nearest-neighbor lateral interactions and construct a sequence of approximations of increasingly higher accuracy, which we compare with KMC and mean-field. The latter is found to perform rather poorly, overestimating the turnover frequency by several orders of magnitude for this system. On the other hand, our approximations, while more computationally intense than the traditional mean-field treatment, still achieve tremendous computational savings compared to KMC simulations, thereby opening the way for employing them in multiscale modeling frameworks.

  15. Double Lynden-Bell structure of low-energy quasistationary distributions in the Hamiltonian mean-field model.

    PubMed

    Konishi, Eiji; Sakagami, Masa-aki

    2015-03-01

    In the Hamiltonian mean-field model, we study the core-halo structure of low-energy quasistationary states under unsteady water-bag type initial conditions. The core-halo structure results in the superposition of two independent Lynden-Bell distributions. We examine the completeness of the Lynden-Bell relaxation and the relaxation between these two Lynden-Bell distributions.

  16. Statistical thermodynamics of lattice models in zeolites: Implications of local versus global mean field interactions

    NASA Astrophysics Data System (ADS)

    Ayappa, K. G.

    1999-09-01

    The statistical thermodynamics of adsorption in caged zeolites is developed by treating the zeolite as an ensemble of M identical cages or subsystems. Within each cage adsorption is assumed to occur onto a lattice of n identical sites. Expressions for the average occupancy per cage are obtained by minimizing the Helmholtz free energy in the canonical ensemble subject to the constraints of constant M and constant number of adsorbates N. Adsorbate-adsorbate interactions in the Brag-Williams or mean field approximation are treated in two ways. The local mean field approximation (LMFA) is based on the local cage occupancy and the global mean field approximation (GMFA) is based on the average coverage of the ensemble. The GMFA is shown to be equivalent in formulation to treating the zeolite as a collection of interacting single site subsystems. In contrast, the treatment in the LMFA retains the description of the zeolite as an ensemble of identical cages, whose thermodynamic properties are conveniently derived in the grand canonical ensemble. For a z coordinated lattice within the zeolite cage, with ɛaa as the adsorbate-adsorbate interaction parameter, the comparisons for different values of ɛaa*=ɛaaz/2kT, and number of sites per cage, n, illustrate that for -1<ɛaa*<0 and n⩾10, the adsorption isotherms and heats of adsorption predicted with the two approaches are similar. In general, the deviation between the LMFA and GMFA is greater for smaller n and less sensitive to n for ɛaa*>0. We compare the isotherms predicted with the LMFA with previous GMFA predictions [K. G. Ayappa, C. R. Kamala, and T. A. Abinandanan, J. Chem. Phys. 110, 8714 (1999)] (which incorporates both the site volume reduction and a coverage-dependent ɛaa) for xenon and methane in zeolite NaA. In all cases the predicted isotherms are very similar, with the exception of a small steplike feature present in the LMFA for xenon at higher coverages.

  17. 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.

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

    SciTech Connect

    Daoutidis, J.; Ring, P.

    2009-08-15

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

  19. 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.

  20. Threshold for chaos and thermalization in the one-dimensional mean-field bose-hubbard model.

    PubMed

    Cassidy, Amy C; Mason, Douglas; Dunjko, Vanja; Olshanii, Maxim

    2009-01-16

    We study the threshold for chaos and its relation to thermalization in the 1D mean-field Bose-Hubbard model, which, in particular, describes atoms in optical lattices. We identify the threshold for chaos, which is finite in the thermodynamic limit, and show that it is indeed a precursor of thermalization. Far above the threshold, the state of the system after relaxation is governed by the usual laws of statistical mechanics.

  1. 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.

  2. 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.

  3. 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.

  4. Study of bottleneck effect at an emergency evacuation exit using cellular automata model, mean field approximation analysis, and game theory

    NASA Astrophysics Data System (ADS)

    Tanimoto, Jun; Hagishima, Aya; Tanaka, Yasukaka

    2010-12-01

    An improved cellular automaton model for pedestrian dynamics was established, where both static floor field and collision effect derived from game theory were considered. Several model parameters were carefully determined by previous studies. Results obtained through model-based simulation and analytical approach (derived from mean field approximation) proved that outflow rate from an evacuation exit, which is usually estimated using outflow coefficient in building codes in Japan, can be improved by placing an appropriate obstacle in front of the exit. This can reduce collision probability at the exit by increasing collisions around the obstacles ahead of the exit.

  5. 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.

  6. Multimode mean-field model for the quantum phase transition of a Bose-Einstein condensate in an optical resonator

    NASA Astrophysics Data System (ADS)

    Kónya, G.; Szirmai, G.; Domokos, P.

    2011-11-01

    We develop a mean-field model describing the Hamiltonian interaction of ultracold atoms and the optical field in a cavity. The Bose-Einstein condensate is properly defined by means of a grand-canonical approach. The model is efficient because only the relevant excitation modes are taken into account. However, the model goes beyond the two-mode subspace necessary to describe the self-organization quantum phase transition observed recently. We calculate all the second-order correlations of the coupled atom field and radiation field hybrid bosonic system, including the entanglement between the two types of fields.

  7. Shortcuts to Adiabaticity in the Infinite-Range Ising Model by Mean-Field Counter-Diabatic Driving

    NASA Astrophysics Data System (ADS)

    Hatomura, Takuya

    2017-09-01

    The strategy of shortcuts to adiabaticity enables us to realize adiabatic dynamics in finite time. In the counter-diabatic driving approach, an auxiliary Hamiltonian which is called the counter-diabatic Hamiltonian is appended to an original Hamiltonian to cancel out diabatic transitions. The counter-diabatic Hamiltonian is constructed by using the eigenstates of the original Hamiltonian. Therefore, it is in general difficult to construct the counter-diabatic Hamiltonian for quantum many-body systems. Even if the counter-diabatic Hamiltonian for quantum many-body systems is obtained, it is generally non-local and even diverges at critical points. We construct an approximated counter-diabatic Hamiltonian for the infinite-range Ising model by making use of the mean-field approximation. An advantage of this method is that the mean-field counter-diabatic Hamiltonian is constructed by only local operators. We numerically demonstrate the effectiveness of this method through quantum annealing processes going the vicinity of the critical point. It is also confirmed that the mean-field counter-diabatic Hamiltonian is still well-defined in the limit to the critical point for a certain class of schedules. The present method can take higher order contributions into account and is consistent with the variational approach for local counter-diabatic driving.

  8. 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.

  9. A mean field model for competition: from neutral ecology to the Red Queen.

    PubMed

    O'Dwyer, James P; Chisholm, Ryan

    2014-08-01

    Individual species are distributed inhomogeneously over space and time, yet, within large communities of species, aggregated patterns of biodiversity seem to display nearly universal behaviour. Neutral models assume that an individual's demographic prospects are independent of its species identity. They have successfully predicted certain static, time-independent patterns. But they have generally failed to predict temporal patterns, such as species ages or population dynamics. We construct a new, multispecies framework incorporating competitive differences between species, and assess the impact of this competition on static and dynamic patterns of biodiversity. We solve this model exactly for the special case of a Red Queen hypothesis, where fitter species are continually arising. The model predicts more realistic species ages than neutral models, without greatly changing predictions for static species abundance distributions. Our modelling approach may allow users to incorporate a broad range of ecological mechanisms.

  10. Light cone in the two-dimensional transverse-field Ising model in time-dependent mean-field theory

    NASA Astrophysics Data System (ADS)

    Hafner, J.; Blass, B.; Rieger, H.

    2016-12-01

    We investigate the propagation of a local perturbation in the two-dimensional transverse-field Ising model with a time-dependent application of the mean-field theory based on the BBGKY hierarchy. We show that the perturbation propagates through the system with a finite velocity and that there is a transition from Manhattan to Euclidian metric, resulting in a light cone with an almost circular shape at sufficiently large distances. The propagation velocity of the perturbation defining the front of the light cone is discussed with respect to the parameters of the Hamiltonian and compared to exact results for the transverse-field Ising model in one dimension.

  11. Evidence of Non-Mean-Field-Like Low-Temperature Behavior in the Edwards-Anderson Spin-Glass Model

    NASA Astrophysics Data System (ADS)

    Yucesoy, B.; Katzgraber, Helmut G.; Machta, J.

    2012-10-01

    The three-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick Ising spin glasses are studied via large-scale Monte Carlo simulations at low temperatures, deep within the spin-glass phase. Performing a careful statistical analysis of several thousand independent disorder realizations and using an observable that detects peaks in the overlap distribution, we show that the Sherrington-Kirkpatrick and Edwards-Anderson models have a distinctly different low-temperature behavior. The structure of the spin-glass overlap distribution for the Edwards-Anderson model suggests that its low-temperature phase has only a single pair of pure states.

  12. A unified coarse-grained model of biological macromolecules based on mean-field multipole-multipole interactions.

    PubMed

    Liwo, Adam; Baranowski, Maciej; Czaplewski, Cezary; Gołaś, Ewa; He, Yi; Jagieła, Dawid; Krupa, Paweł; Maciejczyk, Maciej; Makowski, Mariusz; Mozolewska, Magdalena A; Niadzvedtski, Andrei; Ołdziej, Stanisław; Scheraga, Harold A; Sieradzan, Adam K; Slusarz, Rafał; Wirecki, Tomasz; Yin, Yanping; Zaborowski, Bartłomiej

    2014-08-01

    A unified coarse-grained model of three major classes of biological molecules--proteins, nucleic acids, and polysaccharides--has been developed. It is based on the observations that the repeated units of biopolymers (peptide groups, nucleic acid bases, sugar rings) are highly polar and their charge distributions can be represented crudely as point multipoles. The model is an extension of the united residue (UNRES) coarse-grained model of proteins developed previously in our laboratory. The respective force fields are defined as the potentials of mean force of biomacromolecules immersed in water, where all degrees of freedom not considered in the model have been averaged out. Reducing the representation to one center per polar interaction site leads to the representation of average site-site interactions as mean-field dipole-dipole interactions. Further expansion of the potentials of mean force of biopolymer chains into Kubo's cluster-cumulant series leads to the appearance of mean-field dipole-dipole interactions, averaged in the context of local interactions within a biopolymer unit. These mean-field interactions account for the formation of regular structures encountered in biomacromolecules, e.g., α-helices and β-sheets in proteins, double helices in nucleic acids, and helicoidally packed structures in polysaccharides, which enables us to use a greatly reduced number of interacting sites without sacrificing the ability to reproduce the correct architecture. This reduction results in an extension of the simulation timescale by more than four orders of magnitude compared to the all-atom representation. Examples of the performance of the model are presented.

  13. 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.

  14. 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

  15. The hedgehog baryon as a variational mean field solution of the spherical linear chiral soliton model

    NASA Astrophysics Data System (ADS)

    Goeke, K.; Urbano, J. N.; Fiolhais, M.; Harvey, M.

    1985-12-01

    We prove that the hedgehog baryon arises as a variational solution of the linear σ-model, if this is restricted to the chiral circle and if the boson Fock-states are described by coherent states and the valence quarks by a product of three identical wave functions each consisting of an orbital s-state multiplied with the most general one-quark spin-flavour configuration in the ud-sector. The opposite is shown to be not true, i.e., the assumption of a hedgehog state in the linear σ-model does not lead to fields which obey the requirements of the chiral circle.

  16. Aperiodic sequences and magnetic models: non-universal critical behavior within mean-field approximation

    NASA Astrophysics Data System (ADS)

    Branco, Nilton; Faria, Maicon; Tragtenberg, Marcelo

    2007-03-01

    We study the Ising model on a Bethe lattice, such that the exchange constant can assume two values, according to two-letter aperiodic sequences. Critical temperatures and exponents are calculated for three different sequences: Fibonacci, period-doubling and two-letter Rudin-Shapiro ones. These sequences are found to be irrelevant, marginal, and relevant, respectively, in the renormalization-group sense. The Fibonacci sequence presents the same critical behavior as for the uniform model and no log-periodic behavior is observed. For the marginal sequence, critical exponents depend on the ratio between the two possible exchange constants and a log-periodic behavior is clearly determined. Due to computational constraints, our results are not as precise for the Rudin-Shapiro sequence but we obtain evidence that the exponents are different from the classical ones and do not depend on the ratio between the exchange constants.

  17. 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.

  18. 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.

  19. 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.

  20. Mean-field and quantum-fluctuation dynamics in the driven dispersive Jaynes-Cummings model

    NASA Astrophysics Data System (ADS)

    Mavrogordatos, Th.; Szafulski, P.; Ginossar, E.; Szymańska, M. H.

    2016-12-01

    In this work we investigate the regime of amplitude bistability in the driven dissipative Jaynes-Cummings (JC) model. We study the semiclassical equation dynamics in contrast to entangled cavity-photon and qubit quantum trajectories, discussing our results in the context of an out-of-equilibrium first order quantum dissipative phase transition for a single JC resonator. Finally, we compare the switching process between metastable states for the two system degrees of freedom by examining a single realization of the random qubit vector in the Bloch sphere next to the intracavity amplitude quasi distributions at given time instants.

  1. 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.

  2. 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

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

    NASA Astrophysics Data System (ADS)

    Najafi, Saeed; Potestio, Raffaello

    2015-12-01

    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.

  4. 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.

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

    NASA Astrophysics Data System (ADS)

    Le, Duc-Anh; Tran, Minh-Tien

    2015-05-01

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

  6. 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.

  7. 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.

  8. Non-perturbative corrections to mean-field critical behavior: the spherical model on a spider-web graph

    NASA Astrophysics Data System (ADS)

    Balram, Ajit C.; Dhar, Deepak

    2012-03-01

    We consider the spherical model on a spider-web graph. This graph is effectively infinite dimensional, similar to the Bethe lattice, but has loops. We show that these lead to non-trivial corrections to the simple mean-field behavior. We first determine all normal modes of the coupled springs problem on this graph, using its large symmetry group. In the thermodynamic limit, the spectrum is a set of δ-functions, and all the modes are localized. The fractional number of modes with frequency less than ω varies as exp ( - C/ω) for ω tending to zero, where C is a constant. For an unbiased random walk on the vertices of this graph, this implies that the probability of return to the origin at time t varies as exp ( - C‧t1/3), for large t, where C‧ is a constant. For the spherical model, we show that while the critical exponents take the values expected from the mean-field theory, the free energy per site at temperature T, near and above the critical temperature Tc, also has an essential singularity of the type exp [ - K(T - Tc)-1/2].

  9. Self-consistent mean-field model based on molecular dynamics: Application to lipid-cholesterol bilayers

    NASA Astrophysics Data System (ADS)

    Khelashvili, George A.; Pandit, Sagar A.; Scott, H. L.

    2005-07-01

    We have developed a dynamic self-consistent mean-field model, based on molecular-dynamics simulations, to study lipid-cholesterol bilayers. In this model the lipid bilayer is represented as a two-dimensional lattice field in the lipid chain order parameters, while cholesterol molecules are represented by hard rods. The motion of rods in the system is continuous and is not confined to lattice cells. The statistical mechanics of chain ordering is described by a mean field derived from an extension of a model due to Marčelja. The time evolution of the system is governed by stochastic equations. The ensemble of chain configurations required in partition sums, and the energies of interaction, are taken from atomistic level molecular-dynamics simulations of lipid bilayers. The model allows us to simulate systems 500nm in lateral size for 20μs time scales, or greater. We have applied the model to dipalmitoyl-phosphatidylcholine-cholesterol (Chol) bilayers at 50°C for Chol concentrations between 2% and 33%. At low concentrations of Chol (2%-4%), the model predicts the formation of isolated clusters of Chol surrounded by relatively ordered lipid chains, randomly dispersed in the disordered bilayer. With increasing Chol composition, regions of Chol-induced order begin to overlap. Starting from about 11% Chol this ordering effect becomes system wide and regions unaffected by Chol are no longer detectable. From the analysis of properties of the model we conclude that the change in lipid chain order with increasing Chol concentration is continuous over the 20-μs scale of the simulations. We also conclude that at 50°C no large-scale Chol-rich and Chol-depleted coexisting phase-separated regions form at any concentration. At no point in any of the simulations do we observe a higher degree of lateral organization, such as Chol-based superlattice structures.

  10. 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.

  11. 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.

  12. Evidence of Non-Mean-Field-Like Low-Temperature Behavior in the Edwards-Anderson Spin-Glass Model

    NASA Astrophysics Data System (ADS)

    Yucesoy, Burcu; Katzgraber, Helmut G.; Machta, Jonathan

    2013-03-01

    The three and four-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick Ising spin glasses are studied via large-scale Monte Carlo simulations at low temperatures, deep within the spin-glass phase. Performing a careful statistical analysis of several thousand independent disorder realizations and using an observable that detects peaks in the overlap distribution, we show that the Sherrington-Kirkpatrick and Edwards-Anderson models have a distinctly different low-temperature behavior. The structure of the spin-glass overlap distribution for the Edwards-Anderson model suggests that its low-temperature phase has only a single pair of pure states. J. M. and B. Y. are supported in part by the NSF (Grant No. DMR-0907235 and DMR-1208046).

  13. Equivariant mean field flow

    NASA Astrophysics Data System (ADS)

    Castéras, Jean-baptiste

    2013-12-01

    We consider a gradient flow associated to the mean field equation on (M,g), a compact Riemannian surface without boundary. We prove that this flow exists for all time. Moreover, letting G be a group of isometry acting on (M,g), we obtain the convergence of the flow to a solution of the mean field equation under suitable hypothesis on the orbits of points of M under the action of G.

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

    PubMed

    Yoshitake, Junki; Nasu, Joji; Motome, Yukitoshi

    2016-10-07

    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.

  15. 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.

  16. Irreversible mean-field model of the critical behavior of charge-density waves below the threshold for sliding

    NASA Astrophysics Data System (ADS)

    Sornette, Didier

    1993-05-01

    A mean-field (MF) model of the critical behavior of charge-density waves below the threshold for sliding is proposed, which replaces the combined effect of the pinning force and of the forces exerted by the neighbors on a given particle n by an effective force threshold Xn. It allows one to rationalize the numerical results of Middleton and Fisher [Phys. Rev. Lett. 66 (1991) 92] on the divergence of the polarization and of the largest correlation length and of Pla and Nori [Phys. Rev. Lett. 67 (1991) 919] on the distribution D( d) of sliding bursts of size d, measured in narrow intervals of driving fields E at a finite distance below the threshold Ec.

  17. 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.

  18. 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.

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

    NASA Astrophysics Data System (ADS)

    Koehl, Patrice; Orland, Henri; Delarue, Marc

    2011-08-01

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

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

    PubMed

    Koehl, Patrice; Orland, Henri; Delarue, Marc

    2011-08-07

    We present an extension of the self-consistent mean field theory for protein side-chain modeling in which solvation effects are included based on the Poisson-Boltzmann (PB) theory. In this approach, the protein is represented with multiple copies of its side chains. Each copy is assigned a weight that is refined iteratively based on the mean field energy generated by the rest of the protein, until self-consistency is reached. At each cycle, the variational free energy of the multi-copy system is computed; this free energy includes the internal energy of the protein that accounts for vdW and electrostatics interactions and a solvation free energy term that is computed using the PB equation. The method converges in only a few cycles and takes only minutes of central processing unit time on a commodity personal computer. The predicted conformation of each residue is then set to be its copy with the highest weight after convergence. We have tested this method on a database of hundred highly refined NMR structures to circumvent the problems of crystal packing inherent to x-ray structures. The use of the PB-derived solvation free energy significantly improves prediction accuracy for surface side chains. For example, the prediction accuracies for χ(1) for surface cysteine, serine, and threonine residues improve from 68%, 35%, and 43% to 80%, 53%, and 57%, respectively. A comparison with other side-chain prediction algorithms demonstrates that our approach is consistently better in predicting the conformations of exposed side chains.

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

    PubMed Central

    Koehl, Patrice; Orland, Henri; Delarue, Marc

    2011-01-01

    We present an extension of the self-consistent mean field theory for protein side-chain modeling in which solvation effects are included based on the Poisson-Boltzmann (PB) theory. In this approach, the protein is represented with multiple copies of its side chains. Each copy is assigned a weight that is refined iteratively based on the mean field energy generated by the rest of the protein, until self-consistency is reached. At each cycle, the variational free energy of the multi-copy system is computed; this free energy includes the internal energy of the protein that accounts for vdW and electrostatics interactions and a solvation free energy term that is computed using the PB equation. The method converges in only a few cycles and takes only minutes of central processing unit time on a commodity personal computer. The predicted conformation of each residue is then set to be its copy with the highest weight after convergence. We have tested this method on a database of hundred highly refined NMR structures to circumvent the problems of crystal packing inherent to x-ray structures. The use of the PB-derived solvation free energy significantly improves prediction accuracy for surface side chains. For example, the prediction accuracies for χ1 for surface cysteine, serine, and threonine residues improve from 68%, 35%, and 43% to 80%, 53%, and 57%, respectively. A comparison with other side-chain prediction algorithms demonstrates that our approach is consistently better in predicting the conformations of exposed side chains. PMID:21823735

  2. The relativistic Black-Scholes model

    NASA Astrophysics Data System (ADS)

    Trzetrzelewski, Maciej

    2017-02-01

    The Black-Scholes equation, after a certain coordinate transformation, is equivalent to the heat equation. On the other hand the relativistic extension of the latter, the telegraphers equation, can be derived from the Euclidean version of the Dirac equation. Therefore, the relativistic extension of the Black-Scholes model follows from relativistic quantum mechanics quite naturally. We investigate this particular model for the case of European vanilla options. Due to the notion of locality incorporated in this way, one finds that the volatility frown-like effect appears when comparing to the original Black-Scholes model.

  3. Kinetic phase transitions in a surface-reaction model with diffusion: Computer simulations and mean-field theory

    NASA Astrophysics Data System (ADS)

    Jensen, Iwan; Fogedby, Hans C.

    1990-08-01

    A simple surface-reaction model based upon the oxidation of carbon monoxide on a catalytic surface, introduced by Ziff, Gulari, and Barshad (ZGB) [Phys. Rev. Lett. 56, 2553 (1986)], has been extended in order to include diffusion of the adsorbed particles (both O and CO). The ZGB model is a nonequilibrium model exhibiting both a first- and a second-order phase transition. The effects of diffusion on the behavior of the model has been explored by means of computer simulations. The main effect of diffusion is to change the positions of the phase transitions and increase the rate of CO2 formation. Fast diffusion causes the second-order transition to disappear from the system. Simple explanations of these changes are given. The extended version of the ZGB model has furthermore been studied by mean-field theory in the pair approximation. This approach gives qualitatively correct predictions about the effects of diffusion and yields quantitative predictions in good agreement with simulation results in the vicinity of the first-order transition.

  4. 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)

  5. Assessment of mean-field microkinetic models for CO methanation on stepped metal surfaces using accelerated kinetic Monte Carlo

    NASA Astrophysics Data System (ADS)

    Andersen, Mie; Plaisance, Craig P.; Reuter, Karsten

    2017-10-01

    First-principles screening studies aimed at predicting the catalytic activity of transition metal (TM) catalysts have traditionally been based on mean-field (MF) microkinetic models, which neglect the effect of spatial correlations in the adsorbate layer. Here we critically assess the accuracy of such models for the specific case of CO methanation over stepped metals by comparing to spatially resolved kinetic Monte Carlo (kMC) simulations. We find that the typical low diffusion barriers offered by metal surfaces can be significantly increased at step sites, which results in persisting correlations in the adsorbate layer. As a consequence, MF models may overestimate the catalytic activity of TM catalysts by several orders of magnitude. The potential higher accuracy of kMC models comes at a higher computational cost, which can be especially challenging for surface reactions on metals due to a large disparity in the time scales of different processes. In order to overcome this issue, we implement and test a recently developed algorithm for achieving temporal acceleration of kMC simulations. While the algorithm overall performs quite well, we identify some challenging cases which may lead to a breakdown of acceleration algorithms and discuss possible directions for future algorithm development.

  6. Mean-field calculation of critical parameters and log-periodic characterization of an aperiodic-modulated model.

    PubMed

    Oliveira, T P; Branco, N S

    2012-01-01

    We employ a mean-field approximation to study the Ising model with aperiodic modulation of its interactions in one spatial direction. Two different values for the exchange constant, J(A) and J(B), are present, according to the Fibonacci sequence. We calculate the pseudocritical temperatures for finite systems and extrapolate them to the thermodynamic limit. We explicitly obtain the exponents β, δ, and γ and, from the usual scaling relations for anisotropic models at the upper critical dimension (assumed to be 4 for the model we treat), we calculate α, ν, ν(∥), η, and η(∥). Within the framework of a renormalization-group approach, the Fibonacci sequence is a marginal one and we obtain exponents that depend on the ratio r≡J(B)/J(A), as expected; however, the scaling relation γ=β(δ-1) is obeyed for all values of r we studied. We characterize some thermodynamic functions as log-periodic functions of their arguments, as expected for aperiodic-modulated models, and obtain precise values for the exponents from this characterization.

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

    NASA Astrophysics Data System (ADS)

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

    2014-07-01

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

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

    PubMed

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

    2014-07-01

    The mean-field (MF) approximation offers a simple, fast way to infer direct interactions between elements in a network of correlated variables, a common, computationally challenging problem with practical applications in fields ranging from physics and biology to the social sciences. However, MF methods achieve their best performance with strong regularization, well beyond Bayesian expectations, an empirical fact that is poorly understood. In this work, we study the influence of pseudocount and L(2)-norm regularization schemes on the quality of inferred Ising or Potts interaction networks from correlation data within the MF approximation. We argue, based on the analysis of small systems, that the optimal value of the regularization strength remains finite even if the sampling noise tends to zero, in order to correct for systematic biases introduced by the MF approximation. Our claim is corroborated by extensive numerical studies of diverse model systems and by the analytical study of the m-component spin model for large but finite m. Additionally, we find that pseudocount regularization is robust against sampling noise and often outperforms L(2)-norm regularization, particularly when the underlying network of interactions is strongly heterogeneous. Much better performances are generally obtained for the Ising model than for the Potts model, for which only couplings incoming onto medium-frequency symbols are reliably inferred.

  9. Static and dynamic properties of strongly correlated lattice models under electric fields (Dynamical Mean Field Theory approach)

    NASA Astrophysics Data System (ADS)

    Joura, Alexander V.

    In this thesis we study the Falicov-Kimball model within the framework of Dynamical Mean Field Theory (DMFT). We derive expressions for the electrical conductivity, electronic thermal conductivity, Seebeck coefficient (thermopower) and thermoelectric figure of merit (ZT) for the infinite dimensional hypercubic lattice and the Bethe lattice of infinite connectivity within linear response theory. We use these formulas to numerically calculate thermoelectric properties of the model away from half-filling. We also derive explicit analytic formulas for the retarded Green's function, the retarded self-energy and the relaxation time near the pole in the insulating regime on the hypercubic lattice. Using these results we compare thermal and electric transport properties of the correlated insulator to that of a generic insulator in the small temperature regime. Using analytic expressions for the self-energy near the pole in the insulator phase, we derive analytic formulas for the metal-insulator transition Ucr on the hypercubic lattice. For the Bethe lattice we derive explicit analytic formulas for the electric conductivity, the electronic part of the thermal conductivity, the Seebeck coefficient, the Lorentz number and the figure of merit in the low temperature limit. We also examine the problem of calculating the density of states for single-band lattice Hamiltonians with an applied constant and uniform external electric field, when the field is large enough that nonlinear effects are important. To do this we develop a general formalism (based on the nonequilibrium Kadanoff-Baym-Keldysh theory), which can be applied to a wide variety of different many-body Hamiltonians. We assume that the electric field was turned on in the distant past, so the system has reached the steady state. We present numerical solutions of the equations derived for the Falicov-Kimball model within the framework of dynamical mean-field theory. Finally, nonequilibrium properties of the Hubbard model

  10. Analytic models of relativistic accretion disks

    NASA Astrophysics Data System (ADS)

    Zhuravlev, V. V.

    2015-06-01

    We present not a literature review but a description, as detailed and consistent as possible, of two analytic models of disk accretion onto a rotating black hole: a standard relativistic disk and a twisted relativistic disk. Although one of these models is older than the other, both are of topical interest for black hole studies. The treatment is such that the reader with only a limited knowledge of general relativity and relativistic hydrodynamics, with little or no use of additional sources, can gain insight into many technical details lacking in the original papers.

  11. Growth-induced polarity formation in solid solutions of organic molecules: Markov mean-field model and Monte Carlo simulations

    NASA Astrophysics Data System (ADS)

    Wüst, Thomas; Hulliger, Jürg

    2005-02-01

    A layer-by-layer growth model is presented for the theoretical investigation of growth-induced polarity formation in solid solutions H1-XGX of polar (H) and nonpolar (G) molecules (X: molar fraction of G molecules in the solid, 0model is characterized by the assumption of thermal equilibrium formation of adlayers, with respect to the up and down orientation of the dipoles of H molecules and to an exchange of H and G molecules, while previously attached layers are kept frozen. The model is analyzed by means of a Markov mean-field description and Monte Carlo simulations. In solid solutions, polarity results from a combined effect of orientational selectivity by H and G molecules with respect to the alignment of the dipoles of H molecules and miscibility between the two components. Even though both native structures (H,G) may be centrosymmetric, polarity can arise just from the admixture of G molecules in the H crystal upon growth. An overview of possible phenomena is given by random selection of molecular interaction energies within an assumed but realistic energy range. The analytical approach describes sufficiently basic phenomena and is in good agreement with simulations. High probabilities for significant vectorial alignment of H molecules are found for low (X⩽0.2) and high (X⩾0.8) fractions of G molecules, respectively, as well as for ordered HG compounds (X=0.5).

  12. Ground-state properties of rare-earth nuclei in the Nilsson mean-field plus extended-pairing model

    NASA Astrophysics Data System (ADS)

    Guan, Xin; Launey, Kristina D.; Wang, Yin; Pan, Feng; Draayer, Jerry P.

    2015-10-01

    The Nilsson mean-field plus extended-pairing model for deformed nuclei is applied to describe the ground-state properties of selected rare-earth nuclei. Binding energies, even-odd mass differences, energies of the first pairing excitation states, and moments of inertia for the ground-state band of Er-164152, Yb-166154, and Hf-168156 are calculated systematically in the model employing both proton-proton and neutron-neutron pairing interactions. The pairing interaction strengths are determined as a function of the mass number in the isotopic chains. In comparison with the corresponding experimental data, it is shown that pairing interaction is crucial in elucidating the properties of both the ground state and the first pairing excitation state of these rare-earth nuclei. With model parameters determined by fitting the energies of these states, ground-state occupation probabilities of valence nucleon pairs with angular momentum J =0 ,1 ,⋯,12 for even-even Yb-162156 are calculated. It is inferred that the occupation probabilities of valence nucleon pairs with even angular momenta are much higher than those of valence nucleon pairs with odd angular momenta. The results clearly indicate that S , D , and G valence nucleon pairs dominate in the ground state of these nuclei.

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

    NASA Astrophysics Data System (ADS)

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

    2014-01-01

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

  14. 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 .

  15. Fine structure of the spectra of the Kondo lattice model: Two-site cellular dynamical mean-field theory study

    NASA Astrophysics Data System (ADS)

    Osolin, Žiga; Žitko, Rok

    2017-01-01

    We study the antiferromagnetic and paramagnetic Kondo insulator phases of the Kondo lattice model on the cubic lattice at half filling using the cellular dynamical mean-field theory (CDMFT) with the numerical renormalization group (NRG) as the impurity solver, focusing on the fine details of the spectral function and self-energy. We find that the nonlocal correlations increase the gap in both the antiferromagnetic and Kondo insulator phases and shrink the extent of the antiferromagnetic phase in the phase diagram but do not alter any properties qualitatively. The agreement between the numerical CDMFT results and those within a simple hybridization picture, which adequately describes the overall band structure of the system but neglects all effects on the inelastic-scattering processes, is similar to that of the single-site DMFT results; there are deviations that are responsible for the additional fine structure, in particular for the asymmetric spectral resonances or dips that become more pronounced in the strong-coupling regime close to the antiferromagnet-paramagnetic quantum phase transition. These features appear broader in the CDMFT mostly due to numerical artifacts linked to more aggressive state truncation required in the NRG.

  16. Perturbation Theory versus Thermodynamic Integration. Beyond a Mean-Field Treatment of Pair Correlations in a Nematic Model Liquid Crystal.

    PubMed

    Schoen, Martin; Haslam, Andrew J; Jackson, George

    2017-09-05

    The phase behavior and structure of a simple square-well bulk fluid with anisotropic interactions is described in detail. The orientation dependence of the intermolecular interactions allows for the formation of a nematic liquid-crystalline phase in addition to the more conventional isotropic gas and liquid phases. A version of classical density functional theory (DFT) is employed to determine the properties of the model, and comparisons are made with the corresponding data from Monte Carlo (MC) computer simulations in both the grand canonical and canonical ensembles, providing a benchmark to assess the adequacy of the DFT results. A novel element of the DFT approach is the assumption that the structure of the fluid is dominated by intermolecular interactions in the isotropic fluid. A so-called augmented modified mean-field (AMMF) approximation is employed accounting for the influence of anisotropic interactions. The AMMF approximation becomes exact in the limit of vanishing density. We discuss advantages and disadvantages of the AMMF approximation with respect to an accurate description of isotropic and nematic branches of the phase diagram, the degree of orientational order, and orientation-dependent pair correlations. The performance of the AMMF approximations is found to be good in comparison with the MC data; the AMMF approximation has clear advantages with respect to an accurate and more detailed description of the fluid structure. Possible strategies to improve the DFT are discussed.

  17. Static quadrupolar susceptibility for a Blume-Emery-Griffiths model based on the mean-field approximation

    NASA Astrophysics Data System (ADS)

    Pawlak, A.; Gülpınar, G.; Erdem, R.; Ağartıoğlu, M.

    2015-12-01

    The expressions for the dipolar and quadrupolar susceptibilities are obtained within the mean-field approximation in the Blume-Emery-Griffiths model. Temperature as well as crystal field dependences of the susceptibilities are investigated for two different phase diagram topologies which take place for K/J=3 and K/J=5.0.Their behavior near the second and first order transition points as well as multi-critical points such as tricritical, triple and critical endpoint is presented. It is found that in addition to the jumps connected with the phase transitions there are broad peaks in the quadrupolar susceptibility. It is indicated that these broad peaks lie on a prolongation of the first-order line from a triple point to a critical point ending the line of first-order transitions between two distinct paramagnetic phases. It is argued that the broad peaks are a reminiscence of very strong quadrupolar fluctuations at the critical point. The results reveal the fact that near ferromagnetic-paramagnetic phase transitions the quadrupolar susceptibility generally shows a jump whereas near the phase transition between two distinct paramagnetic phases it is an edge-like.

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

    PubMed

    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 P_{ij}∼r^{-α}, where r_{ij} 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)NATUAS0028-083610.1038/35022643]. 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.

  19. 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

  20. Dipolar interaction and demagnetizing effects in magnetic nanoparticle dispersions: Introducing the mean-field interacting superparamagnet model

    NASA Astrophysics Data System (ADS)

    Sánchez, F. H.; Mendoza Zélis, P.; Arciniegas, M. L.; Pasquevich, G. A.; Fernández van Raap, M. B.

    2017-04-01

    Aiming to analyze relevant aspects of interacting magnetic nanoparticle systems (frequently called interacting superparamagnets), a model is built from magnetic dipolar interaction and demagnetizing mean-field concepts. By making reasonable simplifying approximations, a simple and useful expression for effective demagnetizing factors is achieved, which allows the analysis of uniform and nonuniform spatial distributions of nanoparticles, in particular the occurrence of clustering. This expression is a function of demagnetizing factors associated with specimen shape and clusters shape, and of the mean distances between near neighbor nanoparticles and between clusters, relative to the characteristic sizes of each of these two types of objects, respectively. The model explains effects of magnetic dipolar interactions, such as the observation of apparent nanoparticle magnetic moments smaller than real ones and approaching to zero as temperature decreases. It is shown that by performing a minimum set of experimental determinations along principal directions of geometrically well-defined specimens, model application allows retrieval of nanoparticle intrinsic properties, like mean volume, magnetic moment, and susceptibility in the absence of interactions. It also permits the estimation of mean interparticle and intercluster relative distances, as well as mean values of demagnetizing factors associated with clusters shape. An expression for average magnetic dipolar energy per nanoparticle is also derived, which is a function of specimen effective demagnetizing factor and magnetization. Experimental test of the model was performed by analysis of results reported in the literature and of original results reported here. The first case corresponds to oleic-acid-coated 8-nm magnetite particles dispersed in PEGDA-600 polymer, and the second one to polyacrilic-acid-coated 13-nm magnetite particles dispersed in PVA solutions from which ferrogels were later produced by a physical

  1. Exact quantisation of the relativistic Hopfield model

    SciTech Connect

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

    2016-11-15

    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.

  2. 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.

  3. Slave-boson mean-field theory versus variational-wave-function approach for the periodic Anderson model

    NASA Astrophysics Data System (ADS)

    Yang, Min-Fong; Sun, Shih-Jye; Hong, Tzay-Ming

    1993-12-01

    We show that a special kind of slave-boson mean-field approximation, which allows for the symmetry-broken states appropriate for a bipartite lattice, can give essentially the same results as those by the variational-wave-function approach proposed by Gula´csi, Strack, and Vollhardt [Phys. Rev. B 47, 8594 (1993)]. The advantages of our approach are briefly discussed.

  4. Protein Diffusion on Charged Membranes: A Dynamic Mean-Field Model Describes Time Evolution and Lipid Reorganization

    PubMed Central

    Khelashvili, George; Weinstein, Harel; Harries, Daniel

    2008-01-01

    As charged macromolecules adsorb and diffuse on cell membranes in a large variety of cell signaling processes, they can attract or repel oppositely charged lipids. This results in lateral membrane rearrangement and affects the dynamics of protein function. To address such processes quantitatively we introduce a dynamic mean-field scheme that allows self-consistent calculations of the equilibrium state of membrane-protein complexes after such lateral reorganization of the membrane components, and serves to probe kinetic details of the process. Applicable to membranes with heterogeneous compositions containing several types of lipids, this comprehensive method accounts for mobile salt ions and charged macromolecules in three dimensions, as well as for lateral demixing of charged and net-neutral lipids in the membrane plane. In our model, the mobility of membrane components is governed by the diffusion-like Cahn-Hilliard equation, while the local electrochemical potential is based on nonlinear Poisson-Boltzmann theory. We illustrate the method by applying it to the adsorption of the anionic polypeptide poly-Lysine on negatively charged lipid membranes composed of binary mixtures of neutral and monovalent lipids, or onto ternary mixtures of neutral, monovalent, and multivalent lipids. Consistent with previous calculations and experiments, our results show that at steady-state multivalent lipids (such as PIP2), but not monovalent lipid (such as phosphatidylserine), will segregate near the adsorbing macromolecules. To address the corresponding diffusion of the adsorbing protein in the membrane plane, we couple lipid mobility with the propagation of the adsorbing protein through a dynamic Monte Carlo scheme. We find that due to their higher mobility dictated by the electrochemical potential, multivalent lipids such as PIP2 more quickly segregate near oppositely charged proteins than do monovalent lipids, even though their diffusion constants may be similar. The

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

    NASA Astrophysics Data System (ADS)

    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.

  6. Advanced relativistic VLBI model for geodesy

    NASA Astrophysics Data System (ADS)

    Soffel, Michael; Kopeikin, Sergei; Han, Wen-Biao

    2017-07-01

    Our present relativistic part of the geodetic VLBI model for Earthbound antennas is a consensus model which is considered as a standard for processing high-precision VLBI observations. It was created as a compromise between a variety of relativistic VLBI models proposed by different authors as documented in the IERS Conventions 2010. The accuracy of the consensus model is in the picosecond range for the group delay but this is not sufficient for current geodetic purposes. This paper provides a fully documented derivation of a new relativistic model having an accuracy substantially higher than one picosecond and based upon a well accepted formalism of relativistic celestial mechanics, astrometry and geodesy. Our new model fully confirms the consensus model at the picosecond level and in several respects goes to a great extent beyond it. More specifically, terms related to the acceleration of the geocenter are considered and kept in the model, the gravitational time-delay due to a massive body (planet, Sun, etc.) with arbitrary mass and spin-multipole moments is derived taking into account the motion of the body, and a new formalism for the time-delay problem of radio sources located at finite distance from VLBI stations is presented. Thus, the paper presents a substantially elaborated theoretical justification of the consensus model and its significant extension that allows researchers to make concrete estimates of the magnitude of residual terms of this model for any conceivable configuration of the source of light, massive bodies, and VLBI stations. The largest terms in the relativistic time delay which can affect the current VLBI observations are from the quadrupole and the angular momentum of the gravitating bodies that are known from the literature. These terms should be included in the new geodetic VLBI model for improving its consistency.

  7. Advanced relativistic VLBI model for geodesy

    NASA Astrophysics Data System (ADS)

    Soffel, Michael; Kopeikin, Sergei; Han, Wen-Biao

    2016-10-01

    Our present relativistic part of the geodetic VLBI model for Earthbound antennas is a consensus model which is considered as a standard for processing high-precision VLBI observations. It was created as a compromise between a variety of relativistic VLBI models proposed by different authors as documented in the IERS Conventions 2010. The accuracy of the consensus model is in the picosecond range for the group delay but this is not sufficient for current geodetic purposes. This paper provides a fully documented derivation of a new relativistic model having an accuracy substantially higher than one picosecond and based upon a well accepted formalism of relativistic celestial mechanics, astrometry and geodesy. Our new model fully confirms the consensus model at the picosecond level and in several respects goes to a great extent beyond it. More specifically, terms related to the acceleration of the geocenter are considered and kept in the model, the gravitational time-delay due to a massive body (planet, Sun, etc.) with arbitrary mass and spin-multipole moments is derived taking into account the motion of the body, and a new formalism for the time-delay problem of radio sources located at finite distance from VLBI stations is presented. Thus, the paper presents a substantially elaborated theoretical justification of the consensus model and its significant extension that allows researchers to make concrete estimates of the magnitude of residual terms of this model for any conceivable configuration of the source of light, massive bodies, and VLBI stations. The largest terms in the relativistic time delay which can affect the current VLBI observations are from the quadrupole and the angular momentum of the gravitating bodies that are known from the literature. These terms should be included in the new geodetic VLBI model for improving its consistency.

  8. Majorana dynamical mean-field study of spin dynamics at finite temperatures in the honeycomb Kitaev model

    NASA Astrophysics Data System (ADS)

    Yoshitake, Junki; Nasu, Joji; Kato, Yasuyuki; Motome, Yukitoshi

    2017-07-01

    A prominent feature of quantum spin liquids is fractionalization of the spin degree of freedom. Fractionalized excitations have their own dynamics in different energy scales, and hence, affect finite-temperature (T ) properties in a peculiar manner even in the paramagnetic state harboring the quantum spin liquid state. We here present a comprehensive theoretical study of the spin dynamics in a wide T range for the Kitaev model on a honeycomb lattice, whose ground state is a quantum spin liquid. In this model, the fractionalization occurs to break up quantum spins into itinerant matter fermions and localized Z2 fluxes, which results in two crossovers at very different T scales. Extending the previous study for the isotropic coupling case [J. Yoshitake, J. Nasu, and Y. Motome, Phys. Rev. Lett. 117, 157203 (2016), 10.1103/PhysRevLett.117.157203], we calculate the dynamical spin structure factor S (q ,ω ) , the NMR relaxation rate 1 /T1 , and the magnetic susceptibility χ while changing the anisotropy in the exchange coupling constants, by using the dynamical mean-field theory based on a Majorana fermion representation. We describe the details of the methodology including the continuous-time quantum Monte Carlo method for computing dynamical spin correlations and the maximum entropy method for analytic continuation. We confirm that the combined method provides accurate results in a wide T range including the region where the spins are fractionalized. We find that also in the anisotropic cases the system exhibits peculiar behaviors below the high-T crossover whose temperature is comparable to the average of the exchange constants: S (q ,ω ) shows an inelastic response at the energy scale of the averaged exchange constant, 1 /T1 continues to grow even though the equal-time spin correlations are saturated and almost T independent, and χ deviates from the Curie-Weiss behavior. In particular, when the exchange interaction in one direction is stronger than the other two

  9. 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.

  10. Baryon properties in the relativistic quark model

    NASA Astrophysics Data System (ADS)

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

    2017-09-01

    Properties of heavy and strange baryons are investigated in the framework of the relativistic quark-diquark picture. It is based on the relativistic quark model of hadrons, which was previously successfully applied for the calculation of meson properties. It is assumed that two quarks in a baryon form a diquark and baryon is considered as the bound quark-diquark system. The relativistic effects and diquark internal structure are consistently taken into account. Calculations are performed up to rather high orbital and radial excitations of heavy and strange baryons. On this basis the Regge trajectories are constructed. The rates of semileptonic decays of heavy baryons are calculated. The obtained results agree well with available experimental data.

  11. Modeling of Entangled Network Chains and Linear Solvent Chains in a Single-Chain-Mean-Field Slip-Link Model

    DTIC Science & Technology

    2013-09-01

    J. L. Influence of Solvent Size on the Mechanical Properties and Rheology of Polydimethylsiloxane-based Polymeric Gels. Polymer 2011, 52, 3422–3430...2. Schieber, J. Fluctuations in Entanglements of Polymer Liquids. Journal of Chemical Physics 2003, 18 (11), 5162–5166. 3. Schieber, J.; Neergaard, J...Gupta, S. A Full-chain, Temporary Network Model with Sliplinks, Chain-length Fluctuations, Chain Connectivity and Chain Stretching. Journal of

  12. Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model.

    PubMed

    Coen, Stéphane; Randle, Hamish G; Sylvestre, Thibaut; Erkintalo, Miro

    2013-01-01

    A generalized Lugiato-Lefever equation is numerically solved with a Newton-Raphson method to model Kerr frequency combs. We obtain excellent agreement with past experiments, even for an octave-spanning comb. Simulations are much faster than with any other technique despite including more modes than ever before. Our study reveals that Kerr combs are associated with temporal cavity solitons and dispersive waves, and opens up new avenues for the understanding of Kerr-comb formation.

  13. Bilocal model for the relativistic spinning particle

    NASA Astrophysics Data System (ADS)

    Rempel, Trevor; Freidel, Laurent

    2017-05-01

    In this work we show that a relativistic spinning particle can be described at the classical and the quantum level as being composed of two physical constituents which are entangled and separated by a fixed distance. This bilocal model for spinning particles allows for a natural description of particle interactions as a local interaction at each of the constituents. This form of the interaction vertex provides a resolution to a long standing issue on the nature of relativistic interactions for spinning objects in the context of the worldline formalism. It also potentially brings a dynamical explanation for why massive fundamental objects are naturally of lowest spin. We analyze first a nonrelativistic system where spin is modeled as an entangled state of two particles with the entanglement encoded into a set of constraints. It is shown that these constraints can be made relativistic and that the resulting description is isomorphic to the usual description of the phase space of massive relativistic particles with the restriction that the quantum spin has to be an integer.

  14. Screening parameters for the relativistic hydrogenic model

    NASA Astrophysics Data System (ADS)

    Lanzini, Fernando; Di Rocco, Héctor O.

    2015-12-01

    We present a Relativistic Screened Hydrogenic Model (RSHM) where the screening parameters depend on the variables (n , l , j) and the parameters (Z , N) . These screening parameters were derived theoretically in a neat form with no use of experimental values nor numerical values from self-consistent codes. The results of the model compare favorably with those obtained by using more sophisticated approaches. For the interested reader, a copy of our code can be requested from the corresponding author.

  15. 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.

  16. Modeling relativistic plasmas with PIC using VORPAL

    NASA Astrophysics Data System (ADS)

    Nieter, Chet; Cary, John R.

    2002-11-01

    VORPAL, a fully object-oriented, dimension-free plasma simulation code, now has a fully developed PIC model. This PIC model has been applied to studies of Laser Wake Field Acceleration, including the nonlinear structure of the wake field generated in the colliding pulse injection scheme and in the development of a new injection scheme that reduces timing requirements. (See Giacone et al. and Cary et al. at this conference). Since the PIC model was developed using VORPAL's object oriented architecture, it works in any dimension and with both serial and parallel runs. Several different update methods are available, including both relativistic and non-relativistic Boris push and an electrostatic update as well.

  17. Interface-roughening phase diagram of the three-dimensional Ising model for all interaction anisotropies from hard-spin mean-field theory.

    PubMed

    Cağlar, Tolga; Berker, A Nihat

    2011-11-01

    The roughening phase diagram of the d=3 Ising model with uniaxially anisotropic interactions is calculated for the entire range of anisotropy, from decoupled planes to the isotropic model to the solid-on-solid model, using hard-spin mean-field theory. The phase diagram contains the line of ordering phase transitions and, at lower temperatures, the line of roughening phase transitions, where the interface between ordered domains roughens. Upon increasing the anisotropy, roughening transition temperatures settle after the isotropic case, whereas the ordering transition temperature increases to infinity. The calculation is repeated for the d=2 Ising model for the full range of anisotropy, yielding no roughening transition.

  18. Systematics of light nuclei in a relativistic model

    SciTech Connect

    Price, C.E.

    1988-01-01

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

  19. Derivation and analysis of an ordinary differential equation mean-field model for studying clinically recorded epilepsy dynamics.

    PubMed

    Marten, Frank; Rodrigues, Serafim; Suffczynski, Piotr; Richardson, Mark P; Terry, John R

    2009-02-01

    In this paper we describe how an ordinary differential equation model of corticothalamic interactions may be obtained from a more general system of delay differential equations. We demonstrate that transitions to epileptic dynamics via changes in system parameters are qualitatively the same as in the original model with delay, as well as demonstrating that the onset of epileptic activity may arise due to regions of bistability. Hence, the model presents in one unique framework, two competing theories for the genesis of epileptiform activity. Similarities between model transitions and clinical data are presented and we argue that statistics obtained from, and a parameter estimation of this model may be a potential means of classifying and predicting the onset and offset of seizure activity.

  20. Information geometry of mean-field approximation.

    PubMed

    Tanaka, T

    2000-08-01

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

  1. 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.

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

    PubMed

    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.

  3. 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.

  4. Real-space cluster dynamical mean-field approach to the Falicov-Kimball model: An alloy-analogy approach

    NASA Astrophysics Data System (ADS)

    Haldar, P.; Laad, M. S.; Hassan, S. R.

    2017-03-01

    It is long known that the best single-site coherent potential approximation falls short of describing Anderson localization. Here, we study a binary alloy disorder [or equivalently, a spinless Falicov-Kimball (FK)] model and construct a dominantly analytic cluster extension that treats intracluster (1 /d ,d = spatial dimension) correlations exactly. We find that, in general, the irreducible two-particle vertex exhibits clear nonanalyticities before the band splitting transition of the Hubbard type occurs, signaling onset of an unusual type of localization at strong coupling. Using time-dependent response to a sudden local quench as a diagnostic, we find that the long-time wave-function overlap changes from a power-law to an anomalous form at strong coupling, lending additional support to this idea. Our results also imply such "strong" localization in the equivalent FK model, the simplest interacting fermion system.

  5. Mean Field Theory for Collective Motion of Quantum Meson Fields

    NASA Astrophysics Data System (ADS)

    Tsue, Y.; Vautherin, D.; Matsui, T.

    1999-08-01

    Mean field theory for the time evolution of quantum meson fields is studied in terms of the functional Schrödinger picture with a time-dependent Gaussian variational wave functional. We first show that the equations of motion for the variational wavefunctional can be rewritten in a compact form similar to the Hartree-Bogoliubov equations in quantum many-body theory and this result is used to recover the covariance of the theory. We then apply this method to the O(N) model and present analytic solutions of the mean field evolution equations for an N-component scalar field. These solutions correspond to quantum rotations in isospin space and represent generalizations of the classical solutions obtained earlier by Anselm and Ryskin. As compared to classical solutions new effects arise because of the coupling between the average value of the field and its quantum fluctuations. We show how to generalize these solutions to the case of mean field dynamics at finite temperature. The relevance of these solutions for the observation of a coherent collective state or a disoriented chiral condensate in ultra-relativistic nuclear collisions is discussed.

  6. A mean-field model of the alkane-saturated lipid bilayer above its phase transition. I. Development of the model.

    PubMed Central

    Gruen, D W

    1981-01-01

    A statistical mechanical model of a bilayer of dipalmitoyl-3-sn-phosphatidylcholine molecules in equilibrium with an aqueous phase saturated with an n-alkane is presented. A mean-field approach developed in previous work on a solventless bilayer (Gruen, Biochim. Biophys. Acta. 595:161--183, 1980) is extended to allow alkane chains to exist in the hydrophobic core of the membrane. As the alkane chains are chemically similar to the lipid chains, much of the analysis follows directly from the solventless model. Novel features of the present model are the inclusion of (a) a term which models the free energy cost of creating space for alkane conformations, (b) a term which constrains the chains to pack evenly in the hydrophobic region of the membrane, and (c) a term which estimates the free energy of mixing of the lipid and alkane molecules in the plane of the bilayer. On uptake of alkane, the dimensions of the bilayer increase. Allowance is made for an increase in thickness and/or an increase in area per lipid. A thermodynamic framework is established which allows evaluation of the free energy of a bilayer of arbitrary dimensions with a view to predicting the equilibrium structure. PMID:6894396

  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.

  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. Application of the Stoner-Wohlfarth model with interaction for the determination of the saturation magnetisation, anisotropy field, and mean field interaction in bulk amorphous ferromagnets

    NASA Astrophysics Data System (ADS)

    Collocott, S. J.

    2011-08-01

    Magnetic hysteresis curves of bulk amorphous ferromagnet alloys of composition Nd 60Fe 30Al 10, Nd 60Fe 20Co 10Al 10 and Pr 58Fe 24Al 18 have been measured in applied magnetic fields up to 9 T at temperatures in the range 10-350 K. The behaviour of the demagnetisation curve in the first quadrant is interpreted using a mean field interaction model as proposed by Callen et al. [Phys. Rev. B 16 (1977) 263], which extends the Stoner-Wohlfarth model [Philos. Trans. Roy. Soc. A 240 (1948) 599] for a random distribution of non-interacting uniaxial grains. Application of the mean field interaction model enables the determination of the saturation magnetisation Ms, anisotropy field Ha, and interaction parameter d, and from these other magnetic parameters, such as the anisotropy constant, K, are deduced. For the three alloys, the temperature dependent behaviour of Ms, Ha, d and K over the range 20-350 K are found to be qualitatively similar, though there are quantitative differences. In all cases Ms increases with decreasing temperature, both Ha and K increase with decreasing temperature, reaching a peak in the range 75-120 K, and then decreasing, and d decreases approximately linearly as the temperature decreases. The physical mechanisms responsible for coercivity in these materials are discussed in the context of random anisotropy and a strong pinning model of domain walls.

  10. Effect of platykurtic and leptokurtic distributions in the random-field Ising model: mean-field approach.

    PubMed

    Duarte Queirós, Sílvio M; Crokidakis, Nuno; Soares-Pinto, Diogo O

    2009-07-01

    The influence of the tail features of the local magnetic field probability density function (PDF) on the ferromagnetic Ising model is studied in the limit of infinite range interactions. Specifically, we assign a quenched random field whose value is in accordance with a generic distribution that bears platykurtic and leptokurtic distributions depending on a single parameter tau<3 to each site. For tau<5/3, such distributions, which are basically Student-t and r distribution extended for all plausible real degrees of freedom, present a finite standard deviation, if not the distribution has got the same asymptotic power-law behavior as a alpha-stable Lévy distribution with alpha=(3-tau)/(tau-1). For every value of tau, at specific temperature and width of the distribution, the system undergoes a continuous phase transition. Strikingly, we impart the emergence of an inflexion point in the temperature-PDF width phase diagrams for distributions broader than the Cauchy-Lorentz (tau=2) which is accompanied with a divergent free energy per spin (at zero temperature).

  11. Random-phase approximation based on relativistic point-coupling models

    SciTech Connect

    Niksic, T.; Vretenar, D.; Ring, P.

    2005-07-01

    The matrix equations of the random-phase approximation (RPA) are derived for the point-coupling Lagrangian of the relativistic mean-field (RMF) model. Fully consistent RMF plus (quasiparticle) RPA illustrative calculations of the isoscalar monopole, isovector dipole, and isoscalar quadrupole response of spherical medium-heavy and heavy nuclei test the phenomenological effective interactions of the point-coupling RMF model. A comparison with experiment shows that the best point-coupling effective interactions accurately reproduce not only ground-state properties but also data on excitation energies of giant resonances.

  12. 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.

  13. A mean-field renormalisation-group approach to Ising and q = 3-state Potts models with long-range interactions in one dimension

    NASA Astrophysics Data System (ADS)

    Soares, C. E. K.; de Sousa, J. Ricardo; Branco, N. S.

    2017-09-01

    We study the one-dimensional Potts model with long-range interactions decaying with distance r as r 1 + σ. An extended mean-field renormalisation-group procedure is applied, such that three finite-size linear lattices are compared, in order to evaluate critical temperatures and exponents for the q = 2 (Ising model) and q = 3 (such that the transition is a continuous one) cases. Good results are obtained, whenever comparison with exact results or with other procedures is possible. Moreover, we evaluate the surface field exponent for these models. We have been able to go to rather large lattices and then a suitable finite-size scaling procedure is employed to obtain the results in the thermodynamic limit.

  14. 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.

  15. Critical and multicritical behaviors of static and complex magnetic susceptibilities for the mean-field Blume-Capel model with a random crystal field

    NASA Astrophysics Data System (ADS)

    Gülpınar, Gül; Erdem, Rıza; Ağartıoğlu, Mehmet

    2017-10-01

    The static and dynamic linear response functions for the spin-1 mean-field Blume-Capel model with a random diluted single-ion anisotropy are derived using the thermodynamics of linear irreversible processes. Thermal dependence of the static susceptibility is studied in detail. In addition, by utilizing the stationary solution of the kinetic equation in existence of sinusoidal external magnetic field, the low frequency thermal behavior of the magnetic absorption and dispersion factors are investigated. Particularly, we have analyzed the behaviors of these quantities near both first- and second-order transition temperatures and multicritical points such as tricritical point, critical endpoint and double critical endpoint. The static and dynamical mean field critical exponents in hydrodynamic limit are also calculated in order to formulate the critical and multicritical behaviors of the magnetic susceptibility. Finally, a comparison of the findings of this study with previous theoretical and experimental studies is presented and it is shown that a good agreement is found with our results.

  16. Implementation of a finite-amplitude method in a relativistic meson-exchange model

    NASA Astrophysics Data System (ADS)

    Sun, Xuwei; Lu, Dinghui

    2017-08-01

    The finite-amplitude method is a feasible numerical approach to large scale random phase approximation calculations. It avoids the storage and calculation of residual interaction elements as well as the diagonalization of the RPA matrix, which will be prohibitive when the configuration space is huge. In this work we finished the implementation of a finite-amplitude method in a relativistic meson exchange mean field model with axial symmetry. The direct variation approach makes our FAM scheme capable of being extended to the multipole excitation case.

  17. 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.

  18. Meson exchange currents in a relativistic model for electromagnetic one nucleon emission

    NASA Astrophysics Data System (ADS)

    Meucci, Andrea; Giusti, Carlotta; Pacati, Franco Davide

    2002-09-01

    We analyze the role of meson exchange currents (MECs) in photon- and electron-induced one nucleon emission reactions in a fully relativistic model. The relativistic mean-field theory is used for the bound state and the Pauli reduction for the scattering state. Direct one-body and exchange two-body terms in the nuclear current are considered. Results for the 12C(γ,p) and 16O(γ,p) differential cross sections and photon asymmetries are displayed in an energy range between 60 and 196 MeV. The two-body seagull current affects the cross section less than in nonrelativistic analyses. In the case of the 16O(γ,n) differential cross section, MEC effects are large but not sufficient to reproduce the data. MECs have a small effect on (e,e'p) calculations.

  19. Spectral functions of a time-periodically driven Falicov-Kimball model: Real-space Floquet dynamical mean-field theory study

    NASA Astrophysics Data System (ADS)

    Qin, Tao; Hofstetter, Walter

    2017-08-01

    We present a systematic study of the spectral functions of a time-periodically driven Falicov-Kimball Hamiltonian. In the high-frequency limit, this system can be effectively described as a Harper-Hofstadter-Falicov-Kimball model. Using real-space Floquet dynamical mean-field theory (DMFT), we take into account the interaction effects and contributions from higher Floquet bands in a nonperturbative way. Our calculations show a high degree of similarity between the interacting driven system and its effective static counterpart with respect to spectral properties. However, as also illustrated by our results, one should bear in mind that Floquet DMFT describes a nonequilibrium steady state, while an effective static Hamiltonian describes an equilibrium state. We further demonstrate the possibility of using real-space Floquet DMFT to study edge states on a cylinder geometry.

  20. A Generalization of Mean Field Theory in a Cluster with Many Sites on the Ising Model from the Bogoliubov Inequality: Hexagonal Nanowire and Nanotube

    NASA Astrophysics Data System (ADS)

    Santos, Jander P.

    2017-04-01

    A generalization of mean field theory in a cluster with many sites was obtained for the spin-1/2 Ising model from the Gibbs-Bogoliubov inequality. The expressions for the free energy and the magnetization were obtained. The generalization was applied in a structure of the nanowire and nanotube hexagonal lattices, for clusters of seven sites and six sites, respectively. The results for the magnetization, the free energy, the internal energy, the entropy, the specific heat, and the critical frontiers were obtained. The critical temperature and the compensation temperature in a cylindrical Ising nanowire are investigated, in order to clarify the distinction between the ferromagnetic and ferrimagnetic behaviors when the core-shell exchange coupling takes a different sign. The results were compared with other works.

  1. A Generalization of Mean Field Theory in a Cluster with Many Sites on the Ising Model from the Bogoliubov Inequality: Hexagonal Nanowire and Nanotube

    NASA Astrophysics Data System (ADS)

    Santos, Jander P.

    2017-01-01

    A generalization of mean field theory in a cluster with many sites was obtained for the spin-1/2 Ising model from the Gibbs-Bogoliubov inequality. The expressions for the free energy and the magnetization were obtained. The generalization was applied in a structure of the nanowire and nanotube hexagonal lattices, for clusters of seven sites and six sites, respectively. The results for the magnetization, the free energy, the internal energy, the entropy, the specific heat, and the critical frontiers were obtained. The critical temperature and the compensation temperature in a cylindrical Ising nanowire are investigated, in order to clarify the distinction between the ferromagnetic and ferrimagnetic behaviors when the core-shell exchange coupling takes a different sign. The results were compared with other works.

  2. 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.

  3. Lattice Boltzmann model for resistive relativistic magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

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

    2015-08-01

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

  4. 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.

  5. Accurate mean-field modeling of the Barkhausen noise power in ferromagnetic materials, using a positive-feedback theory of ferromagnetism

    NASA Astrophysics Data System (ADS)

    Harrison, R. G.

    2015-07-01

    A mean-field positive-feedback (PFB) theory of ferromagnetism is used to explain the origin of Barkhausen noise (BN) and to show why it is most pronounced in the irreversible regions of the hysteresis loop. By incorporating the ABBM-Sablik model of BN into the PFB theory, we obtain analytical solutions that simultaneously describe both the major hysteresis loop and, by calculating separate expressions for the differential susceptibility in the irreversible and reversible regions, the BN power response at all points of the loop. The PFB theory depends on summing components of the applied field, in particular, the non-monotonic field-magnetization relationship characterizing hysteresis, associated with physical processes occurring in the material. The resulting physical model is then validated by detailed comparisons with measured single-peak BN data in three different steels. It also agrees with the well-known influence of a demagnetizing field on the position and shape of these peaks. The results could form the basis of a physics-based method for modeling and understanding the significance of the observed single-peak (and in multi-constituent materials, multi-peak) BN envelope responses seen in contemporary applications of BN, such as quality control in manufacturing, non-destructive testing, and monitoring the microstructural state of ferromagnetic materials.

  6. Designing a planar vector field to investigate the role of a slow variable in an enhanced mean-field model during general anesthesia

    PubMed Central

    Molaee-Ardekani, Behnam; Shamsollahi, Mohammad-Bagher; Senhadji, Lotfi; Vosoughi-Vahdat, Bijan; Wodey, Eric

    2006-01-01

    Local mean-field models (MFMs) describe regional brain activities by some connected differential equations. In an overall view, constituting variables of these differential equations can be divided to very fast, fast and slow variables. In this article we propose a method that can be used to determine role of a slow variable in behavior of MFMs. Very fast variables can be adiabatically removed from the equations. Isoclines of fast and slow variables and their corresponding vector field can provide valuable information about model behavior and role of the slow variable in it. The vector field of our interested MFM that is an enhanced MFM designed specially for general anesthesia, is a 3D field (one slow and two fast variables) and it is not so convenient for visually inspecting the role of the slow variable in this model. To afford this problem we design a 2D (planar) vector filed that only considers the slow variable and one of the fast variables. PMID:17946364

  7. 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).

  8. "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.

  9. Predictive beyond-mean-field rate equations for multisite lattice–gas models of catalytic surface reactions: CO oxidation on Pd(100)

    DOE PAGES

    Liu, Da -Jiang; Zahariev, Federico; Gordon, Mark S.; ...

    2016-11-29

    Tailored multisite lattice–gas (msLG) models are developed for CO oxidation on Pd(100) at low-pressures. These models include multiple adsorption site types and superlattice adlayer ordering due to short-range exclusion for highly mobile reactant adspecies. However, they are simplified to neglect longer-range weaker adspecies interactions, so that the key energetic parameters are the CO desorption barrier and the reaction barrier. We discuss existing density functional theory results for these energies and present additional analysis for CO adsorption. After also including an appropriate nontrivial specification of the dynamics of adsorption onto mixed reactant adlayers, we develop rate equations for the reaction kinetics.more » Our formulation goes beyond traditional mean-field (MF) Langmuirian treatments by accounting for multiple adsorption sites and for the strong spatial correlations associated with superlattice ordering. Specifically, we utilize factorization approximations based on appropriate site motifs, and also Padé resummation of exact low-coverage expansions for sticking coefficients. Our beyond-MF rate equations are successful in accurately predicting key aspects of reactive steady-state behavior, and thus expand the utility of rate equation formulations in surface chemistry. This is confirmed by comparison with precise kinetic Monte Carlo simulation results. Furthermore, we not only assess bistability and criticality observed for CO oxidation but also find more complex multistability associated with symmetry-breaking transitions in high-coverage CO adlayers.« less

  10. 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.

    PubMed

    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.

  11. Predictive beyond-mean-field rate equations for multisite lattice–gas models of catalytic surface reactions: CO oxidation on Pd(100)

    SciTech Connect

    Liu, Da -Jiang; Zahariev, Federico; Gordon, Mark S.; Evans, James W.

    2016-11-29

    Tailored multisite lattice–gas (msLG) models are developed for CO oxidation on Pd(100) at low-pressures. These models include multiple adsorption site types and superlattice adlayer ordering due to short-range exclusion for highly mobile reactant adspecies. However, they are simplified to neglect longer-range weaker adspecies interactions, so that the key energetic parameters are the CO desorption barrier and the reaction barrier. We discuss existing density functional theory results for these energies and present additional analysis for CO adsorption. After also including an appropriate nontrivial specification of the dynamics of adsorption onto mixed reactant adlayers, we develop rate equations for the reaction kinetics. Our formulation goes beyond traditional mean-field (MF) Langmuirian treatments by accounting for multiple adsorption sites and for the strong spatial correlations associated with superlattice ordering. Specifically, we utilize factorization approximations based on appropriate site motifs, and also Padé resummation of exact low-coverage expansions for sticking coefficients. Our beyond-MF rate equations are successful in accurately predicting key aspects of reactive steady-state behavior, and thus expand the utility of rate equation formulations in surface chemistry. This is confirmed by comparison with precise kinetic Monte Carlo simulation results. Furthermore, we not only assess bistability and criticality observed for CO oxidation but also find more complex multistability associated with symmetry-breaking transitions in high-coverage CO adlayers.

  12. 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

    NASA Astrophysics Data System (ADS)

    PÈ©kalski, J.; Ciach, A.; Almarza, N. G.

    2014-03-01

    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.

  13. 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.

  14. 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

  15. Multiscale Study of Counterion-Induced Attraction and Bundle Formation of F-Actin Using an Ising-like Mean-Field Model

    PubMed Central

    Yu, Xueping; Carlsson, A. E.

    2003-01-01

    An Ising-like counterion-binding model is developed and solved by a mean-field method. For G-actin, the calculated affinity constants of all the binding sites ranging from loose to tight binding match the experimental data. The model is used to calculate the interaction energy between two F-actin filaments. Within a certain counterion concentration range, a rapidly decaying attractive force between two parallel filaments is produced not only by the correlation of the counterion distributions on the two filaments, but also by the correlation of the configurations of the two filaments with fixed counterion positions, which has been ignored in previous calculations. The bundling energy depends strongly on the configuration of the filaments. Upon bundling, the tightly bound counterion site is not affected, but the medium and loosely bound ones are. The model reproduces the observed minimal divalent counterion concentration for bundling, and naturally predicts the resolubilization of bundles which is seen in recent experiments. At the optimal counterion concentration, we obtain a bundling energy of ∼−0.01 eV per monomer along the filament. The counterion valence strongly affects the optimal counterion concentration, but has only minor effects on the optimal bundling energy. We show that the attractive potential between filaments can be simplified as the sum of interactions between their monomers. This simplification makes it possible to calculate the exact free energy of a two-F-actin-filament system. We are thus able to probe the effects of filament length on F-actin bundling and obtain a critical length for bundling of 59 monomers at 1 μM monomer concentration and pH = 7.2. PMID:14645048

  16. Multiscale study of counterion-induced attraction and bundle formation of F-actin using an Ising-like mean-field model.

    PubMed

    Yu, Xueping; Carlsson, A E

    2003-12-01

    An Ising-like counterion-binding model is developed and solved by a mean-field method. For G-actin, the calculated affinity constants of all the binding sites ranging from loose to tight binding match the experimental data. The model is used to calculate the interaction energy between two F-actin filaments. Within a certain counterion concentration range, a rapidly decaying attractive force between two parallel filaments is produced not only by the correlation of the counterion distributions on the two filaments, but also by the correlation of the configurations of the two filaments with fixed counterion positions, which has been ignored in previous calculations. The bundling energy depends strongly on the configuration of the filaments. Upon bundling, the tightly bound counterion site is not affected, but the medium and loosely bound ones are. The model reproduces the observed minimal divalent counterion concentration for bundling, and naturally predicts the resolubilization of bundles which is seen in recent experiments. At the optimal counterion concentration, we obtain a bundling energy of approximately -0.01 eV per monomer along the filament. The counterion valence strongly affects the optimal counterion concentration, but has only minor effects on the optimal bundling energy. We show that the attractive potential between filaments can be simplified as the sum of interactions between their monomers. This simplification makes it possible to calculate the exact free energy of a two-F-actin-filament system. We are thus able to probe the effects of filament length on F-actin bundling and obtain a critical length for bundling of 59 monomers at 1 microM monomer concentration and pH=7.2.

  17. 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.

  18. Mean-field kinetic nucleation theory

    NASA Astrophysics Data System (ADS)

    Kalikmanov, V. I.

    2006-03-01

    A new semiphenomenological model of homogeneous vapor-liquid nucleation is proposed in which the cluster kinetics follows the "kinetic approach to nucleation" and the thermodynamic part is based on the revised Fisher droplet model with the mean-field argument for the cluster configuration integral. The theory is nonperturbative in a cluster size and as such is valid for all clusters down to monomers. It contains two surface tensions: macroscopic (planar) and microscopic. The latter is a temperature dependent quantity related to the vapor compressibility factor at saturation. For Lennard-Jones fluids the microscopic surface tension possesses a universal behavior with the parameters found from the mean-field density functional calculations. The theory is verified against nucleation experiments for argon, nitrogen, water, and mercury, demonstrating very good agreement with experimental data. Classical nucleation theory fails to predict experimental results when a critical cluster becomes small.

  19. Kinetic mean-field theories

    NASA Astrophysics Data System (ADS)

    Karkheck, John; Stell, George

    1981-08-01

    A kinetic mean-field theory for the evolution of the one-particle distribution function is derived from maximizing the entropy. For a potential with a hard-sphere core plus tail, the resulting theory treats the hard-core part as in the revised Enskog theory. The tail, weighted by the hard-sphere pair distribution function, appears linearly in a mean-field term. The kinetic equation is accompanied by an entropy functional for which an H theorem was proven earlier. The revised Enskog theory is obtained by setting the potential tail to zero, the Vlasov equation is obtained by setting the hard-sphere diameter to zero, and an equation of the Enskog-Vlasov type is obtained by effecting the Kac limit on the potential tail. At equilibrium, the theory yields a radial distribution function that is given by the hard-sphere reference system and thus furnishes through the internal energy a thermodynamic description which is exact to first order in inverse temperature. A second natural route to thermodynamics (from the momentum flux which yields an approximate equation of state) gives somewhat different results; both routes coincide and become exact in the Kac limit. Our theory furnishes a conceptual basis for the association in the heuristically based modified Enskog theory (MET) of the contact value of the radial distribution function with the ''thermal pressure'' since this association follows from our theory (using either route to thermodynamics) and moreover becomes exact in the Kac limit. Our transport theory is readily extended to the general case of a soft repulsive core, e.g., as exhibited by the Lennard-Jones potential, via by-now-standard statistical-mechanical methods involving an effective hard-core potential, thus providing a self-contained statistical-mechanical basis for application to such potentials that is lacking in the standard versions of the MET. We obtain very good agreement with experiment for the thermal conductivity and shear viscosity of several

  20. Beyond-mean-field study of the hyperon impurity effect in hypernuclei with shape coexistence

    NASA Astrophysics Data System (ADS)

    Wu, X. Y.; Mei, H.; Yao, J. M.; Zhou, Xian-Rong

    2017-03-01

    Background: The hyperon impurity effect in nuclei has been extensively studied in different mean-field models. Recently, there is a controversy about whether the Λ hyperon is more tightly bound in the normal deformed (ND) states than that in the superdeformed (SD) states. Purpose: This article is aimed to provide a beyond-mean-field study of the low-lying states of hypernuclei with shape coexistence and to shed some light on the controversy. Method: The models of relativistic mean field and beyond based on a relativistic point-coupling energy functional are adopted to study the low-lying states of both Ar37Lambda; and 36Ar. The wave functions of low-lying states are constructed as a superposition of a set of relativistic mean-field states with different values of quadrupole deformation parameter. The projections onto both particle number and angular momentum are considered. Results: The Λ binding energies in both ND and SD states of Ar37Lambda; are studied in the case of the Λ hyperon occupying the s ,p , or d state in the spherical limit, respectively. For comparison, four sets of nucleon-hyperon point-coupling interactions are used, respectively. Moreover, the spectra of low-lying states in 36Ar and Ar Lambda;s37 are calculated based on the same nuclear energy density functional. The results indicate that the SD states exist in Ar37Lambda; for all four effective interactions. Furthermore, the Λs reduces the quadrupole collectivity of ND states to a greater extent than that of SD states. For Ar37Lambda;, the beyond-mean field decreases the Λs binding energy of the SD state by 0.17 MeV, but it almost has no effect on that of the ND state. Conclusions: In Ar Lambda;s37 , the Λp and Λd binding energies of the SD states are always larger than those of the ND states. For Λs, the conclusion depends on the effective nucleon-hyperon interaction. Moreover, the beyond-mean-field model

  1. Mean field and collisions in hot nuclei

    SciTech Connect

    K /umlt o/hler, H.S.

    1989-06-01

    Collisions between heavy nuclei produce nuclear matter of high density and excitation. Brueckner methods are used to calculate the momentum and temperature dependent mean field for nucleons propagating through nuclear matter during these collisions. The mean field is complex and the imaginary part is related to the ''two-body'' collision, while the real part relates to ''one-body'' collisions. A potential model for the N-N interactions is avoided by calculating the Reaction matrix directly from the T-matrix (i.e., N-N phase shifts) using a version of Brueckner theory previously published by the author. Results are presented for nuclear matter at normal and twice normal density and for temperatures up to 50 MeV. 23 refs., 7 figs.

  2. Propagation peculiarities of mean field massive gravity

    DOE PAGES

    Deser, S.; Waldron, A.; Zahariade, G.

    2015-07-28

    Massive gravity (mGR) describes a dynamical “metric” on a fiducial, background one. We investigate fluctuations of the dynamics about mGR solutions, that is about its “mean field theory”. Analyzing mean field massive gravity (m¯GR) propagation characteristics is not only equivalent to studying those of the full non-linear theory, but also in direct correspondence with earlier analyses of charged higher spin systems, the oldest example being the charged, massive spin 3/2 Rarita–Schwinger (RS) theory. The fiducial and mGR mean field background metrics in the m¯GR model correspond to the RS Minkowski metric and external EM field. The common implications in bothmore » systems are that hyperbolicity holds only in a weak background-mean-field limit, immediately ruling both theories out as fundamental theories; a situation in stark contrast with general relativity (GR) which is at least a consistent classical theory. Moreover, even though both m¯GR and RS theories can still in principle be considered as predictive effective models in the weak regime, their lower helicities then exhibit superluminal behavior: lower helicity gravitons are superluminal as compared to photons propagating on either the fiducial or background metric. Thus our approach has uncovered a novel, dispersive, “crystal-like” phenomenon of differing helicities having differing propagation speeds. As a result, this applies both to m¯GR and mGR, and is a peculiar feature that is also problematic for consistent coupling to matter.« less

  3. Gamow-Teller states in relativistic nuclear models

    NASA Astrophysics Data System (ADS)

    Kurasawa, Haruki; Suzuki, Toshio; van Giai, Nguyen

    2003-12-01

    The Gamow-Teller (GT) states are investigated in relativistic models. The Landau-Migdal (LM) parameter is introduced in the Lagrangian as a contact term with the pseudovector coupling. In the relativistic model the total GT strength in the nucleon space is quenched by about 12% in nuclear matter and by about 6% in finite nuclei, compared with the Ikeda-Fujii-Fujita sum rule. The quenched amount is taken by nucleon-antinucleon excitations in the timelike region. Because of the quenching, the relativistic model requires a larger value of the LM parameter than nonrelativistic models in describing the GT excitation energy. On the other hand, the effect of the Pauli blocking terms is not important for the GT states.

  4. 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.

  5. Validating relativistic models of nuclear structure against theoretical, experimental, and observational constraints

    SciTech Connect

    Piekarewicz, J.

    2007-12-15

    Relativistic mean-field models of nuclear structure have been enormously successful at reproducing ground-state properties of finite nuclei throughout the periodic table using a handful of accurately calibrated parameters. In this contribution, we use powerful theoretical, experimental, and observational constraints on the equation of state of asymmetric nuclear matter--not employed in the calibration procedure--to validate two such models: NL3 and FSUGold. It is observed that FSUGold is consistent with all these constraints, except perhaps for a high-density equation of state that appears mildly softer than required by astronomical observations. It is argued that incorporating such constraints goes a long way in removing much of the ambiguity left over from the standard calibrating procedure.

  6. 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.

  7. Mean-field approaches for Ξ- hypernuclei and current experimental data

    NASA Astrophysics Data System (ADS)

    Sun, T. T.; Hiyama, E.; Sagawa, H.; Schulze, H.-J.; Meng, J.

    2016-12-01

    Motivated by the recently observed hypernucleus (Kiso event) C15Ξ (14N+Ξ- ), we identify the state of this system theoretically within the framework of the relativistic-mean-field and Skyrme-Hartree-Fock models. The Ξ N interactions are constructed to reproduce the two possibly observed Ξ- removal energies, 4.38 ±0.25 MeV or 1.11 ±0.25 MeV. The present result is preferable to be 14N(g .s .) +Ξ-(1 p ) , corresponding to the latter value.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  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. Dynamics of capillary condensation in lattice gas models of confined fluids: a comparison of dynamic mean field theory with dynamic Monte Carlo simulations.

    PubMed

    Edison, John R; Monson, Peter A

    2013-06-21

    This article addresses the accuracy of a dynamic mean field theory (DMFT) for fluids in porous materials [P. A. Monson, J. Chem. Phys. 128, 084701 (2008)]. The theory is used to study the relaxation processes of fluids in pores driven by step changes made to a bulk reservoir in contact with the pore. We compare the results of the DMFT to those obtained by averaging over large numbers of dynamic Monte Carlo (DMC) simulation trajectories. The problem chosen for comparison is capillary condensation in slit pores, driven by step changes in the chemical potential in the bulk reservoir and involving a nucleation process via the formation of a liquid bridge. The principal difference between the DMFT results and DMC is the replacement of a distribution of nucleation times and location along the pore for the formation of liquid bridges by a single time and location. DMFT is seen to yield an otherwise qualitatively accurate description of the dynamic behavior.

  14. 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.

  15. Relativistic HD and MHD modelling for AGN jets

    NASA Astrophysics Data System (ADS)

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

    2013-12-01

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

  16. 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.

  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. 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.

  19. Models of Dilute Relativistic Plasmas Around Black Holes

    NASA Astrophysics Data System (ADS)

    Quataert, Eliot

    2016-10-01

    In some regimes, mass flowing onto a central black hole can become sufficiently hot and low density that the collisional mean free path is appreciable compared to the size of the system. I describe new analytical and numerical models of these relativistically hot low collisionality plasmas around black holes. I also describe the application of these models to interpreting observations of the accreting black holes being observed by the Event Horizon Telescope.

  20. Dynamics of capillary condensation in lattice gas models of confined fluids: A comparison of dynamic mean field theory with dynamic Monte Carlo simulations

    NASA Astrophysics Data System (ADS)

    Edison, John R.; Monson, Peter A.

    2013-06-01

    This article addresses the accuracy of a dynamic mean field theory (DMFT) for fluids in porous materials [P. A. Monson, J. Chem. Phys. 128, 084701 (2008)], 10.1063/1.2837287. The theory is used to study the relaxation processes of fluids in pores driven by step changes made to a bulk reservoir in contact with the pore. We compare the results of the DMFT to those obtained by averaging over large numbers of dynamic Monte Carlo (DMC) simulation trajectories. The problem chosen for comparison is capillary condensation in slit pores, driven by step changes in the chemical potential in the bulk reservoir and involving a nucleation process via the formation of a liquid bridge. The principal difference between the DMFT results and DMC is the replacement of a distribution of nucleation times and location along the pore for the formation of liquid bridges by a single time and location. DMFT is seen to yield an otherwise qualitatively accurate description of the dynamic behavior.

  1. 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.

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

    SciTech Connect

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

    2009-04-15

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

  3. Electroexcitation of the Roper resonance in the relativistic quark models

    SciTech Connect

    Inna Aznauryan

    2007-08-01

    The amplitudes of the transition gamma* N -> P11(1440) are calculated within light-front relativistic quark model assuming that the P11(1440) is the first radial excitation of the 3q nucleon state. The results are compared with those obtained in close approaches by other authors and with standard nonrelativistic results. One of the reasons for this study was to present all these results within unified definition of helicity amplitudes consistent with the definition used in the extraction of the helicity amplitudes from experimental data in one-pion electroproduction. The results of relativistic quark models are qualitatively in good agreement with each other and differ strongly from nonrelativistic calculations. At small Q2 , these results for the transverse amplitude A12 are consistent, but fail to reproduce experimental data. The most probable explanation of this discrepancy is the absence of pion cloud contribution in the approaches under consideration.

  4. 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.

  5. 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.

  6. Mean Field Analysis of Quantum Annealing Correction.

    PubMed

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

    2016-06-03

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

  7. Mean-field descriptions of collective migration with strong adhesion.

    PubMed

    Johnston, Stuart T; Simpson, Matthew J; Baker, Ruth E

    2012-05-01

    Random walk models based on an exclusion process with contact effects are often used to represent collective migration where individual agents are affected by agent-to-agent adhesion. Traditional mean-field representations of these processes take the form of a nonlinear diffusion equation which, for strong adhesion, does not predict the averaged discrete behavior. We propose an alternative suite of mean-field representations, showing that collective migration with strong adhesion can be accurately represented using a moment closure approach.

  8. A new class of relativistic stellar models

    NASA Astrophysics Data System (ADS)

    Haggag, Salah

    1995-03-01

    Einstein field equations for a static and spherically symmetric perfect fluid are considered. A formulation given by Patino and Rago is used to obtain a class of nine solutions, two of them are Tolman solutions I, IV and the remaining seven are new. The solutions are the correct ones corresponding to expressions derived by Patino and Rago which have been shown by Knutsen to be incorrect. Similar to Tolan solution IV each of the new solutions satisfies energy conditions inside a sphere in some range of two independent parameters. Besides, each solution could be matched to the exterior Schwarzschild solution at a boundary where the pressure vanishes and thus the solutions constitute a class of new physically reasonable stellar models.

  9. 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)

  10. Deterministic Mean-Field Ensemble Kalman Filtering

    SciTech Connect

    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 < 2κ. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. Lastly, this is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.

  11. 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

  12. Deterministic Mean-Field Ensemble Kalman Filtering

    SciTech Connect

    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 < 2κ. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. Lastly, this is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.

  13. Back-reaction beyond the mean field approximation

    SciTech Connect

    Kluger, Y.

    1993-12-01

    A method for solving an initial value problem of a closed system consisting of an electromagnetic mean field and its quantum fluctuations coupled to fermions is presented. By tailoring the large N{sub f} expansion method to the Schwinger-Keldysh closed time path (CTP) formulation of the quantum effective action, causality of the resulting equations of motion is ensured, and a systematic energy conserving and gauge invariant expansion about the electromagnetic mean field in powers of 1/N{sub f} is developed. The resulting equations may be used to study the quantum nonequilibrium effects of pair creation in strong electric fields and the scattering and transport processes of a relativistic e{sup +}e{sup {minus}} plasma. Using the Bjorken ansatz of boost invariance initial conditions in which the initial electric mean field depends on the proper time only, we show numerical results for the case in which the N{sub f} expansion is truncated in the lowest order, and compare them with those of a phenomenological transport equation.

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

    NASA Astrophysics Data System (ADS)

    Hamlin, Nathaniel; Seyler, Charles

    2014-10-01

    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. A major challenge of a relativistic fluid implementation is the recovery of primitive variables (density, velocity, pressure) from conserved quantities at each time step of a simulation. This recovery, which reduces to straightforward algebra in non-relativistic simulations, becomes more complicated when the equations are made relativistic, and has thus far been a major impediment to two-fluid simulations of relativistic HED plasmas. By suitable formulation of the relativistic generalized Ohm's law as an evolution equation, we have reduced the central part of the primitive variable recovery problem to a straightforward algebraic computation, which enables efficient and accurate relativistic two-fluid simulations. Our code recovers expected non-relativistic results and reveals new physics in the relativistic regime. Work supported by the National Nuclear Security Administration stewardship sciences academic program under Department of Energy cooperative Agreement DE-NA0001836.

  15. Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource

    SciTech Connect

    Graber, P. Jameson

    2016-12-15

    We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of Riccati equations. In certain cases, the solution to the mean field type control is also the equilibrium strategy for a class of mean field games. We use this fact to study an economic model of production of exhaustible resources.

  16. Relativistic models for the BepiColombo radioscience experiment

    NASA Astrophysics Data System (ADS)

    Milani, Andrea; Tommei, Giacomo; Vokrouhlický, David; Latorre, Emanuele; Cicalò, Stefano

    2010-01-01

    To test General Relativity with the tracking data of the BepiColombo Mercury orbiter we need relativistic models for the orbits of Mercury and of the Earth, for the light-time and for all the spatio-temporal reference frames involved, with accuracy corresponding to the measurements: ≃10 cm in range, ≃2 micron/s in range-rate, over 2 years. For the dynamics we start from the Lagrangian post-Newtonian (PN) formulation, using a relativistic equation for the solar system barycenter to avoid rank deficiency. In the determination of the PN parameters, the difficulty in disentangling the effects of β from the ones of the Sun's oblateness is confirmed. We have found a consistent formulation for the preferred frame effects, although the center of mass is not an integral. For the identification of strong equivalence principle (SEP) violations we use a formulation containing both direct and indirect effects (through the modified position of the Sun in a barycentric frame). In the light-time equations, the Shapiro effect is modeled to PN order 1 but with an order 2 correction compatible with (Moyer 2003). The 1.5-PN order corrections containing the Sun's velocity are not relevant at the required level of accuracy. To model the orbit of the probe, we use a mercury-centric reference frame with its own “Mercury Dynamic Time”: this is the largest and the only relativistic correction required, taking into account the major uncertainties introduced by non-gravitational perturbations. A delicate issue is the compatibility of our solution with the ephemerides for the other planets, and for the Moon, which cannot be improved by the BepiColombo data alone. Conversely, we plan to later export the BepiColombo measurements, as normal points, to contribute with their unprecedented accuracy to the global improvement of the planetary ephemerides.

  17. 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.

  18. A relativistic two-fluid model of compact stars

    NASA Astrophysics Data System (ADS)

    Chakraborty, Koushik; Rahaman, Farook; Mallick, Arkopriya

    2017-03-01

    We propose a relativistic model of compact star admitting conformal symmetry. Quark matter and baryonic matter which are considered as two different fluids, constitute the star. We define interaction equations between the normal baryonic matter and the quark matter and study the physical situations for repulsive, attractive and zero interaction between the constituent matters. The measured value of the Bag constant is used to explore the spacetime geometry inside the star. From the observed values of the masses of some compact objects, we have obtained theoretical values of the radii. Theoretical values of the radii match well with the previous predictions for such compact objects.

  19. Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms

    NASA Astrophysics Data System (ADS)

    Gravejat, Philippe; Lewin, Mathieu; Séré, Éric

    2009-02-01

    We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to describe relativistic electrons interacting with the Dirac sea, in an external electrostatic potential. The model can be seen as a mean-field approximation of Quantum Electrodynamics (QED) where photons and the so-called exchange term are neglected. A state of the system is described by its one-body density matrix, an infinite rank self-adjoint operator which is a compact perturbation of the negative spectral projector of the free Dirac operator (the Dirac sea). We study the minimization of the reduced BDF energy under a charge constraint. We prove the existence of minimizers for a large range of values of the charge, and any positive value of the coupling constant α. Our result covers neutral and positively charged molecules, provided that the positive charge is not large enough to create electron-positron pairs. We also prove that the density of any minimizer is an L 1 function and compute the effective charge of the system, recovering the usual renormalization of charge: the physical coupling constant is related to α by the formula αphys ≃ α(1 + 2α/(3π) log Λ)-1, where Λ is the ultraviolet cut-off. We eventually prove an estimate on the highest number of electrons which can be bound by a nucleus of charge Z. In the nonrelativistic limit, we obtain that this number is ≤ 2 Z, recovering a result of Lieb. This work is based on a series of papers by Hainzl, Lewin, Séré and Solovej on the mean-field approximation of no-photon QED.

  20. 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.

  1. The Linear Response of OXYGEN-16 in a Relativistic Particle-Hole Model

    NASA Astrophysics Data System (ADS)

    Price, Michael William

    The nuclear structure of excited states in ('16)O is studied using the particle-hole (p-h) model in a Dirac -Hartree single-particle basis. The excited-states are assumed to be produced by an exter- nal perturbation which acts in first order and can be expressed as a sum of single -nucleon operators (linear response). In this thesis, the excited nuclear states are viewed as a linear combination of p-h states which are mixed by a Lorentz invariant finite -range p-h interaction. The particle- and hole-states are described by the self-consistently determined Dirac-Hartree spinor wave functions of Horowitz and Serot.* The linearized equations of motion are solved for the excited state energies and the corresponding p-h admixture amplitudes in the Tamm -Dancoff and random-phase approximations. In this model, the p-h basis is at first restricted to p-h states allowed from 1-(H/2PI)(omega) transitions (in the language of an oscillator model) and then extended to include particle states that lie at higher energies in the Dirac-Hartree continuum. The p-h interaction is writ- ten as a sum of five Lorentz invariant terms (scalar, vector, pseudo-scalar or pseudo-vector, axial-vector and tensor) and is allowed to assume various parameterizations (strengths and ranges) including (a) those suggested by relativistic mean field theories based on (sigma) and (omega), and (sigma), (omega), (rho) and (pi) meson exchange, and (b) those obtained by means of chi-squared RPA fits to selected experimental energy levels in ('16)O. Throughout this work, the validity of the predicted excited state energy levels arising from the various treatments of the p-h basis and interaction is tested by comparing with experimental energy levels in ('16)O. The calculated admixture amplitudes are used in conjunction with relativistic transition operators to predict transition rates for selected electro-weak processes. It is found that the agreement between these relativistic predictions and experimental

  2. Quadrature-based lattice Boltzmann model for relativistic flows

    NASA Astrophysics Data System (ADS)

    Blaga, Robert; Ambruş, Victor E.

    2017-01-01

    A quadrature-based finite-difference lattice Boltzmann model is developed that is suitable for simulating relativistic flows of massless particles. We briefly review the relativistc Boltzmann equation and present our model. The quadrature is constructed such that the stress-energy tensor is obtained as a second order moment of the distribution function. The results obtained with our model are presented for a particular instance of the Riemann problem (the Sod shock tube). We show that the model is able to accurately capture the behavior across the whole domain of relaxation times, from the hydrodynamic to the ballistic regime. The property of the model of being extendable to arbitrarily high orders is shown to be paramount for the recovery of the analytical result in the ballistic regime.

  3. Mean Field Games with a Dominating Player

    SciTech Connect

    Bensoussan, A.; Chau, M. H. M. Yam, S. C. P.

    2016-08-15

    In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the dominating player. We first provide the general theory and discuss the necessary condition for the optimal controls and equilibrium condition by adopting adjoint equation approach. We then present a special case in the context of linear-quadratic framework, in which a necessary and sufficient condition can be asserted by stochastic maximum principle; we finally establish the sufficient condition that guarantees the unique existence of the equilibrium control. The proof of the convergence result of finite player game to mean field counterpart is provided in Appendix.

  4. Spectra of heavy-light mesons in a relativistic model

    NASA Astrophysics Data System (ADS)

    Liu, Jing-Bin; Lü, Cai-Dian

    2017-05-01

    The spectra and wave functions of heavy-light mesons are calculated within a relativistic quark model which is based on a heavy-quark expansion of the instantaneous Bethe-Salpeter equation by applying the Foldy-Wouthuysen transformation. The kernel we choose is the standard combination of linear scalar and Coulombic vector. The effective Hamiltonian for heavy-light quark-antiquark system is calculated up to order 1/m_Q^2. Our results are in good agreement with available experimental data except for the anomalous D_{s0}^*(2317) and D_{s1}(2460) states. The newly observed heavy-light meson states can be accommodated successfully in the relativistic quark model with their assignments presented. The D_{sJ}^*(2860) can be interpreted as the |1^{3/2}D_1\\rangle and |1^{5/2}D_3\\rangle states being members of the 1D family with J^P=1^- and 3^-.

  5. 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.

  6. Mean Field Type Control with Congestion

    SciTech Connect

    Achdou, Yves Laurière, Mathieu

    2016-06-15

    We analyze some systems of partial differential equations arising in the theory of mean field type control with congestion effects. We look for weak solutions. Our main result is the existence and uniqueness of suitably defined weak solutions, which are characterized as the optima of two optimal control problems in duality.

  7. Semi-relativistic quark-antiquark potential models

    NASA Astrophysics Data System (ADS)

    Basdevant, J. L.; Boukraa, S.

    We study the qualitative and quantitative properties of the spectrum of a two-body hamiltonian with relativistic kinematics. We show that this kinematics leads in a natural way to the observed features of light flavour (u, d, s) spectroscopy. After having established the basic properties of the operator √ p2 + m2 + V(r) in the cases of linear or logarithmic potentials, we show that, to first approximation, all q1 q2 meson states can be reproduced with a very simple universal flavour-independent potential whose parameters are directly related to basic physical quantities : the Regge slopes of light flavours and the quasi-logarithmic coupling strength of heavy quarks. We can derive equivalent effective non-relativistic hamiltonians which justify the successes of NR approaches. The main difficulties encountered, in particular in incorporating spin effects, appear to be due to the fact that, in phenomenological potential models, chiral symmetry and the ensuing Goldstone nature of the pion cannot be implemented in a natural way. Hence, such an approach can take its full predictive power only if it is based on a deeper field-theoretic level. Devant le succès spectaculaire des modèles potentiels pour la spectroscopie des états formés de quarks lourds (cc, bb, etc.), il est tentant d'essayer d'étendre de tels modèles aux états comprenant des quarks légers, u, d et s. En particulier, la spectroscopie des états mésoniques « lourds » est phénoménologiquement dominée par l'existence d'un potentiel confinant universel, quasi logarithmique entre 0,1 fm et 1 fm, tandis que celle des états légers se décrit de façon simple par des trajectoires de Regge linéaires qui ont une pente universelle. 11 est donc légitime de se demander s'il s'agit là de deux secteurs disjoints du monde hadronique, ou bien s'il existe une certaine unité dans la spectroscopie mésonique au plan phénoménologique. Cependant, en présence de quarks légers, voire de masse nulle, les

  8. A "Boosted Fireball" Model for Structured Relativistic Jets

    NASA Astrophysics Data System (ADS)

    Duffell, Paul C.; MacFadyen, Andrew I.

    2013-10-01

    We present a model for relativistic jets which generates a particular angular distribution of Lorentz factor and energy per solid angle. We consider a fireball with specific internal energy E/M launched with bulk Lorentz factor γ B . In its center-of-momentum frame the fireball expands isotropically, converting its internal energy into radially expanding flow with asymptotic Lorentz factor η0 ~ E/M. In the lab frame the flow is beamed, expanding with Lorentz factor Γ = 2η0γ B in the direction of its initial bulk motion and with characteristic opening angle θ0 ~ 1/γ B . The flow is jet-like with Γθ0 ~ 2η0 such that jets with Γ > 1/θ0 are naturally produced. The choice η0 ~ γ B ~ 10 yields a jet with Γ ~ 200 on-axis and angular structure characterized by opening angle θ0 ~ 0.1 of relevance for cosmological gamma-ray bursts (GRBs), while γ B >~ 1 may be relevant for low-luminosity GRBs. The model produces a family of outflows, of relevance for different relativistic phenomena with structures completely determined by η0 and γ B . We calculate the energy per unit solid angle for the model and use it to compute light curves for comparison with the widely used top-hat model. The jet break in the boosted fireball light curve is greatly subdued when compared to the top-hat model because the edge of the jet is smoother than for a top-hat. This may explain missing jet breaks in afterglow light curves.

  9. Mean Field Theories of Icosahedral Quasicrystals.

    NASA Astrophysics Data System (ADS)

    Troian, Sandra Marina

    studied. We also rederive and generalize a model free energy presented by Kalugin et al. to show that their original conclusion of a metastable quasicrystal is invalidated by the inclusion of a local quartic term in the free energy. Lastly, we review three other mean field theories recently proposed to explain the existence of quasicrystals.

  10. Socio-economic applications of finite state mean field games.

    PubMed

    Gomes, Diogo; Velho, Roberto M; Wolfram, Marie-Therese

    2014-11-13

    In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments, which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems.

  11. Radiative leptonic Bc decay in the relativistic independent quark model

    NASA Astrophysics Data System (ADS)

    Barik, N.; Naimuddin, Sk.; Dash, P. C.; Kar, Susmita

    2008-12-01

    The radiative leptonic decay Bc-→μ-ν¯μγ is analyzed in its leading order in a relativistic independent quark model based on a confining potential in an equally mixed scalar-vector harmonic form. The branching ratio for this decay in the vanishing lepton mass limit is obtained as Br(Bc→μνμγ)=6.83×10-5, which includes the contributions of the internal bremsstrahlung and structure-dependent diagrams at the level of the quark constituents. The contributions of the bremsstrahlung and the structure-dependent diagrams, as well as their additive interference parts, are compared and found to be of the same order of magnitude. Finally, the predicted photon energy spectrum is observed here to be almost symmetrical about the peak value of the photon energy at Ẽγ≃(MBc)/(4), which may be quite accessible experimentally at LHC in near future.

  12. Radio spectra of extragalactic sources and the relativistic beaming model

    NASA Astrophysics Data System (ADS)

    Eckart, A.; Hummel, C. A.; Witzel, A.

    1989-07-01

    Multiepoch radio spectra of 308 extragalactic radio sources taken from the 1-Jy catalog (Kuhr et al., 1981) are analyzed, correlating the spectral index, spectral curvature, and degree of variability. These quantities are statistically interdependent, and their distributions can be used to distinguish between galaxies, quasars, optically violent variable sources, and BL Lac objects. These spectral associations are explained using a relativistic beaming model involving a nonvariable steep spectrum component and a core component with an inverted spectrum exhibiting an intrinsic variability of about 30 percent. At 5 GHz, the flux density ratio of the core component (seen at an angle of 90 deg) to the steep-spectrum component is about 0.03 or larger.

  13. 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.

  14. Acceleration of Relativistic Electrons: A Comparison of Two Models

    NASA Astrophysics Data System (ADS)

    Green, J. C.; Kivelson, M. G.

    2001-12-01

    Observations of relativistic electron fluxes show order of magnitude increases during some geomagnetic storms. Many electron acceleration models have been proposed to explain the flux enhancements but attempts to validate these models have yielded ambiguous results. Here we examine two models of electron acceleration, radial diffusion via enhanced ULF wave activity [Elkington et al.,1999] and acceleration by resonant interaction with whistler waves[Summers,1998; Roth et al.,1999]. Two methods are used to compare observations with features predicted by the models. First, the evolution of phase space density as a function of L during flux enhancement events is evaluated. The phase space density (PSD) is calculated at constant first, second and third adiabatic invariants using data obtained by the CEPPAD-HIST instrument and the MFE instrument onboard the Polar spacecraft. Liouville's theorem states that PSD calculated at constant adiabatic invariants does not change with time unless some mechanism violates one of the invariants. The radial diffusion model predicts that only the flux invariant will be violated during the acceleration process while acceleration by whistler waves violates the first invariant. Therefore, the two models predict a different evolution of the PSD as a function of time and L. Previous examinations of the evolution of PSD have yielded ambiguous results because PSD calculations are highly dependent on the global accuracy of magnetic field models. We examine the PSD versus L profiles for a series of geomagnetic storms and in addition determine how errors in the Tsyganenko 96 field model affect the results by comparing the measured magnetic field to the model magnetic field used in the calculations. Second, the evolution of the relativistic electron pitch angle distributions is evaluated. Previous studies of pitch angle distributions were limited because few spacecraft have the necessary instrumentation and global coverage. The CEPPAD

  15. 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

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

    SciTech Connect

    Naito, O.

    2013-04-15

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

  17. Simulations and analytic models of relativistic magnetized jets

    NASA Astrophysics Data System (ADS)

    Tchekhovskoi, Alexandre Dmitrievich

    Astrophysical jets are tightly collimated streams that are often observed to move at velocities close to the speed of light. While many such systems are known, understanding and explaining how jets collimate and accelerate has been a long-standing challenge and is currently an area of active research. Finding analytic solutions for jets is extremely hard because the equations that describe the jets are highly nonlinear and difficult to solve analytically. Only in the last few years has it become possible to simulate ultrarelativistic jets computationally, which has led to unprecedented insights into their structure. We now think that many relativistic jets are produced by magnetic fields twisted by the rotation of a central compact object, which can be a black hole or a neutron star. In this thesis I present numerical and analytical studies of relativistic jets. In Chapter 2, I start with a discussion of a simple, idealized model that has the bare minimum of ingredients needed for the production of jets: regular magnetic field, spinning central compact object, and externally imposed collimation. The model assumes that magnetic field in the jet is so strong that plasma inertia is negligible and can be ignored. The simplicity of this model allows for a fully analytic description and an intuitive understanding of the results. Despite being simple, this model possesses non-trivial properties and has important applications to various astrophysical systems --- compact object binaries, gamma-ray bursts, and active galactic nuclei. Chapters 3 -- 7 add an extra level of realism (and sophistication) into jet models: they account for mass inertia of the jet fluid and study its effects on the jet structure. Chapter 4 discusses the effect of jet confinement on the acceleration of the jet. Chapter 5 shows that deconfinement can also have a dramatic effect on the jet. Chapter 6 studies how the structure of the jet changes if the central object driving the jet is a black hole

  18. Mean-field behavior of cluster dynamics

    NASA Astrophysics Data System (ADS)

    Persky, N.; Ben-Av, R.; Kanter, I.; Domany, E.

    1996-09-01

    The dynamic behavior of cluster algorithms is analyzed in the classical mean-field limit. Rigorous analytical results below Tc establish that the dynamic exponent has the value zSW=1 for the Swendsen-Wang algorithm and zW=0 for the Wolff algorithm. An efficient Monte Carlo implementation is introduced, adapted for using these algorithms for fully connected graphs. Extensive simulations both above and below Tc demonstrate scaling and evaluate the finite-size scaling function by means of a rather impressive collapse of the data.

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

    SciTech Connect

    Agboola, Davids Zhang, Yao-Zhong

    2012-09-15

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

  20. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2015-12-01

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

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

    PubMed

    Zgid, Dominika; Chan, Garnet Kin-Lic

    2011-03-07

    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.

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

    SciTech Connect

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

    2006-01-15

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

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

    PubMed Central

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

    2015-01-01

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

  5. 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.

  6. Nonlocal relativistic diffusion (NoRD) model of cosmic ray propagation

    NASA Astrophysics Data System (ADS)

    Uchaikin, V. V.; Sibatov, R. T.

    2017-01-01

    The problem of physical interpretation of the nonlocal relativistic diffusion (NoRD model) for cosmic ray transport in the Galaxy is discussed. The model accounts for the turbulent character of the interstellar medium and the relativistic principle of the speed limitation. Involving fractional calculus and non-Gaussian Lévy statistics yields numerical results compatible with observation data. A special attention is paid to the knee problem. The relativistic speed limit requirement steepens theoretical background spectrum at certain energies, and the position of the break, its sharpness and slopes of asymptotes depend on Dα (E) and α.

  7. Mean-field theory for inhomogeneous electrolytes.

    PubMed

    Yeh, Shin-Shing; Chen, Peilong

    2005-09-01

    We calculate the free energy density for inhomogeneous electrolytes based on the mean-field Debye-Hückel theory. Derived are the contributions of (1) the differential term for the electrolyte density being slow varying in one direction and (2) the boundary term for an electrolyte confined to one side of a planar interface. These contributions are shown to cause an electrolyte depletion near the air-water interfaces, which makes the surface tension increase, to be significantly larger than those predicted by previous theories. Nonuniform electrolyte densities are also computed near the water-electrolyte and electrolyte-electrolyte interfaces. Finally we calculate the interaction of two uncharged macrospheres due to the electrolyte depletion.

  8. Mean-field avalanches in jammed spheres.

    PubMed

    Franz, S; Spigler, S

    2017-02-01

    Disordered systems are characterized by the existence of many sample-dependent local-energy minima that cause a step-wise response when the system is perturbed. In this article we use an approach based on elementary probabilistic methods to compute the complete probability distribution of the jumps (static avalanches) in the response of mean-field systems described by replica symmetry breaking; we find a precise condition for having a power-law behavior in the distribution of avalanches caused by small perturbations, and we show that our predictions are in remarkable agreement both with previous results and with what is found in simulations of three-dimensional systems of soft spheres, either at jamming or at slightly higher densities.

  9. Mean-field avalanches in jammed spheres

    NASA Astrophysics Data System (ADS)

    Franz, S.; Spigler, S.

    2017-02-01

    Disordered systems are characterized by the existence of many sample-dependent local-energy minima that cause a step-wise response when the system is perturbed. In this article we use an approach based on elementary probabilistic methods to compute the complete probability distribution of the jumps (static avalanches) in the response of mean-field systems described by replica symmetry breaking; we find a precise condition for having a power-law behavior in the distribution of avalanches caused by small perturbations, and we show that our predictions are in remarkable agreement both with previous results and with what is found in simulations of three-dimensional systems of soft spheres, either at jamming or at slightly higher densities.

  10. Schrödinger Approach to Mean Field Games.

    PubMed

    Swiecicki, Igor; Gobron, Thierry; Ullmo, Denis

    2016-03-25

    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.

  11. Mean field theory for scale-free random networks

    NASA Astrophysics Data System (ADS)

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

    1999-10-01

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

  12. Entanglement spectrum in cluster dynamical mean-field theory

    NASA Astrophysics Data System (ADS)

    Udagawa, Masafumi; Motome, Yukitoshi

    2015-01-01

    We study the entanglement spectrum of the Hubbard model at half filling on a kagome lattice. The entanglement spectrum is defined by the set of eigenvalues of a reduced thermal density matrix, which is naturally obtained in the framework of the dynamical mean-field theory. Adopting the cluster dynamical mean-field theory combined with continuous-time auxiliary-field Monte Carlo method, we calculate the entanglement spectrum for a three-site triangular cluster in the kagome Hubbard model. We find that the results at the three-particle sector well capture the qualitative nature of the system. In particular, the eigenvalue of the reduced density matrix, corresponding to the chiral degrees of freedom, exhibits a characteristic temperature scale Tchiral, below which a metallic state with large quasiparticle mass is stabilized. The entanglement spectra at different particle number sectors also exhibit characteristic changes around Tchiral, implying the development of inter-triangular ferromagnetic correlations in the correlated metallic regime.

  13. 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.

  14. Resummed mean-field inference for strongly coupled data

    NASA Astrophysics Data System (ADS)

    Jacquin, Hugo; Rançon, A.

    2016-10-01

    We present a resummed mean-field approximation for inferring the parameters of an Ising or a Potts model from empirical, noisy, one- and two-point correlation functions. Based on a resummation of a class of diagrams of the small correlation expansion of the log-likelihood, the method outperforms standard mean-field inference methods, even when they are regularized. The inference is stable with respect to sampling noise, contrarily to previous works based either on the small correlation expansion, on the Bethe free energy, or on the mean-field and Gaussian models. Because it is mostly analytic, its complexity is still very low, requiring an iterative algorithm to solve for N auxiliary variables, that resorts only to matrix inversions and multiplications. We test our algorithm on the Sherrington-Kirkpatrick model submitted to a random external field and large random couplings, and demonstrate that even without regularization, the inference is stable across the whole phase diagram. In addition, the calculation leads to a consistent estimation of the entropy of the data and allows us to sample form the inferred distribution to obtain artificial data that are consistent with the empirical distribution.

  15. Resummed mean-field inference for strongly coupled data.

    PubMed

    Jacquin, Hugo; Rançon, A

    2016-10-01

    We present a resummed mean-field approximation for inferring the parameters of an Ising or a Potts model from empirical, noisy, one- and two-point correlation functions. Based on a resummation of a class of diagrams of the small correlation expansion of the log-likelihood, the method outperforms standard mean-field inference methods, even when they are regularized. The inference is stable with respect to sampling noise, contrarily to previous works based either on the small correlation expansion, on the Bethe free energy, or on the mean-field and Gaussian models. Because it is mostly analytic, its complexity is still very low, requiring an iterative algorithm to solve for N auxiliary variables, that resorts only to matrix inversions and multiplications. We test our algorithm on the Sherrington-Kirkpatrick model submitted to a random external field and large random couplings, and demonstrate that even without regularization, the inference is stable across the whole phase diagram. In addition, the calculation leads to a consistent estimation of the entropy of the data and allows us to sample form the inferred distribution to obtain artificial data that are consistent with the empirical distribution.

  16. 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.

  17. 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.

  18. Mean-field theory of echo state networks

    NASA Astrophysics Data System (ADS)

    Massar, Marc; Massar, Serge

    2013-04-01

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

  19. HBT Pion Interferometry with Phenomenological Mean Field Interaction

    NASA Astrophysics Data System (ADS)

    Hattori, K.

    2010-11-01

    To extract information on hadron production dynamics in the ultrarelativistic heavy ion collision, the space-time structure of the hadron source has been measured using Hanbury Brown and Twiss interferometry. We study the distortion of the source images due to the effect of a final state interaction. We describe the interaction, taking place during penetrating through a cloud formed by evaporating particles, in terms of a one-body mean field potential localized in the vicinity of the source region. By adopting the semiclassical method, the modification of the propagation of an emitted particle is examined. In analogy to the optical model applied to nuclear reactions, our phenomenological model has an imaginary part of the potential, which describes the absorption in the cloud. In this work, we focus on the pion interferometry and mean field interaction obtained using a phenomenological pipi forward scattering amplitude in the elastic channels. The p-wave scattering wit h rho meson resonance leads to an attractive mean field interaction, and the presence of the absorptive part is mainly attributed to the formation of this resonance. We also incorporate a simple time dependence of the potential reflecting the dynamics of the evaporating source. Using the obtained potential, we examine how and to what extent the so-called HBT Gaussian radius is varied by the modification of the propagation.

  20. 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.

  1. 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.

  2. Relativistic Approach to One Nucleon Knockout Reactions

    NASA Astrophysics Data System (ADS)

    Meucci, Andrea; Giusti, Carlotta; Pacati, Franco Davide

    2003-04-01

    We develop a fully relativistic distorted wave impulse approximation model for electron- and photon-induced one proton knockout reactions. The relativistic mean field for the bound state and the Pauli reduction for the scattering state are used, including a fully relativistic electromagnetic current operator. Results for 16O(e, e'p) cross section and structure functions are shown in various kinematic conditions and compared with nonrelativistic calculations. Nuclear transparency calculations in a Q2 range between 0.3 and 1.8 (GeV/c)2 are presented. Results for 16O(γ,p) differential cross sections are displayed in an energy range between 60 and 150 MeV including two-body seagull contribution in the nuclear current.

  3. Non relativistic limit of integrable QFT and Lieb-Liniger models

    NASA Astrophysics Data System (ADS)

    Bastianello, Alvise; De Luca, Andrea; Mussardo, Giuseppe

    2016-12-01

    In this paper we study a suitable limit of integrable QFT with the aim to identify continuous non-relativistic integrable models with local interactions. This limit amounts to sending to infinity the speed of light c but simultaneously adjusting the coupling constant g of the quantum field theories in such a way to keep finite the energies of the various excitations. The QFT considered here are Toda field theories and the O(N) non-linear sigma model. In both cases the resulting non-relativistic integrable models consist only of Lieb-Liniger models, which are fully decoupled for the Toda theories while symmetrically coupled for the O(N) model. These examples provide explicit evidence of the universality and ubiquity of the Lieb-Liniger models and, at the same time, suggest that these models may exhaust the list of possible non-relativistic integrable theories of bosonic particles with local interactions.

  4. Tensor interaction and short range correlations in relativistic nuclear models

    SciTech Connect

    Panda, Prafulla K.; Providencia, C.; Providencia, J. da

    2007-06-15

    Short range correlations are introduced using a Jastrow factor in a relativistic approach to the equation of state of the infinite nuclear matter in the framework of the Hartree-Fock approximation. The pion exchange, including the tensor contribution, is taken into account. It is shown that both the tensor contribution of pion exchange and short range correlations soften the equation of state. Neutron matter with correlations presents no minimum at low densities.

  5. a Nonlinear Model for Relativistic Electrons at Positive Temperature

    NASA Astrophysics Data System (ADS)

    Hainzl, Christian; Lewin, Mathieu; Seiringer, Robert

    We study the relativistic electron-positron field at positive temperature in the Hartree-Fock approximation. We consider both the case with and without exchange terms, and investigate the existence and properties of minimizers. Our approach is non-perturbative in the sense that the relevant electron subspace is determined in a self-consistent way. The present work is an extension of previous work by Hainzl, Lewin, Séré and Solovej where the case of zero temperature was considered.

  6. Mean field theory studies of surface reactions on disordered substrates

    NASA Astrophysics Data System (ADS)

    Cortés, Joaquín.; Narváez, Ana; Puschmann, Heinrich; Valencia, Eliana

    2003-03-01

    A mean field theory (MFT) in the site and pair approximations of a surface reaction system on a disordered substrate showing geometric heterogeneity is proposed, characterizing the substrate completely through the set { qi} of probabilities that a surface site has i neighbours that belong to the substrate in the model. The MFT results allow the interpretation of the Monte Carlo (MC) simulations carried out for the ZGB algorithm at instantaneous and finite rates over a series heterogeneous substrates corresponding to percolation clusters. The change in the character of the irreversible phase transitions (IPT) with the degree of disorder or branching of the substrate and its theoretical interpretation are analyzed.

  7. Mean field treatment of heterogeneous steady state kinetics

    NASA Astrophysics Data System (ADS)

    Geva, Nadav; Vaissier, Valerie; Shepherd, James; Van Voorhis, Troy

    2017-10-01

    We propose a method to quickly compute steady state populations of species undergoing a set of chemical reactions whose rate constants are heterogeneous. Using an average environment in place of an explicit nearest neighbor configuration, we obtain a set of equations describing a single fluctuating active site in the presence of an averaged bath. We apply this Mean Field Steady State (MFSS) method to a model of H2 production on a disordered surface for which the activation energy for the reaction varies from site to site. The MFSS populations quantitatively reproduce the KMC results across the range of rate parameters considered.

  8. Small-world network spectra in mean-field theory.

    PubMed

    Grabow, Carsten; Grosskinsky, Stefan; Timme, Marc

    2012-05-25

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

  9. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2015-12-01

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

  11. Mean field theory of charged dendrimer molecules

    NASA Astrophysics Data System (ADS)

    Lewis, Thomas; Pryamitsyn, Victor; Ganesan, Venkat

    2011-11-01

    Using self-consistent field theory (SCFT), we study the conformational properties of polyelectrolyte dendrimers. We compare results for three different models of charge distributions on the polyelectrolytes: (1) a smeared, quenched charge distribution characteristic of strong polyelectrolytes; (2) a smeared, annealed charge distribution characteristic of weak polyelectrolytes; and (3) an implicit counterion model with Debye-Huckel interactions between the charged groups. Our results indicate that an explicit treatment of counterions is crucial for the accurate characterization of the conformations of polyelectrolyte dendrimers. In comparing the quenched and annealed models of charge distributions, annealed dendrimers were observed to modulate their charges in response to the density of polymer monomers, counterions, and salt ions. Such phenomena is not accommodated within the quenched model of dendrimers and is shown to lead to significant differences between the predictions of quenched and annealed model of dendrimers. In this regard, our results indicate that the average dissociated charge bar{α } inside the dendrimer serves as a useful parameter to map the effects of different parametric conditions and models onto each other. We also present comparisons to the scaling results proposed to explain the behavior of polyelectrolyte dendrimers. Inspired by the trends indicated by our results, we develop a strong segregation theory model whose predictions are shown to be in very good agreement with the numerical SCFT calculations.

  12. Mean field theory of charged dendrimer molecules.

    PubMed

    Lewis, Thomas; Pryamitsyn, Victor; Ganesan, Venkat

    2011-11-28

    Using self-consistent field theory (SCFT), we study the conformational properties of polyelectrolyte dendrimers. We compare results for three different models of charge distributions on the polyelectrolytes: (1) a smeared, quenched charge distribution characteristic of strong polyelectrolytes; (2) a smeared, annealed charge distribution characteristic of weak polyelectrolytes; and (3) an implicit counterion model with Debye-Huckel interactions between the charged groups. Our results indicate that an explicit treatment of counterions is crucial for the accurate characterization of the conformations of polyelectrolyte dendrimers. In comparing the quenched and annealed models of charge distributions, annealed dendrimers were observed to modulate their charges in response to the density of polymer monomers, counterions, and salt ions. Such phenomena is not accommodated within the quenched model of dendrimers and is shown to lead to significant differences between the predictions of quenched and annealed model of dendrimers. In this regard, our results indicate that the average dissociated charge α inside the dendrimer serves as a useful parameter to map the effects of different parametric conditions and models onto each other. We also present comparisons to the scaling results proposed to explain the behavior of polyelectrolyte dendrimers. Inspired by the trends indicated by our results, we develop a strong segregation theory model whose predictions are shown to be in very good agreement with the numerical SCFT calculations.

  13. Modeling the detector of charge states of relativistic multicharged ions

    NASA Astrophysics Data System (ADS)

    Malyshevsky, V. S.; Fomin, G. V.; Ivanova, I. A.

    2017-01-01

    A way to identify charge distributions of relativistic multicharged ions by recording the angular distribution of the Cherenkov radiation of ions is analyzed; preliminarily, ions with different charges are separated by ion velocities in an external target with a large charge number. As a result, when an ion beam enters the Cherenkov radiator, different charges radiate at different angles to the direction of the ion motion and the radiation intensity is proportional to the fraction of ions with a given charge in the beam.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

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

    NASA Astrophysics Data System (ADS)

    Lee, Edward; Raju, Archishman; Sethna, James

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

  19. Nuclear polaron beyond the mean-field approximation

    NASA Astrophysics Data System (ADS)

    Scalbert, D.

    2017-06-01

    In III-V semiconductors it was shown theoretically that under optical cooling the nuclear-spin polaron bound to neutral donors would form below some critical nuclear-spin temperature Tc [Merkulov, Phys. Solid State 40, 930 (1998), 10.1134/1.1130450]. The predicted critical behavior is a direct consequence of the use of the mean-field approximation. It is known however that in any finite-size system a critical behavior must be absent. Here we develop a model of the optically cooled nuclear polaron, which goes beyond the mean-field approximation. An expression of the generalized free energy of the optically cooled nuclear polaron, valid for a finite, albeit large, number of spins, is derived. This model permits us to describe the continuous transition from the fluctuation dominated regime to the collective regime, as the nuclear-spin temperature decreases. It is shown that due to the finite number of nuclear spins involved in the polaron, the critical effects close to Tc are smoothed by the spin fluctuations. Particularly, instead of a divergence, the nuclear-spin fluctuations exhibit a sharp peak at Tc, before being depressed well below Tc. Interestingly, the formation of the nuclear polaron can, in certain conditions, boost the nuclear polarization beyond the value obtained solely by optical pumping. Finally, we suggest that the nuclear polaron could be detected by spin noise spectroscopy or via its superparamagnetic behavior.

  20. Nuclear equation of state in a relativistic independent quark model with chiral symmetry and dependence on quark masses

    NASA Astrophysics Data System (ADS)

    Barik, N.; Mishra, R. N.; Mohanty, D. K.; Panda, P. K.; Frederico, T.

    2013-07-01

    We have calculated the properties of nuclear matter in a self-consistent manner with a quark-meson coupling mechanism incorporating the structure of nucleons in vacuum through a relativistic potential model; where the dominant confining interaction for the free independent quarks inside a nucleon is represented by a phenomenologically average potential in equally mixed scalar-vector harmonic form. Corrections due to spurious center of mass motion as well as those due to other residual interactions, such as the one gluon exchange at short distances and quark-pion coupling arising out of chiral symmetry restoration, have been considered in a perturbative manner to obtain the nucleon mass in vacuum. The nucleon-nucleon interaction in nuclear matter is then realized by introducing additional quark couplings to σ and ω mesons through mean field approximations. The relevant parameters of the interaction are obtained self-consistently while realizing the saturation properties such as the binding energy, pressure, and compressibility of the nuclear matter. We also discuss some implications of chiral symmetry in nuclear matter along with the nucleon and nuclear σ term and the sensitivity of nuclear matter binding energy with variations in the light quark mass.

  1. Relativistic Disc Line: A Tool to Constrain Neutron Star Equation of State Models

    NASA Astrophysics Data System (ADS)

    Bhattacharyya, Sudip

    2017-09-01

    Relativistic iron Kα spectral emission line from the inner disc of a neutron star Low-Mass X-ray Binary (LMXB) was first detected in 2007. This discovery opened up new ways to probe strong gravity and dense matter. The past decade has seen detections of such a line from many neutron star LMXBs, and confirmation of this line from the same source with several X-ray satellites. These have firmly established the new field of relativistic disc line from neutron star systems in only a decade or so. Fitting the shape of such a line with an appropriate general relativistic model provides the accretion disc inner edge radius to the stellar mass ratio. In this review, we briefly discuss how an accurate measurement of this ratio with a future larger area X-ray instrument can be used to constrain neutron star equation of state models.

  2. Mean-field theory for car accidents

    NASA Astrophysics Data System (ADS)

    Huang, Ding-Wei; Tseng, Wei-Chung

    2001-11-01

    We study analytically the occurrence of car accidents in the Nagel-Schreckenberg traffic model. We obtain exact results for the occurrence of car accidents Pac as a function of the car density ρ and the degree of stochastic braking p1 in the case of speed limit vmax=1. Various quantities are calculated analytically. The nontrivial limit p1-->0 is discussed.

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

    NASA Astrophysics Data System (ADS)

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

    2015-02-01

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

  4. Mean-field theory for car accidents.

    PubMed

    Huang, D W; Tseng, W C

    2001-11-01

    We study analytically the occurrence of car accidents in the Nagel-Schreckenberg traffic model. We obtain exact results for the occurrence of car accidents P(ac) as a function of the car density rho and the degree of stochastic braking p(1) in the case of speed limit v(max)=1. Various quantities are calculated analytically. The nontrivial limit p(1)-->0 is discussed.

  5. 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.

  6. 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.

  7. Models for relativistic coulomb sum rules: Expansions in moments of the nuclear momentum density

    NASA Astrophysics Data System (ADS)

    Donnelly, T. W.; Kronenberg, E. L.; Van Orden, J. W.

    1989-04-01

    Relativistic Coulomb sum rules for quasielastic electron scattering from nuclei are developed using a class of relativistic models for the nuclear ground-state momentum distribution. Approximate sum rules at constant 3- or 4-momentum transfer are expressed as expansions in moments of the momentum distribution. New sum-rule functions are derived which, even for very large values of energy and momentum where relativistic effects become dominant, approach simple asymptotic values; in doing so they approximately retain the flavor of the nonrelativistic Coulomb sum rule which approaches Z. Specific ways of achieving an optimum separation of effects relating to the electromagnetic response of a single nucleon and of a many-body system of structureless particles are discussed, including a study of sensitivities to alternative parameterizations of GEn. Comparisons of results using different momentum distributions for the case of 16O are presented.

  8. Degeneracy and relativistic microreversibility relations for collisional-radiative equilibrium models

    NASA Astrophysics Data System (ADS)

    Faussurier, Gérald; Blancard, Christophe

    2017-06-01

    We present the relativistic expressions of standard nonrelativistic microreversibility relations that can be used in collisional-radiative equilibrium models to calculate the transition rates including the free electron degeneracy for collisional excitation and deexcitation, collisional ionization and three-body recombination, dielectronic capture and autoionization, photoexcitation and photodeexcitation, and radiative recombination and photoionization. Semiempirical expressions or more refined calculations can be used for the cross sections of interest as long as they are calculated by taking into account either nonrelativistic, relativistic, or ultrarelativistic effects for both the bound and free electrons. The bound and the free electrons should be treated on the same footing. This is crucial for the internal consistency of the approach valid at arbitrary degeneracy and relativistic degrees.

  9. Existence of Atoms and Molecules in the Mean-Field Approximation of No-Photon Quantum Electrodynamics

    NASA Astrophysics Data System (ADS)

    Hainzl, Christian; Lewin, Mathieu; Séré, Éric

    2009-06-01

    The Bogoliubov-Dirac-Fock (BDF) model is the mean-field approximation of no-photon quantum electrodynamics. The present paper is devoted to the study of the minimization of the BDF energy functional under a charge constraint. An associated minimizer, if it exists, will usually represent the ground state of a system of N electrons interacting with the Dirac sea, in an external electrostatic field generated by one or several fixed nuclei. We prove that such a minimizer exists when a binding (HVZ-type) condition holds. We also derive, study and interpret the equation satisfied by such a minimizer. Finally, we provide two regimes in which the binding condition is fulfilled, obtaining the existence of a minimizer in these cases. The first is the weak coupling regime for which the coupling constant α is small whereas αZ and the particle number N are fixed. The second is the non-relativistic regime in which the speed of light tends to infinity (or equivalently α tends to zero) and Z, N are fixed. We also prove that the electronic solution converges in the non-relativistic limit towards a Hartree-Fock ground state.

  10. 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.

  11. Modeling some two-dimensional relativistic phenomena using an educational interactive graphics software

    NASA Astrophysics Data System (ADS)

    Sastry, G. P.; Ravuri, Tushar R.

    1990-11-01

    This paper describes several relativistic phenomena in two spatial dimensions that can be modeled using the collision program of Spacetime Software. These include the familiar aberration, the Doppler effect, the headlight effect, and the invariance of the speed of light in vacuum, in addition to the rather unfamiliar effects like the dragging of light in a moving medium, reflection at moving mirrors, Wigner rotation of noncommuting boosts, and relativistic rotation of shrinking and expanding rods. All these phenomena are exhibited by tracings of composite computer printouts of the collision movie. It is concluded that an interactive educational graphics software with pleasing visuals can have considerable investigative power packed within it.

  12. The Gamow-Teller states and sum rule in relativistic models

    NASA Astrophysics Data System (ADS)

    Kurasawa, Haruki; Suzuki, Toshio; Van Giai, Nguyen

    2004-02-01

    The giant Gamow-Teller(GT) states and the CT sum rule are investigated in relativistic models. It is shown that the Ikeda-Fujii-Fujita sum rule value is quenched by 6% owing to relativistic effects. The quenched amount is taken by the nucleon-antinucleon states. This fact, together with the recent experiment which has observed 90% of the sum rule value, implies that the contribution of the Δ-hole states to the quenching is strongly reduced. As a result, the Landau-Migdal parameter g' NΔ which dominates the critical density of the pion condensation becomes much smaller than what was believed before.

  13. A Study of the Mean Field Approach to Knapsack Problems.

    PubMed

    Pi, Hong; Ohlsson, Mattias

    1997-03-01

    The mean field theory approach to knapsack problems is extended to multiple knapsacks and generalized assignment problems with Potts mean field equations governing the dynamics. Numerical tests against "state of the art" conventional algorithms shows good performance for the mean field approach. The inherently parallelism of the mean field equations makes them suitable for direct implementations in microchips. It is demonstrated numerically that the performance is essentially not affected when only a limited number of bits is used in the mean field equations. Also, a hybrid algorithm with linear programming and mean field components is showed to further improve the performance for the difficult homogeneous N x M knapsack problem. Copyright 1997 Elsevier Science Ltd. All Rights Reserved.

  14. Mean-field analysis for parallel asymmetric exclusion process with anticipation effect.

    PubMed

    Hao, Qing-Yi; Jiang, Rui; Hu, Mao-Bin; Wu, Qing-Song

    2010-08-01

    This paper studies an extended parallel asymmetric exclusion process, in which the anticipation effect is taken into account. The fundamental diagram of the model has been investigated via cluster mean field analysis. Different from previous mean field analysis, in which the n -cluster probabilities P(σ{i},…,σ{i+n-1}) involve the (n+2) -cluster probabilities P(τ{i-1},…,τ{i+n}) , our mean-field analysis is asymmetric because the three-cluster probabilities P(σ{i},σ{i+1},σ{i+2}) involve the six-cluster probabilities P(τ{i-1},…,τ{i+4}) . We find an excellent agreement between Monte Carlo simulations and cluster mean field analysis, which indicates that the mean field analysis might give the exact expression.

  15. Quantum critical point revisited by dynamical mean-field theory

    DOE PAGES

    Xu, Wenhu; Kotliar, Gabriel; Tsvelik, Alexei M.

    2017-03-31

    Dynamical mean-field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. We characterize the QCP by a universal scaling form of the self-energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low-energy kink and the high-energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high-energy antiferromagnetic paramagnons. Here, we use the frequency-dependent four-point correlation function of spin operators to calculate the momentum-dependent correction to the electron self-energy. Furthermore, by comparing with the calculations basedmore » on the spin-fermion model, our results indicate the frequency dependence of the quasiparticle-paramagnon vertices is an important factor to capture the momentum dependence in quasiparticle scattering.« less

  16. 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

  17. 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.

  18. 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.

  19. Stochastic two-fluid model for relativistic heavy-ion collisions

    SciTech Connect

    Ayik, S. |; Ivanov, Y.B.; Russkikh, V.N.; Noerenberg, W.

    1993-04-01

    A reduction of the relativistic Boltzmann-Langevin Equation (BLE), to a stochastic two-fluid model is presented, and transport coefficients associated with fluid dynamical variables are extracted. The approach is applied to investigate equilibration in a counter-streaming nuclear system.

  20. Stochastic two-fluid model for relativistic heavy-ion collisions. [Boltzmann[endash]Langevin Equation

    SciTech Connect

    Ayik, S. Joint Inst. for Heavy Ion Research, Oak Ridge, TN ); Ivanov, Y.B.; Russkikh, V.N.; Noerenberg, W. )

    1993-01-01

    A reduction of the relativistic Boltzmann-Langevin Equation (BLE), to a stochastic two-fluid model is presented, and transport coefficients associated with fluid dynamical variables are extracted. The approach is applied to investigate equilibration in a counter-streaming nuclear system.

  1. Numerical calculations in the new framework of the RMF theory with π mean field

    NASA Astrophysics Data System (ADS)

    Sugimoto, S.; Toki, H.; Ikeda, K.

    2001-10-01

    Usually, π meson field is not included in the Relativistic Mean Field(RMF) Theory. Because π meson has pseudo scalar nature, it is not exchanged by single particle orbits under the mean field approximation as far as the parity and charge symmetries hold. It is, however, desirable to revise the RMF theory to include the π meson field because it plays a essentially important role in producing many aspects of nuclear structures. As mentioned before, π meson field dose not contribute to the mean field under the mean field approximation. To make π meson free from this restriction it is necessary to break the parity and charge symmetries of single particle orbits. It means that single particle orbits have not good parity quantum numbers and good charge quantum numbers. They are mixed states of parities and charge states. In this way we incorporate π meson field into the RMF theory on the same footing as other mesons which are usually used in the RMF calculations, for example σ, ω etc. Present study in this new framework is performed for N=Z nuclei in medium heavy region, for example, ^40Ca, ^56Ni, ^80Zr, and ^100Sn. We found that the π meson field has finite expectation value. It contributes to the total energies of those nuclei in the non-negligible way. In this talk we report the formulation and the results. We also mention our plan for the parity and charge projection.

  2. A comparison of a GCM simulation of the seasonal cycle of the atmosphere with observation. I - Mean fields and the annual harmonic. II - Stationary waves and transient fluctuations. [general circulation model

    NASA Technical Reports Server (NTRS)

    Straus, David M.; Shukla, J.

    1988-01-01

    The seasonal cycle of a GCM is analyzed in terms of the behavior of the monthly and seasonal mean fields and the structure of the annual harmonic. The GCM is found to be successful in simulating the Northern Hemisphere sea-level pressure and 200-mb heights over eastern continents and oceans and in the entire Southern Hemisphere. Problems in the simulation include an anomalously deep Aleutian low and low values of the height over Europe in winter. The GCM fails to show the observed amplitude of the annual harmonic in 200-mb temperature over Antarctica. In the second section, the seasonal dependence of the stationary and transient eddies of the GCM are presented for a two-year annual cycle. The accuracy of the wave and eddy simulations is analyzed.

  3. 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.

  4. Mean field theory for U(n) dynamical groups

    NASA Astrophysics Data System (ADS)

    Rosensteel, G.

    2011-04-01

    Algebraic mean field theory (AMFT) is a many-body physics modeling tool which firstly, is a generalization of Hartree-Fock mean field theory, and secondly, an application of the orbit method from Lie representation theory. The AMFT ansatz is that the physical system enjoys a dynamical group, which may be either a strong or a weak dynamical Lie group G. When G is a strong dynamical group, the quantum states are, by definition, vectors in one irreducible unitary representation (irrep) space, and AMFT is equivalent to the Kirillov orbit method for deducing properties of a representation from a direct geometrical analysis of the associated integral co-adjoint orbit. AMFT can be the only tractable method for analyzing some complex many-body systems when the dimension of the irrep space of the strong dynamical group is very large or infinite. When G is a weak dynamical group, the quantum states are not vectors in one irrep space, but AMFT applies if the densities of the states lie on one non-integral co-adjoint orbit. The computational simplicity of AMFT is the same for both strong and weak dynamical groups. This paper formulates AMFT explicitly for unitary Lie algebras, and applies the general method to the Lipkin-Meshkov-Glick {\\mathfrak s}{\\mathfrak u} (2) model and the Elliott {\\mathfrak s}{\\mathfrak u} (3) model. When the energy in the {\\mathfrak s}{\\mathfrak u} (3) theory is a rotational scalar function, Marsden-Weinstein reduction simplifies AMFT dynamics to a two-dimensional phase space.

  5. Combining lightning leader and relativistic feedback discharge models of terrestrial gamma-ray flashes

    NASA Astrophysics Data System (ADS)

    Dwyer, J. R.

    2016-12-01

    Lightning leader models of terrestrial gamma-ray flashes (TGFs) are based on the observations that leaders emit bursts of hard x-rays. These x-rays are thought to be generated by runaway electrons created in the high-field regions associated with the leader tips and/or streamers heads. Inside a thunderstorm, it has been proposed that these runaway electrons may experience additional relativistic runaway electron avalanche (RREA) multiplication, increasing the number and the average energy of the electrons, and possibly resulting in a TGF. When modeling TGFs it is important to include the discharge currents resulting from the ionization produced by the runaway electrons, since these currents may alter the electric fields and affect the TGF. In addition, relativistic feedback effects, caused by backward propagating positrons and backscattered x-rays, need to be included, since relativistic feedback limits the size of the electric field and the amount of a RREA multiplication that may occur. In this presentation, a lightning leader model of terrestrial gamma-ray flashes that includes the effects of the discharge currents and relativistic feedback will be described and compared with observations.

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

    NASA Technical Reports Server (NTRS)

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

    1988-01-01

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

  7. 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.

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

    SciTech Connect

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

    2014-07-20

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

  9. Nuclear mean field on and near the drip lines

    NASA Astrophysics Data System (ADS)

    Otsuka, Takaharu; Fukunishi, Nobuhisa

    1996-01-01

    We discuss two subjects related to the structure of nuclei near the drip lines. The first is the vanishing of N = 20 magic structure in Z ≪ N = 20 nuclei. Large-scale state-of-the-art shell-model calculations with 2sld and lower 2plf shells are shown to present a unified description of N = 20 isotones with Z = 10-20, covering both stable and unstable nuclei. The calculations demonstrate that, although the N = 20 closed-shell structure remains for Z ≥ 14, the N = 20 closed-shell structure vanishes naturally towards nuclei with Z ≤ 12, giving rise to various anomalous features including those in 32Mg and 31Na. It is suggested that, in these nuclei, the deformed mean field overcomes the shell gap created by the spherical mean potential. Furthermore, the almost perfect agreement with a recent experiment is presented for the B(E2; 0 1+ → 2 1+) value of 32Mg. The second part is devoted to the mean field for loosely bound neutrons. The variational shell model (VSM) is explained with an application to the anomalous ground state of 11Be. The VSM has been proposed recently to describe the structure of neutron-rich unstable nuclei. Contrary to the failure of spherical Hartree-Fock, the anomalous {1}/{2}+ ground state and its neutron halo are reproduced with Skyrme SIII interaction. This state is bound due to dynamical coupling between the core and the loosely bound neutron which oscillates between 2 s{1}/{2} and l d{5}/{2} orbits. The direct neutron capture is discussed briefly in its relation to the neutron halo.

  10. 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.

  11. 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.

  12. A generalized Jaynes-Cummings model: The relativistic parametric amplifier and a single trapped ion

    SciTech Connect

    Ojeda-Guillén, D.; Mota, R. D.; Granados, V. D.

    2016-06-15

    We introduce a generalization of the Jaynes-Cummings model and study some of its properties. We obtain the energy spectrum and eigenfunctions of this model by using the tilting transformation and the squeezed number states of the one-dimensional harmonic oscillator. As physical applications, we connect this new model to two important and novelty problems: the relativistic parametric amplifier and the quantum simulation of a single trapped ion.

  13. 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.

  14. Classifying initial conditions of long GRBs modeled with relativistic radiation hydrodynamics

    NASA Astrophysics Data System (ADS)

    Rivera-Paleo, F. J.; López Núñez, C. E.; Guzmán, F. S.; González, J. A.

    2017-06-01

    We present a method to classify initial conditions of a long gamma ray bursts model sourced by a single relativistic shock. It is based on the use of artificial neural networks (ANNs) that are trained with light curves (LC) generated with radiation relativistic hydrodynamics simulations. The model we use consists in a single shock with a highly relativistic injected beam into a stratified surrounding medium with profile 1 /r2. In the process we only consider the bremsstrahlung radiation and Thomson scattering process. The initial conditions we use to train the ANN are three: the rest mass density, Lorentz factor and radiation energy density of the beam that produces the relativistic shock, together with the LC generated during the process. The classification selects the location of a box in the 3d parameter space that better fits a given LC, and in order to decrease the uncertainty of the parameters this box is refined and the classification selects a new box of smaller size.

  15. Advances in nuclear reaction calculations by incorporating information from nuclear mean-field theories

    NASA Astrophysics Data System (ADS)

    Kawano, Toshihiko

    2017-09-01

    Mean-field model calculations for nuclear structure theories are combined with the statistical Hauser-Feshbach code in order to improve predictive capabilities of nuclear reaction for experimentally unknown cross sections. Utilizing the mean-field calculation results we calculate second moments of matrix elements for the residual interaction. The second moments are applied to a microscopic level density model based on the random matrix theory. An example is shown for the 208Pb level density calculation.

  16. Spherical relativistic vacuum core models in a Λ-dominated era

    NASA Astrophysics Data System (ADS)

    Yousaf, Z.

    2017-02-01

    This paper is devoted to analyzing the effects of the cosmological constant in the evolution of exact analytical collapsing vacuum core celestial models. For this purpose, relativistic spherical geometry coupled with null expansion locally anisotropic matter distributions is considered. We have first developed a relation between tidal forces and structural variables. We then explored some viable spherical cosmological models by taking the expansion-free condition. Our first class of spherical models is obtained after constraining system matter content, while the second class is obtained by considering barotropic equation of state. We propose that our calculated solutions could be regarded as a relativistic toy model for those astronomical compact populations where vacuum core is expected to appear, like cosmological voids.

  17. On Social Optima of Non-Cooperative Mean Field Games

    SciTech Connect

    Li, Sen; Zhang, Wei; Zhao, Lin; Lian, Jianming; Kalsi, Karanjit

    2016-12-12

    This paper studies the social optima in noncooperative mean-field games for a large population of agents with heterogeneous stochastic dynamic systems. Each agent seeks to maximize an individual utility functional, and utility functionals of different agents are coupled through a mean field term that depends on the mean of the population states/controls. The paper has the following contributions. First, we derive a set of control strategies for the agents that possess *-Nash equilibrium property, and converge to the mean-field Nash equilibrium as the population size goes to infinity. Second, we study the social optimal in the mean field game. We derive the conditions, termed the socially optimal conditions, under which the *-Nash equilibrium of the mean field game maximizes the social welfare. Third, a primal-dual algorithm is proposed to compute the *-Nash equilibrium of the mean field game. Since the *-Nash equilibrium of the mean field game is socially optimal, we can compute the equilibrium by solving the social welfare maximization problem, which can be addressed by a decentralized primal-dual algorithm. Numerical simulations are presented to demonstrate the effectiveness of the proposed approach.

  18. Relativistic model of 2p-2h meson exchange currents in (anti)neutrino scattering

    NASA Astrophysics Data System (ADS)

    Ruiz Simo, I.; E Amaro, J.; Barbaro, M. B.; De Pace, A.; Caballero, J. A.; Donnelly, T. W.

    2017-06-01

    We develop a model of relativistic, charged meson-exchange currents (MEC) for neutrino-nucleus interactions. The two-body current is the sum of seagull, pion-in-flight, pion-pole and Δ-pole operators. These operators are obtained from the weak pion-production amplitudes for the nucleon derived in the nonlinear σ-model together with weak excitation of the {{Δ }}(1232) resonance and its subsequent decay into Nπ . With these currents we compute the five 2p-2h response functions contributing to ({ν }l,{l}-) and ({\\overline{ν }}l,{l}+) reactions in the relativistic Fermi gas model. The total current is the sum of vector and axial two-body currents. The vector current is related to the electromagnetic MEC operator that contributes to electron scattering. This allows one to check our model by comparison with the results of De Pace et al (2003 Nucl. Phys. A 726 303). Thus, our model is a natural extension of that model to the weak sector with the addition of the axial MEC operator. The dependences of the response functions on several ingredients of the approach are analyzed. Specifically we discuss relativistic effects, quantify the size of the direct-exchange interferences, and the relative importance of the axial versus vector current.

  19. 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.

  20. 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}.

  1. Mean Field Games for Stochastic Growth with Relative Utility

    SciTech Connect

    Huang, Minyi; Nguyen, Son Luu

    2016-12-15

    This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation error estimate.

  2. General relativistic hydrodynamics with Adaptive-Mesh Refinement (AMR) and modeling of accretion disks

    NASA Astrophysics Data System (ADS)

    Donmez, Orhan

    We present a general procedure to solve the General Relativistic Hydrodynamical (GRH) equations with Adaptive-Mesh Refinement (AMR) and model of an accretion disk around a black hole. To do this, the GRH equations are written in a conservative form to exploit their hyperbolic character. The numerical solutions of the general relativistic hydrodynamic equations is done by High Resolution Shock Capturing schemes (HRSC), specifically designed to solve non-linear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. We use Marquina fluxes with MUSCL left and right states to solve GRH equations. First, we carry out different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations to verify the second order convergence of the code in 1D, 2 D and 3D. Second, we solve the GRH equations and use the general relativistic test problems to compare the numerical solutions with analytic ones. In order to this, we couple the flux part of general relativistic hydrodynamic equation with a source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time. The test problems examined include shock tubes, geodesic flows, and circular motion of particle around the black hole. Finally, we apply this code to the accretion disk problems around the black hole using the Schwarzschild metric at the background of the computational domain. We find spiral shocks on the accretion disk. They are observationally expected results. We also examine the star-disk interaction near a massive black hole. We find that when stars are grounded down or a hole is punched on the accretion disk, they create shock waves which destroy the accretion disk.

  3. 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.

  4. 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.

  5. Semileptonic decays of Λ _c baryons in the relativistic quark model

    NASA Astrophysics Data System (ADS)

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

    2016-11-01

    Motivated by recent experimental progress in studying weak decays of the Λ _c baryon we investigate its semileptonic decays in the framework of the relativistic quark model based on the quasipotential approach with the QCD-motivated potential. The form factors of the Λ _c→ Λ lν _l and Λ _c→ nlν _l decays are calculated in the whole accessible kinematical region without extrapolations and additional model assumptions. Relativistic effects are systematically taken into account including transformations of baryon wave functions from the rest to moving reference frame and contributions of the intermediate negative-energy states. Baryon wave functions found in the previous mass spectrum calculations are used for the numerical evaluation. Comprehensive predictions for decay rates, asymmetries and polarization parameters are given. They agree well with available experimental data.

  6. 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.

  7. 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(+/-).

  8. Ultra-relativistic heavy ion collisions in a multi-string model

    SciTech Connect

    Werner, K.

    1987-01-01

    We present a model for ultra-relativistic heavy ion collisions based on color string formation and subsequent independent string fragmentation. Strings are formed due to color exchange between quarks at each individual nucleon nucleon collision. The fragmentation is treated as in e/sup +/e/sup -/ or lepton nucleon scattering. Calculation for pp, pA, and AA were carried out using the Monte Carlo code VENUS for Very Energetic Nuclear Scattering (version 1.0). 20 refs., 6 figs.

  9. Breit and Quantum Electrodynamics Energy Contributions in Multielectron Atoms from the Relativistic Screened Hydrogenic Model

    NASA Astrophysics Data System (ADS)

    Di Rocco, Héctor O.; Lanzini, Fernando

    2016-04-01

    The correction to the Coulomb repulsion between two electrons due to the exchange of a transverse photon, referred to as the Breit interaction, as well as the main quantum electrodynamics contributions to the atomic energies (self-energy and vacuum polarization), are calculated using the recently formulated relativistic screened hydrogenic model. Comparison with the results of multiconfiguration Dirac-Hartree-Fock calculations and experimental X- ray energies is made.

  10. Mean-field theory of meta-learning

    NASA Astrophysics Data System (ADS)

    Plewczynski, Dariusz

    2009-11-01

    We discuss here the mean-field theory for a cellular automata model of meta-learning. Meta-learning is the process of combining outcomes of individual learning procedures in order to determine the final decision with higher accuracy than any single learning method. Our method is constructed from an ensemble of interacting, learning agents that acquire and process incoming information using various types, or different versions, of machine learning algorithms. The abstract learning space, where all agents are located, is constructed here using a fully connected model that couples all agents with random strength values. The cellular automata network simulates the higher level integration of information acquired from the independent learning trials. The final classification of incoming input data is therefore defined as the stationary state of the meta-learning system using simple majority rule, yet the minority clusters that share the opposite classification outcome can be observed in the system. Therefore, the probability of selecting a proper class for a given input data, can be estimated even without the prior knowledge of its affiliation. The fuzzy logic can be easily introduced into the system, even if learning agents are built from simple binary classification machine learning algorithms by calculating the percentage of agreeing agents.

  11. 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.

  12. Weakly nonlinear ion-acoustic excitations in a relativistic model for dense quantum plasma

    NASA Astrophysics Data System (ADS)

    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.

  13. Dynamical systems approach to relativistic spherically symmetric static perfect fluid models

    NASA Astrophysics Data System (ADS)

    Heinzle, J. Mark; Röhr, Niklas; Uggla, Claes

    2003-11-01

    We investigate relativistic spherically symmetric static perfect fluid models with barotropic equations of state that are asymptotically polytropic and linear at low and high pressures, respectively. We generalize standard work on Newtonian polytropes to a relativistic setting and to a much larger class of equations of state. This is accomplished by introducing dimensionless variables that are asymptotically homology invariant in the low pressure regime, which yields a reformulation of the field equations into a regular dynamical system on a three-dimensional compact state space. A global picture of the solution space is thus obtained which makes it possible to derive qualitative features and to prove theorems about mass radius properties. Moreover, the framework is also suited for numerical computations, as illustrated by several numerical examples, e.g., the ideal neutron gas and examples that involve phase transitions.

  14. Breaking of relativistically intense longitudinal space charge waves: A description using Dawson sheet model

    NASA Astrophysics Data System (ADS)

    Sengupta, Sudip

    2014-02-01

    Spatio-temporal evolution of relativistically intense longitudinal space charge waves in a cold homogeneous plasma is studied analytically as well as numerically, as an initial value problem, using Dawson sheet model. It is found that, except for very special initial conditions which generates the well known longitudinal Akhiezer-Polovin mode, for all other initial conditions, the waves break through a novel mechanism called phase mixing at an amplitude well below the Akhiezer-Polovin limit. An immediate consequence of this is, that Akhiezer-Polovin waves break when subjected to arbitrarily small longitudinal perturbations. We demonstrate this by performing extensive numerical simulations. This result may be of direct relevance to ultrashort, ultraintense laser/beam pulse-plasma interaction experiments where relativistically intense waves are routinely excited.

  15. Breaking of relativistically intense longitudinal space charge waves: A description using Dawson sheet model

    SciTech Connect

    Sengupta, Sudip

    2014-02-11

    Spatio-temporal evolution of relativistically intense longitudinal space charge waves in a cold homogeneous plasma is studied analytically as well as numerically, as an initial value problem, using Dawson sheet model. It is found that, except for very special initial conditions which generates the well known longitudinal Akhiezer-Polovin mode, for all other initial conditions, the waves break through a novel mechanism called phase mixing at an amplitude well below the Akhiezer-Polovin limit. An immediate consequence of this is, that Akhiezer-Polovin waves break when subjected to arbitrarily small longitudinal perturbations. We demonstrate this by performing extensive numerical simulations. This result may be of direct relevance to ultrashort, ultraintense laser/beam pulse-plasma interaction experiments where relativistically intense waves are routinely excited.

  16. On magnetostrophic mean-field solutions of the geodynamo equations

    NASA Astrophysics Data System (ADS)

    Wu, Cheng-Chin; Roberts, Paul H.

    2015-01-01

    A dynamo driven by motions unaffected by viscous forces is termed magnetostrophic. Although such a model might describe well magnetic field generation in Earth's core, its existence is in doubt as numerical simulators have to impose substantial viscosity to stabilize solutions of the full MHD dynamo equations. An attempt is made here to revive interest in a procedure proposed by Taylor [Proc. R. Soc. Lond. A, 1963, 274, 274] for finding inertialess magnetostrophic dynamos. The evolution of the magnetic field from the fluid flow follows the usual kinematic path, but the creation of the zero viscosity flow from the magnetic field was reduced by Taylor to the solution of a second-order ordinary differential equation. Roberts and Wu [Geophys. Astrophys. Fluid Dyn., 2014, 108] derived an exact solution of this equation for axisymmetric mean-field dynamos. Numerical solutions of this equation are presented here, leading to the first truly magnetostrophic dynamos ever found. The magnetic field and fluid flow are derived and discussed for α2 - and αω-dynamos.

  17. 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.

  18. One-Dimensional Forward–Forward Mean-Field Games

    SciTech Connect

    Gomes, Diogo A. Nurbekyan, Levon; Sedjro, Marc

    2016-12-15

    While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward–forward problem is still poorly understood—even in the one-dimensional setting. Here, we consider one-dimensional forward–forward MFGs, study the existence of solutions and their long-time convergence. First, we discuss the relation between these models and systems of conservation laws. In particular, we identify new conserved quantities and study some qualitative properties of these systems. Next, we introduce a class of wave-like equations that are equivalent to forward–forward MFGs, and we derive a novel formulation as a system of conservation laws. For first-order logarithmic forward–forward MFG, we establish the existence of a global solution. Then, we consider a class of explicit solutions and show the existence of shocks. Finally, we examine parabolic forward–forward MFGs and establish the long-time convergence of the solutions.

  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. Relativistic modeling of compact stars for anisotropic matter distribution

    NASA Astrophysics Data System (ADS)

    Maurya, S. K.

    2017-05-01

    In this paper we have solved Einstein's field equations of spherically symmetric spacetime for anisotropic matter distribution by assuming physically valid expressions of the metric function e^{λ} and radial pressure (pr). Next we have discussed the physical properties of the model in details by taking the radial pressure pr equal to zero at the boundary of the star. The physical analysis of the star indicates that its model parameters such as density, redshift, radial pressure, transverse pressure and anisotropy are well behaved. Also we have obtained the mass and radius of our compact star which are 2.29M_{⊙} and 11.02 km, respectively. It is observed that the model obtained here for compact stars is compatible with the mass and radius of the strange star PSR 1937 +21.

  1. 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.

  2. Unitary, gauge invariant, relativistic resonance model for pion photoproduction

    SciTech Connect

    Y. Surya; F. Gross

    2000-07-01

    Pion photoproduction up to 770 MeV photon laboratory energy is described by a manifestly covariant wave equation, which includes a treatment of the final state {pi}N interactions consistent with the covariant, unitary, resonance model of pi-N scattering previously developed. The kernel of the equation includes nucleon (N), Roper (N*), Delta, and D{sub 13} poles and their crossed poles, as well as {pi}, {mu}, and w exchange terms. The Kroll-Ruderman term and other interaction currents insure that the model is exactly gauge invariant to all orders in the strong coupling, g{sub {pi}NN}, and that the low energy theorem is satisfied. Unitarity is maintained up to first order in the charge e (Watson theorem). The complete development of this model, which gives a good fit to all the data up to 770 MeV, is presented.

  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. 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.

  6. Euclidean bridge to the relativistic constituent quark model

    NASA Astrophysics Data System (ADS)

    Hobbs, T. J.; Alberg, Mary; Miller, Gerald A.

    2017-03-01

    Background: Knowledge of nucleon structure is today ever more of a precision science, with heightened theoretical and experimental activity expected in coming years. At the same time, a persistent gap lingers between theoretical approaches grounded in Euclidean methods (e.g., lattice QCD, Dyson-Schwinger equations [DSEs]) as opposed to traditional Minkowski field theories (such as light-front constituent quark models). Purpose: Seeking to bridge these complementary world views, we explore the potential of a Euclidean constituent quark model (ECQM). This formalism enables us to study the gluonic dressing of the quark-level axial-vector vertex, which we undertake as a test of the framework. Method: To access its indispensable elements with a minimum of inessential detail, we develop our ECQM using the simplified quark + scalar diquark picture of the nucleon. We construct a hyperspherical formalism involving polynomial expansions of diquark propagators to marry our ECQM with the results of Bethe-Salpeter equation (BSE) analyses, and constrain model parameters by fitting electromagnetic form factor data. Results: From this formalism, we define and compute a new quantity—the Euclidean density function (EDF)—an object that characterizes the nucleon's various charge distributions as functions of the quark's Euclidean momentum. Applying this technology and incorporating information from BSE analyses, we find the quenched dressing effect on the proton's axial-singlet charge to be small in magnitude and consistent with zero, while use of recent determinations of unquenched BSEs results in a large suppression. Conclusions: The quark + scalar diquark ECQM is a step toward a realistic quark model in Euclidean space, and needs additional refinements. The substantial effect we obtain for the impact on the axial-singlet charge of the unquenched dressed vertex compared to the quenched demands further investigation.

  7. A Maximum Principle for SDEs of Mean-Field Type

    SciTech Connect

    Andersson, Daniel Djehiche, Boualem

    2011-06-15

    We study the optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state of the process. Moreover the cost functional is also of mean-field type, which makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. Under the assumption of a convex action space a maximum principle of local form is derived, specifying the necessary conditions for optimality. These are also shown to be sufficient under additional assumptions. This maximum principle differs from the classical one, where the adjoint equation is a linear backward SDE, since here the adjoint equation turns out to be a linear mean-field backward SDE. As an illustration, we apply the result to the mean-variance portfolio selection problem.

  8. Well-behaved relativistic charged super-dense star models

    NASA Astrophysics Data System (ADS)

    Faruqi, Shahab; Pant, Neeraj

    2012-10-01

    A new class of charged super-dense star models is obtained by using an electric intensity, which involves a parameter, K. The metric describing the model shares its metric potential g 44 with that of Durgapal's fourth solution (J. Phys. A, Math. Gen. 15:2637, 1982). The pressure-free surface is kept at the density ρ b =2×1014 g/cm3 and joins smoothly with the Reissner-Nordstrom solution. The charge analogues are well-behaved for a wide range, 0≤ K≤59, with the optimum value of X=0.264 i.e. the pressure, density, pressure-density ratio and velocity of sound are monotonically decreasing and the electric intensity is monotonically increasing in nature for the given range of the parameter K. The maximum mass and the corresponding radius occupied by the neutral solution are 4.22 M Θ and 20 km, respectively for X=0.264. For the charged solution, the maximum mass and radius are defined by the expressions M≈(0.0059 K+4.22) M Θ and r b ≈-0.021464 K+20 km respectively.

  9. Critical rotation of general-relativistic polytropic models revisited

    NASA Astrophysics Data System (ADS)

    Geroyannis, V.; Karageorgopoulos, V.

    2013-09-01

    We develop a perturbation method for computing the critical rotational parameter as a function of the equatorial radius of a rigidly rotating polytropic model in the "post-Newtonia approximation" (PNA). We treat our models as "initial value problems" (IVP) of ordinary differential equations in the complex plane. The computations are carried out by the code dcrkf54.f95 (Geroyannis and Valvi 2012 [P1]; modified Runge-Kutta-Fehlberg code of fourth and fifth order for solving initial value problems in the complex plane). Such a complex-plane treatment removes the syndromes appearing in this particular family of IVPs (see e.g. P1, Sec. 3) and allows continuation of the numerical integrations beyond the surface of the star. Thus all the required values of the Lane-Emden function(s) in the post-Newtonian approximation are calculated by interpolation (so avoiding any extrapolation). An interesting point is that, in our computations, we take into account the complete correction due to the gravitational term, and this issue is a remarkable difference compared to the classical PNA. We solve the generalized density as a function of the equatorial radius and find the critical rotational parameter. Our computations are extended to certain other physical characteristics (like mass, angular momentum, rotational kinetic energy, etc). We find that our method yields results comparable with those of other reliable methods. REFERENCE: V.S. Geroyannis and F.N. Valvi 2012, International Journal of Modern Physics C, 23, No 5, 1250038:1-15.

  10. Collisional energy losses in relativistic nuclear collisions within an effective quasiparticle model

    SciTech Connect

    Tarasov, Yu. A.

    2009-10-15

    We investigate the collisional energy losses of the fast gluons and light quarks in quark-gluon plasma produced in central (Au+Au) collisions at at energies currently available at the BNL Relativistic Heavy Ion Collider (RHIC) ({radical}(s{sub NN})=200 GeV). We use the effective quasiparticle model for investigation of physical characteristic of expanding plasma. We take into account the possibility of hot glue production at the first stage. We calculate these energy losses and compare them with radiative energy losses of gluons and quarks in an analogous model. We show that radiative energy losses exceed considerably the collisional energy losses.

  11. 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.

  12. 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.

  13. A Euclidean bridge to the relativistic constituent quark model

    NASA Astrophysics Data System (ADS)

    Hobbs, Timothy; Alberg, Mary; Miller, Gerald

    2017-01-01

    We explore the potential of a Euclidean constituent quark model (ECQM) to bridge the lingering gap between Euclidean and Minkowski field theories in studies of nucleon structure. Specifically, we develop our ECQM using a simplified quark-scalar diquark picture of the nucleon as a first calculation. Our treatment in Euclidean space necessitates a hyperspherical formalism involving polynomial expansions of diquark propagators in order to marry our ECQM with results from Bethe-Salpeter Equation (BSE) analyses. From this framework, we define and compute a new quantity - a Euclidean density function (EDF) - an object that characterizes the nucleon's various charge distributions as functions of the quark's Euclidean momentum. Applying this technology and incorporating information from BSE analyses, we find the quenched dressing effect on the proton's axial-singlet charge to be small in magnitude and consistent with zero, while use of recent determinations of unquenched BSEs results in a large suppression. The substantial effect we obtain for the impact on the axial-singlet charge of the unquenched dressed vertex compared to the quenched demands further investigation. Work supported by DOE grant DE-FG02-97ER-41014 and NSF Grant No. 1516105.

  14. Simplified method for including spatial correlations in mean-field approximations

    NASA Astrophysics Data System (ADS)

    Markham, Deborah C.; Simpson, Matthew J.; Baker, Ruth E.

    2013-06-01

    Biological systems involving proliferation, migration, and death are observed across all scales. For example, they govern cellular processes such as wound healing, as well as the population dynamics of groups of organisms. In this paper, we provide a simplified method for correcting mean-field approximations of volume-excluding birth-death-movement processes on a regular lattice. An initially uniform distribution of agents on the lattice may give rise to spatial heterogeneity, depending on the relative rates of proliferation, migration, and death. Many frameworks chosen to model these systems neglect spatial correlations, which can lead to inaccurate predictions of their behavior. For example, the logistic model is frequently chosen, which is the mean-field approximation in this case. This mean-field description can be corrected by including a system of ordinary differential equations for pairwise correlations between lattice site occupancies at various lattice distances. In this work we discuss difficulties with this method and provide a simplification in the form of a partial differential equation description for the evolution of pairwise spatial correlations over time. We test our simplified model against the more complex corrected mean-field model, finding excellent agreement. We show how our model successfully predicts system behavior in regions where the mean-field approximation shows large discrepancies. Additionally, we investigate regions of parameter space where migration is reduced relative to proliferation, which has not been examined in detail before and find our method is successful at correcting the deviations observed in the mean-field model in these parameter regimes.

  15. 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.

  16. Mean-field versus microconvection effects in nanofluid thermal conduction.

    PubMed

    Eapen, Jacob; Williams, Wesley C; Buongiorno, Jacopo; Hu, Lin-Wen; Yip, Sidney; Rusconi, Roberto; Piazza, Roberto

    2007-08-31

    Transient hot-wire data on thermal conductivity of suspensions of silica and perfluorinated particles show agreement with the mean-field theory of Maxwell but not with the recently postulated microconvection mechanism. The influence of interfacial thermal resistance, convective effects at microscales, and the possibility of thermal conductivity enhancements beyond the Maxwell limit are discussed.

  17. Beyond-mean-field effects on nuclear triaxiality

    NASA Astrophysics Data System (ADS)

    Ya, Tu; Chen, Yong-Shou; Gao, Zao-Chun; Liu, Ling; Chen, Yong-Jing

    2017-06-01

    The beyond-mean-field effects on nuclear triaxiality are studied by applying the projected total energy surface (PTES) calculations to the light tungsten isotopes -178W170, which have been well described as prolate rotors within the mean-field approximation. The present PTES calculations have well reproduced the experimental energies of the yrast states and the available experimental transition quardrupole moment (Qt) in function of spin. In particular, the results present a considerable large triaxiality for their ground states, with an average triaxial deformation γ ˜15∘ . For a comparison, the total Routhian surface calculations have also been performed for these nuclei, the results show a well-established axial quadrupole deformation in their ground states. The presence of the significant triaxial deformation can be attributed to the beyond-mean-field effect as the angular momentum projection. This effect is therefore essential for a variety of mean-field approaches since it is only associated with the necessary restoration of the rotational symmetry in the laboratory frame, which is spontaneously broken in the intrinsic frame.

  18. Mean-field dynamo action in renovating shearing flows.

    PubMed

    Kolekar, Sanved; Subramanian, Kandaswamy; Sridhar, S

    2012-08-01

    We study mean-field dynamo action in renovating flows with finite and nonzero correlation time (τ) in the presence of shear. Previous results obtained when shear was absent are generalized to the case with shear. The question of whether the mean magnetic field can grow in the presence of shear and nonhelical turbulence, as seen in numerical simulations, is examined. We show in a general manner that, if the motions are strictly nonhelical, then such mean-field dynamo action is not possible. This result is not limited to low (fluid or magnetic) Reynolds numbers nor does it use any closure approximation; it only assumes that the flow renovates itself after each time interval τ. Specifying to a particular form of the renovating flow with helicity, we recover the standard dispersion relation of the α(2)Ω dynamo, in the small τ or large wavelength limit. Thus mean fields grow even in the presence of rapidly growing fluctuations, surprisingly, in a manner predicted by the standard quasilinear closure, even though such a closure is not strictly justified. Our work also suggests the possibility of obtaining mean-field dynamo growth in the presence of helicity fluctuations, although having a coherent helicity will be more efficient.

  19. 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.

  20. Antiferromagnetism, charge density wave, and d-wave superconductivity in the extended t-J-U model: role of intersite Coulomb interaction and a critical overview of renormalized mean field theory.

    PubMed

    Abram, M; Zegrodnik, M; Spałek, J

    2017-09-13

    In the first part of the paper, we study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the t-J-U-V model of strongly correlated electrons by using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term V in stabilizing the CDW phase. In particular, we show that the charge ordering appears only above a critical value of V in a limited hole-doping range δ. The effect of the V term on SC and AF phases is that a strong interaction suppresses SC, whereas the AF order is not significantly influenced by its presence. In the second part, separate calculations for the case of a pure SC phase have been carried out within an extended approach (the diagrammatic expansion for the Gutzwiller wave function, DE-GWF) in order to analyze the influence of the intersite Coulomb repulsion on the SC phase with the higher-order corrections included beyond the SGA method. The upper concentration for the SC disappearance decreases with increasing V, bringing the results closer to experiment. In appendices A and B we discuss the ambiguity connected with the choice of the Gutzwiller renormalization factors within the renormalized mean filed theory when either AF or CDW orders are considered. At the end, we overview briefly the possible extensions of the current models to put descriptions of the SC, AF, and CDW states on equal footing.

  1. Antiferromagnetism, charge density wave, and d-wave superconductivity in the extended t-J-U model: role of intersite Coulomb interaction and a critical overview of renormalized mean field theory

    NASA Astrophysics Data System (ADS)

    Abram, M.; Zegrodnik, M.; Spałek, J.

    2017-09-01

    In the first part of the paper, we study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the t-J-U-V model of strongly correlated electrons by using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term V in stabilizing the CDW phase. In particular, we show that the charge ordering appears only above a critical value of V in a limited hole-doping range δ. The effect of the V term on SC and AF phases is that a strong interaction suppresses SC, whereas the AF order is not significantly influenced by its presence. In the second part, separate calculations for the case of a pure SC phase have been carried out within an extended approach (the diagrammatic expansion for the Gutzwiller wave function, DE-GWF) in order to analyze the influence of the intersite Coulomb repulsion on the SC phase with the higher-order corrections included beyond the SGA method. The upper concentration for the SC disappearance decreases with increasing V, bringing the results closer to experiment. In appendices A and B we discuss the ambiguity connected with the choice of the Gutzwiller renormalization factors within the renormalized mean filed theory when either AF or CDW orders are considered. At the end, we overview briefly the possible extensions of the current models to put descriptions of the SC, AF, and CDW states on equal footing.

  2. 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.

  3. Analysis and modeling of proton beam loss and emittance growth in the Relativistic Heavy Ion Collider

    DOE PAGES

    Luo, Y.; Fischer, W.; White, S.

    2016-02-04

    The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory has been operating since 2000. Over the past decade, thanks to the continuously increased bunch intensity and reduced β*s at the interaction points, the peak luminosity in the polarized proton operation has been increased by more than two orders of magnitude. In this article, we will present the operational observations at the routine proton physics stores. In addition, the mechanisms for the beam loss, transverse emittance growth, and bunch lengthening are analyzed. Lastly, numerical calculations and multiparticle tracking are used to model these observations.

  4. Decay constants and distribution amplitudes of B meson in the relativistic potential model

    NASA Astrophysics Data System (ADS)

    Sun, Hao-Kai; Yang, Mao-Zhi

    2017-06-01

    In this work we study the decay constants of B and Bs mesons based on the wave function obtained in the relativistic potential model. Our results are in good agreement with experimental data which enables us to apply this method to the investigation of B -meson distribution amplitudes. A very compact form of the distribution amplitude is obtained. We also investigate the one-loop QCD corrections to the pure leptonic decays of B mesons. We find that, after subtracting the infrared divergence in the one-loop corrections using the factorization method, the QCD one-loop corrections to the hard amplitude of leptonic decay will be zero.

  5. 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).

  6. Normalizing a Relativistic Model of X-Ray Reflection Definition of the Reflection Fraction and Its Implementation in relxill

    NASA Technical Reports Server (NTRS)

    Dauser, T.; Garcia, J.; Walton, D. J.; Eikmann, W.; Kallman, T.; McClintock, J.; Wilms, J.

    2016-01-01

    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 reflec_frac all flavours of the relxill model, and the non-relativistic reflection model xillver, in v0.4a (18 January 2016).

  7. Normalizing a Relativistic Model of X-Ray Reflection Definition of the Reflection Fraction and Its Implementation in relxill

    NASA Technical Reports Server (NTRS)

    Dauser, T.; Garcia, J.; Walton, D. J.; Eikmann, W.; Kallman, T.; McClintock, J.; Wilms, J.

    2016-01-01

    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 reflec_frac all flavours of the relxill model, and the non-relativistic reflection model xillver, in v0.4a (18 January 2016).

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. Renormalizability of the nuclear many-body problem with the Skyrme interaction beyond mean field

    NASA Astrophysics Data System (ADS)

    Yang, C. J.; Grasso, M.; Moghrabi, K.; van Kolck, U.

    2017-05-01

    Phenomenological effective interactions like Skyrme forces are currently used in mean-field calculations in nuclear physics. Mean-field models have strong analogies with the first order of the perturbative many-body problem and the currently used effective interactions are adjusted at the mean-field level. In this work, we analyze the renormalizability of the nuclear many-body problem in the case where the effective Skyrme interaction is employed in its standard form and the perturbative problem is solved up to second order. We focus on symmetric nuclear matter and its equation of state, which can be calculated analytically at this order. It is shown that only by applying specific density dependence and constraints to the interaction parameters can renormalizability be guaranteed in principle. This indicates that the standard Skyrme interaction does not in general lead to a renormalizable theory. To achieve renormalizability, other terms should be added to the interaction and employed perturbatively only at first order.

  13. Constrained-pairing mean-field theory. V. Triplet pairing formalism.

    PubMed

    Ellis, Jason K; Jiménez-Hoyos, Carlos A; Henderson, Thomas M; Tsuchimochi, Takashi; Scuseria, Gustavo E

    2011-07-21

    Describing strong (also known as static) correlation caused by degenerate or nearly degenerate orbitals near the Fermi level remains a theoretical challenge, particularly in molecular systems. Constrained-pairing mean-field theory has been quite successful, capturing the effects of static correlation in bond formation and breaking in closed-shell molecular systems by using singlet electron entanglement to model static correlation at mean-field computational cost. This work extends the previous formalism to include triplet pairing. Additionally, a spin orbital extension of the "odd-electron" formalism is presented as a method for understanding electron entanglement in molecules.

  14. Covariant mean-field calculations of finite-temperature nuclear matter

    SciTech Connect

    R. J. Furnstahl; Brian D. Serot

    1990-01-01

    Hot nuclear matter is studied in the framework of quantum hadrodynamics. General principles of covariant thermodynamics and thermodynamic consistency are discussed, and these principles are illustrated by computing nuclear matter properties in an arbitrary reference frame, using the mean-field approximation to the Walecka model. The results are shown to be Lorentz covariant, and thermodynamic consistency is demonstrated by proving the equality of the ‘‘thermodynamic’’ and ‘‘hydrostatic’’ pressures. The mean-field results are used in a simple hydrodynamic picture to discuss the phenomenology of heavy-ion collisions and astrophysical systems, with an emphasis on new features that arise in a covariant approach.

  15. 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.

  16. Generalized Mean Fields for Trapped Atomic Bose-Einstein Condensates

    PubMed Central

    Proukakis, N. P.; Burnett, K.

    1996-01-01

    We describe generalized time-dependent mean-field equations for partially condensed samples of trapped and evaporatively cooled atoms. These equations give a way of investigating the various order parameters that may be present as well as the existence of a mean value of the field due to condensed atoms. Our approach provides us with a closed system of self-consistent equations for the order parameters present. The equations we derive are shown to reduce to other treatments in the literature in various limits. We also show how the equation of motion method allows us to construct a formalism that can handle the evolution of these mean fields due to two-loop kinetics. PMID:27805101

  17. Stochastic Mean-Field Dynamics For Nuclear Collisions

    SciTech Connect

    Ayik, Sakir

    2008-11-11

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

  18. A mean field neural network for hierarchical module placement

    NASA Technical Reports Server (NTRS)

    Unaltuna, M. Kemal; Pitchumani, Vijay

    1992-01-01

    This paper proposes a mean field neural network for the two-dimensional module placement problem. An efficient coding scheme with only O(N log N) neurons is employed where N is the number of modules. The neurons are evolved in groups of N in log N iteration steps such that the circuit is recursively partitioned in alternating vertical and horizontal directions. In our simulations, the network was able to find optimal solutions to all test problems with up to 128 modules.

  19. A Mean Field Limit for the Vlasov-Poisson System

    NASA Astrophysics Data System (ADS)

    Lazarovici, Dustin; Pickl, Peter

    2017-09-01

    We present a probabilistic proof of the mean field limit and propagation of chaos N-particle systems in three dimensions with positive (Coulomb) or negative (Newton) 1/ r potentials scaling like 1/ N and an N-dependent cut-off which scales like {N^{-1/3+ ɛ}}. In particular, for typical initial data, we show convergence of the empirical distributions to solutions of the Vlasov-Poisson system with either repulsive electrical or attractive gravitational interactions.

  20. Modeling the relativistic runaway electron avalanche and the feedback mechanism with GEANT4.

    PubMed

    Skeltved, Alexander Broberg; Østgaard, Nikolai; Carlson, Brant; Gjesteland, Thomas; Celestin, Sebastien

    2014-11-01

    This paper presents the first study that uses the GEometry ANd Tracking 4 (GEANT4) toolkit to do quantitative comparisons with other modeling results related to the production of terrestrial gamma ray flashes and high-energy particle emission from thunderstorms. We will study the relativistic runaway electron avalanche (RREA) and the relativistic feedback process, as well as the production of bremsstrahlung photons from runaway electrons. The Monte Carlo simulations take into account the effects of electron ionization, electron by electron (Møller), and electron by positron (Bhabha) scattering as well as the bremsstrahlung process and pair production, in the 250 eV to 100 GeV energy range. Our results indicate that the multiplication of electrons during the development of RREAs and under the influence of feedback are consistent with previous estimates. This is important to validate GEANT4 as a tool to model RREAs and feedback in homogeneous electric fields. We also determine the ratio of bremsstrahlung photons to energetic electrons Nγ /Ne . We then show that the ratio has a dependence on the electric field, which can be expressed by the avalanche time τ(E) and the bremsstrahlung coefficient α(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.